A damage to crack transition framework for ductile materials

The simulation of the whole ductile fracture from the large-scale yielding to the localised crack initiation and propagation, is still challenging for scientists and engineers, especially under complex loading conditions. In this work, we develop a computationally efficient and energetically consistent damage to crack transition framework to address this issue. In addition, we provide an appropriate porous material model as well as the related calibration procedure.

Practically, an implicit non-local damage model represents the first diffuse damage stage, possibly beyond the softening onset. Once a crack insertion criterion is satisfied, a crack is introduced using a cohesive band model (CBM). This latter, contrarily to a cohesive zone model (CZM), accounts for 3D stress states during the crack opening which is mandatory in order to predict accurate results. The framework is implemented inside a Discontinuous Galerkin (DG) framework following the extrinsic CZM/DG formalism. Those choices ensure to the scheme interesting numerical properties demonstrated in this work: robustness upon failure, mesh-independence, energetic consistency and a reasonable trade-off between computational efficiency and simplicity.

The framework is first applied to a damage-enhanced elastic behaviour where the cohesive band thickness, the only introduced numerical parameter by the CBM, is determined from energetic considerations. It is then extended to the context of large strains and porous plasticity. Therewith, a micromechanics model including void nucleation, growth and coalescence, is presented. A suited crack insertion criterion is derived from a micro-mechanics coalescence model. In both cases, the numerical model is validated using experimental results from the literature.

Finally, the damage to crack transition model is validated with respect to an extensive experimental campaign studying a high-strength steel. The material and numerical models parameters are calibrated following micromechanics-based arguments. The framework, hence calibrated, is shown to be able to accurately predict the material behaviour until complete failure under different stress conditions and to include failure anisotropy. In particular, the complex experimental crack path on round bars and on grooved plates in plane strain is reproduced.