A microphysically based material model for the dynamic inelastic response of a brittle material is developed. The progressive loss of strength as well as the post-failure response of a granular material with friction are included. Crack instability conditions (an inelastic surface in stress space) and inelastic strains are obtained by considering the response of individual microcracks to an applied stress field. The assumptions of material isotropy and an exponential distribution for the crack radius are invoked to provide a tractable formulation. The constitutive model requires a minimal number of physical parameters, is compatible with a previously developed ductile fracture model [J. Appl. Phys. 64, 6699 (1988)] that utilizes inelastic surfaces, and can be formulated as an efficient, robust numerical algorithm for use in three-dimensional computer codes. The material model is implemented into a Lagrangian computer formulation for the demonstration of material response to dynamic loading conditions. Comparisons with one-dimensional, uniaxial impact experiments are provided.

We have developed a model for the finite deformation thermomechanical response of α-cyclotrimethylene trinitramine (RDX). Our model accounts for nonlinear thermoelastic lattice deformation through a free energy-based equation of state developed by Cawkwell et al. (2016) in combination with temperature and pressure dependent elastic constants, as well as dislocation-mediated plastic slip on a set of slip systems motivated by experimental observation. The kinetics of crystal plasticity are modeled using the Orowan equation relating slip rate to dislocation density and the dislocation velocity developed by Austin and McDowell (2011), which naturally accounts for transition from thermally-activated to dislocation drag limited regimes. Evolution of dislocation density is specified in terms of local ordinary differential equations reflecting dislocation-dislocation interactions. The paper presents details of the theory and parameterization of the model, followed by discussion of simulations of flyer plate impact experiments. Impact conditions explored within this combined simulation and experimental effort span shock pressures ranging from 1 to 3 GPa for four crystallographic orientations and multiple specimen thicknesses. Simulation results generated using this model are shown to be in strong agreement with velocimetry measurements from the corresponding plate impact experiments. Finally, simulation results are used to motivate conclusions about the nature of dislocation-mediated plasticity in RDX.

A mathematical model of tensile plasticity and void growth based on the Gurson flow surface and associated flow law is developed and applied to the problem of ductile fracture under general tensile loading conditions. The flow surface defines the plastic strain components in the tensile region; conditions of fracture are defined in terms of the plastic deformational strain, porosity, and the ratio of mean stress to shear stress, p/τ. This model reduces to the Carroll and Holt [J. Appl. Phys. 43, 759 (1972)] tensile threshold pressure for void growth, and to the Rice and Tracey [J. Mech. Phys. Solids 17, 201 (1969)] expression relating the fractional change in void radius to the incremental plastic deformational strain and p/τ in a triaxial tensile stress field. The model has sufficient generality to represent plastic flow and fracture in notched and smooth tensile bars as well as in uniaxial-strain spallation tests. One- and two-dimensional finite-difference calculations demonstrate this capability.

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A rate-dependent constitutive model for the dynamic deformation of ductile materials is developed. The model introduces a physical length scale into the equations governing the progressive failure of materials due to void growth. Consequently, mesh sensitivity or localization problems inherent to rate-independent models are precluded. The model is implemented into an explicit, finite-difference computer code. The insensitivity of the model to changes in the mesh size is demonstrated. Comparisons are provided between numerical simulations and data for uniaxial impact experiments. Excellent agreement is established between the final porosity levels and the width of the damage zone. Also, excellent agreement is provided for the stress histories, including the peak stress values and the spall signal.