Multi-scale spallation model for single-crystal ductile metals incorporating microscopic mechanism of void nucleation

Abstract

Spall strength characterizes the tensile performance of materials under high strain rates. However, theoretical prediction of the spall strength has long been a big challenge since it involves information on the damage evolution at multiple length scales. In this work, a multi-scale model is proposed for the spallation of single-crystal ductile metals, which includes both a microscopic model of damage nucleation and an effective correlation between the microscopic physical mechanisms and the macroscopic mechanical behaviors. An energy criterion to predict the threshold stress for damage nucleation is firstly proposed based on a near-realistic three-dimensional configuration of dislocation emission. The statistical characteristics of the damage nucleation threshold are analyzed, based on which a multi-scale spall model is proposed to couple the physical essence at the micro-scale to the macro-scale, revealing the influences of temperature, vacancy concentration, and strain rate on spall strength. An approximate form of the multi-scale model is proposed by dimensional analysis and reasonable approximation, which is consistent with the empirical model summarized from experimental results, and further deduced to a simple scaling law that predicts the transition in the strain rate-sensitivity of spall strength.