Sidney Chocron

Modeling of Fabric Impact With High Speed Imaging and Nickel-Chromium Wires Validation

Ballistic tests were performed on single-yarn, single-layer and ten-layer targets of Kevlar® KM2 (600 and 850 denier), Dyneema® SK-65 and PBO® (500 denier). The objective was to develop data for validation of numerical models so, multiple diagnostic techniques were used: (1) ultra-high speed photography, (2) high-speed video and (3) nickel-chromium wire technique. These techniques allowed thorough validation of the numerical models through five different paths. The first validation set was at the yarn level, where the transverse wave propagation obtained with analytical and numerical simulations was compared to that obtained in the experiments. The second validation path was at the single-layer level: the propagation of the pyramidal wave observed with the high speed camera was compared to the numerical simulations. The third validation consisted of comparing, for the targets with ten layers, the pyramid apex and diagonal positions from tests and simulations. The fourth validation, which is probably the most relevant, consisted of comparing the numerical and experimental ballistic limits. Finally for the fifth validation set, nickel-chromium wires were used to record electronically the waves propagating in the fabrics. It is shown that for the three materials the waves recorded during the tests match well the waves predicted by the numerical model.

Why Impacted Yarns Break at Lower Speed Than Classical Theory Predicts

Fabrics are an extremely important element of body armors and other armors. Understanding fabrics requires understanding how yarns deform. Classical theory has shown very good agreement with the deformation of a single yarn when impacted. However, the speed at which a yarn would break based on this classical theory is not correct; it has been experimentally noted that yarns break when impacted at a lower velocity. This paper explores the mechanism of yarn breakage. The problem of the strike of a yarn by a flat-faced projectile is analytically solved for early times. It is rigorously demonstrated that when a flat-faced projectile strikes a yarn, the breaking speed will always be at least 11% less than the classical-theory result. It is further shown that when the yarn material in front of the projectile is “bounced” off the front surface due to the impact, that the breaking speed is further reduced. If the yarn bounces elastically off the surface due to the impact at twice the impact velocity (the theoretical maximum), there is a 40% reduction in the breaking speed of a yarn. A beautiful theory of yarn deformation under an applied boundary condition was developed by Smith [1,2]. This theory was developed in the context of impact on yarns. There has been extensive experimental work showing that the wave propagation speeds of the longitudinal and transverse waves and the subsequent deflections are well modeled by the theory. However, numerous researchers have realized that the yarn breaking speed inferred from the classical theory is larger than what is observed in experiment. Why are the impacted yarns breaking at lower speeds than the theory predicts? Most often yarns are impacted by fragment simulating projectiles or right circular cylinders. These projectiles have flat impact faces. In our computational investigation of this phenomenon, we have noticed that the flat face impact leads to a “bounce” of the yarn off the impact surface (Fig. 1). A longitudinal and transverse wave are produced in the yarn, originating at the impactor edges, traveling both outward away from the impactor and inward where the waves from opposing impactor edges. The waves meet at the geometric center of the yarn in front of the projectile; the stress and strain in the yarn double, leading to higher stresses. After this first wave effect, we also see, during more complicated wave interactions a small increase in stress until the material is relieved to the classical (Smith) solution stress at later time.

Impacts and Waves in Dyneema® HB80 Strips and Laminates

Single-yarn impact results have been reported by multiple authors in the past, providing insight on the fundamental physics involved in fabric impact. This insight allowed developing full fabric models that were able to reproduce properly wave propagation, deflection, and ballistic limits. This paper proposes a similar experimental methodology but for a specific composite material made of ultra-high molecular weight polyethylene. The presence of the polyurethane matrix in the composite is expected to slow down wave propagation. But the high-speed photographic tests reported in this paper indicate that wave propagation in strips and single-layer material is similar to that expected for dry fiber. An explanation is proposed for this unexpected result. This paper also reports the critical velocities (i.e., impact velocities that fail the fibers immediately) measured for the composite material and compares them to the velocities expected from the theory. The velocity is accurately predicted when taking into account wave interactions in front of the projectile. Finally, tests on multilayer composites are presented. In particular, a flash produced under the projectile during the first few microseconds was recorded with high-speed video cameras. A simplified study of the temperature increment upon impact indicates that the material may be reaching the autoignition point. This mechanism is speculated to be the origin of the flash systematically observed.

Analytical Model of the Confined Compression Test Used to Characterize Brittle Materials

Numerical and analytical simulations of projectiles penetrating brittle materials such as ceramics and glasses are a very challenging problem. The difficulty comes from the fact that the yield surface of brittle materials is not well characterized (or even defined), and the failure process may change the material properties. Recently, some works have shown that it is possible to characterize and find the constitutive equation for brittle materials using a confined compression test, i.e., a test where a cylindrical specimen, surrounded by a confining sleeve, is being compressed axially by a mechanical testing machine. This paper focuses on understanding the confined compression test by presenting an analytical model that explicitly solves for the stresses and strains in the sample and the sleeve, assuming the sleeve is elastic and the specimen is elastoplastic with a Drucker-Prager plasticity model. The first part of the paper briefly explains the experimental technique and how the stress-strain curves obtained during the test are interpreted. A simple and straightforward approach to obtain the constitutive model of the material is then presented. Finally, a full analytical model with explicit solution for displacements, strains, and stresses in the specimen and the sleeve is described. The advantage of the analytical model is that it gives a full understanding of the test, as well as information that can be useful when designing the test (e.g., displacements of the outer radius of the specimen).

A unified model for long-rod penetration in multiple metallic plates

Abstract The Walker–Anderson and Ravid–Bodner analytical models for penetration of projectiles in metallic plates are well known in the ballistics community. The Walker–Anderson model uses the centerline momentum balance in the projectile and target to calculate the penetration history into a semi-infinite medium, while the Ravid–Bodner model uses the upper bound theorem of plasticity theory modified to include dynamic effects. The Ravid–Bodner model also includes a rich selection of failure modes suitable for finite-thick metallic targets. In this paper a blended model is presented: momentum balance is used to calculate the semi-infinite portion penetration (before the back of the target plate begins to flow), and the Ravid–Bodner failure modes are used to determine projectile perforation. In addition, the model has been extended to handle multiple plate impact. Numerical simulations show that after target failure the projectile still continues to erode for some microseconds. This time has been estimated and incorporated into the model. Examples are presented for long-rod projectiles against thick and spaced-plate targets backed by a witness pack that is separated from the main target element(s) by an air gap. Agreement with results from numerical simulations is quite good.

Impact Experiments Into Borosilicate Glass at Three Scale Sizes

Abstract : Glass impact experiments were designed at three different scales--0.22-cal, 0.375-cal, and 0.50-cal--named after the diameter of the bullets. Four experimental series were conducted at the three scale sizes: 1) Lexan-only experiments; 2) monoblock glass experiments; 3) single impact bonded glass experiments, and 4) multi-hit experiments. The experiments were conducted to obtain residual velocity as a function of impact (striking) velocity, including sufficient partial penetrations to calculate a V50. The Vs - Vr data were fit to the Lambert equation, Eqn. (5), to obtain another estimate of V50. Eroded lengths of the bullets were also measured. The objective of the experiments was to investigate whether a time dependency exists in glass damage/failure for ballistic experiments, and if so, try to quantify this dependency. No scale effect was observed in experimental results for the Lexan-only experiments. But a variety of scale effects were observed in the glass impact experiments, suggesting that there exists a time dependency to failure that is important within the timeframe of ballistic events.

Numerical Simulations of the Penetration of Glass Using Two Pressure-Dependent Constitutive Models

Penetration of long gold (Au) rods into borosilicate glass was investigated experimentally as a function of impact velocity [1]. Flash radiography was used to measure the nose position and rod length as a function of time, and high-speed photography was used to measure the position of the failure front as a function of time. It was found that the failure front, which propagates at a speed much faster than the penetrating rod, quickly outdistances the projectile-target interface. Thus, except for the first few moments after impact, the rod presumably penetrates failed glass.

Mesoscale modeling of S-2 glass/SC-15 epoxy composites: Plain-weave architecture

S-2 glass composites can readily serve as backing materials for armor systems due to their light weight and tensile properties. However, high-fidelity ballistic modeling of these composites requires accurate predictions of their nonlinear deformation and failure behaviors, which can prove challenging. This paper describes simulations of a plain-weave S-2 glass composite at the mesoscale using a mesh geometry that individually models the S-2 glass yarns, epoxy resin matrix, and yarn/matrix interfaces as separate entities. Simulation results are compared to a wide variety of mechanical tests designed to measure the response of the composite to tension, shear, and delamination. Although the individual yarns, matrix, and interfaces are described using relatively simple material models, the overall composite model can accurately reproduce behaviors such as nonlinear deformation, yarn breakage, and delamination in both tension and shear.

Role of target strength in momentum enhancement

Experiments with small aluminum spheres striking 2024-T4 and 1100-O aluminum targets at velocities of 4 to 7 km/s have shown an interesting effect in terms of momentum enhancement. Momentum enhancement is the amount of extra momentum delivered to the target due to the ejecta thrown back along the projectiles path. Momentum enhancement is less for the softer 1100-O material, even though the craters are larger [1]. Thus, there is not a correlation between crater volume and ejecta momentum. When computations with hydrocodes are performed where the flow stress is adjusted with a constant-fracture-stress material failure model, this result is not replicated; rather, the opposite occurs in that reduced flow stress for the aluminum target leads to increased momentum enhancement [2]. This paper examines the effect of linking the flow stress behavior to the damage model by maintaining a strain energy to failure for the material. Given this link, the softer material has a larger strain to failure than the stronger...

Testing boron carbide under triaxial compression

This article focuses on the pressure dependence and summarizes the characterization work conducted on intact and predamaged specimens of boron carbide under confinement in a pressure vessel and in a thick steel sleeve. The failure curves obtained are presented, and the data compared to experimental data from the literature.