Predicting mesh-independent ballistic limits for heterogeneous targets by a nonlocal damage computational framework

During highly dynamic and ballistic loading processes, large inelastic deformation associated with high strain rates leads, for a broad class of heterogeneous materials, to degradation and failure by localized damage and fracture. However, as soon as material failure dominates a deformation process, the material increasingly displays strain softening and the finite element predictions of ballistic response are considerably affected by the mesh size. This gives rise to non-physical description of the ballistic behavior and mesh-dependent ballistic limit velocities that may mislead the design of ballistic resistant materials. This paper is concerned with the development and numerical implementation of a coupled thermo-hypoelasto-viscoplastic and thermo-viscodamage constitutive model within the laws of thermodynamics in which an intrinsic material length scale parameter is incorporated through the nonlocal gradient-dependent damage approach. This model is intended for impact and ballistic penetration and perforation problems of heterogeneous metallic targets such as metal matrix composites with dispersed particles at decreasing microstructural length scales. An evolution equation for the material length scale as a function of the material microstructural features (e.g. mean grain size in polycrystalline materials or particle size and inter-particle spacing in metal matrix composites), course of plastic deformation, strain hardening, strain-rate hardening, and temperature is presented. It is shown through simulating plugging failure in ballistic penetration of high-strength steel targets of different thicknesses by a hard blunt projectile that the length scale parameter plays the role of a localization limiter allowing one to obtain meaningful values for the ballistic limit velocity independent of the finite element mesh density. It is also shown that a local damage model incorporating viscosity and heat conduction as localization limiters, which are known to implicitly introduce length scale parameters, is insufficient in illuminating the mesh sensitivity at impact velocities close to the ballistic limit and that the mesh sensitivity increases as the target thickness increases. Therefore, the proposed nonlocal damage model leads to an improvement in the modeling and numerical simulation of high velocity impact related problems.