A gradient-enhanced formulation for thermoviscoplastic metals accounting for ductile damage

Abstract

In this work, we extend a gradient-enhancement formulation for ductile damage analysis to thermoviscoplastic metals. The original contribution of the study is the nonlocal extension of our previously developed thermoviscoplastic Gurson's model accounting for plastic work heat generation, thermal diffusion and void shearing mechanism. The gradient enrichment is applied to the porosity evolution equation by adding a nonlocal length scale parameter together with the Laplacian of the void volume fraction, following a void diffusion law. A mixed finite element formulation is used to discretize the system with an implicit time integration and a monolithic solution of the linearized system at every time step. Three ductile fracture problems involving plates under plane-strain conditions and tensile loading are simulated, in order to compare the local and nonlocal formulations. Results show that the nonlocal term delays the damage evolution and somewhat alleviates mesh sensitivity in terms of the stress-strain response and the porosity distribution along specific lines. Nevertheless, the most notable effect of the nonlocal formulation is the regularization (or smoothing) of the porosity field, reducing its gradients and mesh dependence, and leading to more consistent porosity contours. The choice of the nonlocal parameter is found to be dependent of the strain rate employed. • A gradient-enhanced thermoviscoplastic ductile damage formulation is proposed. • Coupling of Gurson's porous plasticity, void shearing mechanism, thermoviscoplasticity and thermal diffusion. • Three structural problems involving plates under plain strain assumption are numerically analyzed in detail. • The model is suitable to alleviate mesh dependence and to smooth the porosity field.