A mesh-independent, geometrically characteristic and thermodynamic ductile-damage model catalysed by the kinetics of mobile volumetric crystalline defects

Abstract

The article is aimed to address the mesh-dependent and related issues longstanding to damage modelling. The role of crystalline defects that carry out material plasticity is summarised by field quantities characterising the geometric feature of their induced deviatoric macroscopic deformation, while the inelastic volumetric deformation is represented by a measure of the local voiding state, which should be behind material damage. On top of that, the kinetics of mobile volumetric defects exemplified by vacancy and self-interstitial atom, whose evolution boosts damage development, is also formulated. With the interactions between such mobile volumetric defects and other defects modelled in analogy with chemical reaction, a thermodynamically consistent theory is derived, and a thermodynamically favourable path is identified for damage development catalysed by mobile volumetric defect, i.e., voids grow by absorbing vacancies and other atom-missing types of defects generated from nearby deviatoric defects. With numerical examples, we demonstrate the present theory’s capabilities of mimicking (rate-independent) ductile damage and fracture under an isothermal setting (a) without the introduction of artificial internal length scales, (b) without assigning any pre-cracks, (c) with the resulting finite element calculation freed from the restriction that the mesh size must be comparable to any (artificial) internal length scale parameters. Numerical examples on full-life predictions, from an intact state to the final failure, over mechanics performance of structures bearing certain degree of geometric complexity are also given.