A variational phase-field framework for multiphysics modelling of degradation and stress corrosion cracking in biodegradable magnesium alloys

Biodegradable magnesium alloys have been developed as promising biomedical materials for temporary implants. To facilitate the development of implant design, it is essential to understand and quantify the corrosion behaviour of magnesium alloys under mixed chemo-mechanical loadings. In this study, a multiphase-field model is proposed based on the variational principle to capture the interactions between corrosion and ductile fracture in biodegradable magnesium alloys. Multiple order parameters are introduced to track the interfaces associated with crack propagation and magnesium dissolution. The deformation-fracture-corrosion interactions are considered in the energetic variational formulation with coupling functions. The governing equations are discretised using an incremental variational method and solved by a staggered scheme. Parametric studies on the coupling functions are performed to demonstrate the flexibility of the model. The proposed multiphase-field model is calibrated and validated by in vitro experiments with tensile specimens of rare-earth magnesium alloy WE43MEO. The experimental and computational results demonstrate that the proposed model can capture the degradation and stress corrosion cracking behaviours in the immersion tests and slow strain rate tensile-corrosion tests.