W. C. Bell

Material Modeling and Ballistic-Resistance Analysis of Armor-Grade Composites Reinforced with High-Performance Fibers

A new ballistic material model for 0°/90° cross-plied oriented ultra-high molecular weight (UHMW) polyethylene fiber-based armor-grade composite laminates has been constructed using open-literature data for the fiber and polymeric-matrix material properties and the general experimental/field-test observations regarding the deformation and failure modes in these types of materials. The present model is an extension of our recently developed unit cell-based ballistic material model for the same class of composites (M. Grujicic, G. Arakere, T. He,W.C. Bell, B. A. Cheeseman, C.-F. Yen, and B. Scott, A Ballistic Material Model for Cross-Plied Unidirectional Ultra-High Molecular-Weight Polyethylene Fiber-reinforced Armor-Grade Composites, Mater. Sci. Eng, A 2008, 498(1-2), p 231-241) which was found to be physically sound, but computationally not very efficient. The present model is constructed in such a way that it can be readily integrated into commercial finite element programs like ANSYS/Autodyn (ANSYS/Autodyn version 11.0, User Documentation, Century Dynamics Inc., a subsidiary of ANSYS Inc., 2007), as a User Material Subroutine. To validate the model, a series of transient nonlinear dynamics computational analyses of the transverse impact of armor-grade composite laminates with two types of bullets/projectiles is carried out and the computational results compared with their experimental counterparts. Relatively good agreement is found between the experiment and the computational analysis relative to: (a) the success of the armor panels of different areal densities in defeating the bullets at different initial bullet velocities; (b) postmortem spatial distribution of the damage modes and the extents within the panels; (c) the temporal evolution of the armor-panel back-face bulge; and (d) The existence of three distinct armor-penetration stages (i.e., an initial filament shearing/cutting dominated stage, an intermediate stage characterized by pronounced filament/matrix debonding/decohesion, and a final stage associated with the extensive filaments extension and armor-panel back-face bulging).

Filament-Level Modeling of Aramid-Based High-Performance Structural Materials

Molecular statics and molecular dynamics are employed to study the effects of various microstructural and topological defects (e.g., chain ends, axial chain misalignment, inorganic solvent impurities, and sheet stacking faults) on the strength, ductility, and stiffness of p-phenylene terephthalamide (PPTA) fibers/filaments. These fibers can be considered as prototypes for advanced high strength/high-stiffness fibers like Kevlar®, Twaron®, New Star®, etc. While modeling these fibers, it was taken into account that they are essentially crystalline materials consisting of stacks of sheets, with each sheet containing an array of nearly parallel hydrogen-bonded molecules/chains. The inter-sheet bonding, on the other hand, was considered as mainly being of van der Waals or p-electron character. The effects of various deviations of the PPTA fiber structure from that of the perfectly crystalline structure (i.e., microstructural/topological defects) on the material’s mechanical properties are then considered. The results obtained show that while the presence of these defects decreases all the mechanical properties of PPTA fibers, specific properties display an increased level of sensitivity to the presence of certain defects. For example, longitudinal tensile properties are found to be most sensitive to the presence of chain ends, in-sheet transverse properties to the presence of chain misalignments, while cross-sheet transverse properties are found to be most affected by the presence of sheet stacking faults.

Shock-Wave Attenuation and Energy-Dissipation Potential of Granular Materials

The propagation of uniaxial-stress planar shocks in granular materials is analyzed using a conventional shock-physics approach. Within this approach, both compression shocks and decompression waves are treated as (stress, specific volume, particle velocity, mass-based internal energy density, temperature, and mass-based entropy density) propagating discontinuities. In addition, the granular material is considered as being a continuum (i.e., no mesoscale features like grains, voids, and their agglomerates are considered). However, while the granular material is treated as a (smeared-out) continuum, it is recognized that it contains a solid constituent (parent matter), and that the structurodynamic properties (i.e., Equations of State (EOS) and Hugoniot relations) of the granular material are related to its parent matter. Three characteristic shock loading regimes of granular material are considered and, in each case, an analysis is carried out to elucidate shock attenuation and energy dissipation processes. In addition, an attempt is made to identify a metric (a combination of the material parameters) which quantifies the intrinsic ability of a granular material to attenuate a shock and dissipate the energy carried by the shock. Toward that end, the response of a typical granular material to a flat-topped compressive stress pulse is analyzed in each of the three shock loading regimes.

The effect of up‐armoring of the high‐mobility multi‐purpose wheeled vehicle (HMMWV) on the off‐road vehicle performance

Purpose – A parallel finite‐element/multi‐body‐dynamics investigation is carried out of the effect of up‐armoring on the off‐road performance of a prototypical high‐mobility multipurpose‐wheeled vehicle (HMMWV). The paper seeks to investigate the up‐armoring effect on the vehicle performance under the following off‐road maneuvers: straight‐line flatland braking; straight‐line off‐angle downhill braking; and sharp left turn.Design/methodology/approach – For each of the above‐mentioned maneuvers, the appropriate vehicle‐performance criteria are identified and the parameters used to quantify these criteria are defined and assessed. The ability of a computationally efficient multi‐body dynamics approach when combined with a detailed model for tire/soil interactions to yield results qualitatively and quantitatively consistent with their computational counterparts obtained using computationally quite costly finite element analyses is assessed.Findings – The computational results obtained clearly reveal the comp...

An Improved Mechanical Material Model for Ballistic Soda-Lime Glass

In our recent work (Grujicic et al., Int. J. Impact Eng., 2008), various open-literature experimental findings pertaining to the ballistic behavior of soda-lime glass were used to construct a simple, physically based, high strain rate, high-pressure, large-strain mechanical model for this material. The model was structured in such a way that it is suitable for direct incorporation into standard commercial transient non-linear dynamics finite element-based software packages like ANSYS/Autodyn (Century Dynamics Inc., 2007) or ABAQUS/Explicit (Dessault Systems, 2007). To validate the material model, a set of finite element analyses of the edge-on-impact tests was conducted and the results compared with their experimental counterparts obtained in the recent work of Strassburger et al. (Proceedings of the 23rd International Symposium on Ballistics, Spain, April 2007; Proceedings of the 22nd International Symposium on Ballistics, November 2005, Vancouver, Canada). In general, a good agreement was found between the computational and the experimental results relative to: (a) the front shapes and the propagation velocities of the longitudinal and transverse waves generated in the target during impact and (b) the front shapes and propagation velocities of a coherent-damage zone (a zone surrounding the projectile/target contact surface which contains numerous micron and submicron-size cracks). However, substantial computational analysis/experiment disagreements were found relative to the formation of crack centers, i.e. relative to the presence and distribution of isolated millimeter-size cracks nucleated ahead of the advancing coherent-damage zone front. In the present work, it was shown that these disagreements can be substantially reduced if the glass model (Grujicic et al., Int. J. Impact Eng., 2008) is advanced to include a simple macrocracking algorithm based on the linear elastic fracture mechanics.

A computational analysis of survivability of a pick‐up truck subjected to mine detonation loads

Purpose – The purpose of this paper is to analyze, computationally, the kinematic response (including large‐scale rotation and deformation, buckling, plastic yielding, failure initiation, fracture and fragmentation) of a pick‐up truck to the detonation of a landmine (shallow‐buried in one of six different soils, i.e. either sand, clay‐laden sand or sandy gravel, each in either dry or water‐saturated conditions, and detonated underneath the vehicle) using ANSYS/Autodyn, a general‐purpose transient non‐linear dynamics analysis software.Design/methodology/approach – The computational analysis, using ANSYS/Autodyn, a general‐purpose transient non‐linear dynamics analysis software, included the interactions of the gaseous detonation products and the sand ejecta with the vehicle and the transient non‐linear dynamics response of the vehicle.Findings – The results obtained clearly show the differences in the blast loads resulting from the landmine detonation in dry and saturated sand, as well as the associated ki...

Molecular-level simulations of shock generation and propagation in soda-lime glass

A non-equilibrium molecular dynamics method is employed to study the mechanical response of soda-lime glass (a material commonly used in transparent armor applications) when subjected to the loading conditions associated with the generation and propagation of planar shock waves. Specific attention is given to the identification and characterization of various (inelastic-deformation and energy-dissipation) molecular-level phenomena and processes taking place at, or in the vicinity of, the shock front. The results obtained revealed that the shock loading causes a 2-4% (shock strength-dependent) density increase. In addition, an increase in the average coordination number of the silicon atoms is observed along with the creation of smaller Si-O rings. These processes are associated with substantial energy absorption and dissipation and are believed to greatly influence the blast/ballistic impact mitigation potential of soda-lime glass. The present work was also aimed at the determination of the shock Hugoniot (i.e., a set of axial stress vs. density/specific-volume vs. internal energy vs. particle velocity vs. temperature) material states obtained in soda-lime glass after the passage of a shock wave of a given strength (as quantified by the shock speed). The availability of a shock Hugoniot is critical for construction of a high deformation-rate, large-strain, high pressure material model which can be used within a continuum-level computational analysis to capture the response of a soda-lime glass based laminated transparent armor structure (e.g., a military vehicle windshield, door window, etc.) to blast/ballistic impact loading.

The Effect of High-pressure Densification on Ballistic-penetration Resistance of a Soda-lime Glass

Molecular-level modelling and simulations of the high-pressure volumetric response and irreversible densification of a prototypical soda-lime glass are first employed. The molecular-simulation results obtained were next used to modify the pressure versus degree-of-compression (the negative of volumetric strain) and yield strength versus pressure relations in order to account for the effects of irreversible densification. These relations are next used to upgrade the equation of state and the strength constitutive laws of an existing material model for glass. This was followed by a set of transient non-linear dynamics calculations of the transverse impact of a glass test plate with a solid right-circular cylindrical steel projectile. The results obtained show that irreversible densification can provide only a minor improvement in the ballistic resistance of glass and only in the case of high-velocity (ca. 1000 m/s) projectiles. Furthermore, it was demonstrated that if the key irreversible compaction parameters can be adjusted by modifications in glass chemistry and microstructure, significant improvements in the glass ballistic resistance can be attained over a relatively wide range of projectile velocities.

Development, parameterization, and validation of a visco-plastic material model for sand with different levels of water saturation

A new material model for sand has been developed in order to include the effects of the deformation rate and the degree of saturation on the constitutive response of this material. The model is an extension of the original high strain-rate compaction model for sand developed by Laine and Sandvik and an elastic—visco-plastic material model for sand recently proposed by Tong and Tuan in which these effects were neglected. The new material model was parameterized using the available experimental data for sand with different levels of saturation tested mechanically at different strain rates. The model is next used, within a non-linear-dynamics transient computational analysis, to study: (a) various phenomena associated with the explosion of shallow-buried and ground-laid mines and (b) the dynamic behaviour of a vehicle during an off-road ride. The computational results are then compared with the corresponding experimental results. This comparison suggested that the newly developed material model for sand captures the essential features of the dynamic behaviour of sand with different levels of saturation when subjected to realistic high and low strain-rate loading conditions.

Molecular-Level Analysis of Shock-Wave Physics and Derivation of the Hugoniot Relations for Fused Silica

Equilibrium and non-equilibrium molecular-dynamics simulations are employed in this study to investigate various aspects of shock waves in fused silica (a pure SiO2 amorphous material used in transparent-armor applications). Equilibrium molecular-dynamics simulations are used first to validate that the initial (unshocked) fused silica possesses the appropriate mass density and microstructure (as characterized by its partial Si-Si, Si-O, and O-O radial distribution functions). Next, non-equilibrium molecular-dynamics simulations are employed, within a continuously contracting computational-cell scheme, to generate planar longitudinal (uniaxial motion) shocks of different strengths. By examining and quantifying the dynamics of shock-wave motion, the respective shock-Hugoniot relations (i.e., functional relations between various material-state variables in the material states produced by the shocks of different strengths) are determined. This methodology suggested that irreversible non-equilibrium deformation/damage processes play an important role in the mechanical response of fused silica to shock loading and that the “equilibrium” procedures for Hugoniot determination based on the equation of state and the Rankine-Hugoniot equation may not be fully justified. Finally, the non-equilibrium molecular-dynamics simulations were used to identify the main microstructure modifying/altering processes accompanying the shock-wave motion through fused silica.