Phase field fracture in elastoplastic solids: a stress-state, strain-rate, and orientation dependent model in explicit dynamics and its applications to additively manufactured metals

Abstract

Phase field models have gained increasing popularity in analysing fracture behaviour of materials. However, few studies have been explored to simulate dynamic ductile fracture to date. This study aims to develop a phase field framework that considers strain rate, stress state, and orientation dependent ductile fracture under dynamic loading. Firstly, the governing equations of displacement and phase fields are formulated within an explicit finite element framework. Secondly, constitutive relations are established using a hypoelastic-plasticity framework, encompassing the influence of material orientation and strain rate on both plasticity and fracture initiation. Stress state dependent fracture initiation is also considered. Thirdly, the finite element implementation and corotational formulation of constitutive equations are derived. Finally, to validate the proposed model, additively manufactured samples, including material-level and crack propagation specimens, are tested under dynamic loading conditions. Overall, the proposed phase field model can properly reproduce the experimental force-displacement curves and crack paths. Uniaxial tension tests reveal that a higher strain rate can lead to a higher hardening curve and reduced ductility. Other material specimens further demonstrate the model's capability to predict stress state and orientation dependent dynamic fracture. To simulate dynamic crack paths accurately, it is necessary to consider anisotropic fracture initiation. Lastly, the phase field model was applied for the first time to predict the dynamic response of triply periodic minimal surface (TPMS) structures. Dynamic crack patterns were effectively captured, and the fracture mechanisms were thoroughly analysed. This study provides an explicit phase field framework for dynamic ductile fracture, with applications to additively manufactured materials and structures.