Bayesian inference and GPSR-based void nucleation probability model for polycrystalline Al alloys for spall prediction

Abstract

Spallation is a mechanism of dynamic fracture in materials that occurs when a compressive shock reflects from a free surface as a tensile wave, causing nucleation and growth of spall voids. Predicting the conditions under which spall voids nucleate is an important aspect of designing materials to resist spall failure. This paper describes a computational approach involving porous crystal plasticity modeling and Bayesian inference to predict void nucleation in polycrystalline metals, which can lead to spall. The model has three basic components. The first is a unified porous crystal plasticity finite element model (CPFEM) that (i) covers a wide range of strain rates by incorporating thermally-activated and drag-dominated glide of dislocations causing slip, and (ii) predicts porosity evolution in image-based micromechanical simulations. The second component involves a concurrent model that embeds a 3D statistically-equivalent representative volume element (SERVE) modeled by the crystal plasticity FEM in an exterior domain modeled by continuum plasticity, to handle spurious effects associated with the impact boundary conditions. The third component is a probabilistic model for void nucleation under dynamic loading, utilizing Bayesian inference and genetic programming symbolic regression (GPSR), where nucleation is assumed to be a limiting state of the void evolution process, corresponding to a near-zero initial void volume fraction with a positive void growth rate. The paper illustrates the use of this model by predicting the conditions for void nucleation in a polycrystalline aluminum alloy 7085-T711 under dynamic loading conditions. By accounting for complex phenomena like stress wave propagation, drag effects on plastic slip rates, and void nucleation and growth, the methodology developed in this work provides a powerful tool for determining void nucleation evolution in polycrystalline metals under dynamic loading conditions leading to spallation.