A rate-dependent implicit gradient damage model with energy limiter: Ductile fracture analysis and determination of the physical length scale

Abstract

This work presents an implicit gradient-enhanced damage theory for failure in elastoplastic solids under the quasi-static loading condition. Our previous rate-independent gradient-enhanced damage formulation based on the energy limiter concept for brittle fracture in (Tran, Bui et al, CMAME 413:116123, 2023) is extended to ductile damage analysis with the consideration of rate-dependent crack growth characteristics. The present development contains a system of equilibrium and rate-dependent gradient crack evolution equations that describe the deformation of the body and rate-dependent evolution of the smeared damage in metals, respectively. For the nonlocal damage law, it has almost the same form as the one in our mentioned reference, except for the introduced rate-dependent crack growth term. Consistently with the energy limiter idea for fracture analysis, the material constitutive elastoplastic stress–strain relation is derived from the energy limiter formulation developed for ductile crack growth modeling with the von Mises plasticity criterion for an isotropic body under the small strain regime. This study, other than numerical experiments, will present a complete procedure to determine all input parameters used in the current theory for ductile failure analysis including the value of the length scale from reference experimental tests. To the best knowledge of the authors, it will show, for the first time in the literature, that the length scale is an actual physical scalar of the simulated problem and could be estimated from experiments. On the numerical side, ductile failure analyses under the standard finite element method (FEM) with the aid of an iterative staggered algorithm with both two-dimensional (2D) plane strain and general three-dimensional (3D) crack-growth problems are conducted to reveal the performance and capability of the gradient damage formulation based on the energy limiter concept for fracture in metals.