Shock wave mitigation using periodically discrete material layers of variable orientation: Experiments and simulations

In recent decades, there has been substantial research dedicated to the study of shock wave propagation and its consequences.^1–9 Notably, the engineering community has shown a growing interest in layered composites as a means to reduce the mass of structures while maintaining their strength under high dynamic loads, such as blasts and impacts.¹⁰ This shift in focus from monolithic solids to layered systems has significantly improved the performance and resilience of structures.^11–13 However, there remains a relative lack of understanding when it comes to finite amplitude shock wave propagation in heterogeneous media. Much of the existing research has concentrated on the geometric dispersion of elastic waves,^14,15 with limited insights into the role of interference scattering effects on shock wave dispersion and dissipation in heterogeneous solids.^{12,13,16–19}

Earlier studies have shown the feasibility of mitigating stresses and the risk of structural damage by breaking down the shock pulse at the interlayer boundaries into compressive and release wave clusters.^{14,16,17,20,21} An oscillatory behavior has been observed in the stress profiles behind layered composites when extended input pulses are used, which can be attributed to internal ringing between the layers of these composites due to impedance mismatch^16,22,23 or the presence of inherent weak planes that could lead to spallation at bonding locations.² 

Most of the research in this field has been centered on periodically layered and impedance-graded materials. In the case of periodically layered heterogeneous solids, a stable shock front displays a strain rate that increases with the square of the shock stress,^16,22,23 indicating higher shock viscosity (pressure, temperature, density, etc.) in comparison with homogeneous materials. However, careful consideration of the impedance of each layer can affect the transmitted stress, with the caveat of an increased risk of delamination at the material interface due to elevated tensile reflected stress.^{12,13,18,24,25} It should be noted that higher reductions in impedance may result in a more significant reduction in ultimate transmitted stress.²⁶ 

While much of the existing research predominantly focuses on the through-thickness behavior of layered composites, there is a noticeable scarcity of studies that address the behavior of layered composites when they are oriented such that the wave propagates along the fiber or individual layer. Understanding the propagation of shock waves in composites under oblique impact is just as vital as comprehending their behavior in the through-thickness direction since impacts are seldom perpendicular to the surface.

However, in the field of fiber composites, some research has garnered significant attention and has provided valuable insights into various fundamental issues. Notably, these studies have revealed marked differences in the shock response between the in-fiber direction and the through-thickness direction.^27–35 Researchers have posited the presence of two distinct waves that contribute to the dispersion and dissipation of shock energy. A high-velocity wave propagates along the fibers, while a slower wave moves through the matrix.

This paper employs both experimental and numerical modeling approaches to elucidate the development and propagation of waves when periodically layered composites of different orientations are subjected to high-velocity impact. Given the imperative to mitigate shock waves in structures, there is a corresponding interest in examining the mechanisms underlying shock mitigation. Consequently, this study assesses the efficacy of employing layered composites at an angle and investigates the physical mechanisms through which layer orientation achieves mitigating effects. The anticipated outcome of this research is to offer a fresh perspective for enhancing the shock resistance of structures.

Plate-impact experiments were carried out at the University of New South Wales (UNSW) Canberra, located at the Australian Defence Force Academy (ADFA), with a single-stage gas gun equipped with a 13-m-long barrel and a 70 mm bore diameter. The experimental targets comprised periodically layered composites at different orientations, which were constructed by bonding Polymethyl Methacrylate (PMMA) and Oxygen-Free Copper (Cu) plates together using low-viscosity, slow-curing epoxy. The impactor material utilized was Cu. The relevant material properties, sourced from the existing literature, along with the sample dimensions, are presented in Table I. Further elaboration on these aspects can be found in Secs. II B–II D.

The periodically layered heterogeneous samples were prepared using 1 mm thick Cu sheets alternated with 1.5 mm thick PMMA sheets. To enhance the bonding strength between the Cu and PMMA layers, the sheets were subjected to sandblasting to roughen their surfaces. For bonding, a two-part epoxy consisting of 105 epoxy resin® and 206 slow hardener® from the West System was used. After mixing the epoxy components in the correct ratio, they were applied to the roughened surfaces of the plates. The plates were then cured under 5 bars of pressure using a hot press for 24 h to expel any excess epoxy. Subsequently, the curing process continued at atmospheric pressure and temperature for five days to ensure a strong bond. The cured block was machined into cuboidal shapes with a length and width of 65 mm and a thickness ranging from 6 to 8 mm.

The cured samples were carefully lapped on both sides, taking care to prevent delamination due to surface forces between the flat surfaces and the layers of the sample. To address this concern, lapping was minimized, and tolerances were slightly relaxed, accepting a parallelism of 30 μm for the layered composites. As for the cover plates and flyer, a parallelism of 10 μm was deemed acceptable. The flatness of the samples, cover plates, and flyers was assessed using a dial gauge from Mitutoyo Measuring Instruments Co. Ltd.

To match the material of the flyer plate, a 1 mm thick cover plate made of the same material (Cu) was chosen. Once the cover plate, specimen, and flyer met the required criteria of parallelism and flatness, a manganin stress gauge (MicroMeasurements LM-SS-025CH-048) was positioned at the center between the cover plate and the target, referred to as the front gauge. To ensure insulation between the cover plate and specimen, the gauge was encapsulated in a 50 μm Mylar sheet. A second gauge was placed at the back of the specimen, with a Mylar sheet for insulation, and a 3 mm thick PMMA backing plate was attached behind it; this gauge was termed the back gauge. Special care was taken while positioning the manganin gauge to ensure that its active area spanned both the Cu and PMMA regions of the target, maintaining consistent readings throughout the study. Furthermore, both the front and rear gauges were carefully aligned to ensure that they lay on the same axis, ensuring accuracy and uniformity in the measurements. Finally, a 6 mm thick PMMA window was attached to the PMMA backing plate to prevent early release waves from the free surface affecting the stress wave profile. All components were securely bonded together using the previously mentioned two-part epoxy. The complete procedure for assembling the samples took place within a sample holder and a meticulously clean environment to prevent any contamination from dust. Subsequently, the target assembly was positioned within the gas gun to ensure the alignment of the target for a planar impact during the experiment. An illustrative view of the sample assembly for the plate-impact test, inclusive of the flyer, is presented in Fig. 1.

Cu and PMMA were chosen based on their well-defined nature in the shock community and the substantial difference in material impedance, which significantly decreases transmitted stress.²⁶ They have a sonic impedance mismatch ratio of 0.743 as reported by Chen and Chandra.³⁶ The structure of layered composites at several orientations is shown in Fig. 2. It should be noted that the orientation angle is named based on the orientation of Cu and PMMA with respect to the direction of impact. The sample ID indicates the material utilized, followed by the orientation and enclosed in brackets, denoting samples with similar orientations. For instance, CP30(C) signifies the Cu material (C), PMMA (P), and a 30° orientation, with the letter within brackets distinguishing between samples of the same orientation, with “C” representing the third sample at a 30° orientation.

In a plate-impact experiment, the projectile is propelled through the barrel using a pre-compressed helium gas. The gas pressure is carefully selected based on the desired impact velocity and the mass of the projectile to achieve precise experimental conditions. The collision between the flyer and the target results in the generation of planar shock waves that propagate through both materials. To ensure this, the target was carefully aligned in the target chamber with an anticipated alignment of <1 milliradian. For a clearer understanding of the gas gun setup, please refer to Fig. 3, which illustrates a typical gas gun setup and its various components.

Two sets of trigger pins were precisely inserted in front of the target with a measured distance between them. These pins served the dual purpose of triggering the pulse power supply and measuring the impact velocity. It is worth noting that the impact velocity was also measured using a laser-based velocimeter measurement system (VMS2000B) supplied by SYMES. The pulse power supply used to excite the manganin gauges was provided by Dynasen, Inc. (Model CK2-50/0.050-300). The pulse power supply delivered power to the gauges for a duration of 180 μs, which allowed sufficient time to obtain readings from the gauges before they ceased functioning. The trigger pins closest to the cover plate were strategically positioned at a calculated distance to activate the pulse power supply at least 30 μs before impact to minimize noise resulting from the discharge of the power supply’s capacitor. All data were recorded using Tektronix MSO4104 and Tektronix DPO7354C oscilloscopes, utilizing their full bandwidth and resolution capabilities. The calibration of the manganin gauges was carried out following the procedure outlined by Rosenberg et al.³⁷ 

Two-dimensional finite element simulations were performed using the LS-DYNA solver, with LS-PrePost utilized for pre-processing, model setup, and post-analysis. The dimensions of all simulated components were directly based on the measured thicknesses of the flyer plate, the cover plate, the target and its orientations, the backing plate and window, mirroring the parameters of our physical experiments. The primary objective of these simulations was to investigate the mechanisms governing heterogeneous shock structures, while validation against stress values recorded at the front and rear gauges was performed as a necessary prerequisite to establish confidence in the numerical model before further analysis.

For modeling, all components were represented using the SHELL element formulation, considering a plane strain condition with ELFORM 13. This choice was made after consideration of the component dimensions to ensure that results at the point of interest were not influenced by the release wave from the free surface of any component. This approach was designed to minimize computational time and reduce the number of elements involved. An element size of 0.1 mm was chosen to accurately capture the propagation of stress waves within the various components. Although further reducing the element size extended the computational time, it did not significantly impact the results at the point of interest. This was also reported by Fernando et al.,¹² who noted that a mesh size of less than 0.25 mm was sufficient to capture the Hugoniot Elastic Limit (HEL) of the material.

To define the contact between all parts, including the Cu and PMMA materials in the target, the CONTACT_2D_AUTOMATIC_SURFACE_TO_SURFACE card was used. It is noteworthy that nodes between any of the parts in contact were not merged. This choice was consistent with our experimental setup, where epoxy was employed to bond the parts together, but the strength of epoxy was not sufficient to withstand the stress generated by the impact velocity and the tensile stress resulting from the release, or reflected waves at the interfaces.

All shock computations were performed under the assumption of strengthless behavior, consistent with previous studies.^12,19,38 To model this material behavior, the MAT_ELASTIC_PLASTIC_HYDRO material card (010) was utilized. The hydrodynamic pressure was defined by the equation of state (EOS) of the material, and for all materials, the hydrodynamic pressure $(P= ρ 0. U S. u p)$ as a function of particle velocity $( u p)$⁠, shock wave velocity $( U S)$⁠, and density $( ρ 0)$ was described using EOS_GRUNEISEN. Table I provides the material parameters and EOS data for both Cu^39–41 and PMMA,^42,43 which were used in the analyses.

The results of eight plate-impact experiments, summarized in Table II, involved varying flyer velocities and utilizing different target thicknesses with various orientations. Upon impact between the flyer and the cover plate, the shock wave propagated through both materials. For all samples with layer angles less than 90°, the following observations were made: when the shock wave in the target reaches the interface between the cover plate and the PMMA section of the composite, a rarefaction wave is reflected back to the cover plate. Simultaneously, the shock wave is fully transmitted at the interfaces between the cover plate and the Cu section of the composite sample. This transmission resulted in a varying amplitude of the shock wave upon its entry into the angled target. Subsequently, a complex interaction (including geometric dispersion and dissipation) of waves occurred within the target as the shock wave traveled through it, forming a smeared/dispersed stress front before entering the PMMA backing plate, which is then captured by the rear gauge with finite rise time.

As the dispersed stress wave reaches the PMMA backing plate, a media transition occurs, altering the transmitted stress amplitude from the layered composite to the backing plate. This effect is particularly noticeable at the Cu interface at the target–backing plate interface. At this juncture, a portion of the wave is reflected back into the target, while the PMMA interface transmits the entirety of the stress into the backing plate. This makes use of a manganin gauge for such experiments more appropriate as the gauge average out the transmitted stress into the backing plate.

This process of wave transmission and subsequent rarefaction arises due to the difference in impedance between Cu and PMMA. This is further influenced by the geometric dispersion of the wave, which is caused by interfaces of Cu and PMMA situated at an angle to the direction of wave propagation.

In Fig. 4, the stress measured at the front and back of the sample is depicted using the front and back gauge for target CP20(B). It is important to highlight that the back gauge assesses stress at the sample-backing plate interface, specifically measuring the stress transmitted to the PMMA backing plate. Due to the layered composition of the target with significant layer thickness and impedance differences, it is crucial to note that the stress measured by the rear gauge cannot be extrapolated back to the stress within the sample, as demonstrated by Millett et al.²⁸ 

Experiments 1–6 correspond to those conducted at velocities ranging from 240 to 295 m/s, while Experiments 7 and 8 involve relatively higher velocities of 385 and 395 m/s, respectively, resulting in greater stress being induced into the sample.

Figure 5 presents a comparison of the stress profiles on the target–backing plate interface for CP30(C) and CP90(A). It should be noted that the time coordinate has been interpolated to match the arrival of wave for both experiments. Experiments for CP30(C) and CP90(A) were conducted at impact velocities of 285 and 260 m/s, with specimen thicknesses of 6.67 and 5.87 mm, respectively. Examining the profile of the incoming pulse behind the shock front, it is observed that the stress remains relatively constant for approximately 1.9 μs for CP30(C). The time is determined by the arrival of the release wave from the free surface of the window before the arrival of the release wave from the free surface of the 10 mm thick flyer. The heterogeneous nature of layered composite leads to stress oscillation, which complicates the record of the wave pulse for a significantly long duration. The failure of the gauge occurred before stress release was observed experimentally. Arrival of the unloading from the PMMA window is denoted by a vertically down arrow in Fig. 5, which matches with the time required by the release wave from the free surface of the window to reach at the back gauge location. In contrast, for CP90(A), where the Cu and PMMA sheets are oriented at 90° in the direction of impact, a stepped profile is evident. This stepped profile is attributed to the ringing of the stress wave between the layers, and the stress remains nearly constant for 0.5 μs before the arrival of the release wave from the separated layers of target caused by reverberation of waves within layers. The stepped profile for periodically layered structures has also been seen by Zhuang et al.¹⁶ and Oved et al.¹⁷ 

The most significant difference between the stress profile of CP30(C) and CP90(A) is manifested by the formation of a two-wave structure under shock when Cu and PMMA are oriented at a lower angle during rise. Moreover, the two-wave structure is observed in all the experiments with the lower layer orientation, i.e., CP0(A), CP0(B), CP20(A), CP20(B), and CP30(C). It is due to the high-speed propagation of sound disturbance along both Cu and PMMA individually at longitudinal sound wave speed $( c L)$⁠. This observation is consistent with findings by Yuan et al.,⁴⁴ who evaluated Ti–Fe and Mo–Fe as elastic–elastic bilaminate material pairs, as well as Al–PC as an elastic–viscoplastic bilaminate pair where they averaged wave speed for each layer with thickness of each layer. In the case of 0° orientation, the measured primary wave from the back gauge has a speed of 4.7 km/s, which corresponds to the longitudinal sound wave speed of Cu, as seen in Table I. This primary wave is termed as an elastic precursor.

The speed of the primary wave remained almost constant even with increasing impact velocity for the same angle. This signifies that the velocity of the precursor wave remains unaffected by the magnitude of the shock loading, primarily characterized by its predominantly elastic nature. As the orientation of sample increases from 0° to 20° and 30°, the speed of the primary wave tended to decrease and is attributed to the increasing number of interfaces along the direction of wave propagation with increasing angle. The presence of the precursor wave can also be observed in Fig. 4. Additionally, it is evident from the primary wave speed data for CP20(A) and CP20(B) in Table II, where the specimen thickness varied, that the primary wave speed decreased with increasing thickness. This decrease is attributed to the increase in the number of layers in the direction of impact with the increasing sample thickness. For CP0(A) and CP0(B), an increase in the impact velocity results in a corresponding rise in the longitudinal stress wave velocity, from 2.74 to 2.88 km/s, indicating that higher impact stress enhances wave propagation speed along the composite. In contrast, for CP20(A) and CP20(B), the longitudinal stress wave velocity remains nearly constant (2.78 vs 2.77 km/s), suggesting that at 20° fiber orientation, the effect of the impact velocity on the stress wave speed is less significant than at 0° orientation. This behavior is also influenced by the number of interfaces encountered along the wave propagation path, which is further dependent on the thickness of the composite.

With a further increase in orientation, the primary wave cannot be distinguished from the secondary wave, which is a high-amplitude stress wave propagating through the sample at a lower velocity. This can be visualized through wave propagation and mitigation mechanisms discussed in Sec. IV. Furthermore, the observed precursor is a non-negligible fraction of the total loading, and the loading of the sample should be considered a two-step process. In the direction of wave propagation for CP30(C), the shock wave encountered a difference in impedance. This caused the wave to reverberate obliquely between the Cu and PMMA, which smears the shock wave. Eventually, the reverberating wave superposed with the incoming shock wave, resulting in the reloading of the sample. This is why the stress reload had a lower gradient slope. This can be observed in the stress time graph marked as shock reloading in Fig. 5. On the experimental profile, after the shock jump, oscillations are recorded due to the heterogeneous nature of the sample, the oscillations were not periodic in nature, and in most of the cases not noticeable because of unavoidable noise caused by dynamic nature of the experiment.

While summarizing all the experimental data of layered composites at different orientations, it was observed that the rise time of the dispersed stress wave at the rear gauge increased from 250 ns [CP0(A)] to 803 ns [CP90(A)] as the orientation increased. This increase can be attributed to the phenomenon of the stress wave reverberation between layers, which becomes more pronounced with higher orientations. In other words, as the orientation increases, the number of layers through which the shock wave has to pass also increases, thereby dispersing the shock wave and leading to a longer rise time. The rise time is the time between 10% and 90% of an increase in longitudinal stress. As the rise time is directly linked to the strain rate experienced by the material, with the increase in orientation of the sample, the strain rate decreased within the sample. Figure 6(a) shows the rise time from the experiment with the impact velocity below 300 m/s. The rise time does not exhibit a linear relationship, as shown in Fig. 6(b). Notably, at lower angles, the rise time is relatively smaller. Conversely, at higher angles, the rise time increases significantly. Additionally, shock reloading is evident for 20° and 30° orientations based on the gauge trace. However, due to the early failure of the gauge at 45°, there is no confirmed evidence of stress reloading at this angle. Figure 6(b) also compares the experimental results with the results from simulation. The rise time from numerical modeling was slightly lower than that from experiments, and this can be attributed to the presence of mylar and epoxy in between the sample and the backing plate during the experiments, which was not considered for numerical modeling. This difference in rise time can also be observed in Fig. 4. These parameters, which include the amplitude of the elastic precursor and the stress wave, dispersed stress front rise time, normalized stress velocity, elastic wave arrival time, and wave pattern, were also used to validate the numerical model against the experiment. This validation was essential for analyzing the shock mitigation mechanism discussed in Sec. IV. Moreover, there appears to be a notable variance in the maximum stress values, with CP20(A) exhibiting lower stress levels compared to CP30(C). We attribute this distinction to variations in the impact velocity, thus resulting in differences in stress levels.

The differences observed between the numerical and experimental data at the front gauge of Fig. 4 can be attributed to several factors. The experimental data exhibit higher initial peak stress (∼3.0 GPa) and oscillations, which are not as pronounced in the simulation. These discrepancies may result from material model limitations in capturing the strain-rate-dependent behavior of layered composites, numerical damping effects, and localized wave interactions at material interfaces. Additionally, experimental uncertainties, such as gauge placement sensitivity, microstructural heterogeneities, and inherent noise in stress measurements, could contribute to the variations. The slight time delay in shock arrival compared to the simulation suggests differences in wave propagation speed, possibly influenced by assumptions in interface properties, material impedance mismatches, and the presence of epoxy and mylar layers in between the cover plate and the target. However, the back gauge results show strong agreement between numerical and experimental data, indicating that the model effectively captures the bulk shock propagation, while localized effects near the impact interface remain sources of discrepancy.

As observed in Table II, not all the impact velocities were the same, and the longitudinal stress wave velocity, which is the ratio of sample thickness to the time required by the wave to enter and exit the sample, is dependent on the velocity of impact if the material remains the same, as observed by other researchers.^{6,8,9,24,27,28,32,35,45,46} Figure 7 normalizes the stress wave velocity with the velocity of impact and plots it against different orientations. It can be observed that the normalized stress velocity decreases with increasing orientation. The decrease in the shock wave velocity can be attributed to the increased transit time of the shock wave within the sample. This increase in transit time is due to the growing number of different impedance interfaces in the direction of wave propagation as the orientation of the target increases. Additionally, the oblique interface scattering of the wave at the Cu–PMMA interface for 20°, 30°, 45°, and 60° target orientations contributes to this effect. Since normalized stress wave velocity serves as a key validation parameter, Fig. 7 presents a comparison between the modeling results and experimental data. This comparison aims to validate the numerical simulations while providing insights into wave propagation and mitigation mechanisms influenced by the orientation of layered composites. The results demonstrate strong agreement between the experimental findings and finite element simulations.

After validating the numerical modeling with the experimental results, numerical simulations were conducted to understand how the shock wave propagated through the layered composite upon impact. To this end, a 10 mm thick flyer, a 1 mm thick cover plate, and 6 mm thick target at different orientations, backed by a 12 mm thick backing plate, were modeled with a flyer impact velocity of 300 m/s. A thicker backing plate was chosen so that the release wave from the free surface of the backing plate does not affect the wave propagating within the sample. The flyer, the target, and the backing plate were modeled with the same material properties that were used for conducting numerical modeling for validation with the experiment in Sec. III. The numerical modeling has been explained in Sec. II D and material properties in Table I. Figure 8 shows the evolution and propagation of longitudinal stress upon impact in both flyer and target at different orientations with the same velocity of impact. For each orientation, five specific time points were selected for analysis. At 0.5 μs after impact, stress propagation was examined to ensure that the shock front is fully developed in the cover plate before propagating into the target. The analysis then focused on the wave propagation mechanics within the target, particularly the effects of impedance mismatch in both the transverse and impact directions on shock wave behavior and attenuation. Additionally, by evaluating longitudinal stress contours, the arrival of both the elastic precursor and stress waves at the target–backing plate interface was identified, along with the instant when the stress amplitude reached its peak. Moreover, Fig. 9 presents stress levels through the thickness of the target along the centerline, corresponding to the time depicted in the longitudinal stress contour in Fig. 8. This helps in better understanding of a mitigation mechanism with the help of layered samples at different orientations.

As discussed in this section upon impact, an elastic wave is developed in both target and flyer, which moves faster than the high-amplitude stress wave. The elastic wave is clearly visible in a lower orientation with a stress amplitude lower than 0.1 GPa, which is different for Cu and PMMA. The wave appears to move faster in Cu than in PMMA as the velocity of an elastic wave is higher for Cu than PMMA. This can be clearly observed in Fig. 8 where the elastic precursor wave is denoted by EP, which is followed by a high-amplitude stress wave (SW) at 0.5 μs after impact for 0° orientation. During the experiment at a 0° orientation, the gauge recorded a faster-moving EP originating from Cu. In this scenario, there was no alteration in the medium affecting the elastic wave in the direction of impact. The velocity of the recorded precursor wave matched the longitudinal sound wave velocity of Cu, which is 4.7 km/s. As the sample orientation increases from 0°, the EP encounters a change in the impedance of the medium at the interface. This change causes oblique scattering of the wave. This effect is further influenced by the variation in elastic wave velocities across different media. Due to the angled layering, not all incoming elastic waves encounter a change in the medium simultaneously, leading to a gradual transition in the wave velocity. As a result, the precursor wave velocity decreases with increasing orientation. This trend is evident in Table II, where the primary wave velocity consistently decreases as the orientation increases from 0° to 20° and then to 30°. Additionally, numerical simulations in Fig. 8 (arrival of compression stress) further support this observation, showing that the arrival time of the elastic precursor at the interface between the angled target and the backing plate increases with orientation, indicating a slower elastic precursor as fiber orientation increases.

Following the elastic wave, a slower-moving higher amplitude stress wave becomes apparent, as clearly illustrated in both Figs. 8 and 9, exhibiting a higher amplitude than the elastic wave. The shock wave generated after impact undergoes two simultaneous scenarios. Firstly, there is a change in impedance between the cover plate and the target at the PMMA face. Additionally, there is a difference in impedance between the Cu and PMMA layers of the target in the transverse direction as the shock wave propagates through the target, along with discrepancies in impedance between layers at an angle in the direction of impact.

Upon impact, as soon as the shock is generated in the cover plate, it propagates into the target. At the interface between the cover plate and the target, a portion of the wave is transmitted to the target, while another portion is reflected back to the cover plate from the PMMA face of the target, dividing the shock pulse between Cu and PMMA for orientations less than 90°, where both Cu and PMMA are present at the interface. However, for a 90° orientation, since the cover plate and the first layer of the sample share the same impedance, no wave is reflected back to the cover plate until the wave reaches the Cu and PMMA interface of the target in the direction of impact.

As the shock wave progresses through the target, it encounters impedance mismatches in the transverse direction, resulting in a series of reflections and transmissions within the target. As Cu has a higher impedance than PMMA, the reflected wave at the Cu–PMMA interface generates a slight tensile stress within the Cu layer. Although the tensile strength is lower than the spall strength of Cu, preventing spallation, this phenomenon is evident at 0.7 μs for all orientations except 90°, denoted by “T” in Fig. 8, with Fig. 9(a) illustrating the stress levels at that specific time through the thickness of the target. This reflected tensile wave helps in stress relaxation within the target. This series of tension and compression waves traveling through the target disperses or dissipates the shock wave. In simpler terms, the high-amplitude stress wave, initially a shock wave, transitions into a stress wave with a definite rise time and a reduced amplitude as it moves through the target.

It is crucial to note that for angles greater than 0°, the tensile region is a combined effect of layer impedance mismatch in the transverse direction and the presence of different impedance interfaces at an angle in the direction of impact, causing a series of internal reflections and transmissions of the wave leading to oblique interface scattering. The oblique scattered wave, carrying substantial local shear stress, plays a pivotal role in the evolution of the shock structure. Ravichandra et al.⁴⁶ have also reported the impact of oblique scattering on the evolution of a shock structure, particularly in particulate composites. In the case of a 90° orientation, where alternate layers of Cu and PMMA are stacked consecutively, a reverberation and ringing effect of the wave is observed, denoted by “R” in Fig. 8 at 1 μs. This reverberation causes a series of tension and compression within the target, resulting in substantial fluctuations in stress levels as the stress wave propagates, as depicted in Fig. 9(e). This phenomenon has been extensively explained in prior research.^{6,8,13,14,16,17,36,47} Consequently, it leads to a stepped wave profile, as evident in Fig. 5 for the CP90(A) sample.

The stress propagating in the target experiences dispersion, dissipation, and superposition, causing a delayed rise time of the stress wave profile and a consequent decrease in the strain rate with increasing orientation. However, as the number of interfaces increases with orientation, i.e., for 30°, 45°, 60°, and 90° targets, the stress encounters multiple interfaces in the direction of impact, leading to superposition and an increase in stress within the sample.

Plate-impact experiments were conducted with periodically layered Cu and PMMA composites at various orientations. Numerical simulations were carried out to compliment the experimental results. The main findings are outlined below:

1. Due to the heterogeneity in the target, a high-velocity two-part wave propagates along the target at lower orientations, exhibiting a velocity equal to or near the longitudinal sound speed $( c L)$ of Cu, indicating an elastic nature.

2. The velocity of the elastic precursor remains unchanged when the target is oriented at 0°, as there is no alteration in impedance in the direction of impact, regardless of the impact velocity. However, as the target orientation and the sample thickness increase, the number of interfaces with distinct properties also increases. This results in a reduction in the velocity of the precursor wave, which is further influenced by oblique interference scattering at the interface of Cu–PMMA inside the target.

3. The rise time of the shock increases as the orientation angle increases, leading to a decrease in the strain rate within the target material. Additionally, there is a reduction in the shock wave velocity and an increase in the stress amplitude, accompanied by the disappearance of the elastic precursor as the orientation increases.

4. To elucidate the scattering mechanisms arising from the changing orientation of the target, a series of finite element simulations were performed on periodically layered Cu and PMMA target materials at five different orientations, all with the same target thickness and the impact velocity. The simulations revealed a pattern of compressive and tensile stresses at the Cu–PMMA interfaces, providing an explanation for the extended rise time, reduction of the elastic precursor, and an increased stress amplitude at higher orientations. The presence of interfaces at an angle induces oblique scattering of shock waves. Furthermore, the tensile wave formed due to interference scattering alleviates stress in the sample, and these dissipative mechanisms contribute to the development of shock structures.

A combination of experimental and numerical modeling offers a unique perspective on understanding stress wave propagation in layered composites. This approach highlights the significance of impedance mismatch, geometric dispersion, and oblique scattering mechanisms in aiding shock wave dispersion and dissipation within the structure by orienting them at different angles.

The authors acknowledge the University of New South Wales (UNSW) at the Australian Defense Force Academy (ADFA), Australia for their Tuition Fee Scholarship (No. TFS-5306952). The authors also acknowledge Dr. Jianshen Wang for helping us operate the Gas Gun Facility and conducting experiments.

The authors have no conflicts to disclose.

Suman Shah: Conceptualization (equal); Data curation (equal); Formal analysis (equal); Writing – original draft (equal). Paul J. Hazell: Conceptualization (equal); Formal analysis (equal); Supervision (equal); Writing – review & editing (equal). Hongxu Wang: Conceptualization (equal); Data curation (equal); Investigation (equal); Supervision (equal); Writing – review & editing (equal). Juan P. Escobedo: Conceptualization (equal); Data curation (equal); Formal analysis (equal); Writing – review & editing (equal).

The data that support the findings of this study are available from the corresponding author upon reasonable request.