Dynamic Behavior of Materials, Volume 1

Engineering equipment that uses the principles of longitudinal stress wave propagation often utilizes long slender rods to accommodate long-duration stress pulses. Such designs demand larger footprint and higher cost of infrastructure. To remedy this situation, a revolutionary and innovative design concept called “millipede bar” or “stress waveguide” is being proposed. The concept is introduced in this chapter with preliminary results.

Hierarchical reentrant honeycombs (H-ReHs) with a 2nd order triangular hierarchy, an emerging type of lightweight but robust structures, have exhibited prominent energy absorption performance under quasi-static compression. However, due to the structural strain rate effect as well as the viscoelastic nature of the printing material, the crushing behavior of H-ReHs under the dynamic loading condition could be completely different from the quasi-static scenario. Therefore, it is necessary to investigate the crushing behavior of H-ReHs under dynamic impacts, the real loading condition in crashworthiness applications. In this study, the dynamic responses of H-ReHs are characterized by a drop tower apparatus and compared with the quasi-static responses. The results show that the linear elastic and nonlinear post-buckling behaviors of the H-ReHs exhibit different levels of strain rate sensitivity. The strain rate-dependent behaviors are attributed to the micro-inertia effect and the localized deformation modes of the 2nd order triangular hierarchy. In addition, the energy absorption capacity of H-ReHs under dynamic impacts can reach two orders of magnitude higher than that of the quasi-static one. These findings revealed the relationship between the dynamic crushing behaviors of H-ReHs and the structural heterogeneity of the hierarchical structure, which provides a design paradigm for lightweight but robust structures.

Treating Kevlar fabric with nanoparticles is found to augment its mechanical properties. This could lead to more lightweight yet flexible armors for specialized applications. In this study, the ballistic performance of neat and silica nanoparticle-treated Kevlar (SNK) fabrics with various percentages by weight of nanoparticle treatment and number of layers is experimentally evaluated. A colloid-based treatment procedure is used to impregnate dry silica nanoparticles into the fabric. The fabric samples are evaluated using a compressed air gun as per a test methodology adapted from NIJ standard 0108.01. Both penetrative and non-penetrative cases are examined. Addition of nanoparticles improved the fabric’s ballistic performance by providing about a 17% mass advantage (due to three less layers) for the 40 wt.% SNK vis-à-vis neat Kevlar for the non-penetrative case. SEM imaging reveals that at higher treatment levels, the nanoparticles tend to agglomerate in the interstitial spaces of yarn crossover points, which helps better engage secondary yarns away from the impact location of the projectile. Inspecting the back-face damaged zone areas for penetrative cases shows a strong positive correlation with nanoparticle treatment level, indicating that secondary yarns away from the primary zone are engaged in the impact mitigation mechanism for SNK. A semiempirical model is developed to capture and predict the influence of the treatment level and the number of layers on the kinetic energy dissipated by SNK fabrics. The flexibility of SNK fabrics was evaluated using a fixed cantilever length test. The measured tip deflection angle decreases from 33° for the neat fabric to 19° for the 40 wt.% SNK fabric. Although the addition of nanoparticles does diminish the flexibility of the neat fabric, the SNK fabric retains sufficient flexibility to have significant deflection under its self-weight. Using digital image analysis, the deflection curves for the samples are approximated using those for a cantilevered beam with uniform distributed loading. The educed flexural rigidities range from 48.9 Nm² for the neat fabric to 113.7 Nm² for the 40 wt.% SNK. Treating the fabric with nanoparticles tends to restrict the rotational degree of freedom at yarn crossover points to a greater extent, leading to higher flexural rigidity. Further investigations are underway to ascertain the influence of nanoparticle addition on frictional mechanisms using dynamic yarn pullout tests.

Structures often fail under combined tension and shear loads, and hence, it is critical to understand the mixed-mode fracture behavior of materials. In this work, the dynamic mixed-mode fracture of soda-lime glass (SLG) was experimentally investigated using the full-field optical method—digital gradient sensing (DGS). Freestanding single-edge notched specimens were subjected to reverse impact loading using a modified Hopkinson pressure bar. By eccentrically loading the specimens parallel to the initial notch, various mode mixities, from pure mode-I to nearly pure mode-II conditions, were achieved by changing the amount of eccentricity. Ultrahigh-speed photography was utilized in conjunction with DGS methodology to measure the angular deflection of light rays that are proportional to in-plane stress gradients in two orthogonal directions. In this ongoing research, mode-I and mode-II stress intensity factor histories prior to and at crack initiation will be evaluated in the next phase by performing an over-deterministic least squares analysis on optically measured full-field data. From the critical stress intensity factors at crack initiation, a fracture envelope for SLG encompassing different mode mixities will be developed. From the fractured samples, kink angles will be measured and compared with established fracture criteria.

Cone cylinders measuring 25 mm in diameter and weighing 108 g were shot into dense silica sand beds, mostly at 200 m/s, using a vertical-firing 75-mm diameter compressed-air gun. Velocity-time records were obtained with a multichannel homodyne photon Doppler velocimeter (PDV). Good values for deceleration were obtained below about 150 m/s. In terms of Poncelet parameters, the Poncelet drag coefficient for dense sand was bivalued, being 2.0 above about 80 m/s and 1.5 below that, and was unaffected by saturation. It was about 1.0 for medium dense sand. Values of the R term were 250–450 kPa.

Polymers are widely used as damping materials in vibration and impact applications. Liquid crystal elastomers (LCEs) are a unique class of polymers that may offer the potential for enhanced energy absorption capacity under impact conditions over conventional polymers due to their ability to align the nematic phase during loading. Being a relatively new material, the high rate compressive properties of LCEs have been minimally studied. Here, we investigated the high strain rate compression behavior of different solid LCEs, including cast polydomain and 3D-printed, preferentially oriented monodomain samples. Direct ink write (DIW) 3D printed samples allow unique sample designs, namely, a specific orientation of mesogens with respect to the loading direction. Loading the sample in different orientations can induce mesogen rotation during mechanical loading and subsequently different stress-strain responses under impact. We also used a reference polymer, bisphenol-A (BPA) cross-linked resin, to contrast LCE behavior with conventional elastomer behavior.

This work presents a new experimental configuration for studying material behavior under extreme thermomechanical conditions. Deformation strains up to 10, strain rates up to 10⁶ 1/s, and temperatures close to melting are achievable. The new configuration makes a rigid and hard tool strike a specimen that protrudes from the surface of a substrate. The fin-like specimen is deformed in simple shear by the fast-moving tool. The particular geometry of the specimen creates a shear band that travels nearly one-dimensionally across the fin, from the point of impact. The one-dimensional shear band is characterized by uniform stress, strain, strain rate, and temperature. The configuration is an attractive platform for the accurate development of constitutive models, under simultaneous extreme strain and strain rate. The deformation force can be measured with simple devices. This paper presents a proof of concept for the platform. The deformation is modeled using high-resolution finite element analysis. Deformation force, stress, strain, strain rate, and temperature are obtained from this numerical experiment. Simple analytical models are fitted to the data to infer the constitutive model of the material. The inferred constitutive model is compared to the one given as input to the finite element experiment. The comparisons show minimal deviations, which indicate that real experiments should produce highly accurate flow stress measurements, if the shear band propagates one-dimensionally. The numerical experiments were performed using the Johnson-Cook model for AISI 4340. It is important to note that the numerical experiments resulted in adiabatic shear bands without material damage criteria.

A comprehensive study of the mechanical response of a 316 stainless steel is presented. The split-Hopkinson bar technique was used to evaluate the mechanical behavior at dynamic strain rates of 500 s⁻¹, 1500 s⁻¹, and 3000 s⁻¹ and temperatures of 22 °C and 300 °C under tension and compression loading, while the Drop-Hopkinson bar was used to characterize the tension behavior at an intermediate strain rate of 200 s⁻¹. The experimental results show that the tension and compression flow stress are reasonably symmetric, exhibit positive strain rate sensitivity, and are inversely dependent on temperature. The true failure strain was determined by measuring the minimum diameter of the post-test tension specimen. The 316 stainless steel exhibited a ductile response, and the true failure strain increased with increasing temperature and decreased with increasing strain rate.

Understanding the dynamic failure mechanisms of shale is critical for optimizing oil and gas extraction from unconventional resources. This work presents the experimental investigation of the mechanism of nonlocal damage distribution in shale material under dynamic loading conditions. A circular disk specimen is subjected to local biaxial loading conditions and tested under two different experimental configurations. First, dynamic damage is investigated when the material is under tensile load along the bedding direction and compressive load perpendicular to the bedding direction. Second, the disk is rotated 90°, and the damage is investigated when a compressive load is applied in the bedding direction and a tensile load in the perpendicular direction. The specimens are dynamically loaded using a split Hopkinson pressure bar (SHPB). A noncontact optical technique, digital image correlation, is utilized to monitor the full-field strain and nonlocal damage initiation. As a result, two different dynamic damages are observed and discussed. The experimental setup and the nonlocal damage as a function of the bedding direction are also discussed.

In recent studies, laser powder bed fusion (LPBF) additive manufacturing has created structural beam components possessing internal pockets containing unfused metallic powder. Compared to fully fused beams, these pocketed beams have demonstrated a remarkable improvement in damping performance, suppressing vibrations by as much as 95%. This suggests that internal geometries containing unfused powder can be a significant design feature to reduce vibration and extend the life of structural components. However, additional studies and improvements are needed before these designs can become widespread. For example, it has been observed that the unfused powder begins to fuse to the walls of the pockets when subjected to high strain loading, reducing their damping abilities. This study investigates the effects of the thickness of the beams and the pocket’s axial location in LPBF nickel-based alloy 718 beams on their damping sustainability after being subjected to high strain loads. The beams are subjected to successive resonance dwells with increasing strain amplitude. After each dwell, the damping performance is assessed via frequency sweeps. Results from this study indicate that the decrease in damping performance follows the same relative trend regardless of the beam thickness. The axial location of the pockets affects the initial damping and also influences when the powder begins to fuse.

Concrete is a widely used building material and is integral in the construction of protective structures used by the U.S. Army. These protective structures are designed to resist extreme loading such as blast and penetration, which requires an accurate assessment of concrete strength. The curing and subsequent drying process of massive concrete structures is a slow phenomenon. This leads to the assumption that massive concrete structures, such as personnel bunkers, may remain saturated at their core throughout their lifetime, long after the exterior has dried. Preliminary data exists concerning saturation ratio effects on high-pressure triaxial loading of conventional strength concrete (CSC), which showed that increasing the degree of saturation of CSC lowered the proportional strength of the material at high confining pressures. In order to further expand on this area of research, depth of penetration experiments were performed using CSC targets at three highly controlled saturation ratios: ambient cured, saturated, and oven-dried. The depth of penetration experiments are ideal experiments for probing the saturation effects on the concrete due to the high pressures induced by impact. Spherical projectiles will be fired at velocities ranging between 343 m/s and 6.8 km/s, and trends will be identified between the degree of saturation and the depth of penetration and overall crater size.

Polymer-bonded explosives (PBXs) contain explosive crystals bonded together by a polymeric binder and are widely used in extreme loading conditions such as rocket propellants and explosive munitions because of their high performance and low sensitivity. PBXs typically constitute 80–95% of energetic crystals and 5–20% of a soft polymer binder. The particle size of crystals has a significant effect on the mechanical properties of most polymer particulate composites. In this paper, the effect of particle size on the deformation behavior of PBX under dynamic loading is investigated. This study involves testing polymer-bonded sugar (PBS) samples, a well-known mechanical simulant of PBXs, with four different crystal sizes – coarse, intermediate, fine, and superfine – with corresponding crystal sizes of 600–850 μm, 425–600 μm, 212–425 μm, and 100–212 μm, respectively. A dynamic compression load is applied to these samples using a split Hopkinson pressure bar (SHPB). The macroscale and local dynamic deformation of the samples are captured by taking a series of images of the samples as they deform using a high-speed camera. From the macroscale experiment, it was observed that as the crystal size increases from superfine crystal size to coarse crystal size, the ultimate compressive stress of the PBS decreases. The mesoscale experiment shows that the local von Mises strain field of PBS for different crystal size specimens is different. The von Mises strain field in higher crystal size specimens such as coarse crystal size specimens is highly localized in the polymer-rich regions while more dispersed across the specimens with lower crystal size, particularly superfine crystal size. This study would give an in-depth knowledge and understanding of how the crystal size affects the deformation mechanics of energetic and other particulate polymer composites.

CuCrZr alloys achieve high mechanical properties by thermal (e.g., supersaturated temper and aging), mechanical (e.g., ECAP), or thermomechanical treatments (solution annealing, cold working, and aging). This alloy can be considered a functional material, and it can be exploited in different application fields, thanks to a combination of thermal, electrical, and strength properties. In this work, tensile tests at different strain rates have been conducted on CuCrZr specimens produced by additive manufacturing. As-built and heat-treated conditions have been considered. The quasi-static tests have been performed by an electromechanical testing machine, while the high strain rate tests have been performed by a direct-tension split Hopkinson bar. The geometry of the samples has been selected based on the requirements of the dynamic tests, and the same geometry was used in quasi-static tests for the sake of comparison. High-speed imaging has been used to capture the real strain of the specimens. The results showed a limited positive strain rate sensitivity in terms of flow stress for as-built conditions, whereas negative strain rate sensitivity was observed for the heat-treated samples, but positive sensitivity in terms of ductility was observed for as-built, whereas uncertain results occurred in the case of heat-treated material.

The operation of a vertical-firing ballistic range is described, along with instrumentation to produce high-resolution velocity-time measurements of projectile penetration in sand targets. The range comprises a single-stage gas gun with a 14.45-mm-inner-diameter smooth-bore barrel and a maximum operating pressure of 300 bar. The launch mechanism is a combination of an electropneumatic solenoid valve and a fast-acting shuttle valve. The gun loading curve is determined for projectiles having a mass of approximately 35 g. The launcher efficiency, defined as the ratio of the actual muzzle velocity to the theoretical prediction, assuming the isentropic expansion of the compressed helium gas, is calculated as a function of the reservoir pressure. A conventional photon Doppler velocimeter (PDV) was designed and assembled on the range to directly measure the projectile velocity-time history during flight and penetration into soil targets. Magnetic sensors were used to trigger the data acquisition system. Additional magnetic sensors were assembled to measure the projectile muzzle velocity when steel projectiles were used. Loose- and Densely-packed soil targets were prepared by means of pluviation. Results from shots into loose and dense sand were analyzed, demonstrating the significance of the soil target packing in the penetration resistance of sand.

Results of a high strain rate unconfined compression test on a clay soil sample and corresponding finite element simulations are presented. A drop tower was adapted to drop weights onto a saturated cylindrical kaolin clay soil sample. The engineering stress-strain response was found using piezoelectric load cells and a high-speed camera. Remolded cylindrical clay samples were prepared by the static compaction of hydrated clay in a cylindrical mold. The drop tower experiment featured a mass of 13.4 kg dropped from a height of 1.5 m, resulting in an impact velocity of 4.15 m/s and a constant strain rate of 56/s on the soil sample. Results of the high strain rate experiments revealed that the saturated kaolin clay strength, as quantified using the unconfined compressive strength, exhibited significant strain-rate dependence. An approximately 100% increase in the unconfined compressive strength was observed at a strain rate of 56/s compared to the quasi-static strength. Three-dimensional finite element simulations of the drop tower setup were then used to replicate the observed response. A penalty contact algorithm, available in the commercial finite element code Abaqus/Explicit, was used to simulate the soil-loading ram interactions. Elastic-purely plastic extended Tresca constitutive equations with strain rate and strain softening inclusions were used to capture the strain rate dependence of clay. A comparison of the experiments and the simulations revealed that the modeling procedures and the constitutive model used were able to capture the salient features of the response observed from the drop tower experiments.

A miniature tensile Kolsky bar has been developed. The bars are steel and 1.6 mm in diameter. Because of the small size, each bar is instrumented with a normal displacement interferometer instead of strain gages. The projectile is accelerated with a spring to avoid the complexities of building a gas gun on this small scale. The bar is used to test pure aluminum samples with gage lengths of 1.0 mm and rectangular cross sections of 90 μm by 200 μm. A simple gripping design is used where the dog-bone-shaped sample is placed into recesses that are machined into the ends of the bars; the sample is then secured in place with glue. A high-speed camera is used to observe the sample deformation and failure.

Structural adhesives are important structural elements in modern engineering design, particularly for the bonding of composites and dissimilar materials. Structural adhesives enable light-weighted structures and have long supported the use of organic structural designs common in aerospace. These applications often require designed performance under high strain-rate loading, such as crash and impact. Design and simulation with structural adhesives under these high-rate conditions require reliable mechanical failure data.

High-rate tensile failure testing of bonds, such as butt-tension and napkin ring tests, are particularly important characterizations, and several methods of preparing and loading test specimens have been proposed. However, it is not clear how specimen design and test apparatus influence measured adhesive behavior for nominally identical bond geometry.

In order to understand these effects, we evaluate three different test configurations using identical bond geometries and similar engineering strain rates. The first configuration is a conventional napkin ring specimen loaded using a Kolsky bar. The second configuration is a blister-style specimen—similar to those studied by Gollins et al. and Yildiz et al. and previously reported by Carpenter et al.—loaded using a Kolsky bar. Finally, the same blister-style specimen is evaluated using a drop tower. It is hypothesized that differences in load-train compliance and, in the case of the drop tower, apparatus dynamics will substantially influence test results. Understanding the influence of the test method on tensile failure results is critical to the development of predictive adhesive failure models and the validity of data comparisons between different test configurations.

Density-graded cellular polymers have unique mechanical properties, leading to exceptional impact protection. Furthermore, they can be designed for custom requirements. The current study is part of an effort to develop efficient impact-resistant structures. The impact response of density-graded 3D Voronoi cellular structures is studied and compared to its uniform density counterpart. The specimens are fabricated via photopolymer jetting technology, an additive manufacturing technique that enables high accuracy of intricate features and complex shapes that are distinctive of Voronoi cellular structures. The density gradation is achieved by changing the cell size along the impact direction. The foam specimens are impinged by a freely falling rigid mass with the help of a drop tower that allows determining the response at intermediate strain-rate regime. A series of images are captured using a high-speed camera to capture the deformation mechanisms of the specimen, and a piezo-based load cell is used to measure the dynamic force. The performance is analyzed by studying the energy absorption and transmitted force as a function of density gradation. It is found that density-graded Voronoi cellular structures can be designed to mitigate a wide range of impact conditions.

The response of materials to shock loading is important to understand for a variety of applications. When shock physics emerged during and after WWII, direct explosive loading or explosively driven plate impact was the primary tool for these studies. Subsequent decades have seen the widespread use of large caliber guns for plate impact studies, laser-shock facilities, and pulsed power facilities.

INL currently lacks a gun suitable for plate impact or explosives casting and machining facilities; however, it does possess explosives use and handling capabilities. An option for performing plate impact experiments was needed. Therefore, continuum scale models were utilized to explore a few simple donor-acceptor explosive plane wave lens designs, one of which could be hand packed with plastic explosives to launch flyer plates. 2D simulations were performed to study different geometries in an effort to minimize the difference in shock arrival across the central portion of a small copper flyer plate. A shock wave arrival time difference under 50 ns across 50% of the center of the flyer was achieved with a few designs. This work summarizes the computational models and results.

At the earliest timescale after projectile impact on woven composites, stress waves propagate out from the area of impact both radially and through the thickness. At a later timescale, momentum transfer leads to the formation of a deformation cone. Studies of wave propagation in composites typically consider the radial stress wave propagation and the formation of the transverse deformation cone but neglect through-thickness stress waves. This chapter investigates the effects of through-thickness stress wave propagation on damage and delamination under a projectile in a woven composite. This investigation uses a mesoscale model of plain weave composite, validated using 1D stress wave theory. This model uses a cohesive traction-separation law to simulate delamination cracking, inelastic progressive damage composite tows, and rate-dependent matrix. The 1D stress wave theory is generalized for any number of layers. A finite element modeling approach is validated using the generalized 1D theory.

In the present study, shock wave experiments are conducted on General Carbide cemented tungsten carbide with 3.7 wt.% cobalt binder to determine its shock-induced compression behavior up to 100 GPa. The measured wave profiles indicate the cemented tungsten carbide undergoes elastic-plastic deformation during shock compression. A three-stage particle velocity profile is observed in the experiments – an initial elastic rise to the Hugoniot elastic limit (HEL), an elastic-plastic ramp indicating substantial post-yield hardening, and finally a rise to the peak shocked Hugoniot state. The results of the experiments are used to determine the HEL, the shock velocity (U_s) vs. particle velocity (u_p) Hugoniot relation, and the longitudinal stress (σ_x) vs. specific volume (V) curve for the samples. The HEL of the material was determined to lie between 4.41 and 4.58 GPa. The U_s − u_p relation was determined to be U_s = 4.97 + 1.457u_p for particle velocities greater than 0.75 km/s. The measured plastic shock velocities for particle velocities less than 0.7 km/s were found to be larger than those predicted using the linear U_s − u_p Hugoniot relationship, indicating the cemented WC samples to preserve substantial shear strength in the post-yield deformation region. No phase transformation was observed up to 100 GPa.