Implosion and Blast Response of Metallic and Composite Structures in Underwater Environments

Six different experimental studies were conducted to evaluate the dynamic response of marine structures. These studies examine the: implosion performance of polyurea coated aluminum shells; implosion process of marine grade metallic structures; implosion mechanics within a confining environment; the response of confined blast-initiated implosions; generation and mitigation of implosion induced hammer waves; and behavior of artificially aged composite structures subjected to blast loads. During the experiments, two high-speed cameras are used to record the event, and underwater pressure transducers are used to measure the pressure signatures. A high contrast speckle pattern is placed on the specimen so threedimensional Digital Image Correlation can measure full field surface displacement, velocities, and strains. When explosives are in use, a third high-speed camera records the explosive’s behavior and bubble mechanics. For the artificially aged composite study, a Coupled Eulerian-Lagrange finite element model was created to supplement the experimental results. The findings of these studies show that: polyurea coatings can drastically reduce the emitted energy of an implosion event; marine grade metals can release less energy during an implosion event if fracture is present; confined implosions have different collapse mechanics than free-field implosions; confined blast-initiated implosions can have devastating pressure signatures if the hammer pressure is in phase with the bubble pulse; high pressures from water hammer waves are mitigated if a sacrificial foam material is used at the hammer location; and weathered composites have a lower blast performance due to degraded material properties.

This study aims to develop an experimental scheme to determine the localized energy emitted during the dynamic collapse of aluminum structures. Upon collapse, these structures release damaging pressure pulses into the surrounding fluid; to mitigate this effect, the structures are coated with polyurea. The new energy scheme analyzes the energy emission from coated structures. Specifically, aluminum tubular structures with polyurea coatings on their interiors or exteriors are used. Furthermore, the technique combines the information obtained from pressure sensors, located near the collapsing structure, and high-speed images taken during the collapse event. These images are processed through a 3D Digital Image Correlation technique to obtain full deformation and velocity fields. Results show that the energy history can be successfully obtained experimentally. Moreover, the energy emitted from coated aluminum structures is significantly less than the uncoated structures; more so with interior coated structures, and doubling the coating volume does not significantly improve this mitigation effect. Additionally, collapse pressure does not have a direct relationship with the energy released during the implosion process; even though buckling velocities are proportional to collapse pressure. However, collapse volume does have a direct relationship with energy and is the dominant factor in determining the energy release.

Introduction
Submerged hollow structures will become unstable once a critical depth is reached. At this depth, environmental pressures cause the structure to rapidly collapse onto itself (this process is known as dynamic buckling or implosion). During the collapse, the kinetic energy of the surrounding fluid increases and its potential energy decreases, causing a drop in local pressure. When opposite sides of the structure come into contact with one another, sharp acoustic pulses are released. Soon after, the water that surrounds the structure comes to a sudden stop which leads to an abrupt change in momentum, resulting in a considerably high-pressure pulse [1][2][3][4][5].
Implosion has been of interest since the mid-1900s [3][4][5]. However, there is one key accident that renewed the interest in this topic. This accident was the 2001 Super-Kamiokande laboratory accident in Japan where one photomultiplier tube imploded, and the pressure pulses from this implosion caused adjacent tubes to implode; leading to a chain reaction that destroyed 7000 photomultiplier tubes [6]. More recently in 2014, the multi-million dollar underwater vehicle, Nereus, imploded off the coast of New Zealand [7]. These recent events highlight implosion as an ongoing issue.
Early work on implosion characterized the acoustic pulses emitted during the collapse of glass structures, as well as their potential to damage nearby structures [1,3]. This work led to the creation of robust computational models (for fluid-structure interaction during implosion) for the implosion of metallic structures [2]. Later work analyzed the implosion of aluminum structures with varying lengths to produce higher modes of failure (modes II and IV) [8]. Also, an experimental study on brass structures was made with varying geometries to examine the effect of collapse modes on the emitted pressure pulses [9]. Recently, the pressure pulses from imploding structures were linked to full deformation and velocity fields that were captured through a Digital Image Correlation (DIC) technique coupled with high-speed photography [10][11][12].
Even though full-field measures can be obtained from DIC, only localized measures were used in the discussion and results of previous studies due to the human limitation of comparing four-dimensional fields (three spatial and one temporal). For this reason, most of the information available from the full-field analysis goes unused.
To date, there is no work done in the mitigation of the energy emitted during implosion, or in measuring the kinetic energy on the surface of a DIC specimen [13].
Polyurea has gained research interest regarding blast mitigation due to its dynamic properties, such as its stiffness increase at high strain rates. Some of the work available on energy mitigation through polyurea coating is on blast/dynamic loading on structures [14][15][16]. More recently available is a study on coating thin-walled tubular structures with polyurea to mitigate longitudinal acceleration during crushing due to blast loading [17].
This study aims to develop an experimental scheme to determine the localized energy history emitted during the implosion of aluminum structures. Moreover, a numerical method will be established to combine the three spatial domains from the implosion DIC analysis into a volumetric measure. Finally, the new energy scheme will be used to analyze the mitigation effects of polyurea coated aluminum structures and to create an estimation method for the energy released during an implosion process.

Specimen Geometry and Facility
Each specimen is comprised of a 6061-T6 Al tubular structure with 63.5 mm (2.5") diameter and 381mm (15") length (see Figure 1.1). The specimens are sealed from both ends with aluminum end-caps to prevent water penetration. Therefore, during the experiments high-pressure water surrounds the specimen while lowpressure air resides in the specimen.  The sensors are located above and behind the specimen at an 84 mm distance from the surface of the specimen. Also, Sensor 1 and Sensor 5 are mid-length of the tube (see

Polyurea Coating
The polyurea used was the commercially available product HM-VK TM from Specialty Products, Inc. (Lakewood, WA). This is a two-part polyurea that was manually applied over the aluminum tube as it rotated longitudinally. Tape was used at each end of the tube (set to a predetermined thickness) as a scraper guide to wipe off the excess polyurea. Figure 1

Pressure and Impulse
The tubular structure's cross section during implosion is illustrated alongside local dynamic pressure in Figure 1.5 (a). The y-axis in this figure is in terms of dynamic pressure where the value of 0 represents hydrostatic pressure (1.68 +/-0.01 MPa). The pressure history can be broken down into three main stages: I) Structure becomes unstable, II) emission of low-pressure pulses due to the decrease in potential energy, and III) emission of high-pressure pulses due to the abrupt change in water momentum. Also, immediately after the low-pressure region, there is a high acoustic spike (at t=0 ms) caused by structural contact. For structures with high diameter/thickness ratio (such as the one in this study), a second acoustic spike is seen when the opposing walls of the structure come into full contact. Figure 1.5 (b) shows the captured images that can be associated with the pressure history in Figure 1.5 (a).
By comparing the images of t=0 and t = 0.15 ms, it can be determined that the center cross section of the tube completely flattens from a "figure 8" shape, which is the cause of the second acoustic spike. Note that Figure 1.5 (b) is an in-plane image that illustrates out-of-plane deformation; hence, by focusing on the y-dimension change, the out-of-plane change can be intuitively understood.

10
The pressure data can be better represented in terms of impulse by simply integrating the signal. Doing so will take into account the duration of acoustic spikes as well as their magnitude. After integration, an areal impulse is given in terms of Pa•s. This areal impulse is a good representation of the force that adjacent structures to the implodable could experience [1,2]. Figure 1.6 (a) shows the areal impulse of all five cases taken from sensor 1. It is shown that the structures coated with polyurea have the same behavior as the non-coated structure. Also shown is the diminishing of impulse with added coating (more so with interior coating). The maximum impulse for all five cases is given in Table 1.3 as I max .
(a) (b) Figure 1.6 Impulse histories obtained from pressure sensors; (a) sensor 1's areal impulse histories for all five cases; and (b) all sensors' normalized impulse history for the NC case A closer look can be taken in the impulse data if multiplied by the distance from the center of the structure to the sensor location, R s . This new impulse value will be referred to as normalized impulse, I N . Figure 1.6 (b) shows all eight I N histories for the NC case (see Figure 1.3 for sensor locations). It is seen on this plot that most of the normalized history and peak values (of 65.8 +/-4.2 %) are in good correlations. This implies that the pressure wave is traveling with an attenuation factor of 1/R, in turn confirming previous assertions [2,18] of a spherical wave [19].

Collapse Velocities
The reduction in low pressures waves is accompanied by lower collapse velocities.
The EC1 and IC1 (exterior and interior coating with 1:1 volume ratio respectively) cases are seen to have ~15 and 25% reduction in minimum pressure when compared to the NC case, as shown in Figure 1.5 (c). However, the CenterPoint velocities for all five cases are comparable as depicted by their maximum velocities in Table 1.2. The polyurea is a strain rate sensitive material, and it can reduce the bulking velocities during high strain rates. The CenterPoint is located in the "valley" of the tube's cross section, which is a region that experiences relatively low strain rates. It is in the "lobes" of the tube's cross section that high strain rates are expected to occur.
Additionally, this specific tubular geometry tends to collapse into a "figure 8" shape before flattening completely; hence, in this case, the collapse resistance from the polyurea happens mostly near the lobes. However there is still a small reduction in maximum CenterPoint velocity (up to 10%), and this discrepancy increases as measurements are taken closer to the lobes. This is predominantly the cause of the initial reduction in low-pressure waves seen in Figure 1.5 (c) for t<0. Moreover, there is a compressibility effect at the lobe locations for the IC cases that impede complete hinging, leading to even lower pressures as seen in Figure 1.5 (c) at -0.5 ms < t <0. interior coated cases respectively. This change in velocity leads to the reduction in high-pressure waves seen in Figure 1.5 (c) for t>0.

Volumetric Flow
Through the DIC technique, displacement and velocity information are obtained from the images taken during the experiments.

Fluid Energy
The areal impulse can be combined with the volumetric rate of change to give an energy measurement as a function of time as shown in equation (1). This energy is directly related to the kinetic energy of the moving fluid. Also, since the impulse data used is from a sensor, then the energy obtained is a localized measure of energy.
However, since pressure travels at 1/R spherically then energy will travel at 1/R 2 , also spherically [19]; meaning that the energy value reported will be the same on the surface of a sphere with radius equal to the sensor distance from the structural center.
Equation (1) is only valid with the assumption that the fluid flow of the specimen is the same as of the fluid; in other words, any compressibility effect is neglected. In the case of high collapse pressure implosions, where surface cavitation is often common, this method could over predict the energy emitted.
The fluid energy during implosion as a function of time is shown in Figure 1.8 (a) (obtained from sensor 1). The NC case shows more energy release than the coated cases, as expected. Since the time span of energy release is roughly the same, peak energy values can be used as a representation of the polyurea coating's mitigation effects (performance). Interestingly, since the values for all cases scales equally at 1/R 2 , then the performance shown as E 3 in Table 1

Energy Methods Comparison
Previous work shows a method of obtaining the maximum energy release during an implosion by using the peak areal impulse [18,20] as shown in equation (2).
Moreover, this value is taken as a percentage of the total available potential energy, , prior implosion as shown in equation (3). This method will be referred to as Flow Energy Method, while the method described in this study will be referred to as Volumetric Flow Method. Both methods are compared in Figure 1 In equation (2), the [4 2 ] factor represents the surface area of a sphere with radius initializing from the structural center and 0 is the fluid density. Also, the potential energy in the previous study was obtained with the volume displaced by the implodable (outer volume in Table 1.1); but the displaced volume (or collapse volume, V c ) is used instead (inner volume in Table 1.1 minus remaining volume post implosion) to compensate for the polyurea in the interior coated tubes.
Both methods in Figure 1.8 (b) are apart by ~4% of the total available potential energy. As mentioned earlier, if cavitation was present during implosion the Volumetric Flow Method could over predict the energy emitted. In contrast, if cavitation was present, the Flow Energy Method could under predict the energy due to the density term in equation (2). Moreover, the percentage in Figure 1.8 (b) could be scaled by R s 2 /R 2 , where R is the distance in interest and R s is the sensor distance (116.45 mm in this case). By scaling with an R>R s , then the discrepancies between the two methods will decrease; conversely, by scaling with an R<R s , then the discrepancies would increase towards a singularity at R=0.

Influence of Collapse Volume
The critical collapse pressure and collapse volume are the two key parameters when estimating the damage potential of an implodable as shown by equation (

Conclusions
This study aimed to develop an experimental scheme to determine the localized energy history emitted during the implosion of aluminum structures. Moreover, a numerical method was established to combine the three spatial domains from the implosion DIC analysis into a volumetric measure. The new energy scheme created was used to analyze the mitigation effects of polyurea coated aluminum structures.
The completion of this work resulted in the following conclusions (see Table 1

Introduction
An experimental study is conducted to evaluate the implosion pressure pulses and surface velocities of marine grade metallic shells under high hydrostatic pressures.
This research arises from the concern of damage to naval and marine structures such as underwater pipelines, submarines, and autonomous underwater vehicles (AUVs).
When these structures are submerged deep underwater and experience high hydrostatic pressures, they can instantaneously collapse inward and release strong propagating shock waves in the process known as implosion [1][2][3][4][5].
The implosion phenomenon has been of importance to the marine community since the mid-1900s [3][4][5]. However, one key accident renewed the interest in this topic. This was the 2001 Super-Kamiokande laboratory accident in Japan where one photomultiplier tube imploded, and the pressure pulses from this implosion caused adjacent tubes to implode. The implosion of one single tube caused a chain reaction that destroyed 7000 photomultiplier tubes [6]. More recently in 2010, an AUV known as ABE was lost off the coast of Chile due to the buoyancy control glass sphere imploding [7]. Also, in 2014 the multi-million dollar AUV, Nereus, imploded off the coast of New Zealand [8]. These recent events highlight that implosion is still an ongoing issue.
Early work on implosion characterized the acoustic pulses emitted during the collapse of glass structures as well as their potential to damage nearby structures [1,3]. This led to the creation of robust computational models (for fluid-structure interaction during implosion) for the implosion of metallic structures [2]. Later work analyzed the implosion of aluminum structures with varying lengths to produce higher modes of failure (modes 3 and 4) [9]. Furthermore, an experimental study on brass structures was made with varying geometries to examine the effect of collapse modes on the emitted pressure pulses [10]. Studies were also conducted to estimate the structural energy absorption during implosion [11][12][13]. Recently, the pressure pulses from imploding structures were linked to full deformation and velocity fields that were captured through a Digital Image Correlation (DIC) technique coupled with high-speed photography [12][13][14][15][16][17]. None of the studies mentioned characterize the implosion process for marine grade materials, such as AL7075 and SS316, even though these types of materials is typically used in marine applications.
This study aims to understand the fundamental collapse mechanics and failure characteristics of marine grade materials. Specifically, underwater implosions of AL 7075 and SS316 cylindrical shells during mode 2 and mode 3 collapses will be investigated. Also, the failure mechanisms evolution of AL 7075 will be studied by varying collapse pressures. Lastly, a new technique for evaluating the potential energy of a collapse will be demonstrated.

Facility and Specimen Geometry
The experimental facility consists of a 2.1 m semi-spherical pressure vessel and two high-speed cameras. The specimens are sealed from both ends with aluminum end-caps to prevent water penetration. Therefore, during the experiments, highpressure water surrounds the specimen while low-pressure air resides inside. As shown in Figure 2.1, the specimen is then suspended at the center of the tank, and the tank is filled with water and pressurized with compressed nitrogen gas which is introduced from the top of the tank. This simulates increasing water depths in a marine environment. For the experiments performed in this study, the specimens were subjected to pressures ranging from 1.37 to 5.50 MPa (equivalent to 133 to 532 m below sea level respectively).
Cylinders with large L/D ratio ( >6) collapses in a mode 2 shape, while lower ratios will tend to collapse in higher modes [10]. The collapse pressure in equation (1) will be lowest at the dominant collapse mode. Thus, by adjusting the length of the specimen, the collapse mode can be predetermined. Similarly, by adjusting wall thickness, the collapse pressure can be predetermined.
Overall there are seven cases analyzed in this study, which is listed in Table 2.1.
The first four cases (AL1-AL4) are performed to analyze the failure mechanism evolution. For this, a similar geometry is used with increasing collapse pressure. The last four cases (AL4, AL5, SS1, and SS2) are performed to examine the collapse mechanics of different materials and collapse modes. Three experiments were conducted for each case to ensure consistency accuracy in the results.

Compressive Strength
The compressive loading characteristics for AL 6061-T6 (reference material), AL 7075-T6, and SS 316 were obtained for quasistatic and dynamic loading conditions in accordance to ASTM Standard D2412 [19]. The quasistatic and dynamic tests were performed with an Instron 5585 and an Instron 9210 drop weight tower (done with an 8 kg weight and a 5 m/s impact velocity) respectively. A schematic for tests performed is shown in Figure 2.3 (a). The typical result from ASTM Standard D2412 is pipe stiffness; however, the work per unit volume was obtained instead using Eq. (2) to account for the geometrical discrepancies of each material.
Where F is force, ∆Y is tube compression, and V is the material volume to the tube.
In Assuming that the work required to collapse the tubes by parallel-plate loading is the same as hydrostatic loading, the work potential (or potential energy) can be estimated for each implosion case as shown in Figure 2.3 (c) (neglecting the changes in collapse shape near the end caps). Total potential energy available for each case would be when ∆Y/ID = 1. The usual method for estimating potential energy is by multiplying collapse pressure to cylindrical volume [12][13]; however, since collapse pressure drastically drops throughout the implosion process, using a constant pressure leads to unrealistically high estimated values for potential energy.

Collapse Damage
The post-mortem image of one representative implosion experiment for each case is given in Figure 2

Pressure and Velocity Histories
The dynamic pressure histories for the aluminum cases collapsing at mode 2 and  2.5 (a) and (b) shows the emitted pressure waves after it is normalized by its respective collapse pressure (P/P c = 1 represents the collapse pressure; see Table 2.1 for collapse pressure values). The horizontal axis shows time (t = 0 represents structural wall contact between opposing inner surfaces of the cylindrical tube). A representative experiment is shown in these plots and not the average from three experiments.
As collapse pressure increases, there is a decrease in collapse duration as illustrated in Figure  have similar pressure with one minor discrepancy. The collapse behavior of stainless steel is smoother due to its absence of fracture during the collapse.

Emitted Energy
The energy emitted/released during implosion can be obtained from the measured pressure, p, history [12][13]. The energy flux, E F , from a collapsing volume is calculated from the integral of pressure squares times the inverse of the fluid density, ρ 0 , and two times the sensor's standoff distance, R c , as shown in Eq. (3). The flux in Eq. (3) represents the energy released during the under-pressure region of the pressure history (t < 0), which is also the energy stored in the implodable (in the form of compressed air) during collapse [20,21]. The stored energy is released during the over-pressure region of the pressure history (t > 0) similarly to a gas bubble collapse; in other words, the impulse from t < 0 is equal and opposite to the impulse from t > 0 [1][2]. Furthermore, Eq. (3) can be simplified as Eq. (4), where the integral of pressure is the implosion's impulse, I. Lastly, since the pressure emitted from an implodable is a spherical pulse [1][2]13] , then the surface area of a sphere of radius R c can be used to calculate total emitted energy, E T , as shown in Eq. (5).
The total energy emitted for each implosion case is shown in Figure 2.7 (a) as a function of time. The initial increase in energy in Figure 2.7 (a) represents energy being stored in the compressible gas inside the implodable (in the form of lowpressure pulses). Once the tube fully collapses, it starts to release the stored energy into the fluid (in the form of high-pressure pulses) until the stored energy goes back to zero. The peak energy represents the maximum stored energy as well as the total energy released.
As collapse pressure increases, it is expected that the emitted energy also increases. Therefore, to evaluate tubes of different collapse pressures, the total emitted energy needs to be normalized with respect to potential energy during the collapse. In previous studies, the maximum potential energy is estimated by multiplying collapse pressure to cylindrical volume [12][13]. The normalization of the total emitted energy with respect to this maximum potential energy (P c V) is illustrated in Figure 2.7 (b).
Since the driving pressure drastically drops during the implosion process, using a constant pressure leads to an unrealistically high estimation for the maximum potential energy. The new method for estimating potential energy is also used to calculate a normalized emitted energy as shown in Figure 2.7 (c). which is more reasonable than the latter. Also, the AL1 to AL4 implosion cases shows a similarly emitted energy trend in Figure 2.7 (c) as the increase in kinetic energy trend and growth in collapse damage.
For the Mode 3 collapses, the estimated potential energy from based on the parallel plate technique is low. Since the collapsed tube has three lobes and valleys instead of two, its total strain energy is nearly 3/2 of a mode 2 collapse. Hence, more energy from the implosion is used in damaging the specimen so relatively less energy should be transmitted into the fluid in the form of pressure. Table 2.2 summarizes the experimental results and adjusts the collapse potential energy for the Mode 3 collapse (from Figure 2.3 (c) when ∆Y/ID = 1) by a 3/2 factor. An alternative to applying this adjustment factor would be to perform compressive tests using a 3 point compressive fixture with contacts set 120 degrees apart. Table 2.2 shows that mode 3 collapses will release relatively less energy than a mode 2 collapse.

Conclusions
An experimental investigation is conducted to understand the fundamental collapse mechanics and failure characteristics of marine grade materials. Specifically, underwater implosions of AL 7075 and SS316 cylindrical shells during mode 2 and mode 3 collapses were investigated. Both pressure measurements along with highspeed DIC measurements are carried out to correlate the structural deformation with pressure history. The main findings of this study are as follows:  Assuming that the work required to collapse the tubes by parallel-plate loading is the same as hydrostatic loading, the work potential (or potential energy) for implosion can be estimated from simple compression tests.  The similar aluminum and stainless steel cases have similar pressure histories (same normalized maximum and minimum values). However, the collapse behavior of stainless steel is smoother due to its absence of fracture during the collapse.
 The peak and profile of the collapse velocities between the similar aluminum and stainless steel cases in this study are driven predominately by the collapse pressure and not material property.
 The linear increase in velocity means a linear increase in kinetic energy.
Moreover, the linear increase in kinetic energy is responsible for the steady growth in damage seen in Figure 2.4 (a) and is indicative of an increase in emitted energy.
 The collapse energy normalization (from Table 2.2) implies that 70%-90% of the implosion energy from the cases studied is transferred to forms of energy other than pressure. Also, the AL1 to AL4 implosion cases shows a similarly emitted energy trend in Figure 2.7 (c) as the increase in kinetic energy trend and growth in collapse damage.
 Since the collapsed tube has three lobes and valleys instead of two, its total strain energy is nearly 3/2 of a mode 2 collapse. Hence, more energy from the implosion is used in damaging the specimen so relatively less energy should be transmitted into the fluid in the form of pressure. When estimating the potential energy from parallel plate loading, a 3/2 factor should be used to correct for available energy. Additionally, the behavior of the confining environment can be viewed and understood through classical water hammer theory. A one-degree-of-freedom theoretical model was created to predict the impulse pressure history for the particular problem studied.

Introduction
The buckling of cylindrical shell structures has been investigated extensively because of their application in the design of underwater and aerospace structures.
These structures undergo extreme external pressures when used in underwater applications. If the external hydrostatic pressure exceeds a certain value for a given design, the structure loses its structural stability and undergoes buckling. This buckling in underwater situations is a rapid process and causes the entire structure to collapse onto itself. This event commonly referred as "implosion" is shown to be highly violent in nature with resulting high-velocity water motion, strong shock waves, and sound [1]. Several investigations have been reported by researchers in naval and marine communities on the mechanics and fluid-structure interaction during a free-field implosion process [2][3][4][5][6][7][8][9][10][11][12][13]. From the study conducted by Turner and Ambrico [8], the mechanism of implosion process for metallic structures can be described as follows: (1) the initial collapse phase, prior to wall contact, is accompanied by a smooth decrease in pressure in the surrounding water, (2) at the moment that contact is made between opposing sides of the collapsing cylinder at the center, a short duration pressure spike is emitted in the surrounding water, (3) a large positive pressure is produced at the instant that contact between the two opposing sides extends the full width of the cylinder, and (4) as the buckle propagates toward the ends, the pressure pulse continues, but at a lower magnitude, until the buckle reaches the end cap, and the collapse of the cylinder completes.
Although the mechanics of implosion is well established for free-field implosion situations, the studies reporting the implosion occurring in confining environments are very limited. The authors have recently reported the mechanics of implosion of cylindrical shells in a closed confining environment [14][15][16]. The result of these studies indicated that the limited hydrostatic potential energy present in water 49 significantly affects the implosion process in confining environments. The rate and extent of the collapse progression of the implodable volume are dramatically reduced due to the sudden decrease of potential energy inside the confining tube, and the magnitude of the hammer pressure wave is always smaller than the hydrostatic pressure. If the confining tube is open at one end, the mechanics of implosion changes drastically and it leads to generation of extremely strong water hammer waves with significant time period as shown previously by Costa and Turner [17]. Author's recent study on sympathetic implosion inside an open-ended confining tube indicates that these hammer waves can potentially damage even relatively stronger implodable volumes inside the confining tube [17]. Both of these studies measured the dynamic pressure history inside the open ended confining tube to understand the evolution of water hammer waves at the onset of implosion [17][18]. As the development of such implosion waves is a highly fluid structure interaction process, the structural deformations coupled with the surrounding fluid leads to the generation of water hammer waves. Any changes in the design of the structure will alter the fluid structure interaction process and thus the strength of hammer waves. Therefore, in a real design, the mechanics of collapse can be completely different depending upon the geometry/location of the implodable volume inside the confining tube. Thus, there is a need to understand the evolution of these waves from both structural deformation and the fluid mechanics point of view in order to predict the peak strength and total impulse of these harmful water hammer waves. To the best of author's knowledge, higher collapse pressures. Contrary to a free-field implosion process in which the structural velocity is highest right before the initiation of wall contact [10], the confined open tube implosion shows that the structural velocity reaches a peak value well before the wall contact initiation. This is followed by a deceleration phase until the initiation of wall contact.
This chapter has been structured as follows. Section 2 describes the open-ended confining tube pressure vessel facility used to conduct the experiments. This section also details the 3-D DIC calibration procedure followed for quantifying the accuracy of the DIC measurements made through a curved acrylic window. Section 3 discusses the real-time deformation measurements captured using 3-D DIC along with the pressure history. The evolution of structural deformation along with the key parameters such as peak hammer pressure and peak structural velocity are discussed in this section. This section also discusses a single degree of freedom model to describe the evolution of hammer impulse as a function of time and has been compared with experimental results. Section 4 summarizes the major findings of this study.

Implodable Volume and Open-ended Confining Tube
The implosion experiments are conducted inside an underwater pressure vessel  The implodable volumes are placed concentrically inside a confining tube with one open end which sits inside the underwater pressure vessel facility [10]. The schematic of pressure vessel facility with confining tube and implodable volume is shown in 52  The real time deformation of the implosion event is captured using a pair of Photron SA-1 high-speed cameras at 30,000 frames/second. A random intensity pattern is applied on the surface of the implodable volume using flat paint, and the pattern is illuminated using a pair of high-intensity arc lamps [10].

Calibration of 3-D Digital Image Correlation Technique
The authors have recently shown that calibration of extrinsic and intrinsic parameters by using a submerged calibration target can result in high accuracy for both in-plane and out-of-plane displacement measurements using 3-D DIC [10]. As the experimental setup used in this article contains an additional medium in the optical path of the cameras (i.e. cylindrical acrylic window as shown in Figure 3.1), the technique proposed by Gupta et al. [10] requires recalibration in order to estimate the accuracy of measured DIC in-plane/out-of-plane displacements for objects placed inside a cylindrical window. Therefore, two sets of calibration are conducted in this study. The first is an experimental-calibration which is performed in the experimental setup ( Figure 3.1) in order to obtain the relative camera parameters needed to run experiments. The second is an accuracy-calibration which is performed in a custom designed tank (shown in Figure 3.2) to re-evaluate the DIC accuracy.   very well with the true radius of the implodable volume. The radius is found to 19.07 mm ± 0.22 mm (with 95% confidence interval). As the true radius of the specimen is 19.05 mm, the maximum deviation from true radius is found to be 2.25%. Thus, it can be established that both the shape and 3-D deformation of submerged objects behind a cylindrical window can be measured accurately using the accuracy calibration process.

Full-field Structural Velocity Variation with Collapse Pressure
The experimental cases in Table 3.1 are named after their relative wall thickness; for instance, W29 represents a case with 29 thousands of an inch wall thickness. The  Another change in deformation mechanics is also observed during the W29 experiment as compared to a free-field case. The deformation profile along the longitudinal direction has been earlier shown to be a linear/half-sine wave for mode-2 cylindrical geometry [20][21]. In W29 experiment, the linear profiled deformation mode is observed till the instance of peak velocity. Subsequently, it is seen that the points away from the center along the longitudinal direction gain velocity as seen It is interesting to note that the velocity contours for W43, shown in Figure 3.5 (b), are relatively similar as seen in free-field situations due to high collapse pressure of the geometry. The implodable accelerates till time t = 0.81 ms, reaching a peak velocity of 28 m/s. In comparison to W29, a relatively smaller deceleration phase (~ 0.2 ms) is seen, which causes a slight drop in velocity (from 28 m/s to 24 m/s) prior to contact initiation at t = 1.03 ms. The average velocity of contact growth for W43 is ~ 95 m/s, which is 35% higher than W29.

Velocity History Comparison
In order to compare the velocity history for each collapse pressure, the center point velocity for each experiment is plotted in Figure 3.6 (a).  that the velocity at contact initiation is ~ 50% of the peak velocity; W43 exhibits contact at 85% of its peak velocity. Thus, it can be seen that the effect of a confinement on structural deformations is significant in lower collapse pressure.

Pressure History Comparison
The evolution of implosion waves is very similar to all the experiments in this study. To understand the overall behavior of pressure evolution throughout the space, a time evolution of the pressure for each case is shown in Figure 3.7. The pressure contour levels have been normalized with respect to the collapse pressure for relative comparison. Thus the following in-rushing water over-compresses the water in front and a highpressure water hammer forms inside the confining tube at the closed end-plate. As the highest change of momentum occurs at the closed end-plate, the intensity of the hammer pressure is highest at this location similar to seen in [16]. For experiments conducted in this study, the maximum pressure at the end-plate is seen to be between 1.35 c P and 1.92 c P .

Correlation between Pressure History and Structural Deformations
In order to correlate the features in pressure history with structural deformations, the instance is marked by o in Figure 3.7 at which the collapse has propagated to half longitudinal length resulting in the ¾ collapse of the implodable volume. As soon as the collapse is complete, the high-pressure hammer wave is seen to evolve inside the confining tube. This observation can also be understood by the interaction of implosion wave with the confining tube. During collapse, the low-pressure waves are emitted from the surface of implodable. Hence, the low pressures within the confinement don't allow the dynamic pressure surrounding the implodable to rise beyond c P . Only after wall contact, the high pressures above c P are emitted inside the confining tube to rise above c P . Therefore, the time duration of under-pressure region observed near implodable during confined implosions is approximately equal to the duration of the implodable's collapse.
As seen from DIC measurements, higher values of c P generate faster implosions, and so smaller collapse durations. Therefore, the hammer wave evolves faster for higher c P as shown in Figure 3.7. The hammer wave evolves at ~ 2.1 ms for W43, while it evolves at ~ 4.1 ms (approximately two times that for W43) for W29.

Average Hammer Pressure
The average hammer pressure of the first cycle observed at the end-plate during the water hammer wave impact is found to be increasing linearly with c P as shown in

Hammer Pressure Behavior
The behavior of pressure waves inside the semi-confining environment seen during these experiments can be predominantly explained through fluid mechanics of piping systems. Specifically, the impulses caused by the hammer pressures can be derived from Joukouwsky's Equation [22], Eq.
, which represents a weighted average of coupled pressure wave speeds in the aluminum section (  Table 3.2. Experimentally, it is seen that pressure, p, has a sinusoidal behavior that decays at every cycle n by the factor of l as seen in Eq. (6). From this pressure behavior, the total impulse from Eq. (2) can be distributed throughout time (after normalizing it with a factor α) in order to create a function for impulse as shown in Eq. (7).
( ) cos (2 ) Note that the specimen collapse due to the implosion process adds additional energy to the hammer pressure that is not accounted for in the hammer theory by itself. The maximum impulse was observed to be linear with respect to collapse pressure as seen in Figure 3.9 (a), in turn, a correction factor, K , was added to the impulse function in Eq. (7) and is only significant during the first cycle of oscillation.
For the particular case studied, K is also linear with respect to collapse pressure and can be obtained from Figure 3.9 (c) (note that K could also be a function of velocity since there is a relationship between collapse pressure and velocity).  ) (8)

Conclusions
An experimental investigation is conducted to understand the evolution of water  The calibration using a submerged calibration grid can successfully account for the refractive index mismatch between the water/cylindrical acrylic window/flat acrylic window/air. The calibration experiments reveal that the both the in-plane and out-of-plane measurements can be measured using this modified 3-D DIC calibration procedure within 5% error.

Introduction
In this study, an experimental investigation is conducted to evaluate the implosion pressure pulses, water hammer waves, and their mitigation in a confined environment while subjected to shock loadings. This research arises from the concern of damage to naval and marine structures such as underwater pipelines, submarines, and autonomous underwater vehicles (AUVs). When these structures are submerged deep underwater and experience high hydrostatic pressures, they can instantaneously collapse inward and release strong propagating shockwaves in a process known as implosion [1][2][3][4][5]. In a confining environment, the implosion's pressure waves and any induced particle velocity can interact with its surroundings leading to a water hammer wave that is even stronger and more destructive than the implosion's pressure waves.
However, one key accident that renewed the interest in this topic was the 2001 Super-Kamiokande laboratory accident in Japan where one photomultiplier tube imploded, and the pressure pulses from this implosion caused adjacent tubes to implode; leading to a chain reaction that destroyed 7000 photomultiplier tubes [9]. More recently in 2010, an AUV known as ABE was lost off the coast of Chile due to the glass sphere (that controls buoyancy) imploding; which created high pressure pulses that destroyed all onboard systems [10]. Also, in 2014 the multi-million dollar AUV, Nereus, imploded off the coast of New Zealand [11]. These recent events highlight implosion as an ongoing issue.

81
The current work available on implosion characterizes the collapse mechanics for free-field environments [12][13][14][15][16][17]; meaning that the pressure pulses emitted during the implosion travel undisturbed. There is very limited work available on implosions within confining environments. These include implosions within a fully confined environment [18][19][20]; where it was shown that the limited hydrostatic pressure drastically affects the implosion process. Also, the implosions within a confining environment that are open to a larger water body (held at the same hydrostatic pressure) leads to water hammers [6][7][8]. Water hammer is a well-established phenomenon in terms of piping mechanics [21][22][23][24], but there is no work done on implosion-induced water hammers in terms of shock-initiated implosions.
Polyurea has gained research interest in recent years due to its energy absorbing characteristics under dynamic loading. Some of the latest work was done in the mitigation of the energy emitted during a free-field environment implosion, specifically through polyurea coating [25][26][27].

Specimen Geometry and Experimental Facility
To perform the implosion experiments, a 1.  The tank's water is re-filtered (to remain optically clear) and re-used between experiments.
The high-speed images are analyzed using commercially available DIC software (VIC3D 7 from Correlated Solutions, Inc., Columbia, SC) to measure full-field displacements across the viewable surface of the specimen by triangulating the position of each unique feature in the speckle pattern. Previous work [6,15] outlines the calibration procedures that validate the accuracy of the DIC results in the underwater environment (where changes in refractive index are present). It was found that the flat-surface windows (located at the midspan of the pressure vessel) need to be perpendicular to the viewing axis [15], and the cylindrical window (from the confining structure) needs to be concentric to where viewing axis of both cameras meets (optical center) to minimize DIC displacement errors [6]. For this study, the in-plane displacement errors are ~2%, and the out-of-plane errors are ~5%.

Polyurea Coating
The polyurea used (HM-VK TM from Specialty Products, Inc., Lakewood, WA) is a two-part product that is manually applied to the aluminum tube as it rotated longitudinally. Prior to application, the specimen tube was lightly sanded and cleaned with acetone to improve adhesion. Masking tape was used at each end of the tube (set to a predetermined thickness) as a scraper guide to wipe off the excess polyurea. For interior coating, the entire setup is angled so the polyurea can be poured from the center guide's end.
Specimens with polyurea coatings have a uniform coating placed on the exterior or interior of the tube similar to previous work [26,27].

UNDEX Charge Characterization
Experiments were performed without the implodable specimen, and the environmental pressure was set to 1.06 MPa to mimic the UNDEX implosions conditions in order to characterize the explosive and bubble dynamics as shown in

86
The UNDEX pressure can be visualized inside the confinement and throughout time using the history pressure map shown in Figure 4.2 (c). The vertical axis in  Figure   4.2 (c) as P + ) travels down the confining structure, followed by cavitation along the confinement walls (shown in Figure 4.2 (c) as P -). The high pressures and velocities from the explosive charge lead to the formation of a cavitation bubble at the charge location. The bubble grows until the surrounding pressure is sufficiently large to cause the bubble to collapse. When the bubble fully collapses, it emits high-pressure waves which lead to a subsequent cavitation bubble to form and so on [28]. The high pressures of some of the bubble cycles can be seen in Figure 4.2 (c).
A pressure frequency map can also be constructed using the UNDEX pressure data as shown in  The fluid wave speed inside the confining structure, c f , can be estimated using Eq.
(1) which is derived using piping mechanics and represents a weighted average between coupled pressure wave speeds in the aluminum section (

Implodable Collapse Behavior
During hydrostatic implosions inside the confining structure water rushes from the open end towards the closed end as the specimen collapses. Soon after the specimen fully collapses, the rushing water impacts against the closed end causing immense pressure surge (hammer pressure wave). The pressure differential between the environment and confinement causes cyclic loading conditions inside the confinement [21]. The dynamic pressure history (where 0 MPa represents the hydrostatic collapse pressure) inside the confining structure is illustrated in Figure 4.4 (a) (where t =0 is the time of interest that represents initial specimen structural/wall contact).
UNDEX implosions have comparable pressure history maps to the charge characterization map in Figure 4.2 (c). After the charge combusts at t = -6 ms, highpressure wave travels down the confining structure, followed by cavitation along the confinement walls which are shown in Figure 4.4 (b) as P + and Prespectively.
Moreover, as discussed earlier, the charge ignition causes various bubble cycles. Once the initial shock wave passes through the specimen, it vibrates in a mode-2 shape (seen through DIC analyses). When the high-pressure pulse from the first bubble reaches the bottom of the confinement, it reflects as a high-pressure wave (seen between -2 and 0 ms in Figure 4.4 (b)). These high pressures from the first bubble collapse supply sufficient energy to the specimen to make it unstable and collapse. The specimen collapse also emits a high-pressure wave that causes a hammer (shown in    The hydrostatic implosion starts at rest, and the specimen rushes into itself rapidly until it reaches 12 +/-1 m/s and there a sufficient drop in surrounding pressure to decrease the collapse speed to 8 +/-1 m/s, followed by wall contact at t =0 (see Figure   4.6 (a)). This two-phase velocity behavior is common in a confined hydrostatic initiated implosion [6]. The UNDEX implosion starts with cyclic movement caused by the UNDEX and bubble pressure waves. The high-pressure pulse from the first bubble  The first is the pulse from the explosive itself (seen between -6 and -4 ms); the second is the bubble pulse (seen between -2 and 0 ms); and the third is the implosion pulse/hammer (seen between 1 and 4 ms). The areal impulse (defined as ∫ Pdt pressure cavitation/plateau regimes (seen between -5 and -2 ms as well as 0 and 1 ms in Figure 4.6 (b)) are not taken into account; resulting in the areal impulses from the high-pressures only.
The resultant high-pressure impulses from

Polyurea Coatings
For the hydrostatic initiated implosion experiments, the 1:1 volume ratio polyurea coating in the exterior (EC) and interior (IC) provided a small but notable changes in collapse mechanics when compared to the no coating (NC) case. For instance, the implosion process was seen to be prolonged. This is better illustrated by the center point velocity of the specimens as shown in Figure 4.8 (a). The initial rate of collapse is slower for the EC and IC cases which are due to the resistivity of the polyurea coating. For confining conditions, the symbiosis of collapse rate and surrounding pressure is exceptionally sensitive. From the decrease in collapse rate, the drop in surrounding pressure is also affected; leading to a sharper collapse soon after the implosion begins (seen between -2 and 0 ms in Figure 4.8 (a)). illustrates the pressures near the specimen (about 70 mm away) and at the confinement's bottom closed end respectively. It is seen from these figures that pressures are comparable. The largest discrepancy is seen by the slight reduction in peak pressure from the closed end at 2 ms in Figure 4.8 (c). This small reduction is likely due to a phase shift of the implosion pulse rather than energy mitigation through the coating. The pressures at the closed end are a combination of water hammer and implosion pulses [6]. Since the majority of the volumetric displacement happens before wall contact, and there are little changes in out-of-plane velocities between the three hydrostatic cases, then it is reasonable to assume that the low-pressure pulses, water particle velocity, and water hammer pulses are also about the same for these three cases. However, polyurea coatings have a strong delay effect in longitudinal buckle propagation [26]. This delay would also postpone the high-pressure pulses from the implosion as seen by the slight increase in pressure around 3 ms in Figure 4.8 (c). This reduction in velocity and delay is seen in Figure 4.9 (a); note that t =0 represent wall contact, also, the charge ignition happens at -7 ms for the IC, -6 ms for the EC, and -5.5 ms for the NC cases (illustrated by Figure 4.9 (b)). Finally, the peak pressure at the hammer end seems to be lower for both coated cases (shown in Figure 4.9 (c)); some of the higher frequencies from the shock could've been damped as the shock passed through the coated specimen. The implosion pressures seen after 0 ms are also reduced. Like for the hydrostatic case, the reduction in the implosion high-pressures is due to a phase shift in the implosion pulse rather than energy mitigation. The phase shifts in the UNDEX cases are more prominent than the ones from the hydrostatic cases. The initially higher collapse velocities and the strain rate sensitivity of the polyurea coatings are the cause for these stronger shifts. Note that for the IC case, the implosion and water hammer pulses are nearly separated between 1 and 4 ms in Figure   4.9 (c); this is indicative that the IC leads to a larger delay in buckle propagation, which leads to a stronger phase shift when compared to the EC case.

Hammer Energy
The impulse is an excellent representation of the damage potential from a pressure pulse. Also, it can be directly related to the energy flux, E F , of the pressure pulse [27,29]. The energy flux at the confinement radius, R c , up to time, t, is defined in Eq. (3).
Note that impulse is expressed in terms of a pressure integral, thus, it can be simplified into Eq. (4).
Where, p is the dynamic pressure, I is the areal impulse, and ρ 0 is the density of the fluid.
The implosion event generates an energy flux with a spherical surface area [26,27]. Half of the spherical pulse will travel upwards and leave through the open end of the confinement. The second half will travel downwards, transition from half sphere to planar, reach the closed end of the confinement, and reflect upwards. Since the focus of this study is on the closed end, only the second half of the implosion pulse will be considered. To find the energy at the closed end, the energy flux (where p is taken from CH7) is multiplied by the confinement's cross sectional area (2πR c 2 ). The energy at the closed end will be referred to as implosion energy, E I ; this is the energy required to cause the high pressure surge seen in CH7 for all experiments after t=0 ms.
Recall that the low-pressures and cavitation regimes after wall contact are not taken into account in the impulse calculations since discrepancies are only present during the high-pressure pulses. For this reason, the subsequent energy calculations also only pertain to the high-pressure pulses.   Table 4.3. The polyurea coating does not mitigate much of the available energy, but it does cause a phase shift so that the high-pressures from the water hammer does not align with the high pressures from the implosion; this effect is stronger during higher collapse velocities due to the high strain rate sensitivity of the polyurea. It seems plausible that at specific collapse velocities, the high-pressure implosion pulse could be aligned with the low-pressure hammer pulse, and cancel out most of the subsequent oscillatory behavior within the confinement; however, this feat would be beyond the scope of this study.

Implosion Instabilities
Previous work on the collapse behavior of cylindrical shells shows that the quasistatic non-linear pressure-deformation curve of a cylindrical shell characteristically defines the change in structural stiffness in a buckling problem [30][31]. The maximum stiffness of a cylindrical shell is at zero hydrostatic pressure, but with increasing deformation and pressure in the pre-buckling regime, the stiffness of the structure is degraded to the point of instability. Beyond the instability point, the pressure needed to continue deformation decreases with increasing deformation indicating the presence of negative stiffness in the structure. This negative structural stiffness makes the structure more submissive to deformation [20]. The change in volume of the fluid can be assumed to be the same as the collapsing cylindrical tube, thus the work done by the fluid during collapse (dw) can be expressed as Eq. (6).
An instability plot is shown in Figure 4.11 (a) where the left vertical axis is the normalized critical pressure in percentage, the right vertical axis is the potential hydrostatic energy, and the horizontal axis is the change in volume of the specimen.
At nearly 1% volume change (dV), the pressure is 100% of the critical pressure (P cr ), which indicates hydrostatic instability and the natural collapse of the structure.
Everything to the left of the maximum in the instability plot is stable, and everything to the right is unstable at 100% P cr . As pressure drops from critical, then this instability threshold shifts from a maximum at 100% P cr to a value that coincides with the hydrostatic pressure. To collapse a structure from 70% P cr , there needs to be sufficient energy to deform the structure to 3.7% dV which is the unstable threshold for the 70% P cr (from point A to point B in Figure 4.11 (a)).
The strain energy for thin cylindrical shells (U) during changing cylindrical volume can be estimated using Eq. (7) and Eq. (8) [32]. integrated with respect to the radial direction, r from a-h/2 to a+h/2 (inside and outside radius respectively) the strain energy can be obtained in terms of displacements. As mentioned, the radial deformation, w, starts as an elliptical cross-sectional area of the mid-plane and transitions linearly to zero at both end-cap locations. Longitudinal deformation, u, and tangential deformation, v, are assumed to be negligible as well as any strain energy at the end-cap locations due to small changes in curvature. Note that these assumptions and Eq. (7) are only suitable for small deformations where nonlinear effects are not present; in turn, this method cannot be used to estimate required strain energies for very low pre-pressures. Where the parameters represent: Young's modulus, E; Poisson's ration, ν; mean radius, a; shell thickness, h; longitudinal displacement, u; tangential displacement, v; and radial displacement, w.
The energy requirement for dynamic instability (E ins ) is calculated as the energy required to achieve the strain energy at a given deformation and the energy needed to displace the fluid as shown in Eq. (9) and illustrated by Figure 4.11 (b); where the vertical axis is the strain energy of the cylindrical structure plus the work done by the moving fluid, and the horizontal axis is the change in volume of the specimen. For instance, at 70% pre-collapse pressure (1.06 MPa in this case), an additional 305 J is required to cause the cylindrical specimen to volumetrically deform from 0.05% (the dV at 70%P cr ) to 3.7%, which will lead to instability.
E ins = U + dw (9) The impulse delivered to the specimen by the RP-80 charge can be found by using the pressure information at the charge location ( Figure 4.9 (b)) and integrating it with respect to time. The maximum areal impulse at the specimen location is ~1241 Pa·s for all cases. From the impulse, and Eq. (4), the maximum energy flux passing through the specimen due to the UNDEX charge is 8,565 J/m 2 and the energy can be found as 261 J by using the surface area of the specimen. This energy is below the required 305 J for specimen instability. For this reason the specimen oscillates in a stable manner after the initial pressure from the explosive. However, the additional energy supplied by the first bubble collapse is enough to push the specimen to the unstable regime for the 70% hydrostatic pressure as shown in previous sections.

Conclusions
An experimental investigation is conducted to understand the behavior of confined implosions subjected to UNDEX loading. Both pressure measurements along with high-speed DIC measurements are carried out to correlate the structural deformation with pressure history. The key findings of this study are as follows:  The bubble from an explosive will lead to particle movement in a confinement during its contraction phase that can cause a water hammer. However, this hammer wave though prominent in the frequency, is relatively small in magnitude with respect to the magnitude of the pressure waves from the bubble collapse and the explosive charge.
 The implosion pressure pulse of a confined implosion that is hydrostatic and UNDEX initiated are relatively similar, at the closed end, after the wall contact phase.
 The surface center-point velocity from an implosion specimen does not have a two-phase region in cases where the surrounding pressure is much higher than the critical collapse pressure, such as the UNDEX cases in this study (shown in Figure   4.6 (a)).
 The high-pressure's impulse from the first bubble collapse and implosion, in the UNDEX case, is about the same and ~50% higher respectively than the impulse from the explosive itself. This illustrates that volumetric changes within a confinement can be more detrimental than explosives (under the parameters of this study) due to the water hammer effect.
 An UNDEX implosion has two oscillatory components (the bubble collapse pulses and the periodic oscillation within the confinement) that are combined. These superpositioned pulses will lead to either extremely high pressures, or it could also negate each other depending on their respective phase.
 Polyurea coating the specimens does not necessarily help reduce pressure surges within the parameters of this study. However, the coating does cause phase shifts which delays the implosion pulse. The polyurea coating thickness can be used to control the delay period (since coating thickness affects buckle propagation velocity [26]).
 Through polyurea coating, a delay in implosion and lower collapse/buckle velocities can be achieved, which helps reduce the peak implosion pressures by decoupling the water hammer wave and the implosion high-pressures. For the UNDEX cases, where collapse velocities reached greater values, the polyurea coating has a greater delay effect in collapse mechanics due to the strain rate sensitivity of the polyurea when compared to the hydrostatic cases.
 The energy from the high-pressure waves found at the closed end of the confinement is nearly the same for the hydrostatic case, since the polyurea coating did little to mitigate and delay the implosion pulse (due to the lower collapse velocities). However, for the UNDEX initiated cases, polyurea coating caused a longer delay in the implosion pulse which was sufficiently large to reduce the peak energy values by ~35% for external coatings and ~50% for internal coatings.
 A Riks non-linear model can be used to estimate the required energy needed to push a pre-pressurized cylindrical structure into the unstable mode. The structure in this study was found to need an additional 277 J to become unstable at 70% prepressure. The explosive used did not supply sufficient energy for instability.
However, the bubble collapse and confining nature of the problem led to additional energy inputs that caused the implosion instability.

Introduction
In this study, an experimental investigation is conducted to evaluate different pressure mitigation techniques for implosion induced water hammer waves. This research arises from the concern of damage to naval and marine structures such as underwater pipelines, submarines, and autonomous underwater vehicles (AUVs).
When these structures are submerged deep underwater and experience high hydrostatic pressures, they can become unstable, collapse inward, and release powerful propagating shock waves in a process known as implosion [1][2][3][4][5]. In a confining environment, the implosion's pressure waves and any induced particle velocity can interact with its surroundings leading to water hammer waves that are stronger, and more destructive, than the implosion's pressure waves. Previous work shows the water hammer pressures reaching values of 150-200% the implosion's peak pressures [6][7][8][9].
However, one key accident that renewed the interest in this topic was the 2001 Super-Kamiokande laboratory accident in Japan where one photomultiplier tube imploded, and the pressure pulses from this implosion caused adjacent tubes to implode; leading to a chain reaction that destroyed 7000 photomultiplier tubes [10]. More recently in 2010, an AUV known as ABE was lost off the coast of Chile due to the glass sphere (that is used to control buoyancy) imploding; which created high-pressure pulses that destroyed all onboard systems [11]. Also, in 2014 the multi-million dollar AUV, Nereus, imploded off the coast of New Zealand [12]. These recent events highlight implosion as an ongoing issue.
The current work available on implosion characterizes the collapse mechanics for free-field environments [13][14][15][16][17][18]; meaning that the pressure pulses emitted during the implosion travel undisturbed. There is very limited work available on implosions within confining environments. These include implosions within a fully confined environment [19][20][21]; where it was shown that the limited hydrostatic pressure drastically affects the implosion process. Also, the implosions within a confining environment that are open to a larger water body (held at the same hydrostatic pressure) leads to water hammers [6][7][8][9]. Water hammer and its mitigation is a wellestablished phenomenon in terms of piping mechanics [22][23][24][25][26][27].

Specimen Geometry and Testing Facility
The implosion experiments are performed by using an 813 mm (32.0 in) long, thick walled (1 in), cylindrical confinement that is placed inside a 2.1 m diameter semi-spherical pressure tank as shown in Figure 1  Four types of mitigation methods were selected and evaluated in this study as shown in Figure 1 (d). The first method is a baffle system consisting of a 50% blockage ratio baffle. The second technique is granular polypropylene spheres, where 12.7 mm (0.5 in) diameter spheres are stacked in 4 layers (148 spheres per layer). The third approach is by using cylindrical-shaped high-density foams (PVC 130 from Gurit Inc., Bristol, RI). The fourth scheme is using the same high-density foam from the third approach, but with a rod through its center and a smaller diameter such that when the confinement is filled with water, the foam floats and can act as a piston. All four mitigation techniques were placed at the bottom closed-end of the confinement and given a physical restriction of 50.8 mm (2 in) height (or travel distance for the piston case) so that one technique does not outperform the other simply due to its size. More details on each method are listed in Table 5.1.  The high-speed images are analyzed using commercially available DIC software (VIC3D 7 from Correlated Solutions, Inc., Columbia, SC) to measure full-field displacements across the viewable surface of the specimen. Previous work [6,16] outlines the calibration procedures that validate the accuracy of the DIC results in the marine environment (where changes in refractive index are present). It was found that the flat-surface windows (located at the midspan of the pressure vessel) need to be perpendicular to the viewing axis [16], and the cylindrical window (from the confining structure) needs to be concentric to where viewing axis of both cameras meets (optical center) to minimize DIC displacement errors [6]. For this study, the in-plane displacement errors are ~2%, and the out-of-plane errors are ~5%.

Pressure Behavior
The pressure history for the four different types of mitigation techniques is compared to the no mitigation, control case (C1), in Figure 2 (a). It is seen that both the baffles (B1) and spheres (S1) techniques did not affect the magnitude or frequency of the pressure significantly. However, the high-density foam (F1) and foam-piston (P1) had a substantial effect on the frequency and well as the pressure magnitude. To further explore the impact from the high-density foam, the strain energy storage of the foam was optimized by increasing the collapse pressure of the implodable (by decreasing the length of the implodable) as seen by foam F2 in Figure 2 (b). Two additional piston cases were also explored to see the impact of piston diameter (P2) and foam behavior (P3).

Frequency Response
The coupled pressure wave speed in a pipe, f c , can be calculated by Eq. (1) [6,9].  [6,9]. The details for the parameters used in Eq. (1) can be found in Table 5 Table   5.3. For the control case (C1), the frequency is 26 % smaller than the theoretical value; since theory does not take into account any viscous losses or the impact of the implodable specimen [6]. The baffle and spheres cases (B1 and S1) had negligible changes in frequency; similar to the changes in pressure. However, all foam and piston cases (F1, F2, P1, P2, and P3) had a drastic decrease in its dominant frequency from the control case as shown in Table 5.3. The reduction in frequency is not explained by the change in tube length due to the additional of the mitigation technique; as mentioned earlier, decreasing tube length increases natural frequency. Unlike the decrease in pressures, optimizing the foam behavior by increasing the collapse pressure did not decrease frequency significantly. Therefore, both phenomena are not related to each other. Rather, the change in prolonging of the hammer cycle is likely due to the dampening properties of the foam, which is why the smaller diameter foams (piston cases) have a lower frequency reduction.

Conclusions
An experimental investigation was conducted to evaluate mitigation methods for reducing the degree of cavitation at the closed end while simultaneously reducing the damage potential caused by the water hammer wave. Pressure measurements and high-speed DIC measurements were carried out to correlate the structural behavior with pressure history. The main findings of this study are as follows:  The baffles (B1) and spheres (S1) techniques did not affect the magnitude or frequency of the pressure significantly. However, the high-density foam (F1) and foam-piston (P1) had a substantial effect on the frequency and well as the pressure magnitude.
 The foam behavior was optimized by having the collapse pressure (Pcr = 2.79 MPa) to be slightly lower than the foam's quasistatic crushing pressure (P = 2.85 MPa). After the implodable goes unstable and the event become dynamic, the pressure rises until the dynamic crushing strength is reached and the foam fails in the flow region. The crushing of the foam in the flow region mitigates the pressure within the confining tube.
 Unlike the decrease in pressures, optimizing the foam behavior by increasing the collapse pressure did not decrease frequency significantly. Therefore, both phenomena are not related to each other. Rather, the change in prolonging of the hammer cycle is likely due to the dampening properties of the foam, which is why the smaller diameter foams (piston cases) have a lower frequency reduction.

Introduction
In this study, an experimental and numerical investigation was conducted to evaluate the response of weathered unidirectional composite plates subjected to nearfield explosive/blast loading. 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 due to the continuous exposure to an aggressive 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 fatal.
A major cause for 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 many parameters such as temperature, the composition of resin and curing agent, fillers, 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 common and well-accepted model for epoxy resins is a Fickian model [14] which uses Fick's second law to predict how a material's concentration changes over time [19][20].
Previous studies used a 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 due to an increase in mass, internal stresses due to swelling, and loss of interlaminar strength [15][16][17][18]. Current research on the high strain rate response of weathered composites is very limited. Recently, there has been one work that analyzes the shock response of weathered composites plates [21]. Moreover, many experimental and numerical studies analyze the dynamic response of composite plates due to underwater explosives [22][23][24][25][26], but a study on the explosive response has never been made in regards to weathered composites. 60% fiber volume content. Table 6.1 lists the product information and properties of interest for the fiber, fabric, epoxy, and composite plate.

Weathering Facility
The composite materials are placed in a 3.5% NaCl solution (prepared in accordance to ASTM Standard D1141 [32]) as shown in Figure 6.1; this salinity was chosen due to it being a normal concentration of several ocean bodies. Four water heaters (Model LXC from PolyScience in Niles, IL) are used to maintain a temperature of 65˚C. It is important 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; hence, a temperature reasonably lower than the wet glass transition was chosen. 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 activate individual water pumps to replenish the volume lost; thus, the salinity remains constant, the heaters work properly at a low maintenance level, and water passively circulates as room temperature water is introduced. For this study, the composite materials are exposed to the salt water for consecutive 35 and 70 days.
Experiments are initiated immediately after the specimens are removed from the salt water exposure to avoid moisture loss as suggested by ASTM Standard D5229 [33].

Facility and Specimen Details
To perform the blast experiments, the 1. all-around clamping width; leaving a 254x254 mm 2 (10x10 in 2 ) exposed area as shown in Figure 6.2. An RP-503 explosive was used to load the composite structure; it is submerged in the water, centered to the specimen, and placed at a 152 mm (6 in) standoff distance (additional standoff distances were also explored; see Table 6.2 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 6.2) at 152 mm 136 analysis. A third Photron SA1 camera is used (as shown in Figure 6.2) to record the explosive and bubble-to-structure interactions at 10,000 frames per second (with a 576x992 spatial pixel resolution). High-intensity light sources (Super Sun-Gun SSG-400 from Frezzi Energy Systems Inc. in Hawthorne, NJ; not shown in Figure 6.2) are used to illuminate the recorded images. The experimental cases and its details are summarized in Table 6.2. Each experimental case has been repeated two times to validate the results (three for the 45s_0WD_D3 case in Table 6.2). 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 9-12 pixels per dot) on a flat-black painted background until approximately 50% of the surface area of the specimens are covered by the white dots. When clamping the composite plate, a skin layer of silicon 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 commercially available DIC software (VIC3D 7 from Correlated Solutions, Inc., Columbia, SC) to measure full-field displacements across the viewable surface of the specimen 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 optical windows need to be perpendicular to the viewing axis [34] to minimize DIC displacement errors. For this study, the in-plane displacement errors are 1.2%, and the out-of-plane errors are 2.5%.

Numerical Model
experiments, the reflections from the tank walls are relatively small in magnitude and have minor effects on the composite's response. Therefore, the experiments behave as they would in a free-field condition (where no reflections are present), a larger modeling subdomain is not necessary, and the model's external fluid faces are set as non-reflecting boundary conditions.

Weathering
Since the activation energy (E a ) for a material is constant, a mass diffusion study can be performed at various temperatures (different diffusion rates) to obtain the acceleration factor (AF) of submersion at for the material a specific temperature [36].
For this study, moisture absorption was measured for composites submerged in 3.5% NaCl solutions at 5, 25, 45, 65, and 85 ˚C in accordance to ASTM Standard D5229 [33]. The last temperature for moisture absorption (85 ˚C) is slightly higher than the wet glass transition temperature, and it is only used for calculating AF (since E a is constant).
If the diffusivity into the composite plate obeys Fick's second law of diffusion [19] and is one dimensional, then the diffusion coefficient (D) can be calculated using Eq.
(1) [20]. The diffusion coefficient must be calculated from a point that is within the initial linear portion of the mass diffusion curve (≤ 50% mass saturation). The diffusion coefficient can also be related to E a by using Arrhenius' Relation given in Eq.
(2). To solve for E a , Eq. (2) is written in logarithmic form as shown in Eq. (3), then -E a /R can be found on the slope of a linear plot for the various diffusion temperatures [20]. After obtaining the activation energy for the composite material, AF can be found as the ratio of working over experimental diffusion rates as shown in Eq. (4) [36].
Additionally, the submersion experiments are performed at a constant temperature (T 1 = 338K), but the service temperature (T 2 ) can vary depending on application; hence, AF is application dependent. For instance, the AF for a ship operating in the Arctic Ocean will be much higher than one operating in the Mediterranean Sea.
Assuming an average ocean temperature of 16

Composite Plate
To simplify the material model, a plane stress assumption (using shell elements in the numerical model) is made for the composite plate. The elastic modulus (E 1 and E 2 ), Poisson's ratio (v 12 and v 21 ), shear modulus (G 12 ), and failure strains can be found by the standards outlined in Section 2 and are shown in Table 6.5. The elastic modulus and Poisson's ratio was found to be the same in both principle directions (E 1 = E 2 and v 12 = v 21 ). The normal stress has a linear behavior until failure, but the shear stress has a bilinear behavior; the shear yield and failure stresses are listed in Table 6.5. All results for the material properties in Table 6.5 are given as the average from six experiments with its standard deviation.

Explosive Loading
During the experiments, the RP-503 underwater explosive (UNDEX) combusts at t = 0, and high-pressure waves load the composite specimen. The high pressures and velocities from the explosive lead to the formation of a cavitation bubble at the charge location as shown in Figure 6.6 (a) at t = 3 ms. Also, the high pressures loading the specimen leads to more cavitation on its surface as shown Figure 6.6 (a) at t = 15 ms.
The cavitation bubble expands until its surrounding pressure is sufficiently large to cause it to collapse. After the bubble collapses, it emits another high-pressure pulse that causes the specimen's surface cavitation to collapse as well as shown Figure 6.6 (a) at t = 27 ms.
The high pressures from the explosive can be seen in Figure 6.6 (b) for different standoff distances. The shock from the explosive is distinguished by an immediate rise in pressure followed by exponential decay. The pressure, in this case, decreases spherically by 1/R from the explosive location. Also, the reflections from the tank's boundaries are small relative to the initial pressures which justify the non-reflective boundary conditions in the numerical model.

Deformation and Image Analysis
The out of plane deformation obtained from the 3D DIC is shown in Figure 6 Decreasing the standoff distance leads to higher loading pressure and higher deformation rates. The displacement curves for the 76 mm and 114 mm standoff stop when through thickness cracking is observed in the high-speed images; delamination is seen for the 152 mm standoff during post-mortem, but not during the experiments.
For the 152 mm standoff, the specimen flexes towards the air-side until cavitation covers the composite's surface (on its water-side), which causes it to flex towards the

Numerical Results
The JWL EOS and the using just RDX material to model the RP-503 explosive (instead RDX and PETN) worked well for the numerical simulations as shown in The specimens were carefully analyzed in the post-mortem, and no indication that slippage occurred was found near the boundaries. Also, by performing DIC analysis near the boundaries of the fixture, results indicate that in-plane displacements (slippage) were negligible during all experiments. However, some delamination was found near the boundaries of the specimen. With a plane stress assumption, delamination that occurs within the plate's thickness cannot be accounted for [37]; thus, the numerical results cannot represent this type of failure with shell elements.
The shell element formulation can only account for in-plane damage mechanisms (such as fiber/matrix fracture) and not any debonding that occurs within composite's layers.
Delamination can cause the delay in rising time as well as the slower rebound rate with its weakening (damaging) stiffness in the experimental results seen in Figure 6.9 (b). To improve the numerical model solid elements, a tie-break type of contact can be used to simulate delamination damage could be used. This model type of model would require the delamination strength to be equal to the tie-break force in the model.

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 during prolonged exposure to seawater. The main findings of this study are as follows:  The mechanical properties of the carbon-epoxy composite used in this study degraded over 35 and 70 days of artificial weathering (hydrothermal degradation).
Most notably, the shear properties degraded significantly due to the matrix material (epoxy) having a significant impact on the shear properties.