RESPONSE OF COMPOSITE MATERIALS TO DYNAMIC AND LOW TEMPERATURE ENVIRONMENTS

This dissertation is prepared using the manuscript format. The dynamic response of composite materials subjected to underwater and air shock loading conditions has been studied. Additionally, the effects of low temperatures on the mechanical and fracture properties of these materials has been evaluated. The primary contribution of the author is on the computational modeling aspects of each of the dynamic loading studies conducted. The experimental work presented has been completed by the author’s collaborators from the University of Rhode Island. The low temperature effects on the materials is solely an experimental investigation and was undertaken in collaboration with researchers at the Naval Undersea Warfare Center. The objective of the project is to develop a better understanding of the response of composite materials when subjected to shock loading conditions leading to more efficiently designed structures. The work is divided into five phases as described in the following overview. In the first phase of the research the near field underwater explosion response of E-Glass / Epoxy plates was investigated. The study also included the effects of elastomeric polyurea coatings on both the transient response and damage characteristics. The computational models developed in the study were shown to simulate the testing accurately, and using the Russell Error measure, demonstrate model correlation that can be described as excellent. The models are able to accurately simulate the detonation of the explosive charge and the resulting pressure fields and plate deflections. The objective of the second phase of the project was to investigate the effects of material ageing on the response of Carbon-Epoxy laminates when subjected to air blast loading. The shock loading was induced through the use of an air driven shock tube and the effects of seawater exposure were quantified in terms of transient response and material failure onset. Computational models of the experiments were developed through the use of the Ls-Dyna code for both fully clamped and simply supported edge conditions. The models were shown to accurately capture both the timing and displacement magnitudes of the specimens as well as the onset of material failure. The third phase of the project investigates the response of composite cylinders when subjected to near field underwater explosive loading, including the effects of polyurea coatings. The objective is to determine the influence of both charge standoff and coating thickness on the transient response as well as damage mechanisms / evolution during loading. Experiments with corresponding simulations were performed with good agreement between the two in terms of pressure loads and damage extents. The simulations were further utilized to examine the internal and kinetic energy levels and distributions during loading as well as the surface strain characteristics. The effects of material ageing on the response of flat plates subjected to near field explosive loading is the focus of the fourth part of the research. In this investigation, biaxial Carbon/Epoxy laminates with and without long term seawater immersion effects were subject to the explosive loading to determine the influence of material degradation on the panel response. A fully coupled Eulerian-Lagrangian computational approach was utilized for the modeling of the corresponding experiments. The simulations were used to demonstrate an increase of maximum strains with ageing as well as the characteristics of stress wave propagation as a function of laminate architecture. The final aspect of the research presented is aimed at investigating the influence of temperature on the mechanical and fracture performance of composite laminates. The focus is on the low temperatures associated with seawater in the arctic regions and deep depths of the oceans. Mechanical characterization is in the form of tensile, compression, and short beam shear and fracture is evaluated in terms of Mode-I failure. The results show that for both E-Glass and Carbon Epoxy materials there is an influence of temperature on both mechanical and fracture performance of the material.

contribution of the author is on the computational modeling aspects of each of the dynamic loading studies conducted. The experimental work presented has been completed by the author's collaborators from the University of Rhode Island. The low temperature effects on the materials is solely an experimental investigation and was undertaken in collaboration with researchers at the Naval Undersea Warfare Center. The objective of the project is to develop a better understanding of the response of composite materials when subjected to shock loading conditions leading to more efficiently designed structures. The work is divided into five phases as described in the following overview.
In the first phase of the research the near field underwater explosion response of E-Glass / Epoxy plates was investigated. The study also included the effects of elastomeric polyurea coatings on both the transient response and damage characteristics. The computational models developed in the study were shown to simulate the testing accurately, and using the Russell Error measure, demonstrate model correlation that can be described as excellent. The models are able to accurately simulate the detonation of the explosive charge and the resulting pressure fields and plate deflections.
The objective of the second phase of the project was to investigate the effects of material ageing on the response of Carbon-Epoxy laminates when subjected to air blast loading. The shock loading was induced through the use of an air driven shock tube and the effects of seawater exposure were quantified in terms of transient response and material failure onset. Computational models of the experiments were developed through the use of the Ls-Dyna code for both fully clamped and simply supported edge conditions. The models were shown to accurately capture both the timing and displacement magnitudes of the specimens as well as the onset of material failure.
The third phase of the project investigates the response of composite cylinders when subjected to near field underwater explosive loading, including the effects of polyurea coatings. The objective is to determine the influence of both charge standoff and coating thickness on the transient response as well as damage mechanisms / evolution during loading. Experiments with corresponding simulations were performed with good agreement between the two in terms of pressure loads and damage extents. The simulations were further utilized to examine the internal and kinetic energy levels and distributions during loading as well as the surface strain characteristics.
The effects of material ageing on the response of flat plates subjected to near field explosive loading is the focus of the fourth part of the research. In this investigation, biaxial Carbon/Epoxy laminates with and without long term seawater immersion effects were subject to the explosive loading to determine the influence of material degradation on the panel response. A fully coupled Eulerian-Lagrangian computational approach was utilized for the modeling of the corresponding experiments. The simulations were used to demonstrate an increase of maximum strains with ageing as well as the characteristics of stress wave propagation as a function of laminate architecture.
The final aspect of the research presented is aimed at investigating the influence of temperature on the mechanical and fracture performance of composite laminates. The focus is on the low temperatures associated with seawater in the arctic regions and deep depths of the oceans. Mechanical characterization is in the form of tensile, compression, and short beam shear and fracture is evaluated in terms of Mode-I failure. The results show that for both E-Glass and Carbon Epoxy materials there is an influence of temperature on both mechanical and fracture performance of the material. v

ACKNOWLEDGEMENTS
The completion of this degree has caused me to look back through my academic career at URI that started when I first enrolled as an undergraduate student in 1999 to the present. It seems impossible to imagine the experiences and opportunities I have been afforded through my relationship with the university. At the beginning I had my sights set simply on graduating in four years in preparation for the beginning of my career.
Little did I know then, that I would be actively seeking opportunities to remain engaged with the university after 20 years, and that to a large extent research and academics would be the foundation of that career. Looking back, it is difficult to recall all of the professors from whom I have taken courses and all the staff that helped me get to where I am today.
The number is no doubt larger than expected, and for this I am eternally grateful.     Gupta and Shukla investigated the air blast response of foam core sandwich composite panels at 5°F (facesheet)/-40°F(core). At these low temperatures they found that the performance of the panels was degraded as compared with those tested at room temperature. As observed in previous studies, the damage mechanisms were different at low temperatures. Further, the response of the structure was more severe due to shear cracking which developed in the foam core.

Introduction
Within the naval community there is an interest in constructing new vehicles and structures from composite materials. The advantages of these advanced material systems include high strength to weight ratios, lighter structural components, and overall reduced maintenance costs. However, when structures manufactured from these materials are employed in military applications they must also be designed in a manner such that they will be able to survive an underwater explosion (UNDEX) event. When a submerged structure is exposed to an underwater explosion, it undergoes a complex and highly transient loading condition including high peak pressures and spherical wave fronts. When explosions occur at sufficiently large standoff distances from a structure, the shock fronts are nearly planar and act over the entire structure in a nearly uniform manner. This loading results in structural responses consisting primarily of flexure with large center-point deflections. However, there tends to be low levels of material damage (primarily inter-laminar delaminations) and plate perforations / ruptures are minimal. In the absence of plate rupture, the shock wave is almost fully reflected away from the structure, shielding any occupants / internal equipment from the effects of the high pressure waves. Conversely, when an explosion occurs directly on, or very close to, the surface of a structure, the loading area is limited to the vicinity of the detonation itself. The result is highly localized pressure loadings and the structure sustains higher amounts of damage, oftentimes including plate penetration / complete rupture. Upon rupture of the plate the pressure waves enter the structure, subsequently exposing any occupants to the adverse effects of high pressure gases as well as any shrapnel which may become dislodged from the blast area.
Studies on composite materials subjected to high loading rates have utilized both experimental and computational techniques. Work by Latourte et al [1] utilized a scaled fluid structure method [2] to study the failure modes and damage mechanisms in both monolithic and sandwich plates subjected to underwater impulsive loads. Schiffer and Tagarelli [3] have compared the response of glass and carbon reinforced composites and found that the glass reinforced plates had larger blast resistance than the carbon plates due to their higher tensile ductility. Avachat and Zhou [4] studied the effects of underwater shock loading on filament wound and sandwich composite cylinder and found that while both constructions exhibited similar damage mechanisms, including delamination, fiber failure and matrix cracking, the sandwich structure had overall better performance than a monolithic cylinder with similar mass. The same authors [5] also utilized an Underwater Shock Loading Simulator combined with digital image correlation to show that for sandwich constructions lower density cores yield higher blast performance than high density cores due to their larger core compression capability.
LeBlanc and Shukla [6,7] have studied the response of flat and curved composite plates to far field underwater explosive loading through experimental and computational methods. Franz et al. [8] and Mouritz et al. [9] studied the effects of an underwater explosion at different standoff distances on a glass composite laminate. Dear and Brown [10] have conducted a detailed study on the damage mechanisms and energy absorption in composite plates when subjected to impact loading.
In recent years, the use of polyurea materials to enhance the failure resistance of structures subjected to explosive loading has become a topic of interest. Polyurea is a synthetic, high strength / high elongation coating that is typically spray cast onto existing structures to increase their performance under shock and ballistic loading events such as those of a bomb blast. Research efforts have recently studied the effectiveness of polyurea when used with composite materials. LeBlanc et al. [12,13] showed that the transient response of UNDEX loaded composite plates is dependent upon both coating thickness as well as location. Tekalur et al [14] investigated the response of E-Glass composites coated with polyurea subjected to air blast loading. This study indicated that the polyurea coating reduced the transient deflections and post mortem damage levels as compared to the uncoated material. Gardner et al [15] studied the effect of location of the polyurea in relation to the foam core in sandwich composites. It was observed that when a layer of polyurea is placed between the foam core and the back-face of the sandwich the blast resistance is improved, while conversely if the polyurea is placed between the front face and the foam core the performance is degraded. Furthermore, effects of polyurea coatings have been studied through the use of computational simulations. Amirkhizi et al [16] have developed a visco-elastic constitutive material model that describes the behavior of polyurea materials under a broad range of strain rates, and includes pressure and temperature effects. Amini et al [17,18] used LS-DYNA to simulate impact / impulsive loading experiments of polyurea coated steel plates.

Materials
In the current study, E-Glass Epoxy bi-axial laminate composite plates, with and without polyurea coatings are studied. The following section details the materials utilized in the investigation.

Composite
The  Figure 1. From this figure it is seen that the material exhibits strong strain rate dependence and becomes stiffer with increasing loading rate. Furthermore, the material displays a stiffening effect in compression above 300% whereas in tension the response exhibits a stress plateau like behavior.
A summary of the plate thicknesses and areal weights is provided in Table 2, and a schematic of the laminate designs are shown in Figure 2.

Experimental Methods
The experiments conducted in this study make use of a water filled tank coupled with high speed photography and Digital Image Correlation to impart UNDEX loading to fully clamped plates while capturing the transient response. The following are the details of the equipment and methods employed.

Test Tank
The near field UNDEX experiments in this study were conducted in a water filled tank, Figure 3.

Explosive Charge
The explosive used in the near field blast experiments is an RP-503 charge manufactured by Teledyne RISI, Figure 5. The charge is comprised of 454 mg RDX and 167 mg PETN contained within an outer plastic sleeve.

Digital Image Correlation
High speed photography, coupled with three dimensional Digital Image Correlation (DIC) was used to capture the full-field deformation of the back-face (side opposite of the explosive) of the plates during the UNDEX loading. During the experiments two cameras are arranged in a stereo configuration such that they view the back face of the test specimen. To record the transient response with this system, the cameras must be calibrated and have synchronized image recording throughout the event.
The calibration of the cameras is performed by placing a grid containing a known pattern of points (dots) in the test space where the composite sample is located during the experiment. This grid is then translated and rotated in and out of plane while manually recording a series of images this grid pattern is predetermined, the coordinates of the The cameras used during experimentation were Photron FastCam SA1. Each camera is capable of frame rates from 1,000 to 675,000 fps with image resolution ranging from 1,024 x 1,024 to 64 x 16 pixels depending on the frame rate. In the current effort, a frame rate of 27,000 fps was utilized for an inter-frame time of 37μs. The camera resolution at this frame rate is 448 x 480 pixels.

Experimental Methodology
Experiments were preformed to understand the behavior of E-Glass/Epoxy plates subjected to near field underwater explosions. Three plate configurations have been studied: (1) 0.762 mm thick uncoated plate, (2) 1.524 mm thick uncoated plate, and (3) 0.762 mm thick plate with 0.762 mm polyurea coating on the back-face. Two high speed cameras were positioned 330 mm behind the tank walls perpendicular to the viewing windows to avoid any distortion effects from the windows themselves. A third high speed camera was positioned at the side of the tank to view the detonation of the explosive, resulting bubble growth, and interaction of the bubble with the composite plate. Two free field tourmaline pressure sensors are located within the tank to record the pressure field at two distinct standoff distances. Let it be noted that the gages are located at a larger standoff from the charge than the distance between the charge and the composite plate to avoid damage to the sensors. Figure 6 is a combination, isometric view and aerial schematic of the tank providing an overview of the camera, explosive and pressure sensor positioning. An overview of the experimental process is presented in the following discussion.
To begin the experiment, the high speed cameras comprising the DIC system are calibrated to establish a correspondence of the respective camera coordinate systems.
Calibration is conducted according to the previously described method in which images of a calibration grid are captured while rotating and translating the grid. Once acceptable calibration and time syncing of the cameras is established the plate is bolted into the fixture with the DIC speckle pattern facing the cameras (air backed side). When mounting the polyurea coated plates, the coating is located on the back side of the composite plates with respect to the charge location. Once the plate is bolted into the fixture the RP-503 charge is placed within the tank. The charge is suspended by its detonation wire into the tank and placed 50.8 mm from the center of the composite plate.
To ensure consistent charge standoff distances for each experiment a 3. wire which is secured to a weight resting on the bottom of the tank. After the plate is secured in the fixture and the pressure sensors are in place, the tank is filled with water to a depth of 1.06 m. The center of the plate is located 0.55 m below the surface of the water. As mentioned previously, an aerial schematic of the total setup is shown in Figure   6.
Once the tank is filled, and the operation of all measurement equipment is verified, the RP-503 charge is detonated through the use of a detonation box. The box simultaneously sends a high voltage to the RP-503 charge to initiate detonation and a simultaneous 9 volt pulse to the oscilloscope which captures the pressure data. The oscilloscope also relays a negative TTL voltage to all the cameras to capture the high speed photos. The use of this single initiation system to both initiate the charge detonation and trigger the oscilloscope/cameras ensures complete time synchronization between all experimental equipment and a common time zero datum for all measurements. Upon completion of the experiment all images from the DIC cameras are processed through VIC 3D to extract full-field plate deformation.

Results and Discussion
The response of the composite plates in this study is characterized by the transient center-point displacement of the back-face of the plate, deformation evolution mechanisms during the displacement, and full-field DIC observations. All plate deflection data presented for the plates is extracted from the post processed images through DIC.
The pressure profiles resulting from the detonation of the RP-503 charge, as measured by the two free field pressure sensors at 100 and 175 mm standoff distances from the charge, are shown in Figure 7. The pressure profiles display the characteristic components of an UNDEX, namely: a rapid pressure increase associated with the shock front, followed by an exponential decay and a reduction in peak pressure with increasing radial standoff from the charge center. It is noted that for the 100 mm standoff pressure gage there is a sudden drop in pressure occurring at 0.12 ms. This corresponds to the arrival of the reflected pressure wave from the surface of the plate. The peak pressure of the shock front experienced by the plate surface (50.8 mm standoff) is on the order of 40 MPa determined from the computational simulations.
The behavior of the bubble resulting from the detonation and its associated interaction with the composite plate is shown in Figure 8. The sequence of images shows the clear formation of the bubble at 80μs and its subsequent growth in size due to the combustion of the explosive products. Due to the high pressure of these gaseous products the bubble expands, reaching a diameter of ~50 mm at 320 μs at which point it reaches and interacts with the surface of the composite plate. As a result of this interaction with the plate it is prevented from further expansion in the direction of the plate but continues a spherical expansion in the remaining directions. The uncoated plates experience edge tearing (see later discussion) between 1200 μs and 1400 μs during which time the bubble is still expanding and has not yet reached its maximum diameter.
Once tearing of the plate occurs, the plate can no longer be considered a standing plate and any resulting bubble behavior would be heavily influenced by the resulting motion of the plate.  While filling tank with water during the setup of the experiment it was observed that the plates sustain a measurable level of flexure due to the hydrostatic pressure and the thin nature of the plates. The peak center-point deflection of the plates after filling the tank is provided in Table 3. These deflections are determined by taking photographs of the plate surface before and after filling the tank and processing the images through the DIC software. The baseline for all subsequent plate deflection measurements is taken to be the deformed shape after tank filling. As previously described, a constant charge standoff for all plate configurations is achieved through the use of a foam spacer which connects the charge and plate. Although beyond the scope of the current study, it is noted that it is likely that as the initial depth pressure is increased (i.e. a deep diving submersible) the effects of the corresponding pre-stress prior to UNDEX loading should be considered. As the material has a finite strength capability, the additive effect of depth pressure and UNDEX pressure loading will reduce the ability of a structure to resist an explosion event that may have been survivable at shallower depths. The center-point displacement for each respective plate configuration is shown in Figure 9. From this figure it is observed that there are several distinct differences in the overall plate response as influenced by the plate construction. The first difference is the overall center-point deflection of the plates. It is evident that, as compared to the baseline 0.762 mm plate, increasing the plate thickness or including a polyurea coating reduces the peak overall deflection for a given level of loading. The peak displacement for the uncoated 0.762 mm plate is 28 mm, whereas for the 1.524 mm uncoated plate and the 0.762 mm polyurea coated plate the peak deflections are 20.5 mm and 24.8 mm, reductions of 27% and 12% respectively. It is noted that the center-point velocity during the initial deflection is nearly constant for each configuration. The main difference is the time that it takes for the plate to arrest its outward motion and begin to recover, with the 1.524 mm uncoated and the 0.762 mm polyurea coated plates arresting their outward motion ~0.25 ms sooner than the baseline 0.762 mm plate. The peak center-point deflection and time to reach the peak displacement are provided in Table 4. The centerpoint deflection comparison between the 1.524 mm uncoated plate and the 0.762 mm plate with a 0.762 mm coating of polyurea indicate that for a plate thickness it is more advantageous to utilize additional structural plies rather than an elastomeric coating.
However, when a structure has previously been designed and further thickening of the structural shape is not possible, the application of a polyurea coating can improve the transient response to shock loading.
The second primary difference in the response of the plate configurations is the onset of material damage. Both the uncoated 0.762 mm and 1.524 mm specimens experienced significant through-thickness tearing at the plate boundaries at approximately 1.1 and 1.4 msec respectively. Upon rupture of the plate edges water entered the cameras' field of view and caused decorrelation in the DIC images. Their plots, Figure 9, are accordingly abbreviated at the onset of tearing prior to DIC decorrelation due to water intrusion. However, it is further observed that although the 0.762 mm plate with the polyurea coating did experience larger deflections than the 1.524 mm uncoated plate, there was no edge tearing of the plate itself. Thus in terms of reducing material damage itself, the polyurea coatings offer an advantage over a thicker uncoated plate.  The deformation history of the baseline 0.762 mm uncoated composite plate as measured along a horizontal cut though the center of the plate is shown in Figure 10. The deformed profile plotted throughout time is illustrative of the deformation mechanics of the composite plate. From this figure it is seen that for a plate subjected to a centralized near field UNDEX loading, the deformation is initially dominated by localized deflections at the center with minimal deflection near the boundaries. As the plate responds to the pressure loading, it gradually transitions to an overall plate flexure mode as shown by the cross sectional shape at 0.63 and 1.11 ms. At 1.11 ms the plate experiences significant edge tearing and further observations of the plate deformation mechanics would be invalid due to partial rigid body motion of the plate. The significant observation is that the initial plate deformation is governed by the highly localized pressure loading and then subsequently shifts to a mode I flexure deformation profile later in time.
The full-field displacement profiles for the back-face of each plate configuration are provided in Figure 11. The localized center-point deflection can be visualized in the 0.37 ms time frame and is consistent with the cross sectional shape plot, Figure 10.  The transient displacement results discussed thus far indicate a performance advantage when the thickness of the baseline plate is increased, or alternatively a polyurea coating is applied to the surface of the plate. However, when the plate thickness is increased or a coating is applied there is an associated penalty in that the plate weight is correspondingly increased. One means of quantifying the added mass penalty in terms of transient deflection of the respective plates is to establish an Areal Weight Ratio (AWR) between the plate configurations [13]. The AWR is calculated by Equation 1 where W1 is the areal weight of the uncoated 0.762 mm composite baseline plate and W2,3 is the areal weight of the polyurea coated 0.762 mm plate and the and 1.524 mm specimens, respectively. The AWRs for the 1.524 mm plate and the polyurea coated plate are 2 and 1.57 ( Table 2). The AWR is subsequently employed as a multiplier applied to the transient center-point deflection data. The displacement data that has been adjusted (raw data multiplied by AWR) to account for the areal mass increase is shown in Figure   12. This plot shows that when the displacements are adjusted to account for the increased areal weight, the baseline plate outperforms both the thicker and polyurea coated plates.
The normalized deflection of the polyurea coated specimen was 37.9% greater than the uncoated 0.762 mm specimen, and that the normalized deflection of 1.524 mm specimen was similarly 45.4% greater. This suggests that the additional laminate plies and the employed polyurea regime serve to degrade the deflection performance of the plate specimen with respect to AWR. This observation is consistent with previous findings for curved polyurea composite plates subjected to far field UNDEX loading in which polyurea coatings have been seen to result in larger AWR adjusted deflections [13]. It is noted that in the previous study, multiple coating thicknesses were considered and it was found that there are coating thicknesses for which the coated plate outperforms the baseline plate, even when accounting for the AWR penalty. Thus, the findings of the single coating thickness considered in the current study do not preclude the existence of a polyurea coating thickness for composite plates subjected to near field UNDEX loading that both outweighs the weight penalty while also improving the deflection performance.
Further work is needed to identify such a regime in the future. Finally, the 1.524 mm plate and 0.762 mm polyurea coated plates have approximately the same relative performance in terms of adjusted peak displacement when the added mass penalty is taken into consideration.   Table 6. By defining C0, C1, C2, C3, and C6 equal to zero, and C4, and C5 equal to γ-1, a gamma law EOS is achieved. Furthermore, the pressure generated from the detonation in the model is suitably correlated to the corresponding experimental profile. The Material and EOS parameters for the RDX are provided in Table 7 and Table 8.

Table 8 -RDX EOS (JWL) Parameters [19]
The structural aspect of the coupled model consists of the composite plate and polyurea coating. In all models, only the unsupported section of the plates is included. The outer edge of the plate is fully clamped with appropriate boundary conditions, thus negating the need to explicitly model the fixturing in the test setup. It is noted that after the completion of each test there was no slippage observed at the plate boundary. The composite plate in the simulations is modeled using a single layer of shell elements, Figure   14, with an edge length of 2.5 mm. The *Section_Shell property for the shell element allows for the laminate schedule to be defined within the section card, including the angle of each respective ply. By defining the ICOMP parameter to be equal to 1 on the section card, the orthotropic layered composite option is activated. Through the use of this option an arbitrary number of equally distributed integration points may be defined through the thickness of the shell, with each integration point being assigned a material angle. In the current models, each ply is represented as having two integration points so as to capture the correct bending behavior on a per ply level. The polyurea material is represented in the model by solid elements, Figure 14, with a constant stress formulation. Furthermore, the polyurea coatings are assumed to be perfectly bonded to the composite plate and are thus meshed directly to the composite. This assumption is valid as there was no visual debonding between the composite and polyurea observed during testing.
The LS-DYNA material model utilized for the composite plate is Mat_Composite_Damage (Mat_022) [20]. This is an orthotropic material definition The loading of the composite plates in the models occurs in a two-step process.
During the first step a uniform pressure is quasi-statically applied over the entire front face of the plate. This pressure corresponds to the depth pressure (at the mid point of the plate) acting on the submerged plate. During the experiments it was observed that due to the relatively thin nature of the plates as compared to the unsupported dimensions of the plate there was a sufficient level of center-point defection (~5 mm for all plates) such that it should be accounted for during the simulations. Thus this pressure is applied to the plates and any resulting motion is allowed to damp out resulting in a static stress state. At this point the detonation of the explosive charge is initiated and the plate responds transiently.
In all subsequent discussions of plate displacements, the reported values are measured from the preloaded state by subtracting out the displacement resulting from the preload.

Center-point Displacement -Simulation Correlation to Test
The center-point displacement data captured during the experiments with the DIC method is used as a basis to correlate and validate the finite element model results. The quality of the correlation between the test data and numerical results in this study is quantified using the Russell Comprehensive Error measurement. The Russell error technique is one method which evaluates the differences in two transient data sets by quantifying the variation in magnitude and phase. The magnitude and phase error are then combined into a single error measure, the comprehensive error factor. The full derivation of the error measure is provided by Russell [21] with the phase, magnitude, and comprehensive error measures respectively given as: In the above equations ci and mi represent the calculated (simulated) and measured responses respectively. Excellent, acceptable, and poor correlation using the Russell error measure is given as: Excellent -RC≤0.15, Acceptable -0.15<RC≤0.28, and Poor RC>0.28.
The definition of these criteria levels are the result of a study that was undertaken to determine the correlation opinions of a team in support of a ship shock trial. A summary of the process used to determine the criteria is presented by Russell [22].
The center-point time history correlation between the experimental data and the corresponding computational simulation for each respective plate configuration is shown in Figure 15. A summary of the Russell error for each of these comparisons is provided in Table 9.

Summary and Conclusions
The response of submerged, air backed E-Glass / Epoxy composite plates, including polyurea coatings, when subjected to near field underwater explosive loading has been studied through the use of experiments and computational modeling. The focus of the work is on determining how the response of a composite plate subjected to UNDEX is influenced by increased plate thickness or through the application of an elastomeric coating to the baseline plate. A water filled blast tank has been used to impart UNDEX loading to the composite plates in a controlled manner. The Digital Image Correlation system is used to capture the full-field, transient response of the back (dry) surface of the plates.
Computational models of the experiments have been developed utilizing the commercially available LS-DYNA explicit finite element code.
In the study the response of three unique plate configurations is studied: (1)  However, in the case of an existing design the use of polyurea coatings can be an effective retrofitting application to improve the blast resistance of a structure while reducing overall material damage. Furthermore, it has been shown that through the use of an Areal Weight Ratio, there is a tradeoff between increased panel weight and mechanical performance.
Although, both the thicker composite plate and the coated plate outperform the baseline plate, this performance increase comes at a penalty of increased weight. Thus if weight is a strong consideration in a specific application then maximum blast resistance may not be achievable and a relative tradeoff between weight and performance must be considered.

Abstract
An experimental study, with corresponding numerical simulations, was conducted to investigate the blast response of weathered Carbon-Epoxy composite plates. The dynamic behavior of the composite plates with and without prior exposure to an aggressive marine environment was explored using a shock tube apparatus coupled with a high speed photography system. In order to simulate prolonged exposure in an aggressive marine environment, specimens were submerged in an elevated temperature, 3.5% salt solution for 0, 30 and 60 days. The saline solution temperature was maintained at 65°C to accelerate the aging process. Finite element modeling (FEM) for the blast loading experiments was performed using the Ls-Dyna code. Models have been developed for both the simply supported and fixed boundary condition cases.
Tensile and four-point bend tests were performed to characterize the quasi-static mechanical behavior of the composite material before and after prolonged exposure to aggressive marine environments. After 30 and 60 days of submergence, the tensile modulus decreased by 11% and 13%, the ultimate tensile strength decreased by 12% and 13%, and the ultimate flexural strength decreased by 22% and 22%, respectively.
Dynamic blast loading experiments were performed on simply supported and fully clamped specimens, to determine the effects of the boundary conditions on the Carbon-Epoxy specimen response. The Weathered (30 and 60 days) and Non-Weathered (0 day) specimens displayed dramatically different behavior after being subjected to a blast load.
For the simply supported case, Non-Weathered specimens displayed an average maximum out of plane displacement of 20 mm and recovered elastically. Weathered specimens, both 30 and 60 days exhibited similar initial transient behavior but failed catastrophically due to through thickness cracking at the point of maximum deflection.
For the fixed boundary condition, the Non-Weathered specimens displayed an average maximum out of plane displacement of 5.57 mm, whereas the 30 day and 60 day weathered specimens displayed a maximum out of plane displacement of 6.89mm and 6.96mm, respectively. The corresponding numerical simulations matched well with the experimental data. However, for the fixed boundary case, the beam vibration of the simulation was off phase with the experimental results due to imperfect boundary conditions in the experiments.

Introduction
A series of experiments were conducted to study the blast response of weathered Carbon-Epoxy composite plates subjected to simply supported and fully clamped boundary conditions. The blast loading was created using a shock tube and the structural response of the composite plate was recorded using high speed photography in conjunction with a 3D digital image correlation technique used to obtain full-field data.
In the marine community there is an increasing interest to use composite materials for the construction of structures due to their high strength to weight ratio, reduced radar signatures, and noise dampening properties [1]. Composite materials have been used to create small parts within ships such as fins and rudders, thus reducing the weight of vessels [1]. However, composites have lower impact resistance than steels and can degrade due to the undersea environment. Thus, studying the effects of the degradation of mechanical properties of composite materials, in particular on shock response, is of high priority.
To date, there have been numerous studies on the mechanical response of composite materials subjected to a dynamic loading. Abrate has written a detailed review of literature on the impact of laminated composites [2]. The review covers work from the late 1970s to early 1990s with a focus in discussing the experimental and theoretical approaches of early composites work. In the 2000s work by Zaretsky et al [3] and Yuan et al [4] focused on the damage of composite materials when subjected impact loading, specifically low velocity impacts. Current studies by Avachat and Zhou [5] have experimentally and computationally modeled the dynamic failure of sandwich composites subjected to underwater impulsive loads. However, these studies did not focus on the effect of aggressive marine environments on the dynamic response.
Accelerated life testing (ALT) methods simulate long term exposure to marine environments are used to study the effects of exposure on the mechanical properties of materials. In these investigations, composite materials are subjected to marine aging through submersion in seawater baths at elevated temperatures [6][7][8][9][10][11][12][13][14]. Nakada and Miyano [15] have developed prediction methods for the long term fatigue life of fiber reinforced plastic (FRP) laminates under elevated temperature and absorption conditions.
The long term effect of submersion on composite sandwich structures was studied by Siriruk et al [16] with a focus on the interface between the face sheets and the core. Park et al [17] presented the effects of aging after an impact event on polymer composites.
Submersion studies focus on the degradation of material properties due to the diffusion of water into the composite. Elevated temperatures are used to increase this rate of diffusion, therefore requiring additional data to determine the relationship between the exposure time in the accelerated life test and an equivalent time in a typical operating environment.
Diffusion studies to find an acceleration factor relating ALT submersion times to an equivalent time at operating temperatures have been conducted, including studies involving weight gain monitoring of samples to find diffusion coefficients [18]. Rice and Ramotowski [19] used the Arrhenius equation to derive a method for finding this acceleration factor using the matrix material of the composite. The acceleration factor was found to be dependent on the experimentally determined activation energy of the matrix.
Computational investigations of the mechanical response of composite materials have become more prevalent in recent years. LeBlanc et al. [20] were able to correlate experimental results of the dynamic shock response of composite plates with finite element simulations using LS-DYNA. Arbaoui et al. [21] investigated modeling the response of composites in a split Hopkinson pressure bar (SHPB) experiment and were able to successfully correlate experimental data to their simulations.
In the current study, the blast responses of weathered and Non-Weathered Carbon-Epoxy plates are compared. Additionally, computational models for the 0 and 30 day submergence conditions are developed to simulate the dynamic experiments. The simulations are shown to have good correlation to the experimental results.

Material and Specimen Geometry
The composite material used in this investigation is a Carbon-Epoxy (CE) plate produced by Rock West Composites. The carbon fiber is a 2x2 twill weave cured in an epoxy resin. The plate is 2.92 mm thick and composed of a 670 GSM 12k carbon fiber fabric (Aksaca 12K A-42) and PT2712 low viscosity epoxy produced by PTW&W Industries, Inc. Fiber volume fraction of the material is ~60%. The total thickness of the Carbon-Epoxy plate is made up of four twill woven plies, and the density of the composite is 1.45 g/cm 3 . An image of the composite material and the fiber construction is shown in Figure 1.   [23], D7264/D7264M-07 [24]: Procedure B (four point bend) and prior shock tube studies [28]. Prior to mechanical testing, all specimens were desiccated for 48 hours to remove accumulated atmospheric moisture.

Experimental Setups and Methods
To obtain the blast response of the Carbon-Epoxy composite, the specimens were subjected to blast loading using a shock tube apparatus. Prior to blast loading, the specimens underwent a procedure to artificially accelerate the underwater aging of the material. The experimental details of the blast generating apparatus, high speed photography data acquisition, weathering process and the quantification of accumulated weathering are described in detail below.

Shock Tube Apparatus
A shock tube apparatus is used to generate a pre-determined amplitude of blast loading that is imparted to the composite plates. High speed cameras, coupled with 3D DIC were used to record the side and back face transient response during loading. A schematic of the shock tube setup along with high speed cameras is shown in Figure 2. impacts the specimen and the pressure from the impact is reflected back into the muzzle.
The reflected pressure is the loading that the specimen experiences. Figure 3 is a plot of the pressure created by the shock tube apparatus as a function of time, as recorded by a pressure sensor 20 mm from the end of the muzzle exit.

Digital Image Correlation
High speed photography coupled with 3D DIC was utilized to capture full field displacements and velocities on the back surface of the specimens during blast loading.
Two Photron FastCam SA1cameras, coupled with 3D +DIC, were used to track the 3D displacements of the composite plates during blast loading, while a side view camera is positioned to record the out of plane displacements. The specimen was positioned vertically with the muzzle normal to the specimen, with a gap of (~0.1 mm) between the muzzle face and specimen. The processing of the high speed images from the experiments was performed using the VIC-3D software package, which matches common pixel subsets of the random speckle pattern between the deformed and un-deformed images. The matching of pixel subsets was used to calculate the three-dimensional location of distinct points on the face of the plate. This provided a full field displacement history of the transient event through time. For the blast experiments, a frame rate of 50,000 fps was utilized for an inter-frame time of 20μs.

Accelerated Weathering Facility
A submergence tank was created to subject the composite plates to an elevated temperature saline solution. The tank is composed of two high temperature polypropylene reservoirs. A double wall was created by placing the volumetrically smaller tank inside of the larger tank, creating a fluid boundary to separate the immersion heaters from the internal salt solution, and prevent any unwanted salt water corrosion. A 3.5% salt solution fills the internal tank where specimens were submerged for 30 and 60 days. The immersion heaters in the external tank were used to heat the external boundary of deionized water and through convection and conduction, heat the internal saline solution.
The outer tank is insulated and maintained at 65°C which was chosen to increase the rate of water diffusion in the composite material, while remaining below the published 71.7 -95.6 °C glass transition temperature range of the composite's epoxy matrix. The immersion heaters chosen to heat the submergence tank were Cole Parmer PolyScience LX Immersion Circulators. The maximum capacity of each heater is 20 liters of fluid with a temperature range of ambient to 98°C. Temperature stability is ±0.07°C. Figure 4 shows a schematic of the weathering facility.

Determining the Acceleration Factor
The dominant factor contributing to material degradation during prolonged submersion is fluid absorption in the matrix. In order to mathematically relate the experimental submergence of the composite plate to actual service submergence time, a water diffusion study of the matrix material was conducted. The study assumes that the only factor in the degradation of the composite is the accumulated water in the matrix material via diffusion. The relationship between the accelerated life test and service time immersion is governed by the Arrhenius equation (1). This equation describes the temperature dependence of the rate of reaction for a given process.
Where k is a rate constant, A is a prefactor, Ea is the activation energy, R is the universal gas constant, and T is the absolute temperature. A series of three salt water solutions were prepared, and maintained at different temperatures, Ta, Tb and Tc, to determine the diffusion coefficients and water saturation limits for the epoxy matrix. The spread of diffusion coefficients at various temperatures produced Arrhenius activation energy values for the matrix material, mathematically related to an Acceleration Factor (AF).
Disks of the matrix material were submerged in 3.5% saline solution and their weight recorded periodically until the saturation limit was reached. To calculate the diffusion coefficient, the following expression can be used. [27] Where m t is the mass of water absorbed at the time t, m s is saturated water mass, D is the diffusion coefficient, and h is the disk thickness. The diffusion coefficient can be determined through a simplification of Equation (2) when specimens reach 50% of the total saturation. A solution of the diffusion coefficient is approximated as: Where 50 is the time it takes to reach 50% of total saturation. Recasting equation (1) to reflect the diffusion coefficient gives the following expression: Where is an arbitrary constant. Equation (4) can be rewritten as The acceleration factor, AF, is the ratio between the normal working condition reaction rate and a higher test reaction rate. Using equation (5) the acceleration factor is Where T1 is the theoretical service temperature and T2 is the accelerated weathering temperature. To determine the AF, a diffusion study was performed. Three beakers of 3.5% salt solution were prepared and maintained for 60 days at different temperatures: 22, 45, and 65 °C. Three epoxy disks of PT2712 were submerged in each of the three beakers to ensure repeatability at each temperature. All 9 epoxy disks were desiccated for 48 hours to remove moisture and the mass recorded before submergence. Throughout the duration of the experiment, epoxy disks were periodically removed from their beaker, dried, weighed, and placed back in their respective beaker in accordance to ASTM D5229 / D5229M -14 [29]. The percent mass increase was recorded for all epoxy disks for 60 days, and plotted versus time.

Experimental Results and Discussion
The Carbon-Epoxy composite material was subjected to prolonged submergence in a saline solution at high temperature to increase the rate of weathering. A diffusion study was performed to relate the experimental weathering time to service time and quasi-static tests were conducted to determine the effects of weathering on the mechanical behavior of the composite material. In order to evaluate the dynamic behavior of the Carbon-Epoxy composite, shock tube experiments were performed to characterize the effects of weathering on the dynamic response of Carbon-Epoxy composite. The dynamic response of the Carbon-Epoxy composite was also compared with numerical results.

Acceleration Factor Results
The average percent increase in the mass of the epoxy disks for each temperature as a function of time is shown in Figure 5. Total saturation was obtained by the 65 °C samples at 60 days and the remaining temperature trials reached at least 50% saturation during the trial t50.

Figure 5: Average epoxy mass increase over time
Knowing the t50 value and the thickness of the material, the diffusion coefficient D was calculated. Figure 6 shows the natural log of D plotted vs. 1/T. The slope of the linear trend gives the activation energy of the epoxy matrix.

Figure 6: Activation energy calculation
The AF is then solved for, with the experimental submergence temperature (65 °C), and is displayed in Figure 7 (a) and Figure7 (b). Figure 7 shows that with a decrease in service temperature, the AF will increase. Similarly, with increase in service temperature, the AF will decrease.
From the diffusion study, the calculated acceleration factors range from 48 to 18, corresponding to service temperatures of 10 °C to 22 °C respectively. With 30 days of accelerated ageing the real weathering time will be between 1.5 to 4 years of aging due to diffusion, depending on service temperature. For 60 days, the range is between 3 and 8 years. Since the diffusion of water into the epoxy matrix is a dominant factor contributing to composite material degradation, the calculated AF is a strong estimate used to correlate experimental versus service weathering times. However, it should be noted that after prolonged accelerated ageing, there is possible debonding between the fibers and the matrix, leading to further material degradation.

Quasi-Static Test
Material testing was performed to establish the quasi-static mechanical properties of the composite material before and after accelerated environmental exposure.
The average quasi-static behavior of the material before and after submergence is listed in Table 2 with the percent changes provided Table 3. From the quasi-static results it is shown that prolonged submergence reduced the modulus and strength of the Carbon-Epoxy significantly from the Non-Weathered material. The change in quasi-static results between 30 and 60 days is minor which corresponds to the fact that the matrix reached total saturation at 30 days. Since the majority of the degradation effects are accumulated during diffusion, this supports the assumption that water diffusion into the epoxy material is the primary factor in degradation of the mechanical properties of the composite to the ageing time frames considered in this study.

Shock Tube Experimental
The following experimental results of the shock tube study compare the weathered (30 days) and Non-Weathered (0 days) cases. Weathered experiments for 30 and 60 days show similar quasi-static and dynamic behavior, so the comparison between 0 and 30 day blast scenarios will suffice. Two different support conditions for the plate under dynamic loading were considered; a simply supported case and a fixed boundary support. Figure 8 shows a schematic of the simple support boundary and of the fixed boundary case.

Figure 8: (a) Simply supported boundary case (b) Fixed-Fixed boundary case
A series of side view images for the simply supported boundary case, captured throughout the dynamic blast loading event is shown in Figure 9. From 0 to 0.8 ms the   Carbon-Epoxy composite it is 1.7% [25]. This implies that while the damage occurs during the dynamic blast loading, the carbon fibers have not reached their failure limit.
Thus, during blast loading matrix cracking and delamination happens first leading eventually to fiber failure.
The case for the fixed boundary investigates the effect of zero displacements and rotations at the boundaries. In order to fix the boundaries of the composite, two vice clamps with knurled grips were utilized. Figure 12 shows a series of side view images for both the 0 and 30 day weathering cases for the fixed boundary case.  However, for the fixed boundary case, the maximum moments are at the boundaries, which increase the rigidity of the plate, and lower the center point deflection. It should be noted that the maximum moment for the fixed-fixed boundary case is lower than the maximum moment for the simply supported case. Figure 13 shows the full field out of plane displacement evolution for the 0 day and 30 day weathering for the case of fixed boundary conditions. The maximum out of plane displacement occurs at ~0.6 ms. The center point displacement history for this case is given in Figure 14. should be noted that the fixed boundary condition case does sustain minimal grip slippage of less than 0.5 mm. Due to the slight slipping at the boundaries, the ability of the specimen to recover is hindered, since the material that slipped out of the clamps during the outward deflection will encounter a resistive frictional force while it slips back into the clamps during specimen recovery.

Finite Element Modeling
Finite element modeling (FEM) for the blast loading experiments was performed using the Ls-Dyna code available from the Livermore Software Technology Corporation.
Models have been developed for both the simply supported and fixed boundary condition cases. Based on the mechanical testing which indicated minimal additional material degradation beyond 30 day ageing, the 60 day weather scenario is not considered in the the inner shock tube diameter which is equal to the pressure recorded during the experiment. However, as the specimen deforms outwards there is a "venting" of the gas as a gap forms between the shock tube face and the specimen. This results in an expanded loading area over the face of the plate which is assumed to vary linearly from the measured pressure profile at the inner surface of the shock tube to zero at the outer edge of the plate. The linear variation in pressure is accounted for in a stepwise fashion as shown in Figure 16. A similar computational approach is documented by Yazici et al [26].  During the recovery phase this material must be forced back into the grips, which tends to slow down the process as compared to the numerical model. Even a very small amount of material slippage within the grips has the effect of "shortening" the length of a buckled beam and preventing a return to its un-deformed shape. Finally, it is seen from Figure 18 that the onset of damage for the 30 Day Simply Supported case occurs slightly later than the corresponding experimental fracture. Although the computational models utilize experimentally based values of compressive and tensile strengths, these values are a nominal value representing a statistical basis of multiple tests and the true value for any given specimen is +/-from that average. Furthermore, the models assume a uniform specimen in terms of material properties and does not account for manufacturing variability or minor internal defects which can contribute to the onset of damage or slightly weaker/stronger areas of the plates as compared to the gross material strengths.
That the model is able to predict the onset of damage in a consistent manner as observed during the testing is significant. Overall, it is shown that the models are able to accurately predict the transient response of the composite specimens, particularly the initial rise and peak displacement. • After 30 days of exposure, the quasi-static mechanical properties decreased significantly. The tensile modulus, tensile strength, and ultimate flexural strength decreased by 11%, 12%, and 22% respectively.
• After 60 days of submergence the quasi-static mechanical properties of the composite essentially did not change from the properties at 30 days submergence. o For the fixed support case, the 30 day and 60 day plates showed similar out of plane displacements. However, the frequencies of beam oscillations in these cases were lower than the 0 day case. This is due to the reduction in the stiffness of the material with ageing.
• The numerical results for both boundary conditions are in good agreement with the experimental data.

Abstract
The response of composite cylinders to near field underwater explosive (UNDEX) loading, including the effects of polyurea coatings, have been studied through experiments with corresponding computational simulations. Experiments were conducted on woven E-glass/epoxy roll wrapped cylinders in three unique configurations: (1) base composite, (2)  It is also shown that there is in increase in both material internal energies as well as overall strains with increasing coating thickness.

Introduction
Composite materials have several characteristics which make them particularly appealing for utilization in marine environments such as high strength to weight ratios, superior resistance to corrosion, and overall reductions in required maintenance. When structures composed of these advanced materials are fielded in a marine environment, in addition to operational loading, they may be subjected to harsh transient conditions such as underwater explosions. Maximizing the benefit of these materials, particularly for minimum weight and increased survivability, requires a full understanding of the response to such loadings and the effects of any potential mitigators, such as blast resistant polymeric coatings, in order to avoid overly conservative designs.
Studies on the response of composites subjected to UNDEX have generally focused on far field loading in which the encroaching shock front is nearly planar and there is no interaction between the UNDEX bubble and the structure. LeBlanc and Shukla [1,2] have studied the response of both flat and curved E-glass/epoxy composite plates to far field loading through both experimental and computational means. Avachat and Zhou [3] investigated the response of monolithic as well as sandwich structure composite cylinders to underwater impulsive loading imparted via a novel Underwater Shock Loading Simulator. The key findings were that the inclusion of a foam core reduced damage to the cylinder as compared with a monolithic composite wall of similar mass.
Further, decreasing foam core density resulted in a decrease in observed damage.
Mouritz, et al., [4], conducted a study of the development of damage in a glass reinforced composite subjected to underwater explosive loading at increasing pressures. Both air backed and water backed conditions were evaluated. In the case of the water backed laminates no damage or degradation in strength was noted. In the air backed laminates delamination and matrix cracking led to a degradation of the residual strength of the composite.
Near-field loading is generally characterized by a spherical shock front impinging upon the structure as well as interaction of the UNDEX bubble and the target structure.
This can lead to a highly localized damage response in the structure rather than the more global deformation characteristic of the far field loading. In LeBlanc, et al., [5], coated and non-coated flat E-glass/epoxy plates were subjected to near field UNDEX loading.
Deflections and damage extents were compared across the plate configurations. It was found that the application of a polyurea coating reduced the overall response of the plate and significantly reduced damage to the composite. Brett, et al., [6,7], presented a study of steel cylinders subjected to near field UNDEX. They observed that at standoff distances less than the UNDEX bubble radius the bubble was attracted to the cylinder and collapsed upon it resulting in a significant structural response.
Recently polyurea has found interest as a potential blast mitigating coating. It is an easy to apply polymer that exhibits stiffening with increasing strain rate of loading and is finding use as a post-design phase enhancement. Several studies have been conducted to determine polyurea's ability to reduce structural response to blast loading as well as reduce damage in materials. LeBlanc, et al., [8,9] studied the response of composite plates coated with polyurea to UNDEX loading. It was determined that both location and thickness of the coating were important considerations in efforts to reduce damage and deflection. When considering a weight penalty there is a coating thickness at which the polyurea becomes more advantageous in mitigating the out of plane response of the structure than simply increasing the base composite thickness. Tekalur, et al., [10] and Gardner, et al., [11] studied monolithic and sandwich composites, respectively, subjected to air blast loading. It was found that polyurea was able to mitigate damage and deflection in the monolithic plates. For the sandwich composites blast resistance was improved by placing the polyurea between the back face sheet and the foam core; performance was degraded when the polyurea was applied between the front face sheet and the foam core.

Materials
This investigation tested composite cylinders in a base configuration comprised solely of the composite material as well as the base composite with applied polymeric coatings. Material details are outlined in the following two sections.

Composite
The composite cylinders were manufactured by ACP Composites, Inc. of Livermore, CA. The material is a cured, roll-wrapped E-glass/epoxy with a woven 0°/90° structure The material properties, as provided by the manufacturer, are listed in Table 1.

Polyurea
A polyurea coating, Dragonshield-BC, was manufactured and applied via spray-cast by Specialty Products, Inc., of Lakewood, WA. This is a 2-part polymer which may be applied to a variety of surfaces. The coating was applied in two thicknesses, 100% and 200% of the composite wall thickness, to the outer surface of the cylinders and was cured at 160°F for 48hrs. As in the previous study by the authors [5] this configuration is intended to represent the post-design and manufacture application of the coating as reinforcement rather than an integral design aspect.
A characterization of the polyurea material was conducted at strain rates of 0.01s -1 to 100s -1 for both tensile and compressive loading in a previous study, [8]. Additionally, during the same study, strain rates of 2000 s -1 in compression were achieved via a Split Hopkinson Pressure Bar (SHPB). It is assumed that the behavior of the polyurea is similar in tension for the 2000 s -1 strain rate. Figure 1 illustrates the stress-strain behavior of the Dragonshield-BC polyurea monolithic material over the range of tested strain rates.
It is clear from Figure 1 that with increasing strain rate the response of the material becomes stiffer in both tension and compression, exhibiting a distinct plateau in tension.

Experimental Set-up
The following sections detail the experimental set-up for this investigation. A full account is given regarding the specimen geometry, test vessel, and data acquisition system and methods.

Specimen Geometry
The outside diameter of the base composite cylinder is 7.44 cm with a thickness of 1.14 mm. The total length of the cylinder is 40.64 cm with an unsupported length of 38.1 cm. Each end of the cylinder is fitted with an aluminum endcap protruding 12.7 mm into the length of the cylinder which seals against the inner diameter of the cylinder via a rubber o-ring to prevent water infiltration during experiments. The endcaps are held in place and the cylinder further sealed by the application of epoxy to the joints between the endcaps and cylinder. In addition to the base cylinder, cylinders were prepared with either a thick (2.26 mm ± 0.5 mm) or thin (1.19 mm ± 0.3 mm) outer coating of polyurea. Figure 2 provides a schematic of the cylinder construction.

Figure 2 -Cylinder Construction
The areal weights and wall thicknesses of each cylinder configuration is given in Table 2, below.

Explosive Charge
The explosive used in this study is an RP-503 charge manufactured by Teledyne RISI, Inc. of Tracy, CA. It contains 454mg of RDX and 167mg of PETN. A characterization of the explosive was conducted in equivalent test conditions. Figure 3 provides a plot of bubble diameter over time from detonation until the initial collapse of the bubble and it is shown that the maximum bubble diameter was measured to be 21.7 cm. As will be discussed later in the paper, this is significant because the maximum bubble diameter is larger than the charge standoff itself and thus there is an interaction between the bubble and the cylinders. Figure 4 provides the pressure profile in the water at three different radial distances from the charge center. For the purposes of pressure characterization, these pressure profiles are obtained from a free field experiment with no cylinder present. The characteristic 1/R decay of peak pressure with standoff distance is observed. The characterization of the RP-503, as well as all subsequent experiments, was performed at ambient tank pressure with no additional pressure supplied to the tank.

Test Tank
All experiments were conducted in a large diameter (

High Speed Video and Digital Image Correlation
Three high speed video cameras, FastCam SA1, were used to capture video during experiments. One camera was mounted to align with the longitudinal axis of the cylinder, providing a side view of the UNDEX event and two cameras were arranged to provide a stereoscopic view of the cylinder on the opposite side of the explosive. High intensity lights were used to provide the necessary illumination for the high speed video capture. Frame rates of 36,000 fps were used for both the side view and front view cameras.
Each cylinder was prepared for Digital Image Correlation (DIC) data extraction in order to obtain full-field in-and out-of plane displacements of the cylinders during the test event. A coating of white paint was applied to each cylinder and a random pattern of black speckles was applied using flat black paint. Calibration of the DIC system, which includes the two stereoscopic front view cameras, for use in the large diameter test tank was accomplished by Gupta,et al.,in [12]. Post processing of the front view high speed video to obtain full field displacements was accomplished using the VIC-3D software package. Displacements are obtained by comparison of pixel subsets of the random speckles between images as the cylinder deforms and the reference un-deformed state.

Experimental Methodology
For each experiment the cylinder under test was fixed within a wire support cage used to secure the pressure sensors and the explosive at set distances from the cylinder surface. Figure 5 illustrates the arrangement of the pressure sensors around the cylinders. Collars were affixed to the cylinder endcaps to which the wire cage and the support cabling were attached. The cylinder was then firmly secured in the center of the tank using the support cables and the alignment with the high speed video cameras was confirmed. Figure 6 provides a schematic of the test set-up.

Figure 6 -Test Configuration, (a) Tank Schematic, (b) Cylinder in Support Cage
Each cylinder configuration (base composite, thick coating, and thin coating) was tested at two charge stand-offs, 2.54cm and 5.08cm. Two experiments of each cylinder configuration/charge standoff combination were conducted to ensure repeatable results.
The charge distance to the cylinder surface was maintained by fixing the charge within the support cage with monofilament line, see Figure 6b. All experiments were conducted at ambient pressure within the flooded tank.

Bubble-Cylinder Interaction and Local Pressures
The near field nature of experiments resulted in a complex interaction between the UNDEX bubble and the cylinders. In all experiments the interactions were characterized by a splitting of the bubble with one bubble forming in front (non-charge side) of the cylinder and the bulk of the UNDEX bubble remaining behind (charge side) the cylinder.
Initially, as the shock from the explosive detonation passes the cylinder small cavitation bubbles form on the surface of the cylinder. This happens at 0.36 ± 0.08 msec for the 5.08 cm charge standoff and at 0.23 ± 0.05 msec for the 2.54 cm standoff. This is the result of the UNDEX shock wave interacting and passing by the cylinder and is consistent with the observations of Brett and Yiannakopolous [6]. As time progresses, the cavitation bubbles begin to coalesce. Following coalescence the cavitation bubbles collapse in front of the central region of the cylinder after about 1 msec. Figure 7 provides images of key developments observed during the bubble-structure interaction during an experiment conducted at a charge standoff of 2.54 cm on a cylinder with a thick coating applied. Similar features are observed in the experiments with a 5.08 cm charge standoff with difference in timing in accordance with the increased distance between structure and bubble center. No significant differences were noted in the bubble interaction between uncoated and coated cylinders.  The pressure recorded on the non-charge side of the cylinder is shown in Figure 9.
This pressure profile was recorded during the experiment from which the images presented above were taken. At 0.28 msec a second pressure peak (4.23 MPa) is recorded. This is the reflection of the incident shock from the surface of the cylinder. At Due to the low magnitudes of the reflected pressure from the tank walls it is assumed that the primary cylinder damage, when present, occurs due to the initial charge detonation pressure.

Transient Cylinder Response
The physical response of the cylinders to the near field UNDEX loading will be described primarily by the radial displacement of the center point on the non-charge side of each cylinder, determined via image analysis through DIC. Due to the bubble interaction with the cylinder described in the previous section the displacements of the cylinders could not be determined for the entirety of the loading events. Large scale cavitation on the surface of the cylinder and the formation of a bubble between the cylinder and the cameras prevent DIC analysis by obfuscation of the speckle pattern.
Comparisons will be limited to the time period for which DIC results are available and may not include the peak displacements experienced by the cylinder during test.

Charge Standoff -5.08 cm
The radial displacement of the cylinders exposed to an UNDEX at a 5.1 cm charge standoff is characterized by an initial global deformation in the positive radial direction (away from the charge and toward the cameras) followed by an inflection and dimpling in the center of the cylinder away from the camera view and toward the charge location as the cylinder rebounds. Figure 10

Figure 10 -Centerline Displacements for 5.08 cm Standoff
Full field displacement contours over the initial 2.75 msec of the experiments can be seen in Figure 11. The full field contours confirm the general shape suggested by the center line displacements presented in Figure 10 above. Comparisons with the uncoated cylinder are difficult due to obscuration of the speckle pattern in that image set after 1.25 msec.

Figure 11 -Full Field Radial Displacement Contours
In [9] LeBlanc, et al., introduced the areal weight ratio (AWR) as a means to account for the weight penalty associated with adding material, such as a coating, to an existing design. The AWR acts as a multiplier to quantify the added mass penalty associated with any additional material in terms of transient deflection. The AWR is given by Equation 1 as: 1 is the areal weight of the base material. In this case it is the areal weight of the composite from which the cylinder is constructed. 2 is the areal weight of the base material plus any added material or coating. The AWR for each cylinder in this study is given in Table 3.  mm. This degradation in performance was also observed in previous studies by LeBlanc, et al., [5,8,9] on both flat and curved plates subjected to far field loading as well as near field UNDEX loading of flat composite plates. In [9], LeBlanc, et al., studied an array of poylurea coating thicknesses on the response of E-glass/epoxy cross-ply panels and found that there is a coating thickness which does provide an improvement in transient response characteristics even when weight penalty is considered. A similar result for near field UNDEX loading of composite cylinders with polyurea coatings cannot be ruled out by the findings of this study.

Figure 13 -Centerline Displacements for 2.54 cm Standoff
Full field radial displacement contours are shown in Figure 14, below. The bowed shape indicated by the line segment plots in Figure 13 can be discerned in the contour plots.

Figure 14 -Radial Displacement Contours for 2.54 cm Charge Standoff
The center point deflection at 3.0 msec is used to compare the performance of the uncoated and coated cylinders in accordance with the method outlined in the previous section.    For the thinly coated cylinders tested at 2.54 cm the curving cracks are also observed. They occur at a similar angle although extend only 3.8 cm, Error! Reference source not found.(a). The damage to these cylinders is dominated by large circumferential and longitudinal cracks emanating from the point closest to the charge location. At the nexus of the longitudinal and circumferential cracks the damage extends through the thickness of both the composite and coating, Figure 19(b). The circumferential crack continues to extend through the coating to its termination at ±90°.
The longitudinal crack extends through the coating for only 4.1 cm on either side of the center point and then continues an additional 5.6 cm through the thickness of the base composite only. As with the uncoated cylinder, delamination can be observed near the area closest to the charge on the interior and exterior surfaces, Figure 20 (b) and Figure   21 (b).

Figure 19 -Damage in Thin Coated Cylinder -2.54 cm Charge Standoff, (a) Curving Crack, (b) Nexus
In the cylinder with a thick coating of polyurea the damage was similar in character to that observed in the thinly coated cylinder but lesser in extent. Again, longitudinal and circumferential cracks extend from the center point, nearest the charge location. Delaminations can be observed on the interior of the cylinder, Figure 20 (c).
The circumferential crack, which ranges ±90° from the centroid extends through the thickness of the base composite as well as the coating. Fiber pull-out along the interior edge of the crack can be seen in Figure 21 (c). The curving cracks at the termination of the circumferential cracks in the uncoated and thinly coated cylinders are not present in the thickly coated cylinders. The longitudinal crack, visible in Figure 21 (c), runs 7.6 cm along either side of the center point but extends only through the thickness of the base composite.
As would be expected, the damage to the cylinders tested with a charge standoff of 5.08 cm was less severe for all configurations. Figure 20 and Figure

Uncoated, (b) Thin Coating, (c) Thick Coating
In the thinly coated cylinder exposed to a charge standoff of 5.08 cm longitudinal and circumferential cracks can be seen on the interior of the cylinder, Figure 20  The cylinders with the thick polyurea coating (5.08 cm standoff) showed significant reduction in damage even as compared to the thinly coated cylinders. In these cases the damage was confined to two small sections of damage at ±60° from the centroid. These damage areas consisted of circumferential cracks of 2.5 cm length and longitudinal cracks of about 1.3 cm centered against the circumferential cracks. These cracks, which extend only through the base composite, can be seen in Figure 20 (c).

Finite Element Modeling
The experiments which have been previously discussed, have been simulated utilizing the the LS-DYNA finite element code. The purpose of the modeling effort is twofold: (1) Implement a methodology for the simulation of near field UNDEX loading on composite cylinders, and (2)  All models are constructed in the CGS unit system.

Model Overview
The finite element model representation of the cylinder explosive experiments is provided in Figure 22, and consists of the cylinder body / endcap, polyurea coating, surrounding tank water, internal air, and the RP-503 charge. The model represents a selected subdomain of the full experimental test tank for computational efficiency.   Table 5 and Table 6.

Model Correlation
The demonstration that the computational model is accurately representing the corresponding experiments prior to its use for further data analysis is comprised of two key correlation parameters, namely the agreement between the: (1) pressure profiles of the UNDEX detonation, and (2)

3 Energy Comparisons
The internal and kinetic energy of the cylinders during the explosive loading event are provided in Figure 26  it is evident that in terms of the energy experienced by the cylinder itself, there is an increase as a function of coating thickness. The uncoated cylinder has a peak energy of ~51 J, whereas the cylinder with the thick coating experiences a peak value of 56 J, an increase of ~10%. The cylinder with a thin coating has a peak value just lower than that of the thick coating value. Furthermore, for a given coating thickness it is evident that the cylinders themselves comprise ~90% of the total internal energy (cylinder plus coating) sustained with the coatings comprising 10% of the net peak energies occurring at 0.1 ms. This result is anticipated as the composite material is significantly stiffer than the coating and thus for a given deformation would represent the primary load carrying mechanism. Finally, it is noted that as the coating thickness is increased there is a corresponding increase in the amount of internal energy that can be absorbed by the system (cylinder plus coating) as a whole. For the case of an uncoated cylinder, the sole mechanisms for energy absorption/dissipation are strain energy in the composite and fracture energy corresponding to the evolution of damage through fiber and matrix failure. In the presence of the coatings, there is the additional energy absorption/dissipation reservoir of the coating itself. Thus, whereas the uncoated cylinders sustain damage, the coated cylinders can dissipate that energy into the coating itself and reduce the overall composite material loading. Hence, the coated cylinders experience higher levels of loading, but also a corresponding decrease in material damage. In terms of the internal energy observations, though comparison of the energies of the coatings themselves, the thicker coating does experience a higher level of internal energy as compared to the thin coating.
The comparison of the relative kinetic energies is provided in the lower plot of Figure 26. Consistent with the internal energy measures it is seen that the kinetic energy of the respective cylinder configurations increases with increasing coating thickness. As indicated previously, the kinetic energy is presented for the combined composite/coating system as it is a measure of the velocity characteristic of the system. It should be further noted that based on the relative mass values presented, the coated cylinders have respective areal weight ratios of 1.66 and 1.99 as compared to the uncoated cylinder. In order to remove the mass dependence of the kinetic energy results, the respective curves have been normalized by the AWR and are presented in Figure 27. From the normalized time histories it is seen that the coated cylinders have nearly the same kinetic energy values though time and that both are lower than those of the uncoated cylinder.

Strain Comparison
The strain time histories, radial and longitudinal, for the back and top surfaces of the cylinder are presented in Figure 28 and Figure 29 respectively. The strain values which are presented are measured on the surface of the composite cylinder itself rather than the coating surface to allow direct comparison between cylinder configurations. The overall trends in the strain histories are consistent with those observed in the internal energy comparisons. Specifically, there is an increase in overall strain level with increasing coating thickness in both the radial and longitudinal directions. Comparisons of the back face peak strains show that as compared to the uncoated cylinder, there is an increase in both radial and longitudinal strains of ~36% for the thick coating and 25% for the thin coatings. However, it is further noted that in observing the temporal evolution of the strains, the time to reach the peak strains is longer as the coating thickness in increased by approximately 0.02 ms for all cases. The increase in strain as a function of increasing thickness can be attributed to the additional mass that the coatings contribute to the overall structure, while providing limited additional stiffness to the system. A similar effect as was seen in the overall internal energy measures previously discussed. For the case of the cylinders with a thick coating, there is an overall doubling of the structural mass of the composite/coating system. As the cylinders are accelerated and undergo deformation due to the UNDEX pressure loading, the composite cylinder is the primary load carrying mechanism due to its overall higher stiffness as compared to the coating.
During this initial response the coating is adding additional mass to the system which must be arrested primarily by the composite through additional deformation which leads to resulting increases in strain. Additionally, in a similar manner as was observed with the internal energies of the system, the increase in the rear face surface strains with increasing thickness can be partially attributed to the coatings reducing or preventing the onset of material damage. The uncoated cylinders sustain significant material damage on the charge side surface which has the effect of dissipating a certain level of energy. By reducing the damage levels, the coating have the effect of allowing the cylinders to undergo larger overall deformations, and corresponding strains, as the energy is distributed through the system as a whole. The presence of damage only of the charge side of the cylinders indicates that the surface strains would be larger for the uncoated cylinders than for the coated ones, an inverse trend as exhibited on the non-charge side. 3. When a weight penalty is applied to the overall displacement response of the cylinder to account for the weight penalty of the coatings, there is a net degradation of the relative performance on a per unit weight basis.
4. The polyurea coatings had a more beneficial mitigating effect on the center point displacement at the larger charge standoff; however, when accounting for weight penalty the response was degraded on a per unit weight basis.
5. Damage to the coated composites was dramatically reduced as a function of increasing coating thickness as compared with the baseline cylinders.
6. The modeling approach utilized in the study is able to accurately simulate the detonation of the explosive charge as well as predict the overall damage extents in the composite cylinders.

Introduction
An experimental and computational investigation was conducted to evaluate the dynamic response of weathered biaxial composite plates subjected to near-field explosive/blast loadings. This research arises from the concern of damage to naval and marine composite structures such as ships, submarines, and underwater vehicles [1,2].
During the service life of these structures, their mechanical properties degrade from continuous exposure to an aggressive sea environment [3]. In undesirable circumstances, marine structures can be further subjected to shock and blast loadings. If the degradation of mechanical properties is not accounted for under these highly dynamic conditions, the damages and losses could be catastrophic.
A significant cause of mechanical degradation in composites in a marine environment is the diffusion of water into the matrix material [3]. The diffusion process is relatively well established and can be described by a diffusion coefficient that is a function of parameters such as temperature, type of resin and curing agent, surrounding medium composition, fillers, void content, and so on. The value for diffusion coefficient and the theoretical models used to describe the diffusion varies in previous studies of diffusion in composites [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18]. A standard and well-accepted model for epoxy resins, in terms of mass diffusions, is a Fickian model [14] which uses Fick's second law to predict how the concentration of a diffusive substance changes over time within a material [19][20].
Previous works used the Fickian model to study the properties changes during low strain rate loading of diffused composites. These studies agreed that the mechanical property degrades over time from an increase in mass, internal stresses from swelling, and loss of interlaminar strength [15][16][17][18]. Current research on the high strain rate response of weathered composites is limited. Recently, there has been a study that analyzes the shock response of weathered composites plates within an air medium [21]. Moreover, many experimental and numerical studies analyze the dynamic response of non-weathered composite plates subjected to underwater explosives [22][23][24][25][26].
The aim of this study is to understand how a composite's blast performance is affected by prolonged exposure to seawater. This work experimentally and computationally analyses the dynamic response of weathered composite plates subjected to nearfield underwater blasts. In the experimental portion, a 3D Digital Image Correlation (DIC) technique is implemented to capture real-time high-speed deformation to characterize the fluid-structure interaction. In the computational portion, a Coupled Eulerian-Lagrangian (CEL) simulation was used to simulate the experimental conditions to predict the composite's performance in scenarios beyond the experiments performed. The epoxy mixture was drawn into the fabric by vacuum infusion at a constant pressure of 730 mmHg. After hardening, curing was performed by placing the composite plate in an oven at 70 ˚C for 10 hours. All specimens for both layups were cut from a single sizeable composite sheet to minimize variations in the epoxy mixture and fiber content. The final product was a 1.26 mm (0.050 in) thick composite plate with 1% void content (measured in accordance with ASTM Standard D2734 [27]) and 60% fiber volume content. Table 1 lists the product information and properties of interest for the fiber, fabric, epoxy, and composite plate.

Mechanical Testing
Quasi-static tensile and shear properties were obtained by using an Instron 5585 and following ASTM Standards D3039 [28] (with [0, 90]s specimens) and D3518 [29] (with [45, -45]s specimens) respectively. The strain data was measured with 2-D DIC from images captured by a Prosilica camera (model GC2450 from Allied Vision Technologies GmbH in Stadtroda, Germany). The tensile and shear tests were used to calculate the effective material properties used in the computational models. The strain rate sensitivity of carbon/epoxy composites, though not negligible, is minimal (especially for normal stresses) [30]; therefore, numerical results are reasonably comparable to the actual (experimental) results. Lastly, quasi-static compressive tests were performed on postexperiment specimens using ASTM Standard 7137 [31] to measure their residual strength.

Weathering Facility
The composites were submerged in a 3.5% NaCl solution (prepared in accordance with ASTM Standard D1141 [32]) as shown in Figure 1; this salinity matches the concentration of most ocean bodies. Before submersion, all specimens were placed in a desiccator to dry for a minimum of 72 hours. In the submersion tank, four water heaters (Model LXC from PolyScience in Niles, IL) are used to maintain a constant temperature of 65˚C. It is crucial for the solution temperature to be below the wet glass transition temperature of the composite material. Beyond glass transition, there will be changes in the mechanical properties unrelated to the aging aspect of this study [5]. However, a high temperature is still desired to attain a fast acceleration factor. Therefore, a temperature well under the wet glass transition was chosen to weather the experimental specimens.

Figure 1 -Weathering facility setup
Float switches and water pumps are used to maintain a constant water level. As water evaporates, one float switch in the deionized water and one in the saltwater tank will independently activate water pumps to replenish the lost water. For this reason, the salinity remains constant, and water passively circulates as room temperature water is introduced.
Also, the composite materials were exposed to salt water for 35 and 70 days. The blast experiments were performed immediately after the specimens left the salt water bath (to avoid moisture loss) as advised by ASTM Standard D5229 [33].

Blast Facility
To perform the experiments, the underwater blast facility shown in Figure 2 is used.
This facility holds 1800 L (475 gallons) of water (where the charge is placed) and 45 L (12 gallons) of air in a chamber separated by the composite specimen. Also, the facility is made of a steel cubic shell that is dimensioned 1.2x1.2x1.2 m 3 (4x4x4 ft 3 ) with a shell thickness of 12.7 mm (0.5 in). The composite specimen is clamped between the water and air chambers with a 25.4 mm (1 in) all-around clamping width; leaving a 254x254 mm 2 (10x10 in 2 ) exposed area (see Figure 2).

Figure 2 -Underwater blast facility and experimental setup
An RP-503 explosive (from Teledyne RISI, San Joaquin County, CA) was used to load the composite structure. The explosive charge is composed of 454 mg RDX and 167 mg PETN contained within an outer plastic sleeve. For reference, it is energy equivalent to 1.5 grams of TNT. Moreover, the charge is submerged underwater, centered to the specimen, and placed at a 152 mm (6 in) standoff distance (additional standoff distances were also explored; see Table 2 for details). Two dynamic pressure transducers (PCB 138A05, PCB Piezotronics Inc. in Depew, NY) are located next to the specimen and explosive (as illustrated in Figure 2) at 152 mm (6 in) and 203 mm (8in) distances from the explosive.
During the experiments, a Dash 8HF data acquisition system (from AstroNova Inc. in Warwick, RI) captured the pressure data at two mega samples per second.
Furthermore, two Photron SA1 high-speed cameras (from Photron USA Inc. in San Diego, CA) are placed 14˚ apart outside the blast facility and used to record high-speed images of the specimen at 10,000 frames per second. Each image has an 832x748 spatial pixel resolution; which is approximately equivalent to 259x287 cm (10.2x11.3

in) view
from the specimen's center. The photographs from the high-speed cameras are captured through the facility's optical windows. These images are later used for the DIC analysis.
Also, a third Photron SA1 camera is used (as shown in Figure 2) to record the explosive and bubble-to-structure interactions at 10,000 frames per second (with a 576x992 spatial pixel resolution; approximately equivalent to 186x320 cm). High-intensity light sources (Super Sun-Gun SSG-400 from Frezzi Energy Systems Inc. in Hawthorne, NJ; not shown in Figure 2) are used to illuminate the object for recording images. The details of the experimental cases are summarized in Table 2. Each experimental case has been repeated two times to validate the results (three for the E45-0WD case in Table 2).  (6) 70 (20) The composite specimen's 254x254 mm 2 (10x10 in 2 ) exposed area that is facing the high-speed cameras is coated with high-contrast speckle patterns. The speckle patterns are created by randomly placing flat-white paint dots (sized 9 to 12 pixels per dot) on a flatblack painted background until approximately 50% of the surface area of the specimens is covered by the white dots. When clamping the composite plate, a skin layer of silicone adhesive is applied to the clamping surface to avoid water penetration into the air chamber from the clamping boundaries; therefore during the experiments, the specimen has water and air-fluid boundaries similar to a ship hull.

Digital Image Correlation Reliability
The high-speed images are analyzed using the commercially available DIC software VIC3D 7 from Correlated Solutions, Inc., Columbia, SC. During the DIC analysis, measurements of the full-field displacements across the specimen's viewable surface are calculated by triangulating the position of each unique feature in the speckle pattern.
Previous work [34] outlines the calibration procedures that validate the accuracy of the DIC results when capturing images through an optical window (where changes in refractive index are present). It was found that the camera's viewing axis needs to be perpendicular to the optical windows in order to minimize DIC displacement errors. This technique can yield displacement errors in the order of 1.2% and 2.5% for in-plane and out-of-plane measurements, respectively.

Numerical Model
A computational Finite Element Analysis (FEA) model similar to previous work [26] was created with the LS-DYNA code from the Livermore Software Technology Corp. The model uses a CEL formulation that is capable of capturing the fluid-structure interaction between the fluid and composite plate as well as an accurate representation of the explosive's detonation. All models were constructed using the CGS unit system, and   Table 3. More details about EOS models and assumptions can be found in previous work [26].

Weathering
From Arrhenius' methodology, the water diffusion activation energy (Ea) for an epoxy is assumed to be constant [36]. Therefore, a mass diffusion study was performed at various temperatures (different diffusion rates) to obtain a diffusion acceleration factor (AF) with respect to a specific temperature. The moisture absorption was measured for composites submerged in 3.5% NaCl solutions at 5, 25, 45, 65, and 85 ˚C in accordance with ASTM Standard D5229 [33]. Note that the wet glass transition temperature (72˚C) is based on the composite's storage modulus and not its diffusion activation energy. The composite's diffusivity still follows Arrhenius' methodology at 85˚C even though its stiffness is lower at this temperature. Therefore, this high temperature is only used for the mass diffusion study and not for weathering the experimental specimen.
The water diffusivity into the composite plate obeys Fick's second law of diffusion [19]. Fick's second law was simplified into one dimension to calculate the diffusion coefficient (D) using Eq. (1) [20]. The diffusion coefficient was calculated from a point that is within the initial linear portion of the mass diffusion curve (≤ 50% mass saturation).
The diffusion coefficient was related to Ea by using Arrhenius' equation. To solve for Ea, Eq. (2) was written in logarithmic form as shown in Eq. (3), then -Ea/R was found as the slope of the linear trend for the various diffusion temperatures [20]. (1) Where t is time; Mt is the composite's mass at time t; Ms is the composite's saturated mass; h is the composite plate's thickness; C is the diffusion constant; R is the universal gas constant; and T is the temperature in the absolute scale.

Figure 4 -(a) Mass diffusion for five temperatures and (b) logarithmic relationship between diffusivity and temperature
After obtaining the activation energy for the composite material, AF can be found as the ratio of diffusions at different temperatures as shown in Eq. (4)

Mechanical Properties
In the material model, a plane stress assumption is used for the composite plate. The materials tested were from the same batch of materials used to for the experimental specimen. Therefore, effective properties (homogenized laminate properties) [37] were measured instead of ply properties. Table 5 shows the effective elastic modulus (Ex and Ey), Poisson's ratio (vxy), shear modulus (Gxy), and failure strains which were calculated with the standards outlined in Section 2. The effective elastic modulus was the same in both principal directions (Ex = Ey) since the layup is symmetric and evenly balanced. The normal stress has a linear behavior until failure, but the shear stress has a bilinear behavior; the shear yield and failure stresses are also listed in Table 5. Each result for the effective material properties in Table 5 is calculated from six tests.

Blast Response
During the experiments, the RP-503 underwater explosive (UNDEX) combusts at t = 0 as shown in Figure 5 (a). The high pressures from the explosive loads the composite specimen and forms a cavitation bubble at the charge location at t = 3 ms. The cavitation bubble expands spherically until it begins to interact with the composite plate. As a result, its growth is skewed away from the composite. The bubble's expansion peaks at t = 9 ms, which is when the bubble begins to collapse from its low internal cavitation pressure and high external pressure. During this collapse, the surrounding fluid accelerates towards the bubble, which leads to a new surface cavitation on the composite due to its close proximity as seen in Figure 5 (a) at t =15 ms. When the bubble finally collapses at t = 22 ms, the composite's surface is fully engulfed by this new surface cavitation. Therefore, the composite specimen does not react to the bubble collapse. However, the pressures from the bubble collapse initiates the surface cavitation collapse; which does so at t = 24 ms. The bubble pulsation cycle is interrupted by the surface cavitation collapse; hence the loading cycles of interest are completed by this time.
Moreover, the high pressures from the explosive are shown in Figure 5 (b) for different distances (each measured during a different experiment). The shock from the explosive is distinguished by an immediate rise in pressure followed by exponential decay. The amplitude of the explosive pressure decreases spherically by 1/R from the explosive location. When the explosive pressures are normalized in time for charge distance and in magnitude by 1/R, the pressure trends are nearly identical; hence the loading condition is highly repeatable between experiments. Also, the reflections from the tank's boundaries are small relative to the initial explosive pressures. Furthermore, the pressure from the bubble pulse and surface cavitation collapse are shown in Figure 5 (c) for the 152mm standoff case. The bubble pulse has a comparable impulse to the initial explosive pulse due to its long duration. The surface cavitation collapse has low recorded pressure signatures.
However, pressure signatures at this point in time are partially blocked by the bubble. Even so, an acoustic spike is seen when the surface cavitation's water boundary slaps against the composite plate; which leads to a substantial amount of momentum transfer to the composite. Additionally, the bubble pulse was nearly identical in magnitude as well as duration between experiments and the surface cavitation spike is only consistent in time (not shown in Figure 5 (c)).

4 Deformation and Image Analysis
The out of plane deformation from the 3D DIC is illustrated in Figure 6; which shows center point displacements. Each of the displacement curve shown is from one representative experiment. The center point displacements for the non-weathered [45,-45]s composite plate at different standoff distances is shown in Figure 6 (a). Decreasing the standoff distance leads to higher loading pressure and higher deformation rates. The displacement curves for the 76 mm and 114 mm standoff ended when failure (in the form of through-thickness cracking) is observed during the experiment (in the high-speed images). For the 152 mm standoff distance, failure is not observed during the experiments but is seen during the post-mortem analysis.
As loading initiated on the composite's surface, it flexes towards the air-side (forward) to a maximum displacement. When the composite begins to rebound, the surface cavitation (at vacuum pressure) begins at 8 ms, and the specimen rapidly abruptly flexes towards its water-side (backward) to a magnitude beyond its initial displacement (seen 8 and 24 ms).
At t = 24 ms, the surface cavitation collapses, and an abrupt increase in displacement forward occurs once again as shown by the full displacement cycle in Figure 6 (b). Figure   6 (b) also illustrates the repeatability of the three experiments for the E45-0wd case.
Weathering the composite plates led to an increase in maximum displacements for the

Residual Strength
Quasi-static compressive tests were performed on specimens after the explosive/blast experiments using ASTM Standard 7137 [31] to measure and compare compressive residual strength properties between non-weathered and weathered samples. To perform this residual strength tests, the composite specimen was simply supported at the 254x254 mm 2 (10x10 in 2 ) central area (same boundary locations as the blast experiments) as shown in Figure 8 (a). A schematic of the boundary and loading condition is shown in Figure 8 (b) as well as a model for the loading fixture in Figure 8 (c). Figures 8 (d) and (e)

Numerical Model Correlation
The correlation between the computational model and the corresponding experiment in terms of the UNDEX pressure profile is shown in Figure 9 (a) as measured by the 152 mm standoff. The experimental trends seen in Figure 9 (a) and (b) were selected from a representative experiment; experimental variation is shown in Figure 6 (b). In Figure 9 (a), the peak pressure predicted by the simulation is nearly identical to the value observed during the experiment. The simulation shows a longer rise time and similar decay time.
The overall impulse between the two signals is comparable; hence, the UNDEX EOS definition and parameters are deemed to be appropriate for this model. Furthermore, the tank reflections were relatively small compared to the initial load. Therefore, the nonreflective boundary condition is also appropriate for this model. The transient displacement time history of the center point displacement for the E45-0wd and C45-0wd cases are shown in Figure 9 (b). The model captured the peak center point displacements relatively well; with the simulations over predicting the peak by ~10-15%. However, the simulations show notable discrepancies during the flexural motion of the composite. The first discrepancy is the prolonged response in deformation seen between 0.5 and 1.25 ms in the experiments. This same prolonged response behavior in the experimental data can be seen after the plate reaches its maximum displacement and starts to recoil between 3.5 and 5 ms. These discrepancies are believed to be the result of an underdefined material model. The numerical model was from the effective stiffness (homogenized laminate properties) of the composite. Hence, the full stiffness matrix or any rate dependency was not specified in the model. With the current material model, things such as delamination and other out-of-plane failure mechanisms cannot be accounted for.
However, the maximum displacements and, in turn, maximum strains, can still be predicted by the current material model. Moreover, the displacement velocities leading up to the maximum displacement, and velocities that soon follow, are well matched during the simulations. Lastly, the surface cavitation to composite interaction was not predicted by the numerical model. Therefore, nothing after the maximum displacements/strains will be considered in the following discussions.

Maximum Strains
The maximum in-plane εxx strain field for the [45,-45]s non-weathered numerical model is shown in Figure 10 (a). For all simulations, εxx and εyy are nearly the same; hence they will just be referred to as normal strains. The maximum normal strains are located in the lobes of the buckling mode, at 57.2 mm (2.25 inches) away from the corners. Moreover, the maximum strains (normal and shear) for all numerical cases are listed in Table 6. The values in Table 6 are greater than the failure strains listed in Table 5. These higher values are expected since the transverse composite properties are not incorporated into the failure model. However, the maximum simulation strains are still valuable information because they illustrate how the weathering affects strain levels.  The maximum strain values from Table 6 are used to calculate the relative failure probability as a function of weathering time with Eq. (5); where the maximum strains (normal and shear) are subtracted from the non-weathered case strains then divided by its respective failure strain (listed in Table 5). The results from this calculation are illustrated in Figure 10 Table 5); which offsets the failure probability as defined by Eq. (5).
Furthermore, there is also a proportional relationship between the failure probability from normal stresses and damage accumulation in terms of through-thickness cracking for the [45,-45]s cases as illustrated in Figure 10 (c). In turn, damage accumulation is also proportional to weathering time regardless of saturation levels as it was inferred by Figure   7 (b). illustrates how the laminate orientation could be used as "stress guides" to direct the high stresses to areas in a structure (or boundary) that are stronger or has higher dissipation properties (in the case of hybrid composites).

Conclusions
This work experimentally and numerically analyzed the dynamic response of weathered composite plates subjected to nearfield underwater blasts from explosives. The aim of this study was to understand better how a composite plate's blast performance is affected by prolonged exposure to seawater. The main findings of this study are as follows: • The mechanical properties of the carbon-epoxy composites degraded even after its saturation point (after 35 days of weathering) during hydrothermal degradation.
Most notably the shear properties had the highest degradation, which is governed by the matrix material.
• • The effective material properties used in the numerical model led to discrepancies such as simulation rise time and rebound behavior. However, the properties and EOS used in the model was able to predict center point peak displacements, deformation shape, and explosive loading profile. In the future, properties should be obtained from parallel laminates at different angles as well as strain rates and use CLT to build rate-dependent stiffness matrices; this would likely require a user subroutine to define the material in numerical codes. Also, high rate failure properties should be obtained for future studies.
• Based on the normal strain data from Tables 5 and 6, failures from normal stresses are strongly proportional to weathering time regardless of saturation level. From the shear strain data, it is unclear if there is a relationship between failures from shear stresses and weathering time.
• Failure probability from normal stresses is proportional to damage accumulation in terms of through-thickness cracking for the [45,-45]s cases as illustrated in Figure   10 (c). In turn, damage accumulation is also proportional to weathering time regardless of saturation levels as it was inferred by Figure 7 (b) and previous conclusion.
• The laminate orientation could be used as "stress guides" to direct the high stresses to areas in a structure (or boundary) that are stronger or has higher dissipation properties for dynamic applications. beyond what is currently known will greatly advance the ability to design and implement future systems.
Studies of temperature effects on FRP composites have been limited.
Kichhannagari [4] observed from experiments that micro-cracking was more pronounced at cold versus ambient temperatures when specimens were tested under nominal uniaxial and biaxial loads. Thermal contraction causes matrix shrinkage and forms residual interlaminar shear stresses. These stresses degrade the inter-laminar shear strength, fatigue life, and laminate stiffness. Microcracks can lead to increased permeability, creating paths for hygrothermal effects [5,6,7] such as moisture and fluid absorption and swelling at cold temperatures. Swelling is a major source of environmentally-induced stress when laminates are subjected to a freeze-thaw cycling in the presence of water. The generation of microcracks can lead to coalescence which can cause larger meso-scale and macroscale cracks leading to reductions in fracture toughness and damage tolerance. Hybrid laminates with different fiber materials and orientations, show sensitivity to low temperature-induced microcracking. The effects of freeze-thaw cycles when combined with loading cycles are of significant importance and must be addressed in the design process. In order to study these influences, comprehensive testing and analysis must be performed. In general, fracture can occur in one or more of three modes: Mode-I (separation), Mode-II (in-plane shearing), or Mode-III (out-of-plane tearing). The fracture toughness of a given material is defined by the mixed mode critical strain energy release rate, GC. Fracture propagation occurs when the total strain energy release rate acting on the material, GT, exceeds the critical strain energy release rate GC.
Improving fracture toughness of FRP composites is of greater importance when severe loading events including blast, ballistic impact, UNDEX shock, wave slap, and implosion may occur in cold environments. Controlled laboratory experiments can be performed to simulate these events by which the effects of cold temperatures on static and dynamic fracture toughnesses can be characterized for optimizing material selections in design.
Increased knowledge of cold temperature effects on the fracture response of FRP composites will advance the structural integrity and reliability of future Navy systems.
The vast majority of loading conditions upon a material consist of a combination of Mode-I, Mode-II, and Mode-III loadings. Investigating fracture toughness when subjected to mixed mode loading at varying temperatures and moisture levels provides a more complete scope of the failure mechanisms associated with a given composite construction and its operating environment. For applications where blast, ballistic impact, or UNDEX shock are a concern, fracture toughness as it relates to mixed mode failure is vital in preventing structural failure of critical composite components.
This investigation provides an overview of the effects of decreasing temperature on the material and fracture properties of carbon and E-glass composites

Materials
The materials studied in the current investigation consisted of carbon/epoxy and E-glass epoxy laminates. In each laminate the base fabric was a "plain weave" style in which the yarns are woven in a one-over one-under pattern as shown in Figure 1.

Tensile Testing
Tensile testing was conducted on the carbon and E-glass laminates to determine the effect of decreasing temperature on these properties.

Figure 4 -Tensile Test Setup
The results for the E-glass tensile tests conducted at 5 °C are shown in figure 5 which highlights the repeatability of the results across the six test specimens. Similar repeatability was seen across both sets of materials and across the temperatures considered. From the figure it was shown that material response is nearly linear up to failure and the failure was classified as brittle in nature such that there was minimal plastic response prior to failure.

Figure 5 -Tension Test Results, E-Glass at 5 °C
The tensile characterization results for each material are summarized in   Compressive test data for the carbon/epoxy laminate at a temperature of 5 °C is provided in figure 10. As previously shown for the tensile testing, the results were repeatable across each specimen evaluated. The compressive behavior of the E-glass was consistent with the carbon in that each material was nearly linear up to failure and the failure was characterized by a sudden drop in load-carrying capacity with very little reduction in stiffness occurring prior to failure. Table 2 summarizes the compression characterization results for each material with the details provided in figures 11 and 12 for the E-glass and carbon respectively. From these results there are several trends that were identified:

Figure 10 -Compression Test Results, Carbon at 5 °C
-Both the carbon and E-glass laminates are significantly less stiff in compression than in tension. The E-glass laminate was ~4.5 times stiffer in tension and the carbon laminate was on the order of 10 times stiffer in tension.
-Specific to the compressive behavior, the carbon-based laminates were about two times stiffer than the E-glass laminates across all temperatures.
-The carbon laminates had approximately 2.5 times the compressive strength of the E-glass laminates across the temperature range.
-The specific E-glass/epoxy material utilized in this study exhibited differing trends in moduli and strength with decreasing temperature. As evidenced from figure 11, it was seen that with decreasing temperature there was a decrease in modulus but a corresponding increase in strength.
In other words, as the temperature is reduced, the material got softer but stronger.
-The carbon/epoxy laminate exhibited a clear trend in decreasing with decreasing temperature, a decrease of 30% over the range from 20 °C to -2 °C. Similarly, the material strength exhibited a decrease from 20 °C to 5 °C, but then remained statistically constant from 5 °C to -2 °C.   Short beam shear test data in the form of stress vs. displacement for tests conducted at 20 °C, 5 °C, and -2 °C is provided in figures 15 and 16 for the carbon/epoxy and Eglass epoxy laminates respectively. At a given temperature the results were shown to be highly repeatable for each temperature. The E-glass specimens were characterized by a linear ramping of stress followed by a flat plateau in the stress response. Similarly, the carbon specimens exhibited the same linear ramp up of stress during the initial loading, but displayed a decrease in stress capacity after reaching the maximum value rather than a flat plateau. Table 3 summarizes the short beam shear strength for each material and the trends were graphically highlighted in figure 17. From these results there were several trends that are identified:

Figure 16 -Carbon Short Beam Shear Stress Results
-In terms of overall short beam shear strength, the carbon laminates exhibited approximately twice the strength as compared to the E-glass laminates at a given temperature.
-The E-glass/epoxy laminates were characterized by a flat plateau in stress with increasing displacement after reaching maximum load whereas the carbon laminates exhibited decreasing stress capacity after maximum load.
-The carbon and E-glass laminates exhibited a 20% increase in short beam shear strength over the range from 20 °C to -2 °C.

Fracture Testing
Mode-I fracture tests were conducted to measure the effects of decreasing temperature on the Mode-I (see figure 18) critical strain energy release rates GIC for both the carbon and E-glass laminates. The Mode-I fracture tests were performed at 20 °C, 5 °C, and -2°C to ensure consistency across the mechanical characterization study. The specimens were double cantilever beam (DCB) type and fracture gauges were bonded to the specimen edges to measure the crack lengths, crack growth stability and GIC. The free end of each specimen was not restrained. Loading was applied in displacement control mode at a crosshead rate of 0.20 inch/min. Crack gauges from Vishay Precision Group, Inc. (Part No. TK-09-CPC03-003/DP) were used to monitor crack growth.
Single crack gauges were bonded to one side of each specimen and were connected to a data acquisition system. Each gauge consisted of 20 strands oriented along the specimen crack direction with a strand spacing of 0.08-inch. As the crack front propagated across each strand, the strands broke consecutively and the change in gauge resistance was recorded. The instantaneous crack length was tracked by monitoring the time-history changes in gauge resistance. Additionally, the load and deflection time histories were recorded by the test machine. Using the time history data, crack growth and GIC values were characterized.

Figure 20 -Fracture Test Configuration
A description of the fracture behavior in the laminated DCB specimens follows.
Upon loading, strain energy is produced in the specimen and a critical load Pc is reached.
At this load, the corresponding strain energy causes crack initiation to occur at the Teflon insert. The DCB loading arrangement generates a Mode-I crack extending from the Teflon insert along the specimen mid-plane. As the deflection of each beam increases further, increases in crack length occur, strain energy is released (lost) and compliance is increased. (Note that the crosshead extension δ for symmetric laminates is assumed to equal 2x the deflection of an individual beam or arm.) The load versus deflection curve for the -2 °C E-glass fracture test is shown in figure 21 and was representative of the DCB Mode-I fracture test specimen behavior of all samples tested.

Figure 21 -Typical Load vs. Extension for Fracture Test
Strain energy released through Mode-I fracture was calculated by continually monitoring the loads and deflections for each crack length prior to the next increment of crack growth. The overall crack lengths were measured by monitoring the resistance changes across the crack gauges. The data acquisition system recorded the crack gauge voltages over the time duration of the test. Discrete jumps in the crack gauge voltage were due to failures of the individual strands within the gauges as shown in figure 22. Each jump in voltage corresponded to an incremental increase of 0.08-inch in crack length.

Strain Energy Release Rate Calculation
The critical strain energy release rate is defined as the strain energy released per unit area of new crack surface generated. The method of calculating in the current study is the modified beam theory (MBT) approach.
The modified beam theory governing equation is shown in equation 1. Load and deflection data are determined experimentally, therefore the sum of the laminate bending and transverse shearing components of deflection is treated as the total bending deflection of the beam. If the laminate thickness is small and the transverse shearing deformations can be neglected, MBT can be used. GIC can be plotted vs. crack length a by using each crack gauge strand location. With the exception of the first few gauge strand locations, which are close to the initial crack front, GIC is consistent along the crack path.
The values of GIC were calculated for each material and temperature considered using equation (10) with the E-glass and carbon laminate results provided in figures 23 and 24 respectively. From these figure it is seen that each laminate material exhibits a direct dependence of GIC on temperature. It is evident that with decreasing temperature there is a corresponding decrease in GIC. For the E-glass laminate the GIC value (8 lbin/in 2 ) at -2°C is ~65% of the corresponding value at 20 °C (12 lb-in/in 2 ). The Carbon laminate exhibits less of a dependence on temperature as seen in the E-Glass material.
There is a very small decrease in GIC from 20 to 5°C, and a statistically constant value from 5 to -2°C. The differing trends in fracture behavior between the materials indicates that the strain energy release rate, GIC, is primarily a function of fiber type and not matrix material for the current laminates. Each laminate in this study utilized the same resin composition.

Conclusions
A detailed experimental and analytical investigation of the effects of low temperature on the mechanical, water ingression/diffusion, and acoustic properties of E-Glass/Epoxy and Carbon/Epoxy laminates has been conducted. The investigation was primarily aimed at establishing a foundational understanding of the temperature effects on composite laminates at temperatures of interest to the undersea warfare community.
Historically, mechanical and acoustic properties at operating temperatures in the range of ~15 -20 °C have been evaluated, with minimal data pertaining to the temperatures associated with arctic seawater in the ~2 -4 °C regime.
The key findings of the study were as follows: • Mechanical Performance  The E-glass laminate had a GIC value of 8 lb-in/in 2 at -2 °C which was ~65% of the corresponding value at 20 °C, 12 lb-in/in 2 .

CONCLUSIONS
This research has studied the response and structural performance of composite materials when subjected to extreme loading conditions, namely in the form of shock and low temperatures. The studies consisted of experimental work with corresponding numerical simulations, with the primary contributions of this author being the numerical modeling. The fundamental objective of the study as a whole was to develop a better understanding of the response of composite materials leading to more efficiently designed structures while understanding the effects of elastomeric coatings, long term seawater immersion/degradation, and low temperature exposure. The relevant findings resulting from the present study are presented below.
(1) Through an experimental and numerical study, the response of flat composite plates subjected to near field underwater explosive loading was investigated, including the influence of polyurea coatings. The relative performance of the plate configurations was evaluated in terms of center-point and full-field time histories of the deflection of the back-face of the plates, as well as level of material damage.
It was shown that the use of the coatings reduced both the transient deflections as well as the material damage. The computational models developed in the study were shown to accurately simulate the testing with good correlation between the transient responses. Additionally, the models are able to accurately simulate the detonation of the explosive charge and the resulting pressure fields and plate deflections.
(2) The effects of material degradation due to long term seawater immersion on the air blast response of a Carbon-Epoxy material was investigated through experimental and numerical approaches. It was shown that when ageing effects were included, both the transient deflections under load increased and the material suffered material failure. The corresponding numerical simulations matched well with the experimental data. However, for the fixed boundary case, the beam vibration of the simulation was off phase with the experimental results due to imperfect boundary conditions in the experiments.
(3) The response of composite cylinders, including elastomeric coatings, subjected to near field UNDEX loading was studied through a combined experimental and computational approach. The primary parameters of interest in the study were transient response, damage extents, energy levels, and material strains. Damage to the coated composites was dramatically reduced as a function of increasing coating thickness as compared with the baseline cylinders. The modeling approach utilized in the study is able to accurately simulate the detonation of the explosive charge as well as predict the overall damage extents in the composite cylinders. During the transient loading of the cylinders, both the internal material energy and the overall system kinetic energy increase with increasing coating thickness.
(4) A detailed experimental study was conducted to investigate the influence of low temperatures associated with arctic and deep ocean seawater on the mechanical performance of Carbon and E-Glass / Epoxy laminates. The study showed that both the moduli (stiffness) and the strength of the materials considered were effected in the temperature range considered. Furthermore, the fracture toughness of the materials decreased with decreasing temperature.

FUTURE WORK
The current investigation has provided a basis for the development of numerical modeling approaches for the simulation of composite materials when subjected to dynamic loading conditions, namely air and underwater shock loading. It has also presented the effects of reduced temperatures on the mechanical characteristics of similar laminates. As with all research, there remains a significant body of work to be completed in this area before the dynamic response of these materials matures to an equivalent level of understanding as that for metallic materials. This work includes further experimental and computational studies as well as work which correlates the two. This will effectively lead to validated modeling practices that can be applied during the design phase of composite structures. The proposed potential future projects are summarized as follows: 1. Perform additional experimental dynamic loading studies involving additional material combinations and/or laminate architectures to further populate the available data to support model validation. Composite materials are inherently unique and dependent upon material construction, further data will help to quantify the variability under dynamic loading of these materials to allow for design considerations. The performance of other materials such as S-Glass and Kevlar should be examined as well as the possibility of hybrid materials such as Glass / Carbon constructions. The performance of these materials needs to be understood as they inherently have different characteristics. Furthermore, there now exist three dimensional (3D) fabrics which include through thickness fibers which are interwoven through the cloth. These through thickness fibers may improve the performance of the laminates in terms of reducing the delamination damage.
2. Conduct shock experiments in which the complexity of the geometry of the test articles is further increased. More complex geometries could include doubly curved surfaces, oblong spheroids, and plates with abrupt angle changes. The goal should be to incorporate real world design shapes into the test article geometry. The current finite element modeling methodology should also be expanded to simulate these experiments to ensure it is able to accurately simulate the geometrical effects.
3. Conduct experimental work in which the influence of low temperatures under dynamic loading conditions are evaluated. The current study performed mechanical characterization at quasi-static loading, although of far more interest is those loading rates associated with impact, ballistic, and shock conditions.