NOVEL COMPOSITE MATERIALS AND SANDWICH STRUCTURES FOR BLAST MITIGATION

An experimental study has been conducted to investigate the blast resistance and mitigation behaviors of novel composites and sandwich structures. Understanding the overall behaviors and failure mechanisms will aid in the development of optimally designed light-weight structures that can mitigate energy and maintain structural integrity when subjected to blast loadings. Due to the increased threat of damage to civilian and defense structures in the form of terrorist attacks and blast loading, a comprehensive understanding on blast mitigation of composites and sandwich structures, as well as an optimal design, is essential. The dynamic behavior of various sandwich composites made of E-glass VinylEster (EVE) facesheets and Corecell TM A-series styrene acrylonitrile (SAN) foam core was studied using a shock tube apparatus. The overall specimen dimensions were held constant for all core configurations studied, more specifically the foam core thickness. Prior to shock tube testing, the quasi-static and dynamic constitutive behavior of the facesheets (tensile/compressive) and foam (compressive) was evaluated. During the shock tube testing, a high-speed photography system was utilized to capture the real-time deformation process, as well as mechanisms of failure. In the later studies, high-speed photography was coupled with the optical technique of 3-D Digital Image Correlation (DIC) to obtain the real-time, full-field deformation process, including the out-of-plane deflection and velocity, as well as in-plane strain. Post-mortem analysis was also carried out to evaluate the overall blast performance of these configurations. First, shock tube experiments were performed to study the dynamic response of sandwich panels with E-glass Vinyl-Ester (EVE) composite facesheets and stepwise graded styrene acrylonitrile (SAN) foam cores. Two types of core configurations, with identical areal density, were subjected to the shock wave loading. The core layers were arranged according to the density of the respective foam; configuration 1 consisted of low / middle / high density foams and configuration 2 consisted of middle / low / high density foams. The method to calculate the incident and reflected energies of the shock wave, as well as the deformation energy of the specimen, were proposed based on the shock wave pressure profiles and the high-speed deflection images that were obtained. The experimental results showed that configuration 1 outperformed configuration 2 in regards to their blast resistance. Significant core material compression was observed in configuration 1, while in configuration 2 the core layers disintegrated and the front skin (blast side) fractured into two pieces along the midsection. The foam core compression in configuration 1 reduced the dynamic pressures seen on the back facesheet, and thus limited the total amount of damage imparted on the specimen. The estimated energies were then calculated for both configurations. The total energy difference between the incident and reflected energies was almost identical, even though the deformation energy for configuration 2 was larger. Since it was observed that a stepwise graded foam core allows for more compression in the core, thus reducing dynamic pressures seen on the back facesheet, and limiting the total amount of damage imparted on the specimen, the study was then continued to investigate the influence of the number of foam core layers, as well as material interfaces, on the dynamic response of sandwich structures. Four types of core configurations were subjected to the shock wave loading. The foam core was monotonically graded based on increasing acoustic wave impedance, with the foam core layer of lowest wave impedance facing the blast. The specimen dimensions were held constant for all core configurations, while the number of core layers varied, resulting in specimens with one layer, two layer, three layer, and four layers of foam core gradation. The results indicated that even though each configuration allowed for a stepwise compression of the core, the number of core layers has an influence on the dynamic response of the structure under blast loading. More specifically, by increasing the number of monotonically graded layers, the acoustic wave impedance mismatch between successive layers is reduced. Therefore, the strength of the initial shock wave (stress wave) can be weakened by the time it reaches the back facesheet, resulting in lower back face deflection, in-plane strain, and velocity. More importantly, the overall damage imparted on the structure can be reduced and structural integrity can be maintained. Due to the fact that higher levels of core gradation helped maintain structural integrity and improved the overall blast performance of sandwich structures, the study was then continued to investigate the blast response of sandwich structures with a functionally graded core and polyurea (PU) interlayer, and more importantly how the location of this polyurea interlayer affects the overall behavior and blast performance. Two types of core configurations were subjected to shock wave loading. The materials, as well as the core layer arrangements, were identical, with the only difference arising in the location of the polyurea interlayer. The foam core itself was layered with monotonically increasing wave impedance of the core layers, with the lowest wave impedance facing the shock loading. For configuration 1, the polyurea interlayer was placed behind the front facesheet, in front of the foam core, while in configuration 2 it was placed behind the foam core, in front of the back facesheet. The results indicated that applying polyurea behind the foam core and in front of the back facesheet will reduce the back face deflection, particle velocity, and in-plane strain, thus improving the overall blast performance and maintaining structural integrity. Since an optimized core configuration was determined, the study was continued to investigate the relationship between the weight of the panel and its overall blast performance. Two types of core configuration were subjected to shock wave loading. The materials, as well as the core layer arrangements, and overall specimen dimensions were identical, with the only difference appearing in the core layers; one configuration utilized equivalent core layer thickness, while the other configuration utilized equivalent core layer mass. The foam core itself was layered based on monotonically increasing the acoustic wave impedance of the core layers, with the lowest wave impedance facing the shock loading. The results indicated that with a decrease in areal density of ~ 1 kg/m 2 (5%) from the sandwich composites with equivalent core layer thickness to the sandwich composites with equivalent core layer mass, an increase in deflection (20%), in-plain strain (8%) and velocity (8%) was observed. Finally, since an optimal core configuration was developed to better mitigate blast loadings, and an in-depth study was performed on the relationship between the weight of the panel and its overall blast performance, the research was continued with composite facesheet designs to better mitigate impact and blast loadings. Two types of core configurations were subjected to shock wave loading. The core material and thickness, as well as overall specimen dimensions were held constant, with the only difference arising in the resin system used during the infusion. The non-core-shell rubber toughened resin system (Non-CSR) consisted of a Vinyl-Ester resin only; while the CSR toughened resin consisted of the same Vinyl-Ester resin, but with Kane Ace MX-153 nano-scale core-shell rubber particles added to the mixture. Results indicated that adding nano-scale core-shell rubber (CSR) particles to sandwich composites, aids in dispersing the initial shock wave loading, thus reducing the overall deflection, strain, and velocity and improving the overall blast resistance of the structure.

First, shock tube experiments were performed to study the dynamic response of sandwich panels with E-glass Vinyl-Ester (EVE) composite facesheets and stepwise graded styrene acrylonitrile (SAN) foam cores. Two types of core configurations, with identical areal density, were subjected to the shock wave loading. The core layers were arranged according to the density of the respective foam; configuration 1 consisted of low / middle / high density foams and configuration 2 consisted of middle / low / high density foams. The method to calculate the incident and reflected energies of the shock wave, as well as the deformation energy of the specimen, were proposed based on the shock wave pressure profiles and the high-speed deflection images that were obtained. The experimental results showed that configuration 1 outperformed configuration 2 in regards to their blast resistance. Significant core material compression was observed in configuration 1, while in configuration 2 the core layers disintegrated and the front skin (blast side) fractured into two pieces along the midsection. The foam core compression in configuration 1 reduced the dynamic pressures seen on the back facesheet, and thus limited the total amount of damage imparted on the specimen. The estimated energies were then calculated for both configurations. The total energy difference between the incident and reflected energies was almost identical, even though the deformation energy for configuration 2 was larger.
Since it was observed that a stepwise graded foam core allows for more compression in the core, thus reducing dynamic pressures seen on the back facesheet, and limiting the total amount of damage imparted on the specimen, the study was then continued to investigate the influence of the number of foam core layers, as well as material interfaces, on the dynamic response of sandwich structures. Four types of core configurations were subjected to the shock wave loading. The foam core was monotonically graded based on increasing acoustic wave impedance, with the foam core layer of lowest wave impedance facing the blast. The specimen dimensions were held constant for all core configurations, while the number of core layers varied, resulting in specimens with one layer, two layer, three layer, and four layers of foam core gradation. The results indicated that even though each configuration allowed for a stepwise compression of the core, the number of core layers has an influence on the dynamic response of the structure under blast loading. More specifically, by increasing the number of monotonically graded layers, the acoustic wave impedance mismatch between successive layers is reduced. Therefore, the strength of the initial shock wave (stress wave) can be weakened by the time it reaches the back facesheet, resulting in lower back face deflection, in-plane strain, and velocity. More importantly, the overall damage imparted on the structure can be reduced and structural integrity can be maintained.
Due to the fact that higher levels of core gradation helped maintain structural integrity and improved the overall blast performance of sandwich structures, the study was then continued to investigate the blast response of sandwich structures with a functionally graded core and polyurea (PU) interlayer, and more importantly how the location of this polyurea interlayer affects the overall behavior and blast performance.
Two types of core configurations were subjected to shock wave loading. The materials, as well as the core layer arrangements, were identical, with the only difference arising in the location of the polyurea interlayer. The foam core itself was layered with monotonically increasing wave impedance of the core layers, with the lowest wave impedance facing the shock loading. For configuration 1, the polyurea interlayer was placed behind the front facesheet, in front of the foam core, while in configuration 2 it was placed behind the foam core, in front of the back facesheet. The results indicated that applying polyurea behind the foam core and in front of the back facesheet will reduce the back face deflection, particle velocity, and in-plane strain, thus improving the overall blast performance and maintaining structural integrity.
Since an optimized core configuration was determined, the study was continued to investigate the relationship between the weight of the panel and its overall blast performance. Two types of core configuration were subjected to shock wave loading.
The materials, as well as the core layer arrangements, and overall specimen dimensions were identical, with the only difference appearing in the core layers; one configuration utilized equivalent core layer thickness, while the other configuration utilized equivalent core layer mass. The foam core itself was layered based on monotonically increasing the acoustic wave impedance of the core layers, with the lowest wave impedance facing the shock loading. The results indicated that with a decrease in areal density of ~ 1 kg/m 2 (5%) from the sandwich composites with equivalent core layer thickness to the sandwich composites with equivalent core layer mass, an increase in deflection (20%), in-plain strain (8%) and velocity (8%) was observed.
Finally, since an optimal core configuration was developed to better mitigate blast loadings, and an in-depth study was performed on the relationship between the weight of the panel and its overall blast performance, the research was continued with composite facesheet designs to better mitigate impact and blast loadings. Two types of core configurations were subjected to shock wave loading. The core material and thickness, as well as overall specimen dimensions were held constant, with the only difference arising in the resin system used during the infusion. The non-core-shell rubber toughened resin system (Non-CSR) consisted of a Vinyl-Ester resin only; while the CSR toughened resin consisted of the same Vinyl-Ester resin, but with Kane Ace MX-153 nano-scale core-shell rubber particles added to the mixture. Results indicated that adding nano-scale core-shell rubber (CSR) particles to sandwich composites, aids in dispersing the initial shock wave loading, thus reducing the overall deflection, strain, and velocity and improving the overall blast resistance of the structure.   With growing concerns on safety and human lives involved, the significance of such research cannot be understated.

Sandwich structures have very important applications in the naval and aerospace
industry. Due to their construction they have many advantages that include high strength/weight ratio, high stiffness/weight ratio, and energy absorption capabilities.
Sandwich structures consist of two thin, stiff facesheets, usually the same thickness, separated by a lightweight, thicker core. The facesheets carry almost all of the bending and in-plane loads, while the core helps to stabilize the facesheets and defines the flexural stiffness and out-of-plane shear and compressive behavior. When sandwich structures are subjected to high-intensity impulse loadings, such as air blasts, the core materials play a crucial role in the dynamic behavior and overall structural response.
Their properties assist in dispersing the mechanical impulse that is transmitted into the structure, and thus protect anything located behind it [3][4][5].
2 Common cores are made of metallic and non-metallic honeycombs, cellular foams, balsa wood, PVC, truss and lattice structures. Extensive research exists in the literature regarding the dynamic response of sandwich structures consisting of the various core materials and geometric structures. Dharmasena et al. [5], Zhu et al. [6], and Nurick et al. [7] have tested sandwich structures with a metallic honeycomb core material. Their results indicated that the parameters of core materials can effectively reduce the transmitted impulse and damage of the back facesheet. Tagarielli et al. [8] has investigated the dynamic response of sandwich beams with PVC and balsa wood cores. Radford et al. [9] has conducted metal foam projectile impact experiments to simulate a blast loading on sandwich structures with metal foam cores. McShane et al. [10,11] have investigated the underwater blast response of sandwich composites with a prismatic lattice (Y-frame, corrugated), as well as simulated an air blast, using metal foam projectiles, on sandwich composites with a pyramidal lattice cores. These studies have indicated that advanced sandwich structures can potentially have significant advantages over monolithic plates of equivalent mass in absorbing the blast energy, whether in air or underwater.
In recent years, functionally graded materials, where the material properties vary gradually or layer by layer within the material itself, have gained much attention.
Hossain et al. [12] have experimentally studied the compressive behavior of a functionally graded foam material system and energy absorption under quasi-static loading conditions. The results indicated stepwise crushing from the lower density to the higher density foams. Kiernan et al. [13] numerically investigated the propagation of a stress wave through a virtual functionally graded foam material (FGFM). It was 3 concluded that the amplitude of a stress wave propagating through a FGFM can be shaped by the gradient functions according to which the foam density varies through the direction of wave propagation. Cui et al. [14] proposed a functionally graded foam model to improve the energy absorption characteristics offered by uniform foams. In this model, the characteristics of the foam (e.g. density) are varied through the thickness. Results indicated that for high energy impacts, increasing the density range can decrease the performance of the graded foams over conventional foams of uniform density. Consequently, decreasing the density range can increase the performance of the graded foams over conventional foams of uniform density.
Since the properties of the layered/graded material can be designed and controlled, they show great potential to be an effective core material for energy absorption and blast mitigation. To date, there have been very little results published regarding the dynamic impact response of sandwich composites with a functionally graded core, and even less regarding the blast response. Li et al. [15] numerically examined the response of layered and graded metal-ceramic structures under impulsive loadings. It was concluded that the choice of gradation has a great significance on the impact applications and the particular design can exhibit better energy dissipation properties. Apetre et al. [16]  Apart from the various core materials, the facesheet also plays an important role in the blast mitigation properties of the structure. In fact, the facesheet is the part of the structure which is directly exposed to the blast loading. Adhesive and fibercomposite materials are commonly based on epoxy polymers. The epoxies are highly cross-linked thermosetting polymers, which exhibit good elevated temperature resistance and low creep. However their high cross-link densities cause them to be relatively brittle in nature. This limits their applications as structural materials, as they have a poor resistance to crack initiation and growth.
The behavior of rubber toughened and core-shell rubber toughened epoxy resin has been extensively studied in the literature [27,28,[39][40][41][42][43][44][45]. The core-shell rubber particles consist of two parts, a core which is rubber for impact resistance, and a shell 6 which is a co-polymer compatible with epoxy resin. Note for these investigations, most of these rubber particles were on the micro-scale level. Results of these investigations indicated that the addition of rubber particles to epoxy resins can aid in increasing the fracture toughness, lap shear / T-peel strength, and fatigue resistance, as well as allow for no loss of T g or thermal properties (during infusion process), consistent morphology and a wide cure window. Therefore, the addition of rubber particles to current resin systems allows the once-brittle by nature resin to become toughened and subsequently more impact resistant.
Due to the improvement in mechanical properties, these rubber toughened epoxies can be used as the matrices for fiber-reinforced composite systems. However, the addition of these tougheners or pre-formed rubber particles, in the concentrations required to sufficiently enhance the toughness, can significantly increase the viscosity of the matrix resin. Also, conventional pre-formed particles generally have a particle diameter larger than the inter-fiber spacing, and particles are filtered out during infusion. This has led to the development of nano-scale rubber particles [44], defined as rubber particles less than 100 nm in diameter, since these particles will flow between the fibers during infusion [45]. However, research investigating nano-scale rubber toughened fiber-reinforced composite systems is extremely limited. 13

Abstract
Shock tube experiments were performed to study the dynamic response of sandwich panels with E-glass Vinyl-Ester (EVE) composite facesheets and stepwise graded styrene acrylonitrile (SAN) foam cores. Two types of core configurations, with identical areal density, were subjected to the shock wave loading. The core layers were arranged according to the density of the respective foam; configuration 1 consisted of low / middle / high density foams and configuration 2 consisted of middle / low / high density foams. The method to calculate the incident and reflected energies of the shock wave, as well as the deformation energy of the specimen, were proposed based on the shock wave pressure profiles and the high-speed deflection images that were obtained. The experimental results showed that configuration 1 outperformed configuration 2 in regards to their blast resistance. Significant core material compression was observed in configuration 1, while in configuration 2 the core layers disintegrated and the front skin (blast side) fractured into two pieces along the midsection. The estimated energies were then calculated for both configurations. The total energy difference between the incident and reflected energies was almost identical, even though the deformation energy for configuration 2 was larger. The present study focuses on the blast resistance and energy absorption of sandwich composites with a stepwise graded foam core when experimentally subjected to a shock wave loading. The results will help to understand the performance and the mechanisms of failure of sandwich composites with a stepwise graded core under blast loading and provide a guideline for a better core design. The quasi-static and dynamic constitutive behaviors of the foam core materials were first studied using a modified SHPB device with a hollow transmitter bar. The sandwich composites with two types of layered foam core arrangements were then fabricated and subjected to shock wave loading generated by a shock tube. The two types of sandwich composites have identical core materials but different core layer arrangements. The shock pressure profiles and real-time deflection images were carefully analyzed to reveal the failure mechanisms of these sandwich composites.
Based on the experimental data, the methods to calculate the energies of the incident shock wave (incident energy), the reflected shock wave (reflected energy) and the energy that deforms the specimen (deformation energy) were proposed and implemented. The energy redistribution in the system was analyzed, and the results showed that only a small amount of incident energy of the shock wave was transferred into the sandwich composites during the shock wave loading process.

Energy Evaluation
The incident energy, the reflected energy, and the deformation energy were calculated based on the shock wave pressure profiles and the high-speed deflection images obtained from the shock tube experiment. Fig. 1 shows a shock wave loading process with a shock tube. The definite state of the gas can be defined using the following physical parameters: p the pressure  the gas density u the gas particle speed c the speed of sound in gas The subscript 0 on the parameters denotes the initial state of the gas. Subscript 1 represents the state of the gas located behind the incident shock wave front and it will be defined as the incident state. Subscript 2 represents the state of the gas located behind the reflected shock wave front and it will be defined as the reflected state.

The Incident and Reflected Energies
The calculation of the incident and reflected energies is based on the incident and reflected shock wave pressure profiles. When a planar shock wave impacts a planar panel, the energy stored in the gas, which is located behind the shock wave front, will impinge on the structure. The stored energy in the gas is equivalent to the work done by the gas as it propagates through the cross-section of the shock tube. Note that the particle speed, u , of the gas located behind the shock wave front is important in evaluating the energies, and it is always less than the propagating speed, U , of the wave front. When a shock wave with a pressure profile, () pt , propagates within a (a) Incident shock process (b) Reflected shock process Fig. 1 Sketch of the incident and the reflected shock process shock tube with a cross-sectional area, S , it induces a particle speed, u and impacts a specimen, then the energy stored in the impinging gas during element time, dt , is equivalent to ( )* * * p t S u dt . Therefore, the total energy can be obtained by integrating ( )* * * p t S u dt with respect to time. The formulas for E incident and E reflected are as follows, where, 1 () pt is the incident pressure profile, 1 u is the particle speed behind the incident shock front, 2 () pt is the reflected pressure profile, and 2 u is the particle speed behind the reflected shock front. The incident energy, E incident , is the energy stored in the impinging gas, while the reflected energy, E reflected , is the energy stored in the gas after the incident shock wave impacted the specimen.
In Eq. (1) and Eq. (2), the cross sectional area, S , of the shock tube is known and the incident and reflected pressure profiles, 1 () pt and 2 () pt, can be measured. The particle velocities, 1 u and 2 u behind the incident and reflected shock front can be calculated using the theory of gas dynamics (Courant and Friedrichs, 1948).
Based on the Hugoniot relation of the polytropic gas and the jump conditions for the shock wave, we can derive the following equations (using incident shock process in Fig. 1a as an example), By assuming these particle speeds to be constant during the shock wave loading process, the incident and reflected energies can then be calculated by substituting Eq.

The Deformation Energy
The calculation of the deformation energy is based on the reflected shock wave pressure profile and the high-speed deflection images. The main idea is to obtain the deflection-time data from the high-speed deflection images and the force-time data from the reflected pressure profile. Combining the deflection-time data and the forcetime data will result in force-deflection data. Then the deformation energy can be obtained by integrating the force-deflection data. The measurement of the deflection is the most important step in this energy calculation. Since the force is only applied on the front face of the specimen, the deflection of the front face of the specimen is what we need. As shown in Fig. 2a, seven points were chosen along the profile of the front face of the specimen in the high-speed images, and a spline curve fitting was applied to match the shape of the front face. After calibrating the distance and choosing the reference point, we can calculate the deflection of every point on the front face. Thus, the deflection-time data can be obtained. Fig. 2b shows the typical deflection-time data obtained from this process. By assuming that the pressure applied on the shock area is uniform and combining the pressure-time data and the deflection-time data, the pressure-deflection profile can be obtained, as shown in Fig. 2c. Therefore, the deformation energy (E deformation ) can be calculated by integrating the pressure-deflection profile of every point inside the shock area. The formula is as follows:

Skin and Core Materials
The skin materials that were utilized in this study were E-glass Vinyl-Ester (EVE) specifically for marine sandwich composite applications. The three types of Corecell TM A-series foam that were used in the present study were A300, A500, and A800. Table 1 lists the important material properties of the three foams from the manufacturer's data (http://www.gurit.com).
The cell structures for the three foams were very similar and the only difference appears in the cell wall thickness and node sizes, which accounted for the different densities of the foams.

Sandwich Panels with Stepwise Graded Core Layer Arrangement
The 23 A300/A500/ A800 (low / middle / high density), and configuration 2 consisted of a core gradation of A500/A300/A800 (middle / low / high density). With these configurations it should be noted that the first core layer was the one first subjected to the shock wave loading. An actual sample can be seen in Fig. 3b.

Shock Tube
A shock tube apparatus was utilized to obtain the controlled blast loading (Fig.   5a). It had an overall length of 8 m, consisting of a driver, driven and muzzle section.
The high-pressure driver section and the low pressure driven section were separated by a diaphragm. By pressurizing the high-pressure section, a pressure difference across the diaphragm was created. When this difference reached a critical value, the diaphragms ruptured. This rapid release of gas created a shock wave, which travelled down the tube to impart dynamic loading on the specimen.  Reflected Pulse the muzzle section to measure the pressure profiles during the experiment. The final muzzle diameter was 0.0762 m. The distance between the two sensors was 0.16 m and the distance between the second sensor and the end of the muzzle was ~0.02 m. The specimen was placed in the support fixture, which ensured simply supported boundary conditions with a 0.1524 m span. The front face of the specimen was normal to the axis of the shock tube and had a ~1.6 mm initial gap to the muzzle end.

Experimental Procedure and Parameters
In the present study, a simply stacked diaphragm of 5 plies of 0.254 mm mylar sheets with a total thickness of 1.270 mm was utilized to generate an impulse loading on the specimen with an incident peak pressure of approximately

Dynamic Behavior of Core Materials
The As seen in Fig. 8, the quasi-static and dynamic stress-strain responses had an obvious trend for the different types of foams. Lower density foam has a lower strength and stiffness, as well as a larger strain range for the plateau stress.
The high strain-rate yield stresses and plateau stresses were much higher than the quasi-static ones for the same type of foam. Table 2 showed the quasi-static and high strain-rate yield stresses. The dynamic strength of A500 and A800 increased approximately 100% in comparison to their quasi-static strength, while A300 increased approximately 50%. The high yield stresses and long stress plateaus indicated that these foams can bear higher stresses and absorb larger amounts of energy. Therefore, they showed great potential in being used as core materials in sandwich structures subjected to high intensity blast loading.

Real-time Deformation
The real-time observations of the transient behavior of configuration 1 (A300/A500/A800) and configuration 2 (A500/A300/ A800) under shock wave loading were shown in Fig. 9 and Fig. 10 respectively. The shock wave propagated from the right side of the image to the left side and some detailed deformation mechanisms were pointed out in the figures.
For configuration 1, as shown in Fig. 9, the first core layer subjected to the shock wave was A300 and the core gradation was from the foam of least density and lowest strength to the foam of highest density and highest strength.

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In this case, two deformation mechanisms were observed during the panel deflection: core compression and global bending. The indentation failure of the front skin can be observed at t = 70 µs. Core compression of the A300 foam, the first core layer of gradation, can initially be observed at 140 µs. At this time there is no compression in the other two core layers of foam. Due to the compression of the foam, the high dynamic pressure applied to the front skin was substantially weakened by the time it reached the back skin. The measurements showed that at t = 420 µs and onward

Fig. 9
Real-time side view images of configuration 1 (A300/A500/A800) under shock loading the central deflection of the A300 foam was approximately 25% more than that of the A500 and A800 foams. This deflection can be directly related to the density of the A300 foam and its compressive strength. The double-winged deformation shape showed that the core of the sandwich structure was under intense shear loading. The onset of core failure, where core cracking begins, was observed at t = 280 µs and the initial separation / delamination of the front skin from the core was observed at t = 770 µs; this indicated relatively weak adhesion. Even though the onset of core failure began at t = 280 µs, complete core collapse and failure was not observed in this configuration.
In configuration 2, as shown in Fig. 10, A500 was the first core layer subjected to the shock wave and the core gradation began with the foam of middle density and middle strength, next the foam of least density and lowest strength, and then the highest density and highest strength foam.
The images in Fig. 10 show that indentation failure of the front skin began at t = 70 µs. Also note that the central core compression was not as prominent in this sandwich as can be seen in configuration 1. The initial separation / delamination of the core began at t = 350 µs and was located between the A500 and A300 foams. The onset of core failure, where core cracking began, can be seen at t = 140 µs and the onset of complete collapse of the core initiates at t = 490 µs, where the core cracking had traveled completely through the core. In this case, the only deformation mechanism observed was global bending.

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The major failure mechanism in configuration 2 was progressive damage of the core and the sandwich, which initiated at the back skin and was evident in Fig. 10.
This crack became a large inclined crack and propagated through the core from the back skin to the front skin. By t = 490 µs the crack had extended completely through the core and delamination between the A300 and A500 foam was very prominent.
Also at this time, many cracks were visible in the core which is followed by a rapid crushing of the core and catastrophic failure of the sandwich structure. This showed that configuration 2 cannot withstand the applied shock wave pressure, which had a peak value of ~4.83MPa.
Contrary to the case of configuration 2 the real-time deformation sequences observed in Fig. 9 for configuration 1 indicated that the major failure mechanism was core compression. The results showed that the core lay-up improved the overall performance of the structure. The onset of core failure took twice as long to be visible in this configuration as opposed to configuration 2 and no complete core collapse was evident. Even though delamination did occur, it was between the facesheet and foam core only. Overall configuration 1 outperformed configuration 2, and this was related to the dynamic constitutive behaviors of the foam core materials and the order of the core layer arrangements. For configuration 1, the strength of the core layers increase monotonously from the front facesheet to the back facesheet. Due to the low yield stress of the first core layer, A300, under dynamic loading, core compression occurred before the sandwich panel exhibited any bending (indentation failure in Fig. 9) and the core layers were compressed layer by layer. For configuration 2, the strength of the core layers did not increase monotonously from the front facesheet to the back facesheet. Here the first core layer, A500, had higher strength in comparison to A300 foam. These factors neutralized the core compression even though the core materials were identical. Thus bending occurred before the sandwich panel exhibited core compression.

Deflection
The mid-point deflections of each graded sandwich panel and all of its constituents were obtained from the high-speed images. The deflection of the front face (front skin), interface 1 (between first and second core layer), interface 2 (between second and third core layer), and back face (back skin) for configuration 1 and configuration 2 were plotted in Fig. 11 and Fig. 12. It can be seen in Fig. 11 for configuration 1 that the front face deflects to ~33 mm at ~t = 840 µs, which was approximately 25% more than the other three constituents. Note that the difference between the front face (skin) and interface 1 was the A300 foam, which was the weakest foam in three types of foams, and almost all compression occurs here (~7 mm).
On the contrary, all of the constituents of configuration 2 deflect in the same manner (shown in Fig. 12). This showed almost no obvious compression, even though the core foams of configuration 1 and configuration 2 were identical, but in a different gradation. Also this graded sandwich panel only deflected to ~29 mm at ~t = 840 µs.

Post-mortem Analysis
The damage patterns in the graded sandwich composites after the shock event occurred were visually examined and recorded using a high resolution digital camera and were shown in Fig. 13.
When configuration 1 was subjected to the highly transient loading, the damage was confined to the area where the supports were located in the shock tube and core cracking was visible in these two areas. Delamination was visible between the front skin and the foam core, as well as the back skin and the foam core. The core compression can be seen clearly and distinctively in the A300 foam.
Microscopic analysis of the failure and compression observed in configuration 1 was done using a Nikon SMZ microscope. Pre and post-blast core cell structures for the three layers of gradation were shown in Fig. 14. Note the heavy amount of compression seen in the A300 foam core cell structure. Also the cell structure for the 35 A500 foam did indeed compress, but not nearly as much as can be seen in the A300 foam. Likewise, the A800 foam core cell structure did compress, but only minimally.
Unlike the damage visible in configuration 1, configuration 2 suffered catastrophic damage as shown in Fig. 13. The core of the sandwich disintegrated and the front skin (blast side) of the sandwich fractured into two pieces at the midsection.
The back skin showed an extensive amount of fiber delamination in the central region as well.  surfaces show that the delamination surfaces exhibit similar material granules as those observed in a pure tension test.

Energy Evaluation
The energies calculated by the methods described in section 2 were shown in Fig.   16 and Fig. 17. With regards to the choice of the adiabatic component,  , the following explanation was offered. In the present shock tube experiments, prior to the diaphragm rupturing, one side of the diaphragm was helium (driver side), while the other side of the diaphragm was air (driven side). After the diaphragm ruptured the compressive shock wave travelled in the direction of higher pressure to lower pressure (helium -> air). Since the particle speed of the gas (helium) located behind the shock front was less than the speed of the shock front itself, air passed over the shock front and occupied the space located between the gas (helium) and the shock front during 37 the propagation of the shock wave. Therefore, by the time the shock wave reached the specimen, the gas located to the front and back side of the shock front were both airs.
Thus, the adiabatic exponent of air, 1.4   , was used in the energy calculations. Fig. 16 shows the incident and reflected energy calculated for configuration 1(A300/500/800). The difference between the incident and reflected energies was the total energy lost during the shock wave loading process. It included the energy absorbed by the composite structures, sound, light, heat, rigid body motion and other forms of energy. We defined it as the total amount of energy loss. It can be seen that there is a large amount of energy lost during the shock wave loading process.
The initial gap between the specimen and the muzzle end (~1.6 mm) increased after the impingement of shock on the specimen as the specimen deformed in a concave manner. The gas leak from this gap did affect the reflected energy calculation as it influenced the reflected pressure drop. Therefore, a fraction of energy was lost due to the gas that escaped from this gap. This lost energy was included in our estimation of the total energy loss.  Fig. 17a that the total energy loss for both configurations was almost identical. The deformation energy of configuration 2(A500/300/800) was a slightly higher than that of configuration 1(A300/500/800). This minimal difference can be ignored due to the error that arose showed no obvious structural collapse while configuration 2(A500/300/800) exhibited total structural collapse. Therefore, it can be concluded that configuration 1(A300/500/800) can withstand a higher blast loading than configuration 2(A500/300/800) and thus overall outperformed configuration 2.
Due to the fact that the deformation energy ( Fig. 17b) was much less than the total amount of energy loss (Fig. 17a), it can be concluded that only a small amount of energy was transferred into the sandwich structure. At 0.6 ms, the total energy loss was approximately 1300 J, while the deformation energy was only ~350 J. This indicated that only ~ 25% of the total energy lost was transferred into the specimen and most of the energy actually dissipated into other forms of energy (sound, heat, light, rigid body motion and various other forms).

Conclusions
(1) The dynamic stress-strain response was significantly higher than the quasistatic response for every type of Corecell TM A-series foam studied. Both quasistatic and dynamic constitutive behaviors of Corecell TM A-series foams (A300, A500, A800) showed an increasing trend.
Large compression was visible in the core when the least density foam (A300) is first in contact with the blast loading. This configuration reduced the dynamic pressures seen on the back facesheet, and thus limited the total amount of damage imparted on the specimen. When using the A500 foam first in contact with the blast loading, the overall deformation process of the sample was completely different. Compression in the core was limited, and thus the specimen showed a heavy amount of damage.
(3) The methods used to calculate the energy of the incident energy, the reflected energy and the deformation energy were proposed and implemented. The difference between the total incident and reflected energy was defined as the total energy loss in the system during the shock loading process. Only a small amount of energy was transferred into the specimens during the shock loading process. The total energy loss in the two configurations as well as their deformation energy was almost identical. Therefore, since configuration 2(A500/A300/A800) showed heavy damage and failure, it can be concluded that overall configuration 1(A300/A500/A800) outperformed configuration 2(A500/A300/A800).

Acknowledgements
Dr. Stephen Nolet and TPI Composites for providing the facility for creating the materials used in this study.

Abstract
The dynamic behavior of sandwich composites made of E-glass Vinyl-Ester (EVE) facesheets and graded Corecell TM A-series foam was studied using a shock tube apparatus. The foam core was monotonically graded based on increasing acoustic wave impedance, with the foam core layer of lowest wave impedance facing the blast.
The specimen dimensions were held constant for all core configurations, while the number of core layers varied, resulting in specimens with one layer, two layer, three layer, and four layers of foam core gradation. Prior to shock tube testing, the quasistatic and dynamic constitutive behavior (compressive) of each type of foam was evaluated. During the shock tube testing, high-speed photography coupled with the optical technique of Digital Image Correlation (DIC) was utilized to capture the realtime deformation process as well as mechanisms of failure. Post-mortem analysis was also carried out to evaluate the overall blast performance of these configurations. The results indicated that increasing the number of monotonically graded foam core layers, thus reducing the acoustic wave impedance mismatch between successive layers, helped maintain structural integrity and increased the blast performance of the sandwich composite.

Keywords: Sandwich Structures, Functionally Graded Materials, Acoustic Wave
Impedance, Blast Loading, High-Speed Photography

Introduction
Sandwich structures have very important applications in the naval and aerospace industry. Due to their construction they have many advantages that include high strength/weight ratio, high stiffness/weight ratio, and energy absorption capabilities.

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Sandwich structures consist of two thin, stiff facesheets, usually the same thickness, separated by a lightweight, thicker core. The facesheets carry almost all of the bending and in-plane loads, while the core helps to stabilize the facesheets and defines the flexural stiffness and out-of-plane shear and compressive behavior. When sandwich structures are subjected to high-intensity impulse loadings, such as air blasts, the core materials play a crucial role in the dynamic behavior and overall structural response.
Their properties assist in dispersing the mechanical impulse that is transmitted into the structure, and thus protect anything located behind it [1][2][3]. al. [4], and Nurick et al. [5] have tested sandwich structures with a metallic honeycomb core material. Their results indicated that the parameters of core materials can effectively reduce the transmitted impulse and damage of the back facesheet.
Radford et al. [6] and Wang et al. [7] have conducted metal foam projectile impact experiments to simulate a blast loading on sandwich structures with metal foam cores.
Tagarielli et al. [8] and Atas et al. [9] have investigated the dynamic response of sandwich beams with PVC and balsa wood cores. McShane et al. [10,11] have investigated the underwater blast response of sandwich composites with a prismatic lattice (Y-frame, corrugated), as well as simulated an air blast, using metal foam projectiles, on sandwich composites with a pyramidal lattice cores. These studies have indicated that advanced sandwich structures can potentially have significant advantages over monolithic plates of equivalent mass in absorbing the blast energy, whether in air or underwater.
In recent years, functionally graded materials, where the material properties vary gradually or layer by layer within the material itself, have gained much attention.
Hossain et al. [12] have experimentally studied the compressive behavior of a functionally graded foam material system and energy absorption under quasi-static loading conditions. The results indicated stepwise crushing from the lower density to the higher density foams. Kiernan et al. [13] numerically investigated the propagation of a stress wave through a virtual functionally graded foam material (FGFM). It was concluded that the amplitude of a stress wave propagating through a FGFM can be shaped by the gradient functions according to which the foam density varies through the direction of wave propagation. Cui et al. [14] proposed a functionally graded foam model to improve the energy absorption characteristics offered by uniform foams. In this model, the characteristics of the foam (e.g. density) are varied through the thickness. Results indicated that for high energy impacts, increasing the density range can decrease the performance of the graded foams over conventional foams of uniform density. Consequently, decreasing the density range can increase the performance of the graded foams over conventional foams of uniform density.
Since the properties of the layered/graded material can be designed and controlled, they show great potential to be an effective core material for energy absorption and blast mitigation. To date, there have been very little results published regarding the dynamic impact response of sandwich composites with a functionally graded core, and even less regarding the blast response. Li et al. [15] numerically examined the response of layered and graded metal-ceramic structures under impulsive loadings. It was concluded that the choice of gradation has a great significance on the impact applications and the particular design can exhibit better energy dissipation properties. Apetre et al. [16] numerically investigated the impact response of sandwich beams with a functionally graded core. Their results showed that a reasonable core design can effectively reduce the shear forces and strains within the structure. Consequently, they can mitigate or completely prevent impact damage on sandwich composites. In the previous work by the authors [17] they investigated the blast resistance of sandwich composites with a discretely layered foam core. They concluded that monotonically increasing the density of the foam core allows for a stepwise compression of the core layers and thus reduces the dynamic pressures imparted on the back facesheet.
Due to the fact that the authors' earlier work [17] was limited to sandwich composites with one specific foam core configuration (i.e. 3 layers of core gradation), the current study will expand upon the previous work and investigate the influence of the number of monotonically graded foam core layers (based on increasing acoustic wave impedance) on the overall blast response of the sandwich structure. For this investigation a series of four (4) different foam core layer arrangements were studied, which consisted of one layer, two layers, three layers, and four layers of gradation respectively. The purpose of this investigation was to study the role of material interfaces and the acoustic wave impedance mismatch between consecutive core layers on the dynamic behavior and blast response of the structure, and the results will help provide an optimal core design to help mitigate the high-intensity impulse 48 loading. More importantly, the rationale for this series was based off of creating a sandwich composite structure with enough foam core layers to reduce impedance mismatch between successive layers, therefore creating a theoretical "continuous" gradation. The quasi-static and dynamic constitutive behaviors of the foam core materials were first studied using a modified SHPB device with a hollow transmitted bar. The sandwich composites with different core layer arrangements were then fabricated and subjected to shock wave loading generated by a shock tube. All of the sandwich composites have an identical core thickness and overall specimen geometry, but a different number of core layers and overall areal densities. The shock pressure profiles and real-time deformation images were carefully analyzed to reveal the failure mechanisms of these sandwich composites. Digital Image Correlation (DIC) analysis was implemented to investigate the real-time deflection, in-plane strain and velocity of the back face of the specimens. Post-mortem analysis was also carried out to evaluate the overall blast performance of these sandwich structures.

Skin and Core Materials
The skin materials that were utilized in this study are E-glass Vinyl-Ester (EVE)  A-series foam that were used in present study were A300, A400, A500, and A800. Table 1 lists important material properties of the four foams from the manufacturer's data [18], as well as the material properties of the facesheet. The material properties of the facesheet and the core materials were determined using proper ASTM standards, D 3410 and D 1621 respectively, as well as Rule of Mixtures (ROM) formula (transverse material properties).
In Table 1, the A300 foam has the lowest nominal density (ρ), as well as compressive modulus (E) of the four foams, followed by the A400, A500 and A800 foams respectively. Since both the nominal density and the compressive modulus are increasing from A300 to A800 foam, the one-dimensional acoustic wave impedance (Z) also increases, and shows the following relationship, The cell structures for the four foams are very similar and the only difference appears in the cell wall thickness and node sizes, which accounts for the different densities of the foams. The SEM images of the cell microstructures can be seen in Fig. 2.

Sandwich Panels with Functionally Graded Core Layer Arrangement
The Vacuum Assisted Resin Transfer Molding (VARTM) process was utilized to fabricate the sandwich specimens. During the VARTM process, the sandwich specimens were infused under the same conditions, i.e. temperature, humidity, and vacuum pressure (760 mmHg (1 atm)), with the same volume of resin. The overall dimensions for the samples were approximately 102 mm wide, 254 mm long and 48 mm thick. The foam core itself was approximately 38 mm thick, while the skin thickness was approximately 5 mm.  Table 2. Foam core gradation and thickness For the sandwich composites with a functionally graded/layered core, a series of four different core layer arrangements were studied (as shown in Fig. 3a). The four different core layer arrangements/gradations, along with their respected foam thickness and overall average areal densities are shown in Table 2. These core layer arrangements were functionally graded by monotonically increasing the onedimensional acoustic wave impedance.
For one layer of core gradation, sandwich composites were created using A500 foam alone, and the core layer arrangement was A500/A500 (middle / middle density).
For two layers of core gradation, sandwich composites were fabricated using A300 and A800 foams, and the core layer gradation was A300/A800 (lowest / high density).
For three layers of core gradation, sandwich composites were created using A300, A500 and A800 foams, and the core layer gradation was A300/A500/A800 (lowest / middle / high density). Finally, for four layers of core gradation, sandwich composites were fabricated using A300, A400, A500, and A800 foams, and the core layer gradation was A300/A400/A500/A800 (lowest / low / middle / high density). With these configurations it should be noted that the first core layer is the one first subjected to the shock wave loading. Actual samples can be seen in Fig.3b. At the head and at the end of the hollow transmission bar, end caps made of the same material as the bar were press fitted into the hollow tube. By applying pulse shapers, the effect of the end caps on the stress waves can be minimized. The details of the

Shock Tube
The shock tube apparatus was utilized to obtain the controlled blast loading (Fig.   5a). It has an overall length of 8 m, consisting of a driver, driven and muzzle section.
The high-pressure driver section and the low-pressure driven section are separated by a diaphragm. By pressurizing the high-pressure section, a pressure difference across the diaphragm is created. When this difference reaches a critical value, the diaphragms rupture. This rapid release of gas creates a pressure wave that develops into a shock wave as it travels down the tube to impart dynamic loading on the specimen.

High-speed Photography Systems
Two high-speed photography systems were used in the present study, as shown in

Experimental Procedure and Parameters
In the present study, a simply stacked diaphragm of 5 plies of 0.254 mm mylar sheets with a total thickness of 1.270 mm was utilized to generate an impulse loading on the specimen with an incident peak pressure of approximately 1 MPa, a reflected peak pressure of approximately 5 MPa and a shock wave speed of approximately 1000 m/s. For each configuration, at least three samples were tested. A typical pressure profile obtained from the transducer closest to the specimen (~ 0.020 m away) can be seen in Fig. 7. It should be noted that both pressure transducers were utilized to obtain the shock wave history, i.e. incident / reflected pressure and incident / reflected velocity. However, only the pressure transducer closest to the specimen was utilized to obtain the pressure applied on the specimen. 57

Dynamic Behavior of Core Material
The four types of Corecell TM A-series foams have different quasi-static and dynamic compressive behavior. For the same type of Corecell TM foam, the material shows strain rate dependency from quasi-static to dynamic loading.   Table 3. Flow stresses (plateau) of Corecell TM A-series foams [19] regions; (I) the linear elastic region, (II) the plateau stress (plastic yielding) region and (III) the densification region [21]. For high strain rate compressive behavior, the stress-strain curves also show the three deformation regions, even though the densification region is much harder to achieve. Note the plateau stress regions for both instances have a large strain range.
As seen in Fig. 8, the quasi-static and dynamic stress-strain responses have an obvious trend for the different types of foams. Lower density foam has a lower strength and stiffness, as well as a larger strain range for the plateau stress.
The high strain rate yield stresses and plateau (flow) stresses are much higher than the quasi-static ones for the same type of foams. Table 3 shows the quasi-static and high strain rate plateau stresses (measured in the plateau stress region). The dynamic strengths of A500 and A800 foam increase approximately 100% in comparison to their quasi-static strengths, while the dynamic strengths of A300 and A400 foam increase approximately 50% in comparison to their quasi-static strengths.
The high yield stresses and long stress plateaus indicate that these foams can withstand higher stresses and absorb larger amounts of energy. Therefore, they show great potential in being used as core materials in sandwich structures subjected to high intensity blast loading.

Real-time Deformation
The real-time observations of the transient behavior for all types of configurations subjected to shock wave loading are shown in Fig. 9. The shock wave (pressure wave) propagates from the right side of the image to the left side and some detailed deformation mechanisms are pointed out in the figures. It should be noted that the time scheme used to represent the images in each configuration is identical. Therefore, for each of the four configurations investigated, the images are correlated based on the same time per frame. This allows for a better comparison between the different configurations in regards to the failure mechanisms and extent of damage observed.
Also, since each configuration is graded monotonically by increasing the acoustic wave impedance, the damage processes are identical. First, indentation failure (initiation of core compression) is observed; followed by core compression, core cracking, and then finally delamination, either between the skin and core or at the core layer interfaces. Fig. 9a shows the real-time blast loading response for the sandwich composites with one layer of core gradation. From these images, it can be seen that the indentation failure begins at approximately t = 100 μs. At t = 400 μs core cracking is evident. The crack starts at the lower support and propagates from the back face towards the front face. By t = 700 μs more core cracking is observed and delamination between the core layers can be seen. Skin delamination is evident at t = 1000 μs between the front facesheet and first core layer of foam, along with heavy first layer core compression.
By t = 1600 μs the core cracks have propagated completely through the core from the Core Layer Delamination back face to the front face, and the amount of delamination has increased. Also, the first layer core compression has reached a maximum, approximately 30% of its original thickness.
The real-time blast loading response for the sandwich composites with two layers of core gradation can be seen in Fig. 9b. Indentation failure for this configuration is observed at approximately t = 100 μs. By t = 400 μs, first layer core compression is very evident (A300). Also at this time, core cracking starting from the back facesheet where the lower support is located can be seen. By t = 700 μs more core cracking can be observed, as well as skin delamination between the front skin and the first core layer of foam (located at the bottom of the specimen). At t = 1000 μs more skin delamination can be observed between the front facesheet and the first core layer of foam, but this time it is located at the top of the specimen. By t = 1600 μs, the core cracks have propagated completely through the core from the back facesheet to the front facesheet. Also, the core compression in the first core layer has reached a maximum, approximately 75% of its original layer thickness. with three layers of core gradation. It can be seen from these images that the indentation failure begins at approximately t = 100 μs. Following indentation failure, heavy first layer (A300) core compression is observed as well as core cracking by approximately t = 400 μs. By t = 700 μs, the first core layer has compressed to a maximum, reaching a critical strain level and initiating the onset of indentation and compression in the second core layer of foam (A500). Also at this time, skin delamination between the front skin and the first core layer of foam is evident at the bottom of the specimen. At t = 1000 μs, more core compression is observed in the second core layer. Finally by t = 1600 μs, skin delamination can be seen at the top of the specimen between the front facesheet and the first core layer of foam. The core cracking has propagated completely through the core from the back facesheet to the front facesheet. Also at this time, the core compression in the first and second layers has reached a maximum, approximately 70% and 50% respectively.

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The real-time blast loading response for the sandwich composites with four layers of core gradation are shown in Fig. 9d. From these images, indentation failure is observed at approximately t = 100 μs. At t = 400 μs, heavy core compression is observed in the first core layer (A300). Also at this time, core cracking has initiated and is located at the bottom of the specimen where the supports are. By t = 700 μs a second core crack is evident at the top of the specimen where the upper support is located. Delamination is evident at the bottom of the specimen, between the first and second core layers of foam. Also at this time, the first core layer of foam has compressed to a maximum, reaching a critical strain level and initiating the onset of indentation and compression in the second core layer of foam (A400). By t = 1000 μs, the second core layer has compressed to a maximum, reaching a critical strain level, causing indentation and compression in the third core layer of foam (A500). Finally by t = 1600 μs, the total core compression has reached a maximum, the first layer and second core layer have compressed approximately 65%, while the third layer has compressed approximately 30%. Also at this time, delamination between the first and second core layer of foam is evident, and occurs at the top of the specimen. The core cracks have stopped propagating towards the front facesheet, and unlike the other configurations studied, these core cracks never propagated completely through the core.
In order to better evaluate the blast performance of the four different core layer arrangements studied, a more in depth look at the later time frames (t = 1000 μs and onward) of the high-speed images ( Fig. 9) must be investigated. For the sandwich composite with one layer of core gradation (as shown in Fig. 9a), it is evident at t = 63 1000 μs there are approximately four (4) major damage areas present. These damage areas consist of two heavy core cracks occurring in the central region of the specimen, one where the bottom support is located and the other just below the top support, as well as core delamination at the top of the specimen between the foam core layers, and skin delamination at the bottom of the specimen between the front facesheet and first core layer of foam.
Using two layers of core gradation, as shown in Fig. 9b, at t = 1000 μs again four For the sandwich composite with four layers of core gradation, as shown in Fig.   9d, again it can be observed that at t = 1000 μs only three (3) areas of damage are present. These damage areas consist of two core cracks occurring wear the supports are located and propagating into the central region of the specimen. Also at this time core delamination can be observed, which occurs at the bottom of the specimen between the first and second core layer of foam. The fourth damage zone can be observed at t =1600 μs. This damage area consists of core delamination at the top of the specimen, which occurs between the first and second core layer of foam.
Therefore, by looking at Fig. 9, it is clearly evident that when using sandwich composites with one and two layers of core gradation, four damage areas are present by t = 1000 μs. When using sandwich composites with three and four layers of core gradation, only three (3) damage areas are present at t = 1000 μs. The fourth damage zone isn't observed until later in the panel deformation. Therefore, it can be concluded that higher levels of core layer gradation (i.e. 3 and 4 layers), allow for a delay in the arrival of the fourth damage zone.

Deflection
The mid-point deflections of each graded sandwich panel and all of its constituents were obtained from the high-speed images and a typical response can be seen in Fig. 10. For one layer gradation, the midpoint deflection for the front face (front skin) and back face (back skin) of the specimen was plotted and can be seen in Therefore, the difference between the deflection of the front face and deflection of the back face signifies the total amount of compression observed in the core. Therefore, it can be concluded that the core compressed approximately 11 mm, which is 30% of its original thickness (38 mm).
When using two layers of core gradation, the midpoint deflection of the front face (front skin), interface (between first and second core layer), and back face of the specimen were plotted and are shown in Fig. 10b. It can be seen from the figure that at t = 1600 μs, the front face has deflected to approximately 46 mm, while the interface and the back face deflect to approximately 33 mm. The difference between the deflection of the front face and deflection of the interface indicates the total amount of compression observed in the first core layer of foam (A300 layer). Therefore, the first core layer of foam (A300) compressed approximately 13 mm, or 75% of its original thickness (19.05 mm). Since the interface and the back face deflect in an identical For three layers of core gradation, the midpoint deflection for the front face (front skin), interface 1 (between first and second core layer), interface 2 (between second and third core layer), and back face (back skin) were plotted and can be seen in Again, since interface 2 and the back face deflect in an identical manner to the same value of 31 mm, it can be concluded that no compression was observed in the third core layer of foam (A800).
Finally, when using four layers of core gradation, the midpoint deflection of the front face (front skin), interface 1 (between first and second core layer), interface 2 (between second and third core layer), interface 3 (between third and fourth core layer), and back face (back skin) were plotted and are shown in Fig. 10d. It can be seen from the figure that at t = 1600 μs, the front face has deflected to approximately 67 46 mm, while interface 1 has deflected to approximately 39 mm, interface 2 has deflected to approximately 33 mm, while interface 3 and the back facesheet deflect to approximately 29 mm. The difference between the deflection of the front face and the deflection of interface 1 signifies the total amount of compression in the first core layer of foam (A300). Therefore, it can be seen that A300 foam compresses approximately 7 mm, which is ~ 70% of its original thickness (9.53 mm). Looking at the difference between the deflection of interface 1 and the deflection of interface 2, the amount of compression observed in the second core layer of foam (A400) can be obtained. It can be seen that the A400 foam compresses approximately 6 mm, or ~ 65% of its original thickness (9.53 mm). The difference between the deflection of interface 2 and the deflection of interface 3 indicates the total amount of compression observed in the third layer of foam (A500). Therefore, it is evident that the A500 foam compressed approximately 4 mm, which is ~ 40% of its original thickness (9.53 mm).
Since interface 3 and the back face deflect in an identical manner to the same value of 29 mm, it can be concluded that no compression was observed in the fourth core layer of foam (A800).
It should be noted that for all of the configurations studied, the core layers were graded monotonically by increasing the acoustic wave impedance, and therefore allowing for a stepwise compression of the core. This stepwise compression is more evident in the three and four layer core configurations, i.e. Fig. 10c and Fig. 10d.
From the deflection data of each interface in Fig. 10, the deformation of each core layer along the mid-line (line of symmetry) can be obtained by subtracting the core layers' back side deflection from the core layers' front side deflection. Sequentially, the strain along the line of symmetry of each core layer can be obtained using the where, l original is the original thickness of the each core layer.
The strain histories of the core layers for each configuration, as calculated from Eq. (3) using the mid-point deflection data from Fig. 10, are shown in Fig. 11 respectively. Since there is no compression in the A800 foam core layer, its strain history is not shown here.
It is evident from the figure when using sandwich composites with higher levels of core gradation, the maximum strain levels achieved in the same individual core layer of foam is reduced. For the A300 foam core layer, the maximum strain level When using higher levels of core gradation, three and four layers ( Fig.11c and Fig.   11d), the A300 layer exhibits a maximum strain level of approximately 70% and 65% respectively. For the A500 foam core layer, the maximum strain level achieved using three layers of core gradation (Fig. 11c) was approximately 50%, while the strain level was reduced to approximately 30% when using four layers of core gradation (Fig.   11d). Note that even though the A500 foam core layer exhibited its lowest maximum strain value when using one layer of core gradation (Fig. 11a), heavy core cracking was observed early in the deformation history and subsequently its strain values and overall behavior will not be discussed in full.
For the sandwich composite with two layers of core gradation (Fig. 11b), the A300 core layer exhibited a maximum strain level of approximately 75% -80% at t = 500 μs, which corresponds to a stress level of approximately 3.8 MPa (Fig. 8b). Note that the stress level required to initiate compression (increase strain) in the second core layer (A800) is approximately 4.0 MPa (Fig. 8b). Therefore, no compression (strain) is observed in the A800 foam layer.
For the sandwich composite with three layers of core gradation (Fig. 11c), the maximum strain level achieved in the A300 foam was approximately 70% at t = 400 μs, which corresponds to a stress level of 2.8 MPa (Fig. 8b). Note that the stress level required to initiate compression (increase strain) in the second core layer (A500) is approximately 1.6 MPa (Fig. 8b). Therefore, core compression (strain) is expected in this layer of foam by t = 400 μs. In regards to the A500 layer, this layer exhibited a maximum strain level of approximately 50% at t = 900 μs, which corresponds to a 70 stress level of approximately 2.6 MPa (Fig. 8b). Note that the stress level required to initiate compression (increase strain) in the third core layer (A800) is approximately 4.0 MPa (Fig. 8b). Therefore, no compression (strain) is observed in the A800 foam layer.
For the sandwich composite with four layers of core gradation (Fig. 11d), the maximum strain level achieved in the A300 foam was approximately 60% -65% by t = 600 μs, which corresponds to a stress level of approximately 2 MPa (Fig. 8b). Note that the stress level required to initiate compression (increase strain) of the second core layer (A400) is approximately 0.9 MPa (Fig. 8b). Therefore, core compression (strain) is expected in this layer of foam by t = 600 μs. For the A400 foam core layer, this layer exhibited a maximum strain level of approximately 60 -65% by t = 600 μs, which corresponds to a stress level of approximately 2.1 MPa (Fig. 8b). Note that the stress level required to initiate compression (increase strain) of the third core layer (A500) is approximately 1.6 MPa (Fig. 8b). Therefore, core compression (strain) is expected in this layer of foam by t = 600 μs. For the A500 foam core layer, this layer exhibited a maximum strain level of approximately 30%, which corresponds to a stress level of approximately 1.8 MPa (Fig. 8b). Note that the stress level required to initiate compression (increase strain) of the fourth core layer (A800) is approximately 4.0 MPa (Fig. 8b). Therefore, no compression (strain) will be observed in the A800 foam layer. Table 4 shows the exact strain (dynamic) values necessary to initiate compression in each of the subsequent foam core layers, as generated from Fig. 8b. Correlating these strain values, to the strain-time history plot in Fig. 11, the exact time of Table 4. Dynamic strain required to initiate compression in subsequent foam core layers compression in each of the successive foam core layers for all gradations can be generated.
An interesting phenomenon can be observed from deflection data and strain results in Fig. 10 and Fig. 11 respectively. By looking at the deflection data ( Fig. 10) for two, three and four layers of core gradation by t = ~ 600 μs, the foam core of each configuration has compressed the same amount, approximately 13 mm. Using the same time, t = ~ 600 μs, and referring to the strain history of each configuration (Fig   11), for a sandwich composite with two layers of core gradation, only the first foam core layer (A300) is compressed. For higher levels of core gradation, i.e. three and four layers, by t = 600 μs, compression in multiple layers has initiated, and thus increasing strain values in subsequent layers can be observed. In regards to the sandwich composite with three layers of core gradation, both the first (A300) and second (A500) core layers exhibit increasing levels of strain (compression). When using four layers of core gradation, the first (A300), second (A400) and third (A500) foam core layer all show increasing levels of strain (compression). Even though the total amount of core compression is the same (~ 13 mm) in all core configurations, the Foam Type A300 A400 A500 A800 A300 -30% (300μs) 60% (400-500 μs) 80%

A400
--55% (500-600 μs) 75% compression of the denser foams (A400 and A500) in the panels with higher levels of gradation (three and four layers), signifies their ability to absorb more energy. Fig. 12 shows a comparison between the front face deflection (a) and the back face deflection (b) for the four different core configurations. It is evident from Fig.   12a, that at t = 1600 μs, the front face deflection for all core configurations are in excellent agreement (within 5%) It can also be observed that two layers of core gradation showed the most front face deflection, followed by three layers of core gradation. This is due to the thickness of the A300 foam layer (lowest density) located behind the front facesheet and its ability to compress. For two layer gradation and three layer gradation, the A300 layer of foam is approximately 19.05 mm and 12.70 mm respectively.
When looking at Fig. 12b, an interesting phenomenon is observed. At t = 1600 μs, the back face deflection for the sandwich composite with one layer of core gradation is approximately 35 mm, which is followed by two layer gradation, three layer gradation, and four layer gradation, with back face deflections of approximately 33 mm, 31 mm and 29 mm respectively. Therefore, in relation to the back face deflection of the sandwich composite with one layer gradation, two layer gradation deflects ~ 6% less, three layer gradation deflects ~ 11% less, and four layer gradation deflects ~ 17% less.

Digital Image Correlation (DIC) Analysis
Utilizing the Digital Image Correlation (DIC) technique, the full-field deflection, in-plane strain and particle velocity of the back facesheet of each configuration was generated. Figures 13, 14, 15 show the full-field results for the back facesheet of all core gradations respectively. Fig. 13 shows the full-field out-of-plane deflection (W) during the initial fluid-structure interaction (t ≤ ~ 250 μs, [22]), with an emphasis on the shape of the loading, as indicated by the localized areas of larger deflection. Note that the scale used to represent each core gradation is different in order to highlight these areas. For one layer core gradation, as shown in When using two layers of core gradation (Fig. 14b), it can be seen that at t = 1600 μs, t = 100 μs t = 400 μs t = 1000 μs t = 1600 μs t = 700 μs  conclusive, but the trend is evident. When using more than one layer of core gradation, it can be seen that the strain distribution is altered, resulting in a reduction of maximum in-plane strain values observed on the back facesheet.
Using the point inspection tool from the Digital Image Correlation (DIC) software, a point directly in the center of the back face of each specimen was chosen.
The out-of-plane deflection (W) showed excellent agreement with the results generated utilizing the high-speed images and therefore only the in-plane strain (ε yy ) and out-of-plane velocity (dW/dt) results are shown. Fig. 16 and Fig. 17 show the inplane strain and out-of-plane velocity values obtained. Looking at the in-plane strain values ( Fig. 16) it can be seen that at t = 1600 μs, the maximum in-plane strain value at the central point of the back facesheet for one layer core gradation is approximately 2.4%. When using more layers of core gradation, i.e. two, three and four layers, at t = 1600 μs the maximum in-plane strain values are reduced to 2.3%, 2.2% and 2.1% respectively. Therefore, it can be concluded that using more layers of core gradation, the maximum in-plane strain values are reduced by 4%, 8% and 12.5% for two, three and four layer gradation in comparison to one layer of core gradation. 79

Post-mortem Analysis
After the blast loading event occurred, the damage patterns of the sandwich composites with four different core layer arrangements were visually examined and recorded using a high resolution digital camera and are shown in Fig.18. When the sandwich composite with one layer core gradation was subjected to highly-transient loading, as shown in Fig. 18a, the damage was confined to the areas where the supports were located in the shock tube and core cracking is visible in these two areas.
The core cracks propagated completely through the foam core. Core delamination is visible between the two core layers of A500 foam. Also one of the core cracks lead to back skin delamination, where the core separated from the back facesheet. Some core compression is also visible in the first core layer of A500 foam.
For the sandwich composite with two layers of core gradation, the damage patterns after being subjected to the shock loading are shown in Fig. 18b. For this core configuration, the damage was again confined to the areas where the supports were located in the shock tube and core cracking is evident. The core cracks propagated completely through the foam core. Skin delamination is obvious between the front facesheet and the foam core, as well as back skin delamination between the back facesheet and the foam core. Core delamination between the first and second core layers of foam, A300 and A800 respectively, is also evident, along with core compression in the first core layer of foam (A300). Fig. 18c shows the damage patterns of the sandwich composite with three layers of core gradation after the blast loading event occurred. Again, the damage to this core configuration was confined to the areas where the supports were located in the shock tube and core cracking is visible in these two areas. These core cracks propagated completely through the foam core. Also skin delamination is visible between the front facesheet and the foam core, as well as back skin delamination located between the 82 back facesheet and the foam core. Core compression is also evident in both the first and second core layers of foam, A300 and A500 respectively.
When the sandwich composite with four layers of core gradation was subjected to the shock loading, as shown in Fig. 18d, the damage was again confined to the areas where the supports from the shock tube were located and core cracking is evident in these two areas. Unlike the previous three configurations, the core cracks did not propagate completely through the foam core. Core delamination is obvious between the first and second core layers of foam, A300 and A400, as well as back skin delamination between the back facesheet and the foam core. Core compression is very obvious in this configuration. The first, second and third layer of foam, A300, A400 and A500 respectively, all exhibit various amounts of core compression.

Permanent Deformation
The permanent deflection (deformation) for each graded core configuration was measured after the shock loading experiment. A schematic of the specimen and how the measurements were taken can be seen in Fig. 19. The distance between the top dotted line (red) and the front surface of the front facesheet is defined as the permanent deflection of the front face. Similarly, the distance between the bottom dotted line and the top surface of the back facesheet is defined as the permanent deflection of the back face. Subtracting the total permanent deflection of the back face from the front face, the final core thickness and thus total core compression (permanent) can be obtained. These values are shown in Table 5. This results in a total core compression of approximately 5.6 mm (15%). When using four layers of core gradation, the front face shows approximately 12. 4 mm of permanent deflection, while the back face shows 6.1 mm. Consequently, the total permanent compression of the core is 6.3 mm (17%). Therefore, increasing the number of monotonically graded core layers results in higher levels of permanent core compression, but lower levels of permanent back face deflections.

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The total core compression observed during the experiment, as measured from the high-speed images and shown in Fig. 10 is listed in Table 5 (Real-time core compression). Subtracting the total permanent core compression from the real-time core compression, the total amount of core compression recovered can be measured.
When using one and two layers of core gradation, the amount of core compression recovered is almost the same, approximately 8.4 mm and 8.1 mm respectively. When using three and four layers of core gradation, the total amount of core compression recovered is 9.4 mm and 10.7 mm. Thus, higher levels of core gradation allow for larger amounts of real-time compression to be recovered. This can be directly related to the strain-time history data in Fig. 11 and discussed in Section 4.2.2. When using higher levels of core gradation, the maximum strain values achieved in the same individual foam core layers was reduced. For the A300 foam core layer, the maximum amount of strain was reduced from approximately 80% for two layer gradation, to 70% and 65% for three and four layers of core gradation respectively. For the A500 foam core layer, the maximum amount of strain was reduced from 50% for three layers gradation to 30% for four layer of core gradation. Therefore, with higher levels of core gradation, the same individual foam core layers exhibit less strain, thus allowing for more real-time core compression to be restored post-blast.
The post-mortem images in Fig. 18, along with the results generated in Table 5, indicate the ability of functionally graded sandwich composites with higher levels of core gradation (three and four) to better mitigate blast energy. The sandwich panels with three and four layers of core gradation exhibited the largest amount of total core compression, 5.6 mm (15%) and 6.3 mm (17%), but the least amount of permanent Table 5. Permanent deflection and core compression back face deflection, 7.3 mm and 6.1 mm. Also, these sandwich panels showed the largest amount of real-time core compression recovered, 9.4 mm (25%) and 10.7 mm (28%).

Materials
The stress wave propagation in functionally graded/layered materials has been extensively investigated by [23 -29]. Note for these investigations the wave interactions within the specimens were treated as one-dimensional, and without dispersion and compression waves. Makris et al. and Nerenberg et al. [23,24] studied the attenuation of a blast wave with a cellular material (polymeric foam) and found that if a foam layer is loaded by a decaying blast wave, as opposed to a shock wave with a constant pressure profile, the shock wave transmitted through the foam may either be amplified or attenuated, depending on the blast wave strength and duration as well as the foam stiffness and thickness. Attention must be paid to the sequence and ordering of the layers, which introduces interfaces and affects the stress transmission greatly [25]. The stress at an interface with a large variation in impedances will mainly be governed by the properties of the material with lower impedance. Similarly, the equilibrium motion of the interface is governed by the material with high impedance [26]. Changjing et al. [27] found that during dynamic compression, the increase in the acoustic impedance should be small, and a better matching of wave impedance for layered media can change the stress peak value, duration, and energy distribution based on the consideration of wave attenuation and energy dissipation.
These results demonstrated that combining materials with pronounced differences in material properties, in an optimal configuration and arrangement, can lead to efficient wave attenuation. There are two ways in which the peak pressure of a compression or shock wave can be attenuated: through expansion of the high pressure shock wave (energy dissipation mechanism) or through scattering/dispersion of the wave through interface variations. During blast wave loading, the expansion wave following the shock wave is the main cause of the attenuation. As the rarefraction wavelets propagate faster in the compacted foam than the shock wave in the porous foam, the expansion fan is able to catch up to the shock wave and attenuate it gradually in a sufficiently thick foam layer [23,24]. By altering the number of interfaces and distribution of materials within a composite structure, the wave decoupling (scattering/dispersion) effect could be optimized. In other words, as the number of interfaces is increased, the number of wave reflections within the material system is greatly increased as well. These reflections lengthen the timescales for pressure rise across the sample [26,28] allowing for a time-delay of the peak stress arrival, which in turn delays the time of damage initiation [29].
Even though it is nearly impossible to conclude which mechanism had a more important role in attenuating the stress wave, thus improving the dynamic performance of the structure when subjected to a blast loading, we do know that both mechanisms played a vital role. By inspecting the high-speed images in Fig. 9 and deflection plots in Fig 10, it can be observed that increasing the number of core layers allows for a stepwise compression of the core (energy dissipation mechanism). The scattering method of wave attenuation (time-delay phenomena) can be observed in the out-ofplane velocity (dW/dt), Fig. 17, as well as the high-speed images, Fig. 9. When using three and four layers of core gradation, the maximum velocities are reached 100 μs and 200 μs respectively after the sandwich composites with one and two layers of core gradation (Fig. 17). This time-delay in the maximum velocity in turn delays the time of damage initiation, as seen in Fig. 9 and discussed in Section 4.2.1. When using more layers of core gradation (three and four), and thus introducing more material interfaces, the onset of the fourth damage zone was delayed (~ 200 μs).

Conclusions
The following is the summary of the investigation: (1) The dynamic stress-strain response is significantly higher than the quasi-static response for every type of Corecell TM A foam studied. Both quasi-static and dynamic constitutive behaviors of Corecell TM A series foams (A300, A400, A500, and A800) show an increasing trend. The increase in the yield strength from quasi-static response to dynamic response, along with the longer stress plateau, indicates that these foam materials show great potential in absorbing large amounts of energy.

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(2) Sandwich composites with four different core layer arrangements, one, two, three and four layers respectively, were subjected to shock wave loading. The overall performance of the sandwich composite with four layers of core gradation is the best, followed by the sandwich composites with three, two and one layer gradation respectively. Even though each configuration allowed for a stepwise compression of the core, it was shown that the number of core layers has an influence on the dynamic response of the structure under blast loading.
More specifically, by increasing the number of monotonically graded layers, the acoustic wave impedance mismatch between successive layers is reduced.
Therefore, the strength of the initial shock wave (stress wave) can be weakened by the time it reaches the back facesheet, resulting in lower back face deflection, in-plane strain, and velocity. More importantly, the overall damage imparted on the structure can be reduced and structural integrity can be maintained.
(3) Increasing the number of monotonically graded foam core layers, thus introducing more material interfaces, allows for blast wave (stress wave) attenuation through the following mechanisms: (1) stepwise compression of the core (energy dissipation mechanism) and (2) scattering/dispersion of the wave through interface variations. Combining these mechanisms results in lengthened timescales for pressure rises across the samples, allowing for a time-delay of the peak stress arrival, and thus delaying the time of damage initiation.
(4) When using higher levels of core gradation, i.e. two, three and four layers respectively, the amount of stress transferred to subsequent layers is diminished, thereby subjecting the back face to reduced loadings and blast pressures.

Acknowledgements
The authors kindly acknowledge the financial support provided by Dr. Yapa D. S. 94

Abstract
The dynamic behavior of two types of sandwich composites made of E-glass Vinyl-Ester (EVE) facesheets and Corecell TM A-series foam with a polyurea interlayer was studied using a shock tube apparatus. The materials, as well as the core layer arrangements, were identical, with the only difference arising in the location of the polyurea interlayer. The foam core itself was layered with monotonically increasing wave impedance of the core layers, with the lowest wave impedance facing the shock loading. For configuration 1, the polyurea interlayer was placed behind the front facesheet, in front of the foam core, while in configuration 2 it was placed behind the foam core, in front of the back facesheet. A high-speed side-view camera, along with a high-speed back-view 3-D Digital Image Correlation (DIC) system, was utilized to capture the real-time deformation process as well as mechanisms of failure. Postmortem analysis was also carried out to evaluate the overall blast performance of these two configurations. The results indicated that applying polyurea behind the foam core and in front of the back facesheet will reduce the back face deflection, particle velocity, and in-plane strain, thus improving the overall blast performance and maintaining structural integrity.

Introduction
Core materials play a crucial role in the dynamic behavior of sandwich structures when they are subjected to high-intensity impulse loadings such as air blasts. Their properties assist in dispersing the mechanical impulse that is transmitted into the structure and thus protect anything located behind it [1][2][3]. Stepwise graded materials, where the material properties vary gradually or layer by layer within the material itself, were utilized as a core material in sandwich composites due to the fact that their properties can be designed and controlled. Typical core materials utilized in blast loading applications are generally foam, due to their ability to compress and withstand highly transient loadings. In recent years, with its ability to improve structural performance and damage resistance of structures, as well as effectively dissipate blast energy, the application of polyurea to sandwich structures has become a new area of interest The numerical investigation by Apetre et al. [4] on the impact damage of sandwich structures with a graded core (density) has shown that a reasonable core design can effectively reduce the shear forces and strains within the structures.
Consequently, they can mitigate or completely prevent impact damage on sandwich composites. Li et al. [5] examined the impact response of layered and graded metalceramic structures numerically. He found that the choice of gradation has a great significance on the impact applications and the particular design can exhibit better energy dissipation properties. In their previous work, the authors experimentally investigated the blast resistance of sandwich composites with stepwise graded foam cores [6]. Two types of core configurations were studied and the sandwich composites were layered / graded based on the densities of the given foams, i.e. monotonically and non-monotonically. The results indicated that monotonically increasing the wave impedance of the foam core, thus reducing the wave impedance mismatch between successive foam layers, will introduce a stepwise core compression, greatly enhancing the overall blast resistance of sandwich composites.
Although the behavior of polyurea has been investigated [7][8][9][10], there have been no studies regarding the dynamic behavior of functionally graded core with a polyurea interlayer. Tekalur et al. [11] experimentally studied the blast resistance and response of polyurea based layered composite materials subjected to blast loading. Results The present study focuses on the blast response of sandwich composites with a functionally graded core and a polyurea (PU) interlayer. Two different core layer configurations were investigated, with the only difference arising in the location of the polyurea (PU) interlayer. The quasi-static and dynamic constitutive behaviors of the foam core materials, as well as the polyurea, were first experimentally studied using a modified SHPB device with a hollow transmitted bar. The sandwich composites were then subjected to shock wave loading generated by a shock tube. The shock pressure profiles, real-time deflection images, and post-mortem images were carefully analyzed to reveal the mechanisms of dynamic failure of these sandwich composites. Digital Image Correlation (DIC) analysis was implemented to investigate the real-time deflection, strain, and particle velocity.

Skin and Core Materials
The skin materials that were utilized in this study are E-glass Vinyl-Ester (EVE)   Table 1 lists important material properties from the manufacturer's data of the three foams [17], as well as the Dragonshield-HT polyurea [18] and the material properties of the facesheet as determined using ASTM standards.
In Table 1, the A300 foam has the lowest nominal density (ρ), as well as compressive modulus (E) of the three foams, followed by the A500 and A800 foams respectively.
Since both the nominal density and the compressive modulus are increasing from A300 to A800 foam, the wave impedance also increases.
The cell structures for the three foams are very similar and the only difference appears in the cell wall thickness and node sizes, which accounts for the different densities of the foams. The SEM images of the cell microstructures can be seen in Fig.   2.  Table 1 Material properties for foam core [17] and polyurea [18] 100 Two core configurations, which consisted of identical core materials, were studied (as shown in Fig. 3a). For configuration 1, the polyurea interlayer was placed behind the front facesheet and in front of the foam core (PU/A300/A500/A800). For configuration 2, the polyurea interlayer was placed behind the foam core, and in front of the back facesheet (A300/A500/A800/PU). With these configurations it should be noted that the first core layer is the one first subjected to the shock wave loading.
Actual samples can be seen in Fig.3b.

Shock Tube
The shock tube apparatus was utilized to obtain the controlled blast loading (Fig.   5a). It has an overall length of 8 m, consisting of a driver, driven and muzzle section.
The high-pressure driver section and the low pressure driven section are separated by a diaphragm. By pressurizing the high-pressure section, a pressure difference across the diaphragm is created. When this difference reaches a critical value, the diaphragms

High-speed Photography Systems
Two high-speed photography systems were used in the present study, as shown in  Another high-speed digital camera, [Photron SA1], was placed perpendicular to the side surface of the specimen to capture the side-view deformation images. A framing rate of 20,000 fps was utilized which gives an interframe time of approximately 50 μs.

Experimental Procedure and Parameters
An initial series of experiments was conducted for both configurations and three samples were tested for each. This was followed by a second set of experiments, in

Dynamic Behavior of Core Material
The quasi-static and dynamic stress-strain curves for the core materials are obtained and shown in Fig.8. The four types of core materials used in the present study have different quasi-static and dynamic behavior. For the same type of Corecell TM A foam and Dragonshield-HT polyurea, the material behavior under high strain rate loading is significantly different from its behavior under quasi-static loading.
The yield stresses of core materials under quasi-static and high strain rate loading are listed in Table 2. The dynamic yield stress of A500 and A800 increases approximately 100% in comparison to their quasi-static yield stress, while the dynamic yield stress of A300 increases approximately 50% in comparison to its quasistatic yield stress. Also it can be observed that the high strain-rate yield stress of  First Layer Compression high strain-rates for all core materials used in the present study signifies their ability to absorb more energy under high strain-rate dynamic loading.

Real-time Deformation
The real-time observations of the transient behavior for both core configurations subjected to shock wave loading are shown in Fig. 9 and Fig. 10. The real-time blast loading response of configuration 1 (PU/A300/A500/A800) is shown in Fig. 9. It can be observed from the images that indentation failure (initiation  The real-time blast loading response of configuration 2 (A300/A500/A800/PU) is shown in Fig. 10. It is evident from the figure that indentation failure begins at t = 150 μs. After indentation failure is observed, heavy core compression is observed in the first core layer (A300 foam). By t = 650 μs the first layer of foam (A300) has compressed to a maximum, reaching its densification level, and the shock wave has now propagated into the second foam core layer (A500), initiating compression of this core layer. Also at this time, a core crack has initiated at the bottom of the specimen where the support is located. Skin delamination is evident between the front skin and the foam core, and is located at the bottom of the specimen. At t = 1150 μs skin delamination can be observed at the top of the specimen between the front facesheet and the foam core. Also at this time the compression in the second foam core layer has increased to its maximum and no more compression is observed in the core, resulting in a global bending response. Between t = 1150 μs and t = 1800 μs, no new failure mechanisms were observed. The core crack continues to propagate through the third layer of the foam core (A800) and skin delamination at the bottom of the specimen has increased between the front facesheet and the foam core.
Comparing the deformation mechanisms observed in configuration 1 and configuration 2, the location of the polyurea interlayer affects the order and level of different failure mechanisms, such as core compression, core cracking and interface delamination, as well as the time at which they are first observed. In configuration 1, indentation failure (core compression) is followed by delamination in the core and then core cracking. Unlike configuration 1, the indentation failure of configuration 2 is followed by heavy core compression, core cracking and then skin delamination.
Comparing both configurations, the indentation failure is observed at approximately the same time, while core cracking and delamination initiate in configuration 1 earlier in the deformation, approximately 100 μs and 250 μs respectively, than in configuration 2.
The location of the polyurea interlayer also affects the core deformation mode for each configuration. In configuration 1 the initial blast loading is uniformly distributed over the polyurea layer, resulting in a global uniform compression of the first layer of the foam core (A300). On the contrary, in configuration 2 the initial impulse is nonuniformly distributed into the foam core, resulting in a local compression in the central region of the first layer of the foam core (A300) where the shock loading was applied.
This indicates that the polyurea interlayer has the ability to disperse the shock loading.
Also, the deformation shape for both configurations is much different. For configuration 1, the specimen exhibits a double-winged deformation shape until approximately t = 400-500 μs, then the polyurea layer begins to delaminate from the core, exhibiting a shape much like a specimen in pure bending. For configuration 2, the specimen exhibits a double-winged deformation shape throughout the entire blast loading event. Therefore, configuration 2 has the ability to support the shear stresses that are present during the event, while configuration 1 could not.

Deflection
The mid-point deflections of the constituents of sandwich composites with different core configuration were obtained from the high-speed side-view images and shown in Fig. 11. For configuration 1, the mid-point deflection of the front face (front skin), interface 1 (between first and second core layer), interface 2 (between second and third core layer), interface 3 (between third and fourth core layer), and back face (A300 foam). Therefore, it can be observed that the A300 foam layer compressed approximately 9 mm, or 75% of its original thickness (12.7 mm). Again, noting the difference between the deflection of interface 1 and interface 2 the amount of compression in the second core layer (A500 foam) can be obtained. By inspection the A500 foam core layer compresses approximately 3 mm, which is approximately 25% of its original thickness. Finally, since interface 2, interface 3 and the back face all deflected in a similar manner to the same value of approximately 21 mm, it can be concluded that there was no compression in the third and fourth core layer (A500 112 foam layer and the polyurea interlayer). Therefore, the core arrangement of configuration 2 allows for a stepwise compression through the core and the front face and back face deflect to approximately 33 mm and 21 mm respectively.
From the deflection data of each interface in Fig. 11, the deformation of each core layer along the mid-line (line of symmetry) can be obtained by subtracting the core layers' back side deflection from the core layers' front side deflection. Sequentially, the strain rate along the line of symmetry of each core layer can be obtained using the following equation, where, l original is the original thickness of the each core layer and Δl/dt is the deformation rate.
The strain and strain rate histories of the core layers for each configuration, as calculated from Eq. (1) and Eq. (2) using the mid-point deflection data from Fig.11 are shown in Fig. 12. For those layers exhibiting no compression, their strain and strain rate results (0 s -1 ) are not shown here. The strain results are shown in Fig. 12a and Fig.   12b, while the strain rate results are shown in Fig. 12c and Fig. 12d.
It can be seen that in both configurations, the A300 foam layer exhibits approximately the same amount of maximum strain, however the time in which the maximum strain was reached varied. For configuration 1, distributing the initial loading uniformly results in densification of the A300 foam much later in the deformation history, more mitigation of the initial shock loading and thus less transmission of the load to the A500 layer, resulting in no compression in this layer. For configuration 2, unlike configuration 1, localized loading allowed for densification of the A300 foam layer much earlier in the deformation history, and consequently transmitted more shock loading into the A500 layer. Therefore, the A500 layer also showed compression. However, the deformation in configuration 2 is constrained to the central region where the initial loading was applied.
The strain rate plots of configuration 1 and configuration 2 show that the A300 layer of configuration 2 reached a much higher strain rate than the A300 layer of configuration, which was expected since the maximum level of strain in configuration 2 was achieved approximately twice as fast (~800 μs earlier) than in configuration 1. It should be noted that in configuration 2 the core stops compressing by approximately t = 800 μs, thus the oscillations that are observed in the strain rate plot after this time can be correlated to the errors in data recording, and consequently neglected.
From the mid-point deflection data in Fig. 11a and Fig. 11b,  [20] and Tilbrook et al. [21]. When the front and back face velocities equalize early in the deformation history, this response is labeled as a hard core type response. In contrast, when the back face begins to decelerate while the core is still compressing, this response is labeled as a soft core type response. Therefore, it can be concluded that configuration 1 exhibits a hard core type response, while configuration 2 exhibits a soft core type response. The authors [20,21] suggested that the optimal performance of sandwich beams is attained for soft core designs, which allows for a reduction in the transmitted impulse during the initial fluid-structure interaction stage.

Digital Image Correlation (DIC) Analysis
Utilizing the Digital Image Correlation (DIC) technique, the deflection, in-plane strain and particle velocity contours of the back facesheet for each configuration were generated. Fig. 14 -Fig 16 show the full-field results for the back facesheet of configuration 1 and configuration 2 respectively. Fig. 14 shows the full-field out-ofplane deflection (W) with a scale of 0 mm (purple) to 32 mm (red). It is evident from the figure that for configuration 1, as shown in Fig. 14a, the back face exhibits very  The full-field out-of-plane velocity (dW/dt) of the back face is shown in Fig. 16 for both configurations with a scale from 0 mm/s (purple) to 30,000 mm/s (red), or 0  Utilizing a point-inspection tool from digital image correlation, the data at the center point of the back facesheet for each configuration was evaluated and plotted.
The out-of plane deflection, as well as the back face velocity, showed excellent agreement with the results generated utilizing the side-view high-speed images, and therefore only the in-plane strain results are shown in Fig. 17. The back face of configuration 1 exhibits a maximum in-plane strain (ε yy ) of approximately 2.4% at t = 1800 μs. For configuration 2, the back face shows a maximum in-plane-strain (ε yy ) of approximately 1.6% at t = 1800 μs. Configuration 2 exhibits approximately 35% less in-plane-strain (ε yy ) than configuration 1.

Post-mortem Analysis
After the blast loading event occurred, the damage patterns of both configuration 1 and configuration 2 were visually examined and recorded using a high resolution digital camera and are shown in Fig. 18. When configuration 1 was subjected to transient shock wave loading, as shown in Fig. 18a, the damage was confined to the areas where the supports were located in the shock tube and core cracking is visible in 120 Fig. 18 Visual examination of both configurations after being subjected to high intensity blast load (Incident peak pressure ~1.0 MPa)

Core Compression Delamination
Core cracking (a) Configuration 1 (PU/A300/A500/A800) Core Compression Delamination Core cracking (b) Configuration 2 (A300/A500/A800/PU) these two areas. The core cracks propagated completely through the foam core to the polyurea interlayer. Core delamination is visible between the polyurea interlayer, and the first layer of the foam core (A300). Core compression is visible in the first core layer of A300 foam.
When configuration 2 was subjected to transient shock wave loading, the damage patterns can be seen in Fig. 18b. For this configuration, very little core damage was observed. Core delamination between the first two layers of the foam core (A300 and A500) led to a crack that propagated through the first foam core layer (A300) to the front facesheet. Skin delamination was evident between the front face and the first foam core layer (A300). Also core compression can be observed in the first two layers of the foam core (A300 and A500).  Fig. 19 shows the damage patterns of both configuration 1 and configuration 2 after they were subjected to the higher levels of blast loading (incident peak pressure ~ 1.5 MPa, reflected peak pressure ~7.5 MPa, wave velocity of 1300 m/s). It can be seen from the figure that when configuration 1, as seen in Fig. 19a, was subjected to a higher level of blast loading, the core exhibited heavy core cracking which lead to catastrophic failure. The font face showed heavy fiber delamination and cracking across the central region, while the back face delaminated completely from the core.
Configuration 2 on the other hand, as seen in Fig. 19b, remained structurally intact after the higher level of blast loading. The front face showed minor fiber delamination, while the core exhibited cracking along the central region where the supports were located. Minor front skin delamination was evident between the front 122 face and the first foam core layer (A300). Also core compression can be observed in the first and second core layers of foam, A300 and A500 respectively.

Energy Redistribution Behavior
The energy redistribution behavior of both configurations was next analyzed using the methods described by Wang et al. [22]. The total energy loss and the total deformation energy of both configuration 1 and configuration 2 during the blast loading event are shown in Fig. 20 and Fig. 21 respectively. Total energy loss is characterized as the difference between the incident and remaining energies of the gas and total deformation energy is defined as the work done by the gas to deform the specimen. It can be observed in Fig. 20 and Fig. 21 that at t = 1800 μs, the total energy loss of configuration 1, as well as the deformation energy, is approximately 25% more than that of configuration 2. This indicates that configuration 1 has the ability to consume more energy during the shock loading process, as discussed in Section 4.2.1, but results in heavier core damage as observed in Fig. 18a and Fig. 19a.
This phenomenon is directly related to the location of the polyurea layer and has been described by Amini et al. [13][14][15][16]. Polyurea is a highly pressure sensitive elastomer with its shear and bulk stiffness increasing remarkably with increasing pressure [8].
When polyurea is applied to the front of the specimen, behind the facesheet and in front of the foam core, the confined polyurea is loaded in compression, increasing its bulk stiffness and thus attaining a better impedance match with the facesheet.
Consequently, more of the blast energy is transferred to the foam core.
On the contrary, when polyurea is applied to the back of the specimen, behind the foam core and in front of the facesheet, the foam core is loaded first and then a part of this energy is transferred to the polyurea. This compresses the polyurea layer, thus increasing its stiffness, and therefore increasing the amount of energy that it captures.
This behavior can be elucidated by the fact that as the pressure-pulse travels through the polyurea layer and subsequently through the back facesheet, it is reflected back off its free-face surface as a tensile release wave. This results in a substantial decrease in the polyurea's shear stiffness and concurrently substantial increase in its dissipative ability due to its viscoelasticity. This phenomenon can be observed in the overall behavior of configuration 2. From the high-speed images in Fig. 10, it can be seen that the foam core is loaded first, resulting in heavy core compression as discussed in Section 4.2.1 and shown in Fig. 18b and Fig 19b. In comparison to configuration 1, the peak values of back face deflection, strain and velocity are reduced by 35%, 35% and 15% respectively, as shown in Fig. 11b, 13b and 17. This means the energy that is transferred to the back face of configuration 2 is less than that of configuration 1.

Conclusions
The following is the summary of the investigation: (1) The dynamic stress-strain response is significantly higher than the quasi-static response for each type of core material used in the present study, Corecell TM A-series foam and Dragonshield-HT polyurea respectively. The quasi-static and dynamic constitutive behaviors of Corecell TM A series foams (A300, A500, and A800) as well as the polyurea interlayer show an increasing trend.
The increase in the yield strength from quasi-static response to dynamic 125 response, along with the longer stress plateau, indicates that these core materials show great potential in absorbing large amounts of energy.
(2) Sandwich composites with two types of core layer arrangements were subjected to shock wave loading. Both core configurations consisted of three  (4) The methods used to evaluate the energy as described by Wang et al. [22] were implemented and the results analyzed. It was observed that the location of the polyurea layer has a significant positive effect on the response of composite sandwich panels to shock wave loading, both in terms of failure mitigation and energy absorption, if it is placed opposite the blast-receiving side (configuration 2). On the contrary, the presence of polyurea on the blastreceiving side (configuration 1), amplifies the destructive effect of the blast, promoting (rather than mitigating) the failure of the composite sandwich panels.

Acknowledgements
The

Introduction
Sandwich structures have very important applications in the naval and aerospace industry. Due to their construction they have many advantages that include high 131 strength/weight ratio, high stiffness/weight ratio, and energy absorption capabilities.
Sandwich structures consist of two thin, stiff facesheets, usually the same thickness, separated by a lightweight, thicker core. The facesheets carry almost all of the bending and in-plane loads, while the core helps to stabilize the facesheets and defines the flexural stiffness and out-of-plane shear and compressive behavior. When sandwich structures are subjected to high-intensity impulse loadings, such as air blasts, the core materials play a crucial role in the dynamic behavior and overall structural response.
Their properties assist in dispersing the mechanical impulse that is transmitted into the structure, and thus protect anything located behind it [1][2][3]. In recent years, functionally graded materials, where the material properties vary gradually or layer by layer within the material itself, have gained much attention.
Since the properties of the layered/graded material can be designed and controlled, they show great potential to be an effective core material for energy absorption and blast mitigation [12][13][14][15][16][17][18]. Li et al. [15] numerically examined the response of layered and graded metal-ceramic structures under impulsive loadings. It was concluded that the choice of gradation has a great significance on the impact applications and the particular design can exhibit better energy dissipation properties. Apetre et al. [16] numerically investigated the impact response of sandwich beams with a functionally graded core. Their results showed that a reasonable core design can effectively reduce the shear forces and strains within the structure. Consequently, they can mitigate or completely prevent impact damage on sandwich composites. In the previous work done by the authors [17,18], they experimentally investigated the blast resistance of sandwich composites with a functionally graded foam cores. Results indicated that monotonically increasing the wave impedance of the foam core, thus reducing the wave impedance mismatch between successive foam layers, will introduce a stepwise core compression, greatly enhancing the overall blast resistance of sandwich composites. It was also concluded that increasing the number of foam core layers, thus introducing more material interfaces, allows for blast wave (stress wave) attenuation: resulting in a time-delay of the peak stress arrival and consequently delaying the time of damage initiation.
In [17] two types of core configurations were studied and the sandwich composites were layered / graded based on the wave impedance of the given foams, i.e. monotonically and non-monotonically. In [18] four types of core configurations were investigated and the sandwich composites had a monotonically graded core based on increasing wave impedance, where the core gradations consisted of one, two, three and four layers respectively. The specimen dimensions and overall thickness were held constant, and each individual core layer was of equivalent thickness, i.e. for two layers of core gradation, each core layer was 19.0 mm, while with four layers of core gradation, each core layer was 9.5 mm.
The current investigation is an extension of the author's previous work and focuses on the blast response of sandwich composites with equivalent core layer mass.
By using sandwich composites with equivalent core layer mass, the overall areal density of the specimen is reduced in comparison to its sandwich composite counterpart with equivalent core layer thickness. The quasi-static and dynamic constitutive behaviors of the foam core materials were first studied using a modified SHPB device with a hollow transmitted bar. The sandwich composites were then fabricated and subjected to shock wave loading generated by a shock tube. The materials, as well as the core layer arrangements, and overall specimen dimensions were identical; the only difference arises in the core layers, where one configuration has equivalent core layer thickness, and the other configuration has equivalent core layer mass. The shock pressure profiles and real-time deflection images were carefully analyzed to reveal the mechanisms of dynamic failure of these sandwich composites. Digital Image Correlation (DIC) analysis was implemented to investigate the real-time full-field deflection, in-plane-strain, and particle velocity on the back face of the specimens. Post-mortem analysis was also carried out to better evaluate the overall blast performance of the specimens (structural integrity).

Skin (Facesheet) and Core Materials
The facesheet materials that were utilized in this study are E-glass Vinyl-Ester consisting of identical layups and materials. The EVE composite consisted of a 55% / 45% volume fraction of glass (fiber) to resin, as determined using proper ASTM standard D 2584. Fig. 1 shows a schematic of the sandwich composite with skin and core materials.
The core materials used in the present study are Corecell TM A-series styrene acrylonitrile (SAN) foams, which are manufactured by Gurit SP Technologies specifically for marine sandwich composite applications. The two types of Corecell TM A-series foam that were used in present study were A300 and A800. Table 1 lists important material properties of the two foams from the manufacturer's data [19], as well as the material properties of the facesheet [18]. The material properties of the 135

E-Glass Vinyl Ester Facesheets
Foam Core Fig. 1 Schematic of sandwich composite with skin and core Table 1. Quasi-static material properties of foam core [18] and EVE facesheet facesheet and the core materials were determined using proper ASTM standards, D 3410 and D 1621 respectively.
In Table 1, the A300 foam has a lower nominal density (ρ) and compressive modulus (E) than the A800 foam. Since both the nominal density and the compressive modulus are lower in the A300 foam than the A800 foam, the one-dimensional acoustic wave impedance (Z) is also lower, and shows the following relationship, The cell structures for the two foams are similar and the only difference appears in the cell wall thickness and node sizes, which accounts for the different densities of the foams. The SEM images of the cell microstructures can be seen in Fig. 2.

Layer Mass
The For the sandwich composites utilized in this study, two different core layer arrangements were investigated (as shown in Fig. 3). Both configurations consisted of two core layers of foam, A300 and A800 respectively, and were arranged based on monotonically increasing the acoustic wave impedance (A300/A800). It should be 137 noted that the first core layer of foam, A300, is the one first exposed to the shock wave loading. For the sandwich composites with equivalent core layer thickness, both foam layers had equivalent layer thickness (19 mm), resulting in an overall areal density of approximately 18.5 kg/m 2 . For the sandwich composites with equivalent core layer mass, the mass of the individual foam layers was equivalent. The following equations were used to obtain the required foam core thickness in order to equalize the mass of the A300 and A800 foam core layers, First the overall thickness, t foam_overal , must remain equal, To maintain equivalent mass, m, where ρ is the nominal density and V is the volume where A is the individual foam layer area, then Eq. (4) becomes A300 A300 A300 A800 A800 A800 Substituting Eq. (3) into Eq. (7) yields From Table 1, ρ A300 = 58.5 kg/m 3 and ρ A800 = 150 kg/m 3 , which yields

Shock Tube
The shock tube apparatus used to obtain the controlled dynamic loading is shown in Fig. 5(a). Shock tubes offer the advantages of plane wave fronts, wave parameters that are easily controllable and repeatable, and uniform loading over shock tube muzzle diameter [21]. A complete description of the shock tube and its calibration can be found in ref. [22]. In principle, the shock tube consists of a long rigid cylinder, divided into a high-pressure driver section and a low pressure driven section, which are separated by a diaphragm. By pressurizing the high-pressure driver section, a pressure difference across the diaphragm is created. When this pressure differential reaches a critical value, the diaphragm ruptures. The subsequent rapid release of gas creates a shock wave, which travels down the shock tube to impart shock loading on the specimen at the muzzle end.
When the shock wave impacts the specimen located at the end of the muzzle, the wave is reflected at a higher pressure than that of the incident shock pressure. The theoretical details on the equations for shock tubes have been previously established in the literature [23]. There are four basic theoretical assumptions which are used to describe the gas flow in shock tube: 1. The gas flow is one-dimensional.
2. The gas is ideal and has constant specific heats.
3. Heat transfer and viscosity effects are neglected.
4. Diaphragm rupture is instantaneous and does not disturb the subsequent gas flow.
Using conservation of energy, mass, and momentum as described by Wright [23], the following relationships for pressure, temperature and density across a shock front can be derived: where, P 1 , T 1 and ρ 1 , are pressure, temperature and density ahead of the shock front and, P 2 , T 2 and ρ 2 , are the pressure, temperature and density behind the shock front, γ is the adiabatic gas constant, and M 1 is the mach number of the shock wave relative to the driven gas. The pressure imparted on the specimen can be controlled by varying the above parameters in equations 9, 10, and 11. Different gases, such as nitrogen, and helium, were used in the shock tube and it was found that helium is the most suitable gas to replicate blast loading conditions and also offered the added advantage of repeatability.
The shock tube apparatus utilized in the present study has an overall length of 8 m, consisting of a driver, driven, converging and muzzle section. The diameter of the driver and driven section is 0.15 m. The final muzzle diameter is 0.07 m. Fig. 5b shows

High-speed Photography Systems
Two high-speed photography systems were used in the present study, as shown in

Experimental Procedure and Parameters
In the present study, a simply stacked diaphragm  Fig. 7. It should be noted that both pressure transducers were utilized to obtain the shock wave history, i.e. incident / reflected pressure and incident / reflected velocity. However, only the pressure transducer closest to the specimen was utilized to obtain the pressure applied on the specimen. Fig.8 shows the quasi-static (Fig. 8a) and high strain rate (Fig. 8b) compressive behavior of the different types of Corecell TM A-series foams [18]. For the quasi-static compressive behavior (Fig. 8a), the stress-strain curves show three deformation regions; (I) the linear elastic region, (II) the plateau stress (plastic yielding) region and (III) the densification region [26]. For high strain rate compressive behavior, the 146 stress-strain curves also show the three deformation regions, even though the densification region is much harder to achieve. Note the plateau stress regions for both instances have a large strain range.

Dynamic Behavior of Core Material
As seen in Fig.8 Table 2 shows the quasi-static and high strain rate plateau stresses (measured in the plateau stress region).
The dynamic strength of A800 foam increases approximately 100% in comparison to its quasi-static strength, while the dynamic strength of A300 foam increases approximately 50% in comparison to its quasi-static strength. The improvement of the mechanical behavior from quasi-static to high strain-rates in these core materials, as well as their long stress plateaus, signifies their ability to absorb large amounts of energy under high strain-rate dynamic loading. Therefore, they show great potential in being used as core materials in sandwich structures subjected to high intensity air blasts.

Blast Response of Sandwich Composites with Equivalent Core Layer
Thickness and Equivalent Core Layer Mass

Real-time Deformation
The real-time observations of the transient behavior for both sandwich composite panels subjected to shock wave loading are shown in Fig. 9  For the sandwich composites with equivalent core layer thickness, as shown in Fig. 9a, it can be observed that at t = 100 μs indentation failure of the core has initiated. This means that compression has initiated in the first core layer of foam (A300). By t = 400 μs, the A300 layer has continued to compress and core cracking has initiated in the A800 layer where the supports are located. By t = 700 μs more core cracking can be observed, as well as skin delamination between the front skin and the first core layer of foam (located at the top and bottom of the specimen). Also at this time, the core compression in the first layer of foam (A300) has reached a maximum (13 mm), approximately 75% of its original layer thickness (19 mm). After this time, the response of the specimen is global bending and by t = 1600 μs, no new failure mechanisms were observed. Also the core cracks have propagated completely through the foam core to the front facesheet, and there is heavy skin delamination between the front facesheet and the first core layer of foam.
For the sandwich composites with equivalent core layer mass, as shown in Fig.   9b, it can be observed that at t = 100 μs indentation failure of the core has initiated.
This means that compression has initiated in the first core layer of foam (A300). By t = 400 μs, the A300 layer has continued to compress and core cracking has initiated in the A800 layer where the supports are located. By t = 700 μs more core cracking can be observed, as well as skin delamination between the front skin and the first core It was observed in both configurations, equivalent core layer thickness and equivalent core layer mass, that the deformation mechanisms were identical. Both configurations exhibited a double-winged deformation shape which means both configurations were under shear loading. Indentation failure was followed by core compression of the first layer of foam (A300) and core cracking, and finally skin delamination between the front facesheet and foam core. The extent of the damage mechanisms varies between configurations, but the time at which the damage mechanisms were observed is identical.

Deflection
The mid-point deflections of each configuration and all of its constituents were obtained from the high-speed images, and a typical response can be seen in Fig. 10.
For the sandwich composites with equivalent core layer thickness (Fig. 10a), it can be seen that at t = 1600 μs the front face (front skin), interface 1 (between first and second core layer) and the back face (back skin) deflect to approximately 46 mm, 33 mm and 33 mm respectively. Since the A300 foam core layer is located between the front skin and interface 1, the difference in deflection between the front skin and interface 1 indicates the total amount of compression in the A300 layer. Therefore, it is evident that the A300 foam compresses approximately 13 mm, which is 75% of its original thickness (19 mm). Also note that the deflection curves for interface 1 and the back face follow the same trend and deflect to the same value at t = 1600 μs (33 mm).
Therefore, no compression was observed in the A800 core layer of foam.
For the sandwich composites with equivalent core layer mass, the mid-point deflections are shown in Fig. 10b. It can be seen that at t = 1600 μs, the front skin, interface 1, and the back skin deflect to approximately 60 mm, 41 mm and 41 mm respectively. Since the A300 foam core layer is located between the front skin and interface 1, the difference in deflection between the front skin and interface 1 shows the amount of compression in the A300 layer. Therefore, it can be observed that the A300 foam compresses approximately 19 mm, which is 75% of its original thickness (25.4 mm). Also note that the deflection curves for interface 1 and the back face follow the same trend and deflect to the same value at t = 1600 μs (41 mm). Therefore, no compression was observed in the A800 core layer of foam.  where, l original is the original thickness of the each core layer.
The strain history of the A300 foam core layer of both configurations, as calculated from Eq. (12) using the mid-point deflection data from Fig. 10, is shown in Fig. 12. Since there is no compression in the A800 foam core layer, its strain history is not shown here. It can be seen that in both configurations, the A300 foam layer exhibits approximately the same amount of maximum strain, 75% -80%, however the time in which the maximum strain was reached varied. For the sandwich composites with equivalent core layer thickness, the maximum strain value was achieved by ~ t = 500 μs. For the sandwich composites with equivalent core layer mass, the maximum Eq. Thickness Eq. Mass strain value was achieved by ~t = 1000 μs. Therefore, since the maximum strain value of the A300 foam layer for the sandwich composites with equivalent core layer mass was achieved in half the time in comparison to that of the sandwich composites with equivalent core layer mass, the behavior of the stiffer, A800 foam layer came into effect much earlier in the panels' deformation history.

Digital Image Correlation (DIC) Analysis
Utilizing the Digital Image Correlation (DIC) technique, the full-field deflection (W), in-plane strain (ε yy ) and particle velocity (dW/dt) of the back facesheet of each configuration were generated. Fig. 13 -Fig. 15 shows the full-field results for the back facesheet of both core arrangements respectively.  Fig. 13a, it can be observed that at t = 1600 μs, the central region of the panel has deflected approximately 33 mm. When using sandwich composites with equivalent core layer mass (Fig. 13b), it can be seen that at t = 1600 μs, the central region of the panel has deflected approximately 41 mm. Therefore, it can be concluded that when using a core configuration with equivalent layer thickness, the deflection across the central region of the back facesheet is reduced approximately 20%.
The full-field, in-plane strain (ε yy ) is shown in Fig 14 for both configurations with a scale of 0 (purple) to .025 (red), or 0% to 2.5% respectively. It can be observed in the figure that the back face of both core configurations exhibits very minimal in-plane strain (ε yy ) prior to t = 100 μs. Between t = 100 μs and t = 1600 μs, both of these configurations continue bending and the in-plane strain values continue to increase. For the sandwich composite with equivalent core layer thickness, as shown in Fig.   14a, it can be observed that at t = 1600 μs, the central region of the panel exhibits an in-plane strain of approximately .022, or 2.2%. When using sandwich composites with equivalent core layer mass (Fig. 14b), it can be seen that at t = 1600 μs, the central region of the panel exhibits an in-plane strain of approximately .024, or 2.4%.
Therefore, it can be concluded that when using a core configuration with equivalent layer thickness, the maximum in-plane strain across the central region of the back facesheet reduced approximately 8%.

Post-mortem Analysis
After the blast loading event occurred, the damage patterns of the sandwich composites with both core layer arrangements were visually examined and recorded using a high resolution digital camera and are shown in Fig.18. Note the locations and damage mechanisms were identical for both configurations; the only difference was in the extent of damage observed. When the sandwich composite with equivalent core layer thickness was subjected to highly-transient loading, as shown in Fig. 18a, the damage was confined to the areas where the supports were located in the shock tube and core cracking is visible in these two areas. The core cracks propagated completely through the foam core. Core delamination is visible between the front facesheet and the foam core. Also, the core cracks lead to back skin delamination, where the core separated from the back facesheet. Some core compression is also visible in the first core layer (A300) of foam.
For the sandwich composite with equivalent core layer mass, the damage patterns after being subjected to the shock loading are shown in Fig. 18b. For this core configuration, the damage was again confined to the areas where the supports were located in the shock tube and core cracking is evident. The core cracks propagated completely through the foam core. Skin delamination is obvious between the front facesheet and the foam core, as well as back skin delamination between the back facesheet and the foam core. Also, heavy front face fiber delamination and core compression in the first layer of foam (A300) can be observed.

Energy Redistribution Behavior
The energy redistribution behavior of both configurations was next analyzed using the methods described by Wang et al. [27]. The total energy loss and the total deformation energy of the sandwich composites with equivalent core layer thickness and equivalent core layer mass, as calculated during the blast loading event are shown in Fig. 19. Total energy loss is characterized as the difference between the incident and remaining energies of the gas and total deformation energy is defined as the work done by the gas to deform the specimen. This total energy loss is consumed in panel deformation energy, panel kinetic energy, heat, sound, light and any energy lost out of the side of the panel during bending.

Eq. Mass
It can be observed in Fig. 19a and Fig. 19b that at t = 1800 μs, the total energy loss and the deformation energy of the sandwich composite with equivalent core layer mass are approximately 20% and 15% more than that of the sandwich composites with equivalent core layer thickness. This indicates that using equivalent core layer mass, thus increasing the thickness of the A300 (softer) foam core layer allows for more energy to be consumed during the shock loading process, resulting in heavier core damage as observed in Fig. 18b. Also note that a very small amount of energy, approximately 5% of the total energy loss, is used to deform the panel, and the bulk of the energy is lost elsewhere.
Using Matlab, seven points were chosen (between the simple-supports) along the profile of the front face of the panel using the high-speed images (Fig. 9). The splinecurve fitting method was utilized to track the deformation of the front face throughout the shock wave loading event. The reconstructed shapes, as generated by the seven data points, are shown in Fig. 20. Since the deformation energy of both configurations ( Fig. 19b) is very similar prior to t = 600 µs, the reconstructed shapes of the front face of both configurations was carried out to include this time (up to approximately t = 800 µs). Through this reconstruction method, the deflection data of each point of the front face of each panel (such as Fig. 20a) can be obtained and utilized in the calculation of the deformation energy (Fig. 19b). Therefore, it can be observed that the shape of the front face of the panel with equivalent core layer mass exhibits a sharper bending profile in comparison to the panel with equivalent core layer thickness. Due to the increased thickness of the A300 (softer) foam core layer and the decreased thickness of the A800 (stiffer layer), this configuration (equivalent core layer mass) results in a core which allows for more localized compression (muzzle diameter) and a larger amount of bending. This in turn results in more gas escaping out the sides and more damage during deformation, which lowers the reflected pressures and allows for a higher total energy loss.

Bending Stiffness and Strength of Sandwich Beams
In order to achieve a better understanding of the performance of these sandwich panels and the phenomena observed, the bending stiffness (flexural rigidity) and strength of each configuration will be calculated and compared. For simplicity the shock loading event, which utilizes a beam (specimen), held in simple-supports, will be modeled as a sandwich beam centrally loaded under three-point bending (quasistatic). This type of analysis on the bending stiffness and strength of sandwich beams has been extensively investigated by [28][29][30][31][32][33][34]. Note this general theory is based on the shear deformable beams theory and has been discussed in detail by Allen [28]. This theory uses the assumption of uniform deflection and a linear longitudinal displacement field in the core through its thickness. Also, the facesheets and foam core materials are assumed to be homogeneous and isotropic.  Allen [28] gives the total deflection δ at the mid-point of a sandwich beam loaded in three-point bending as the sum of the deflections due to bending of the facesheets and the shear of the core: where (EI) eq is the equivalent flexural rigidity  Table 3. Specimen dimensions and three-point bending schematic variables (Fig. 22) were used in Eq. (14) and Eq. (15) respectively. Also note, the load P was left as a variable, since the same load was applied to both configurations.
Therefore, it can be observed in Table 4, that the sandwich composites with equivalent core layer mass, thus a thicker A300 (softer) foam core layer and a thinner A800 (stiffer) foam core layer, the equivalent flexural rigidity (EI eq ) and shear rigidity (AG eq ) are reduced 18% and 33% respectively. This results in a quasi-static deflection under three-point bending that is 18% larger for the sandwich composite with equivalent core layer mass than the sandwich composite with equivalent core layer thickness. These quasi-static results can be extended to the dynamic performance of the sandwich panel with equivalent core layer mass under shock wave loading, and it can be seen that a higher back face deflection, in-plane-stain and velocity, as described in section 4.2.3 (Digital Image Correlation (DIC) Analysis) was achieved.
For a sandwich beam in three-point bending, as shown in Fig.21, the predicted collapse loads are as follows: For face yielding or microbuckling, For face wrinkling, 168 note, this expression includes a knockdown factor of almost two (2) associated with the assumed geometrical imperfections of the facesheet [28].
For core shear failure, where eq. (18(a)) results in the same yield load as eq. (18(b)) but includes a postyield hardening response with a slope controlled by the bending stiffness of the facesheets [33].
For indentation failure (core compressive yield) [ (19) which assumes that the compressive sandwich face behaves as an elastic beam-column with the core as a rigid-ideally plastic foundation.
For the purposes of this investigation, only face yielding, core shear and indentation (core compressive yield) failure loads will be investigated and compared. Table 5 summarizes the results as obtained using Eq. (16)-Eq. (19) coupled with the corresponding material properties of the given facesheet and foam core material (Table 1), as well as the specimen dimensions (Table 3) and loading conditions (Fig.   22). Note, when applying the above equations, to sandwich composites with more than one core layer, the shear strength and the compressive strength of the foam core, τ c and σ c respectively, were calculated again using a weighted average, i.e., 1  where c 1 and c 2 are the respective core thicknesses of A300 and A800 for the sandwich composites with equivalent core layer thickness (denoted with subscript a) and equivalent core layer mass (denoted with subscript b). These weighted averages were used in Eq. (18) and Eq. (19) respectively. Also note, the deflection, δ, was left as a variable, since it's a function of the applied load, P.
Therefore, it can be observed in Table 5, that the sandwich composites with equivalent core layer mass, thus a thicker A300 (softer) foam core layer and a thinner A800 (stiffer) foam core layer, failure modes occur at a load which is approximately 15% less than that of the sandwich composites with equivalent core layer thickness.
This results in panel which exhibits more damage, as described in section 4.2.4 (Postmortem analysis).

Conclusions
The following is a summary of this investigation: (1) The dynamic stress-strain response is significantly higher than the quasi-static response for the two type of Corecell TM A-series foam studied. Both quasi- indicates that these foam materials show great potential in absorbing large amounts of energy.
(2) Sandwich composites with two types of monotonically graded cores based on increasing wave impedance were subjected to blast loading. In order to reduce areal density, a sandwich composite with equivalent core layer mass was fabricated and its blast performance was compared to its sandwich composite counterpart with equivalent core layer thickness. Table 6 lists the overall results of this investigation.
(3) The flexural stiffness and shear rigidity were numerically investigated to achieve a better understanding on the overall behavior of the two types of sandwich composites. It was observed that utilizing a sandwich composite with equivalent core layer mass, thus increasing the thickness of the A300 (softer) layer, decreasing the thickness of the A800 (stiffer) layer and reducing the overall areal density, results in specimen whose stiffness and strength is significantly lower (~20%) in comparison to the sandwich specimen with equivalent core layer thickness.

Acknowledgements
The

Introduction
Sandwich structures have very important applications in naval and aerospace industry. Due to their construction they have many advantages that include high strength/weight ratio, high stiffness/weight ratio, and energy absorption capabilities.
Sandwich structures consist of two thin, stiff facesheets, usually of the same thickness, separated by a lightweight, thicker core. The facesheets carry almost all of the bending and in-plane loads, while the core helps to stabilize the facesheets and defines the flexural stiffness and out-of-plane shear and compressive behavior. When sandwich structures are subjected to high-intensity impulse loadings, such as air blasts, the core materials play a crucial role in the dynamic behavior and overall structural response.
Their properties assist in dispersing the mechanical impulse that is transmitted into the structure, and thus protect anything located behind it [1][2][3].
Common cores are made of metallic and non-metallic honeycombs, cellular foams, balsa wood, PVC, truss and lattice structures. Extensive research exists in the literature regarding the dynamic response of sandwich structures consisting of the various core materials and geometric structures [3][4][5][6][7][8][9]. These studies have indicated that advanced sandwich structures can potentially have significant advantages over monolithic plates of equivalent mass in absorbing the blast energy, whether in air or underwater. Apart from the various core materials and structures, the facesheet also plays an important role in the blast mitigation properties of the structure. In fact, the facesheet is the part of the structure which is directly exposed to the blast loading.
For marine applications, fiber-composite (facesheet) materials are commonly based on epoxies and other thermosetting polymers. This is due to the fact that these thermosetting polymers are highly cross-linked resulting in materials which exhibit good elevated temperature resistance and low creep. However, their high cross-link densities cause them to be relatively brittle in nature. This limits their applications as structural materials, as they have a poor resistance to crack initiation and growth. To overcome this deficiency and increase toughness, a commonly used method is the addition of a second dispersed particulate phase (during infusion). This second dispersed particulate phase can either be initially soluble in the epoxy resin and which then phase separates during curing to form or it can be of pre-formed particles. For the phase-separable tougheners, both rubbers (carboxyl-terminated butadiene-acrylonitrile (CBTN) [10,11]) and thermoplastics [12][13][14] have been investigated. Pre-formed particles that have been studied include ceramic particles (glass [15,16], alumina [17], or silica [18,19]), metal particles (aluminum [18]), polymers [20,21] and core-shell rubber particles [22][23][24][25][26][27].
The behavior of rubber toughened and core-shell rubber toughened epoxy resin has been extensively studied in the literature [10,11,[22][23][24][25][26][27]. The core-shell rubber particles consist of two parts, a core which is rubber for impact resistance, and a shell which is a co-polymer compatible with epoxy resin. Note for these investigations, most of these rubber particles were on the micro-scale level. Results of these investigations indicated that the addition of rubber particles to epoxy resins can aid in increasing the fracture toughness, lap shear / T-peel strength, and fatigue resistance, as well as allow for no loss of Tg or thermal properties (during infusion process), consistent morphology and a wide cure window. Therefore, the addition of rubber particles to current resin systems allows the once-brittle by nature resin to become toughened and subsequently more impact resistant.
Due to the improvement in mechanical properties, these rubber toughened epoxies can be used as the matrices for fiber-reinforced composite systems. However, the addition of these tougheners or pre-formed rubber particles, in the concentrations required to sufficiently enhance the toughness, can significantly increase the viscosity of the matrix resin. Also, conventional pre-formed particles generally have a particle diameter larger than the inter-fiber spacing, and particles are filtered out during infusion. This has led to the development of nano-scale rubber particles [27], defined as rubber particles less than 100 nm in diameter, since these particles will flow between the fibers during infusion [28].
Even though the behavior of rubber toughened epoxy systems has been extensively investigated in the literature, investigations regarding the behavior of glass-fiber reinforced composites and sandwich structures are limited. Therefore, the current study will investigate the influence of nano-scale core-shell rubber (CSR) particles [Kane Ace MX 153] on the behavior and performance of E-glass Vinyl-Ester (EVE) composite panels and sandwich structures. It will expand upon the authors' previous work [29][30][31], for which the blast performance of sandwich composites made of E-glass Vinyl-Ester (EVE) facesheets and Corecell TM A-series foam was studied.
The quasi-static and dynamic constitutive behaviors of the facesheets (both with and without CSR) and foam core material were first studied using a Split Hopkinson Pressure Bar (SHPB) device. The sandwich composites were then fabricated and subjected to shock wave loading generated by a shock tube. Both sandwich composites consisted of identical materials, core thickness and overall dimensions, with the only difference arising in the resin system. The non-core-shell rubber toughened resin system (Non-CSR) consisted of a vinyl-ester resin only; while the CSR toughened resin consisted of the same vinyl-ester resin, but with Kane Ace MX-180 153 nano-scale core-shell rubber particles added to the mixture. The shock pressure profiles and real-time deformation images were carefully analyzed to reveal the failure mechanisms of these sandwich composites. Digital Image Correlation (DIC) analysis was implemented to investigate the real-time deflection, strain and velocity of the back face of the specimens. Post-mortem analysis was also carried out to evaluate the overall blast performance of these sandwich structures.

Skin (Facesheet) and Core Materials
The facesheet materials that were utilized in this study are E-glass Vinyl-Ester MX153 is stable and the CSR remains completely dispersed under normal handling, formulating and curing conditions. Fig. 2 shows an SEM image of nano-scale coreshell rubber particles [27].
Due to the fact that resin viscosity is important during the infusion process  Table 1. Quasi-static material properties of foam core [35] and EVE facesheet [29] Core: Co-Polymer I designed for impact resistance

Shell:
Co-Polymer II designed to be compatible with thermosetting resins Fig. 2 SEM image of nano-scale core-shell rubber (CSR) particles [27].
The core material used in the present study is Corecell TM A500, which is a styrene acrylonitrile (SAN) foam manufactured by Gurit SP Technologies specifically for marine sandwich composite applications. Table 1 lists important material properties of the foam from the manufacturer's data [35], as well as the material properties of the facesheet [29]. The material properties of the facesheet and the core materials were determined using proper ASTM standards, D 3410 and D 1621 respectively. The SEM images of the A500 foam cell microstructure can be seen in Fig. 3.  For the sandwich composites utilized in this study, two different resin systems were used; one configuration utilized a simple vinyl-ester resin system, while the other configuration utilized the same vinyl-ester resin system but with nano-scale core-shell rubber (CSR) toughening. The sandwich composite panels can be seen in Fig. 4. Both configurations consisted of one core layer of foam, A500. Since the core material and thickness, as well as overall specimen dimensions were identical, with the only difference arising in the resin system used during the infusion, the areal density of the two configurations was within 3%, i.e. the areal density of the Non-CSR toughened sandwich composite was 19 kg/m 2 , and the CSR toughened sandwich composite was 18.5 kg/m 2

Quasi-Static Loading
The quasi-static loading was implemented by a screw-driven testing machine

Drop-weight Impact Tower
The dynamic loading was implemented by a drop-weight impact tower apparatus Normally specimens are held within the drop tower enclosure during experiments.
To allow the use of an environmental chamber or testing of specimens too large to fit in the enclosure, the 9210 can be modified. Specimens that do not fit in the enclosure can be fixed within the support base, outside of the enclosure. A simple support fixture Table 2. Mass of drop-weight components contributing to impact was built that resides in the support base (see Figure 6b). Note the span width between supports is approximately 152 mm, which is identical to the simple support span in the shock loading experiments. The positioning of the specimen outside of the enclosure also allowed the specimen to be oriented in such a way that a high-speed photography system could be employed during testing. The use of the high-speed photography system was to ensure proper results, i.e. duration of event (prior to impacting support fixture), no slipping of the specimen, and proper loading (center).
To perform an experiment several steps must be taken. The crosshead mass and drop height must be determined. Given that highest energy output was to be used the cross head was loaded with the maximum weight. All weights are stamped with their mass. The additional mass of the crosshead, reaction plate, reaction plate bolts, tup, tup bolts, and striker were taken into account. The mass of the crosshead, reaction plate and bolts are labeled from the manufacturer. The tup, tup bolt and striker were weighed to determine their mass. where E is the desired energy, m is the mass of the drop-weight, and g is the acceleration due to gravity.
After the drop height was determined, the drop tower velocity was tested. The specimen was placed in the fixture and the cross head was lowered until it came into contact with the specimen. The velocity sensor must be adjusted so that the velocity flag attached to the crosshead is in line with the bottom of the sensor. With the sensor adjusted, the number indicated on the scale was taken as a datum point and the calculated drop height was set from the datum. The crosshead was raised to the appropriate height and the specimen removed. A velocity test was then completed to ensure that the proper velocity was reached. Impact velocities were checked against a calculated velocity determined by Before experiments were performed, the data acquisition system was configured.
Each tub has a calibration factor that must be input into the software. The system was configured using the correct calibration factor for the 44 KN (10,000 lb) tup. After the calibration factor was entered, the sampling rate was properly chosen. The sampling rate will determine if the entire event is captured. The data acquisition system will record 8192 data points regardless of the sampling rate, therefore it is important to know the duration of the impact event. For the given study, the event duration was approximately 12 ms. A sampling rate of 410kHz was chosen as this corresponds to 20 ms allowing for a proper margin of safety. Figure 7 shows a specimen placed in the simple supports with the hemispherical impactor in contact with the specimen.

Shock Tube
The shock tube apparatus used to obtain the controlled dynamic loading is shown in Fig. 9(a). Shock tubes offer the advantages of plane wave fronts, wave parameters that are easily controllable and repeatable, and uniform loading over shock tube muzzle diameter [37]. A complete description of the shock tube and its calibration can be found in ref. [38]. In principle, the shock tube consists of a long rigid cylinder, divided into a high-pressure driver section and a low pressure driven section, which are separated by a diaphragm. By pressurizing the high-pressure driver section, a pressure difference across the diaphragm is created. When this pressure differential Reflected Pulse reaches a critical value, the diaphragm ruptures. The subsequent rapid release of gas creates a shock wave, which travels down the shock tube to impart shock loading on the specimen at the muzzle end.
When the shock wave impacts the specimen located at the end of the muzzle, the wave is reflected at a higher pressure than that of the incident shock pressure. The theoretical details on the equations for shock tubes have been previously established in the literature [39]. There are four basic theoretical assumptions which are used to describe the gas flow in shock tube: 1. The gas flow is one-dimensional.
2. The gas is ideal and has constant specific heats.
3. Heat transfer and viscosity effects are neglected.
4. Diaphragm rupture is instantaneous and does not disturb the subsequent gas flow.
Using conservation of energy, mass, and momentum as described by Wright [39], the following relationships for pressure, temperature and density across a shock front can be derived: where, P 1 , T 1 and ρ 1 , are pressure, temperature and density ahead of the shock front and, P 2 , T 2 and ρ 2 , are the pressure, temperature and density behind the shock front, γ is the adiabatic gas constant, and M 1 is the mach number of the shock wave relative to 193 (c) Detailed dimensions of the muzzle (a) Shock tube facility at URI (b) Schematic of shock tube Fig. 9 Shock tube apparatus the driven gas. The pressure imparted on the specimen can be controlled by varying the above parameters in equations 1, 2, and 3. Different gases, such as nitrogen, and helium, were used in the shock tube and it was found that helium is the most suitable gas to replicate blast loading conditions and also offered the added advantage of repeatability. 194 The shock tube apparatus utilized in the present study has an overall length of 8 m, consisting of a driver, driven, converging and muzzle section. The diameter of the driver and driven section is 0.15 m. The final muzzle diameter is 0.07 m. Fig. 9b shows

High-speed Photography Systems
Two high-speed photography systems were used in the present study, as shown in

Quasi-Static Behavior
The quasi-static behavior of the facesheet and core materials were first investigated using an Instron 5582 screw-driven testing machine. The compressive properties of the A500 foam, as well as the tensile and compressive properties of the two composite facesheet panels (Non-CSR and CSR toughened) was studied to better understand the individual behavior of all of the constituents used in the sandwich composite structure. Understanding the individual properties of each material will allow for a better understanding of the entire material system, i.e. sandwich structure.
Due to the fact that during a shock wave loading event the facesheet materials exhibit very little compression(transverse and longitudinally), only the tensile behavior of the facesheet material will be presented here, as shown in Fig. 13a.  For the quasi-static compressive behavior of the A500 foam core material, as shown in Fig. 13b, the stress-strain curves show three deformation regions; (I) the linear elastic region, (II) the plateau stress (plastic yielding) region and (III) the densification region [43]. It can be observed that the plateau stress of the A500 foam is approximately 0.88MPa.

Drop-weight Impact
Both types of composite panels were subjected to low velocity high mass

High Strain Rate (SHPB) Behavior
The high strain rate behavior of the facesheet and core materials was investigated using a SHPB apparatus. For the dynamic behavior of the facesheet materials, Fig.   15a, it can be observed that the Engineering stress-strain response shows two distinct Core Layer Delamination t = 100 μs t = 400 μs t = 700 μs t = 1000 μs t = 1600 μs t = 0 μs mechanical behavior from quasi-static to high strain-rates in this core material, as well its long stress plateaus, signifies its ability to absorb large amounts of energy under high strain-rate dynamic loading. Therefore, it shows great potential in being used as a core material in sandwich structures subjected to high intensity air blasts.

Deflection
The mid-point deflection of each sandwich panel and all of its constituents was obtained from the high-speed images and a typical response can be seen in Fig. 17. For both configurations studied, the midpoint deflection of the front face (front skin) and back face (back skin) of the specimen was plotted. For the sandwich composite without core-shell rubber (Non-CSR), as shown in Fig 17a, it is evident that at t = 1600 μs the front face deflects to approximately 46 mm, while the back facesheet deflects approximately 35 mm. Therefore, the difference between the deflection of the front face and deflection of the back face signifies the total amount of compression observed in the core. Therefore, it can be concluded that the core compressed approximately 11 mm, which is 30% of its original thickness (38 mm).
For the core-shell rubber (CSR) toughened sandwich composite, as shown in Fig   17b, it is evident that at t = 1600 μs the front face deflects to approximately 45 mm, while the back facesheet deflects approximately 32 mm. Therefore, the difference between the deflection of the front face and deflection of the back face signifies the total amount of compression observed in the core. Therefore, it can be concluded that the core compressed approximately 12mm, which is 30 % of its original thickness (38 mm).

Digital Image Correlation (DIC) Analysis
Utilizing the Digital Image Correlation (DIC) technique, the full-field deflection (W), in-plane strain (ε yy ) and particle velocity (dW/dt) of the back facesheet of each configuration were generated. Fig. 18 -Fig. 21 show the full-field results for the back facesheet of both configurations respectively. Fig. 18 shows the full-field out-of-plane deflection (W) during the initial fluid-structure interaction (t ≤ ~ 250 μs, [22] Fig. 19a, it can be observed that at t = 1600 μs, the central region of the panel has deflected approximately 35 mm. When using CSR toughened sandwich composites (Fig. 19b), it can be seen that at t = 1600 μs, the central region of the panel has deflected approximately 32 mm. Therefore, it can be concluded that  The out-of-plane deflection (W) showed excellent agreement with the results generated utilizing the high-speed images and therefore, only the in-plane strain (ε yy ) and out-of-plane velocity (dW/dt) results are shown. Fig. 22 and Fig. 23 show   It can be observed from the figure that by t = 3200 µs, the Non-CSR toughened sandwich composite exhibits a crack across the central region. Also note, the amount of bending in the Non-CSR composite facesheets is higher than the CSR toughened facesheet.

Residual Compressive Strength
After the blast loading event occurred on the facesheets, both types of composite facesheets were subjected to post-blast residual compressive strength measurements.
For each composite panel system, at least two samples were tested. A typical response is shown in Fig. 25. It can be observed that after the blast loading event, the Non-CSR toughened composite facesheet achieved a maximum residual strength of 15 MPa, at a strain level of approximately 1%. Following this, the composite facesheet exhibited brooming due to cracking and heavy fiber delamination (Fig. 25b). Therefore, it can be concluded that the addition of nano-scale CSR particles to the composite facesheet allows for a post-blast residual strength which is approximately 300% higher than that of the Non-CSR toughened facesheet.

Post-mortem Analysis
After the quasi-static (Drop-weight) and dynamic events (SHPB and Shock Tube) occurred, the damage patterns were visually examined and recorded using a high resolution digital camera and are shown in Fig. 26 -Fig. 29. The damage patterns of both types of composite facesheets subjected to a 150 J drop-weight impact event are  Fig. 26. For the Non-CSR toughened composite facesheet, heavy fiber delamination can be observed along the central region of the facesheet (Fig. 26a). For the CSR toughened composite facesheet, as shown in Fig. 26b, very little damage can be observed.  The damage patterns of both types of sandwich composite panels subjected to an incident peak pressure of 1.0 MPa, a reflected peak pressure of 5.0 MPa, and an incident velocity of 1000 m/s using the shock tube apparatus are shown in Fig. 28.
When the Non-CSR toughened sandwich composite was subjected to high-intensity loading, as shown in Fig. 28a, the damage was confined to the areas where the supports were located in the shock tube and core cracking is visible in these two areas.
The core cracks propagated completely through the foam core. Core delamination is visible between the two core layers of A500 foam. Also one of the core cracks lead to back skin delamination, where the core separated from the back facesheet. Some core compression is visible in the first core layer of A500 foam. Also heavy fiber delamination and cracking is visible along the front facesheet.  When the CSR toughened sandwich composite was subjected to high-intensity loading, as shown in Fig. 28b, the damage was again confined to the areas where the supports were located in the shock tube and core cracking is visible in these two areas.
The core cracks propagated completely through the foam core. Core delamination is visible between the two core layers of A500 foam. Also, the core cracks lead to back skin delamination, where the core separated from the back facesheet. Some core compression is visible in the first core layer of A500 foam. Also, fiber delamination is visible along the front facesheet. MPa, and an incident velocity of 650 m/s using the shock tube apparatus. When the Non-CSR toughened facesheet was subjected to the blast loading, heavy fiber delamination and a large central crack was observed, as shown in Fig. 29a. When the 219 CSR toughened facesheet was subjected to the blast loading, heavy delamination was observed, as shown in Fig. 29b.
The results of the post-mortem analysis, Fig. 26 -Fig. 29, show that using a coreshell rubber (CSR) toughened epoxy system allows for a more impact resistant composite system, and aids in dispersing the high-intensity dynamic loadings. The CSR toughened panels exhibited heavy amounts of delamination, but the structural integrity was maintained. On the contrary, the Non-CSR toughened sandwich panels exhibited heavy fiber delamination and cracking. For the Non-CSR toughened composite facesheets, these panels failed catastrophically and structural integrity was lost.

Conclusions
The following is the summary of the investigation: (1) Core-shell rubber particles (CSR) have a significant effect on the quasi-static and dynamic behavior of composite materials and sandwich structures. It was observed that the addition of 4% CSR to E-glass Vinyl-Ester (EVE) composite facesheets increased the tensile strength (~10%) and drop-weight impact resistance (~10%),. After the dynamic loading, such as SHPB and shock wave loading, the CSR toughened facesheets maintained structural integrity, while the Non-CSR facesheets did not.
(2) The dynamic stress-strain response is significantly higher than the quasi-static response for the Corecell TM A500 foam studied. The increase in the yield strength from quasi-static response to dynamic response, along with the longer stress plateau, indicates that this core material shows great potential in absorbing large amounts of energy.
(3) Two types of sandwich composites were fabricated, one with the addition of nano-scale core-shell rubber (CSR) particles during infusion, and one without (Non-CSR). The core material and thickness, as well as overall specimen dimensions were held constant. Results indicated that the addition of nanoscale core-shell rubber (CSR) particles to the panels allows for an increase in blast performance. By dispersing the initial loading, the CSR toughened sandwich composites exhibit lower amounts of out-of-plane deflection and velocity, as well as in-plane strain, approximately 8%, 12% and 20% respectively.

Acknowledgements
The authors kindly acknowledge the financial support provided by Dr. Yapa D. S.

Conclusions
The main objective of this investigation has been to investigate the blast resistance and mitigation behaviors of novel composites and sandwich structures.
Various composite panels and sandwich structures were designed and fabricated with an overall aim to create an optimal structure to withstand high-intensity air-blast loadings. Different materials, ranging from facesheet materials made of E-glass Vinyl-Ester (EVE) and nano-scale core-shell rubber (CSR) toughened particles, to core materials including functionally graded styrene acrylonitrile foams (SAN) and Dragonshield polyurea were designed and fabricated. Using the shock tube facility, an air-blast loading, equivalent to those experienced and generated during real-life explosions was applied to the various composites and sandwich structures. 3D-Digital Image Correlation (3D DIC) technique coupled with high-speed imaging was used to obtain the back face out-of-plane deflections and velocities, as well as the in-plane strains during the experiments. Understanding the overall behaviors and failure mechanisms will lead to optimally designed light-weight structures that can mitigate energy and maintain structural integrity when subjected to blast loadings. Due to the increased threat of damage to civilian and defense structures in the form of terrorist attacks and blast loading, a comprehensive understanding on blast mitigation of composites and sandwich structures, as well as an optimal design to withstand these loadings, is pivotal. The findings from the present study are summarized below.
(1) The dynamic stress-strain response is significantly higher than the quasi-static response for every type of Corecell TM A-series foam studied, as well as the Dragonshield-HT Polyurea (PU) interlayer. Both quasi-static and dynamic constitutive behaviors of Corecell TM A-series foams (A300, A400, A500, and A800), as well as the PU interlayer show an increasing trend. The improvement of the mechanical behavior from quasi-static to high strain-rates in these core materials, as well as their long stress plateaus, signifies their ability to absorb large amounts of energy under high strain-rate dynamic loading. Therefore, they show great potential in being used as core materials in sandwich structures subjected to high intensity air blasts.
(2) The sandwich specimens with two different core arrangements, configuration 1 (A300/A500/A800) and configuration 2 (A500/A300/A800), were subjected to shock wave loading. The overall specimen dimensions and areal density were held constant; the only difference was in the gradation of the foam core layers.
Configuration 1 was monotonically graded based on increasing the density of the core layers from low/middle/high density, while configuration 2was nonmonotonically graded, i.e. middle/low/high density foam. The overall performance of configuration 1 (A300/A500/A800) was better than that of configuration 2 (A500/A300/A800). Large compression was visible in the core when the least density foam (A300) is first in contact with the blast loading. This configuration reduced the dynamic pressures seen on the back facesheet, and thus limited the total amount of damage imparted on the specimen. When using the A500 foam first in contact with the blast loading, 227 the overall deformation process of the sample was completely different.
Compression in the core was limited, and thus the specimen showed a heavy amount of damage.
(3) Sandwich composites with four different core layer arrangements, one, two, three and four layers respectively, were subjected to shock wave loading. The foam core was monotonically graded based on increasing acoustic wave impedance (increasing density and stiffness, E and ρ respectively), with the foam core layer of lowest wave impedance facing the blast. The specimen dimensions were held constant for all core configurations, while the number of core layers varied. The overall performance of the sandwich composite with four layers of core gradation is the best, followed by the sandwich composites with three, two and one layer gradation respectively. Even though each configuration allowed for a stepwise compression of the core, it was shown that the number of core layers has an influence on the dynamic response of the structure under blast loading. More specifically, by increasing the number of monotonically graded layers, the acoustic wave impedance mismatch between successive layers is reduced. Therefore, the strength of the initial shock wave (stress wave) can be weakened by the time it reaches the back facesheet, resulting in lower back face deflection, in-plane strain, and velocity. More importantly, the overall damage imparted on the structure can be reduced and structural integrity can be maintained.
(4) Increasing the number of monotonically graded foam core layers, thus introducing more material interfaces, allows for blast wave (stress wave) attenuation through the following mechanisms: (1) stepwise compression of the core (energy dissipation mechanism) and (2) scattering/dispersion of the wave through interface variations. Combining these mechanisms results in lengthened timescales for pressure rises across the samples, allowing for a time-delay of the peak stress arrival, and thus delaying the time of damage initiation.
(5) When using higher levels of core gradation, i.e. two, three and four layers respectively, the amount of stress transferred to subsequent layers is diminished, thereby subjecting the back face to reduced loadings and blast pressures. The foam core was monotonically graded based on increasing wave impedance and the only difference between the two core configurations arose in the location of the polyurea interlayer. It was observed that when the polyurea interlayer is located behind the graded foam core, and in front of the back face (i.e. configuration 2), the core layer arrangement allows for a stepwise compression of the core. Larger compression was visible in the A300 and A500 foam core layers of configuration 2 than configuration 1. This compression lowers the strength of the initial shock wave by the time it reaches the back facesheet and thus the overall deflection, in-plane strain, and velocity were reduced in comparison to the sandwich composite with the polyurea 229 interlayer located behind the front facesheet and in front of the foam core (i.e. configuration 1). Therefore, it can be concluded that placing the polyurea interlayer behind the foam core and in front of the back facesheet (configuration 2) improves the blast resistance of the sandwich composite and better maintains structural integrity.

(7)
Comparison of the mid-point deflection of both configurations was made using high-speed photography (side-view images) and the Digital Image Correlation (DIC) technique. Results obtained using both methods of analysis showed excellent agreement with a small margin of error (< 5%).

(8)
The methods used to evaluate the energy as described by  were implemented and the results analyzed. It was observed that the location of the polyurea layer has a significant positive effect on the response of composite sandwich panels to shock wave loading, both in terms of failure mitigation and energy absorption, if it is placed opposite the blast-receiving side (configuration 2). On the contrary, the presence of polyurea on the blastreceiving side (configuration 1), amplifies the destructive effect of the blast, promoting (rather than mitigating) the failure of the composite sandwich panels.
(9) Sandwich composites with two types of monotonically graded cores based on increasing wave impedance were subjected to blast loading. In order to reduce areal density, a sandwich composite with equivalent core layer mass was fabricated and its blast performance was compared to its sandwich composite counterpart with equivalent core layer thickness. The materials, as well as the 230 core layer arrangements, and overall specimen dimensions were identical, with the only difference appearing in the thickness of the individual core layers of each specimen (equivalent layer thickness and equivalent layer mass). Table 1 lists the overall results of this specific investigation.

(10)
The flexural stiffness and shear rigidity were numerically investigated to achieve a better understanding on the overall behavior of the two types of sandwich composites. It was observed that utilizing a sandwich composite with equivalent core layer mass, thus increasing the thickness of the A300 (softer) layer, decreasing the thickness of the A800 (stiffer) layer and reducing the overall areal density, results in specimen whose stiffness and strength is significantly lower (~20%) in comparison to the sandwich specimen with equivalent core layer thickness. (2) Conduct a comprehensive study to understand the effect of nano-scale coreshell (CSR) rubber particle weight percentages on the quasi-static and dynamic behaviors of glass-fiber reinforced panels. Due to the fact that CSR particles cause an increase in resin viscosity, the weight percentages of CSR cannot exceed 10% without compromising proper infusion. Specimens will be 233 fabricated and subjected to various quasi-static and dynamic loading conditions including, drop-weight impact, Split Hopkinson Pressure Bar (SHPB) and shock tube loading. Also residual strength measurements of the panels will be conducted both pre-and post-loading.

Units
(3) Results from the composite panel tests will aid in the optimal design of a sandwich structure to mitigate energy and maintain structural integrity.
Depending upon the weight-percentage of CSR that provides the best increase in mechanical properties, sandwich panels will be fabricated using the same amount of CSR in the resin system. A shock tube apparatus will be utilized to conduct a controllable and repeatable air-blast loading on the sandwich structure. During the shock tube testing, a high-speed photography system coupled with the optical technique of 3-D Digital Image Correlation (DIC) will be utilized to capture the real-time deformation process as well as mechanisms of failure. Post-mortem analysis will be carried out to evaluate the overall blast performance of this structure. There exists an optimal thickness, depending upon application, which allows for the highest mechanical property increase, without compromising the overall areal density/weight.

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(5) Also the idea of a functionally graded polyurea system could have a significant effect on retrofitting pre-existing structures, and creating more improved blast resistant structures. Using cenospheres or fly ash to increase the density of the polyurea coating would allow for a functionally graded material system based on increasing density. Since polyurea has the ability to be spray cast, functionally grading the polyurea and applying it to structures shows great promise. with an ability to be formed easily and accurately into virtually and complex geometric shape. Some advantages of composites include high strength and stiffness, low weight-mass ratio, dimensional stability and exceptional formability.
When these composites are made in the most economical way, they are inferior to those that take much more time and money to construct. Developing a method that is fast and reliable is crucial. A controlled set up must be designed in order to optimize the resin infusion. The experimental process in which infusion is accomplished is known as Vacuum Assisted Resin Transfer Molding (VARTM). In this process a vacuum pulls resin in from a feed tube to distribute it evenly into the preform.
There are several different steps that must be followed in order to run a VARTM infusion. A selection of materials that will be infused must be acquired. panel and is the preform that will be infused (Figure 1a). The foam core has been previously laid out in a configuration that was tailored to meet specific demands. Once the core was laid out, 3/16 inch holes were drilled approximately two inches apart and off center (Figure 1b). This ensures that the resin will flow through the entire preform and infuse properly.

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The preform is placed on a large glass table that has already been coated with a few layers of high-temperature Mold Release (T.R. Industries). This is a substance that deters two substances from bonding together, also known as a buffer. This is important so that the finished panel does not stick to the glass and can easily be removed. The next step is to place a sheet of peel ply on top of the preform, so the vacuum bag does not stick to the finished composite panel (Figure 2a). The peel ply is a highly permeable fabric allowing resin to flow through it, but not hardening with the preform.
When the process is finished, the peel ply allows the preform to have uniform texture.
After the peel ply is laid down, a piece of mesh is cut to approximately the dimensions as the top of the preform (~1 in. on all sides), and placed on top of the peel ply. This mesh helps ensure proper infusion across the perform (Figure 2b). Next, a distribution medium (knitted fabric) is placed alongside the performs to ensure that thorough wetting out is achieved quickly. This entire process is known as SCRIMP (Seemann Composite Resin Infusion Molding Process) Tacky tape forms the perimeter around the entire preform. It is placed about two (2) to three (3) inches wider than the preform to give adequate room for tubing and bagging. A piece of coiled tubing, which has been cut to the approximate length of the preform, is placed on the sides of the preform. Another piece of tubing, which is connected to the vacuum pot, is inserted into the coiled tubing. The vacuum pot is a sealed bucket that collects any excess resin that comes out of the preform. This is important because the vacuum pump would be ruined if resin enters the vacuum line.
A feed line is then installed on top of the preform. Again, a piece of coiled tubing is cut to the approximate length of the preform. Once the coiled tubing is in place, it is wrapped with mesh and a piece of tubing, which is connected to the resin bucket, is inserted into the coiled tubing. These lines are made airtight by wrapping tacky tape around the edges that cross the previously constructed tacky tape perimeter ( Figure 5).
The final step in the set-up is the addition of the vacuum bag. The bag is adhered to the tacky tape and positioned around the tubes ( Figure 6). When there is excess bag in an area, an "ear" is formed with tacky tape to guarantee that the bag will be airtight.

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This is a critical step due to the fact that any small holes could cause loss of a full vacuum.
Once the entire set-up is complete, a vacuum check is made. This is done by using a vacuum gage to test how well it was holding a vacuum. After the vacuum check is made, and an adequate vacuum is reached, the clamp is turned off and the infusion begins (Fig. 4). Numerous factors in the set-up process can modify the desired final product. A correct bagging job is one that is not too tight and has no leaks or creases. A bag that is too tight could leave channels running on the sides of the preform, causing the resin to move around the piece on the sides rather than through the preform. This occurs because fluids travel through the path of least resistance. Most of the resin will flow in these voids and leave through the vacuum tube. Therefore, only some resin will enter the piece leaving dry spots and thus weakening the composite.
Another variable is the time needed to perform an infusion. There were a total of sixteen plies of E-glass and a foam core infused at once. The time needed depends on the resin used and the temperature and humidity in the room where the infusion took place. Not enough humidity and/or too low of a temperature can cause the resin to become more viscous. This will lead to improper infusion due to the fact that the resin will harden before the entire sample is infused.
Atmospheric pressure plays another role in the VARTM process. There is pressure pushing against the vacuum bag and pressure pushing against the bucket of resin. If the pressure is higher, the vacuum on the piece will be much higher. The atmospheric pressure pushes on the vacuum bag, causing more air to be withdrawn by the vacuum pump.
Maintaining a perfect vacuum is very important as well. An ideal vacuum is 30" Hg. There are many places where leaks could exist. The vacuum pot must be tightly shut so that no air can leak in from the sides of the lid. In some cases, air that is between the clamp on the feed tube and the resin bucket will get into the piece as the resin follows. This air makes the piece fluctuate rapidly during the entire infusion.
Placing the vacuum and feed tubes in the correct locations can determine how quickly and effectively the resin flows into the preform. Feed tubes should not exceed the length of the preform. The tube should go on top of the preform and in the center.
This will prevent dry spots from occurring by forcing the resin to flow through the piece instead of down the sides.
If the coil tubing on top of the preform became loose, it could puncture the vacuum bag. This would hinder the quality of the vacuum, making the infusion process take longer and weaken the compression that the bag puts on the piece. Also, 240 if the tacky tape does not stay sealed to the glass table, it can create holes in which air will leak in. This could destroy the vacuum and any chance for a quality piece to form.
When the infusion process is completed, the piece must be left to cure. This is the process in which the resin will harden. There are a couple of ways in which the piece can cure. It can either be left at room temperature for approximately forty-eight (48) hours, or, to speed up the process, it can be placed in an oven. Leaving the piece on the table, and allowing it to cure, is the best method because it will ensure that the piece remains flat and no bowing occurs. Also, if the temperature of the oven is set too high, the sides of the piece will flare up and the entire piece will become less dense.
This will lead to an offset of the strength properties of the piece.   2. Then select the pressure bars (steel or Aluminum) closer to the impedance of the specimen. We also have different diameters for the pressure bars.

References
Note: The basic thumb rule is that we use steel bars for the harder materials to bar center. We generally use clay and lead pulse shapers. These give us very good results for harder materials, but for the softer materials, you can try different pulse shapers. These include paper, copper etc..
(m) Release the nitrogen gas from the gas tank into the gas gun chamber until the required pressure level is achieved.
(n) Arm the oscillation to capture the strain gage voltage signals and make sure the arm holds until you release the projectile. If the arm is not holding, adjust trigger levels. (Note: if you are getting high noise in your signals more than 20mv, turn off the lights before the experiment).
(o) Once again, ensure that the specimen is well aligned between the bars and verify the status of the trigger hold before pressing the solenoid valve release button.
(p) Press solenoid valve control box button to release the projectile.
(q) Save captured voltage pulses onto a USB drive for further analysis of the data.
(r) A MATLAB program is written to read the data from the pulses and analyze the pulses using the one-dimensional wave theory stress and strain equations. After the experiments are performed, the pulses are used along with the MATLAB program to determine the equilibrium and true stressstrain plots of the specimen.
(s) After the experiment is completed, turn off the cylinder and make sure all the left over nitrogen gas in the gas chamber is released.
(t) After the data is transferred from the oscilloscope to USB drive, verify that in your computer and turn off the amplifier and oscilloscope.
Analyzing the results: 1. There are two MATLAB codes to analyze the data. 1. Verify_Equilibrium and 2. Steel/aluminum_SHPB. Use the appropriate codes to analyze the data.
Depending on the bars you used, the respective code has to be used.
2. Make sure the code has the right properties and dimensions of the pressure bars you used. These include the bar diameters and proper wave speed of bar material.

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3. If we use hollow bars, make sure you have the right dimensions in the code.
For solid bars, dimensions for the hollow bar should be zero. 4. First run the verify equilibrium code. Make sure the data you get from the oscilloscope has the following names for the four channels. TEK00000, TEK00001, TEK00002,and TEK00003. The code recognizes these names.
Make sure the codes and the data are in the same folder. 8. When you run the code, you get two figures. Figure 1 gives the incident and reflected pulses. Figure 2 gives the transmitted pulse.  10. Input the values you found out and press 'ENTER'. 11. Now you will get 3 more figures. Figure 3 shows the incident, reflected and transmitted pulses. Figure 4 shows the incident, reflected and transmitted pulses you picked on before. Figure 5 shows the force ratio. Front face represents the forces calculated on the incident and reflected pulses. Back face represents the force calculated on the transmitted pulse. Ideally, these two fronts and back face should match perfectly.
12. Various factors decide the equilibrium. These include type of material tested, strain rate etc.. 13. Make sure the incident and reflected pulses start at the same time on 16. Now open the SHPB code and make sure you have the same value for filter as in the verify_equilibrium code.
17. Enter the specimen thickness and diameter in inches. 18. Again, you get two figures. Figure 1 gives the incident and reflected pulses. 24. Go to MATLAB main window and you can see the strain rate. Note down this value. Next you will end up with final figure (Figure 6). This is eng. strain rate vs. time. 2. Selecting the bar is same as explained before.
3. Experimental procedure is also similar to the above. Here, you place the pulse shaper on the flange. You can use paper, clay or lead. 4. Different striker bars can be used to perform experiments at different strain rates. Make sure the striker bar slides freely on the bars. 5. The specimen will be threaded at both ends to the pressure bars. There is no need to use the lubricant. 6. The connections remain the same as explained before. You can use the same amplifier and oscilloscope, and same settings.  1. The tungsten carbide inserts will be used. The specimen will be sandwiched between these inserts.
2. The diameter of the specimen should be smaller than the inserts. The below figure shows the set up. 3. For experiments at elevated temperatures, the SHPB apparatus in conjunction with the induction coil heating system will be utilized as shown in Fig. 2. 4. A special fixture is used to load the specimen. 5. The inserts were used to eliminate the temperature gradient in the bars and thus protect the strain gages mounted on them.
6. The impedance of the inserts was matched with the bars; hence they do not disturb the stress wave profiles in the bar. The impedance matching requires the diameter of these tungsten carbide inserts to be smaller than the main pressure bars. This is the reason for the specimen diameter for high temperature testing being smaller than that for room temperature testing. 7. By varying the power, higher temperatures can be achieved. 8. The induction coil heating system has a power control box, remote to start and stop, a cooling unit and cooling supply (blue box) to reserve water. Make sure the blue box has sufficient distilled water. The copper coils are connected to the cooling unit and it is places around the inserts.  9. First turn ON the blue box, then the power supply. The power supply needs the larger output in the DPML lab. 10. Make sure the wheel on the cooling unit is pinning smoothly and fast. If not, do not do the experiment. Increase the power supply, to heat the specimen. 11. When the regulator is turned ON, it should give a click sound after around 30s.
If it does not, turn it off and try again. If the problem persists, turn off the regulator and the problem can be determined.
12. Turning ON the power supply regulator, it will read 'cycle continuous' on the remote (smallest one), which is desired. 13. The system should already be set to manual power output again, which will allow to control the power. If it is not set, you can do by using the switch located to the immediate right of the dial on the regulator.
14. Make sure the dial on the regulator is zero, so there will be no immediate power output. 15. Now press 'start' button on the remote (small one that reads the display). 16. The bars were kept apart initially, later the specimen and carbide inserts were heated in isolation to the desired temperature (usually about 20-50°C higher than the test temperature) and soon after the bars were brought manually into contact with the specimen. The temperature of the specimen was monitored using a 0.127mm chromel/alumel thermocouple, which was spot welded onto the specimen. 17. In most of the experiments, it takes less than two minutes to heat the specimen to the required temperature and it takes less than 10 seconds to bring the pressure bars into contact with the tungsten inserts and fire the gun. 18. Once the temperature is reached, hit 'stop' on the display and turn off the regulator and the induction heater. Now trigger the oscilloscope. If you trigger the oscilloscope before, due to magnetic fields from the induction heater, you will see lot of noise. 19. Allow the cooling unit to run for some time son that it reaches room temperature. 252 20. All other experimental procedure, data capturing, and analyzing the results remain the same as explained in compression SHPB section.

Note:
1. Always make sure the yield strength of the material you are testing is never beyond the yield strength pressure bars.
2. For testing ceramics of high strength, we need to use inserts so as to protect the bars from plastic deformation.

ENERGY ANALYSIS
This manual is designed for the steps to use the energy and impulse analysis code.
(1) Obtain the original data The original data of shock tube experiments are from the Tektronix oscilloscope (TDS3014 or 3014C). The data must have following name: First channel: TEK00000.csv Second channel: TEK00001.csv Normally, there are two columns in these files. The unit of the first column is second (s). The unit of the second column is voltage (v).Please copy these files into the folder named "experimental data backup".
(2) Analyze the original data. This step is to analyze the original data to obtain the shock wave velocity, the peak pressure and the modified pressure profiles.
This step is carried out in the folder named "original data analysis". In this folder, the m file named profile_analysis.m is necessary. Other files can be deleted or replaced.
You must copy the original data files into this folder and then run the code. The running process is as follow, (1) The code will first ask you how many plys you use in the experiment. This information is only for your record. It does not matter the analysis process.
(2) The code will ask you the sensitivity of the sensors. This value is given in the box of the sensors. This value means how many milli-voltage related to 1 psi. (4) Then the code will inform you as follow, "The peak and velocity data have been saved into the file, which is named peak&velocity.txt and in the same folder of this code.
There are two more pressure data files in this folder: inc_sp.dat ref_sp.dat They can be used for energy and impulse evaluation.
The code will give some plots to verify your data.
Please double check them very carefully.
press any key to continue" (5) After pressing any key, the code will give four images:  The first two files will be used to analyze the energy and impulse. There are two column data in these two files. The first column is time with unit second (s). The second column is pressure data with unit psi.
The last file records the physical parameters, which needs to be input in the energy and impulse analysis.
(7) Please cut these three data files into the folder named "experimental data backup" and delete all of these files in the current folder.
(3) Analyze the incident and remaining energy and impulse This step is to use the data obtained in step 2 to analyze the incident and remaining energy and impulse in a shock tube experiment.
This step is carried out in the folder named "gas energy and impulse analysis". In this folder, seven m files are necessary. They are, Main code: energy_impulse_analysis.m Other files can be deleted or replaced. You must copy the data files: inc_sp.dat and ref_sp.dat, into this folder and the correlated blank test data file, inc.dat, from the folder named "blank test data". The code running process is as follow, (1) The code will first show the format and unit of the data. Please be sure that the data should be the exact format.
(2) Then the code will give the total number of the data and ask you how many Skip two points 266 (3) Then the code will ask you to input physical parameters obtained in step 2 (saved in peak&velocity.txt).
(4) The code will calculate the physical parameter profiles. This process is automatic.
(5) Then the code will integrate the parameter profiles to obtain the energy components. This process is automatic.
(6) Finally, the code will ask you to input the name of the file which you want to save data into. Then all of the data will be saved into Please copy and save these data into a safe folder.
(4) Analyze the deformation energy of the gas, momentum and kinetic energy of the specimen This step is to use the data obtained in step 2 and the high-speed side-view images to analyze the deformation energy of the gas, momentum and kinetic energy of the specimen in a shock tube experiment.

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This step is carried out in the folder named "specimen momentum and energy". In this folder, only one m files, Deformation_momentum_kinetic_photron.m, are necessary.
Other files can be deleted or replaced. You must copy the data files: ref_sp.dat, and a series of high-speed images into this folder. The code running process is as follow, (1) The code will first show the format and unit of the data. Please be sure that the data should be the exact format.
(2) load the time series of the images You will have three ways to load the time series of the images.
(i) The time between two frames is same. You can input total number of frames and time between two frames. Then the code will generate the time series automatically.
(ii) The time between two frames is not same. You can input total number of frames and input time between two frames frame by frame.
(iii)The time between two frames is not same. The time between two frames is not same. Then you can just load that time series data file.
You can choose anyone and following the instruction.
(3) Length calibration. You can choose any image for length calibration. You will need to choose two points on this image and the vertical distance between these two points will be used to calibrate the length. Therefore, you need to know one real vertical scale between two points on the image.
For example: (i) the span of the supports is 6 inches (ii) the outer diameter of the shock tube is 5 inches The process will repeat three times. Thus, totally you will pick six times.
Please follow the instruction. . Make sure to yell "firing" when experiment is about to be run and SHPB is being pressurized, keep outside doors closed so no one walks in 7. Make sure everyone in the lab, helping or not with the experiment, is aware an experiment will be taking place