Modeling diffusive phase transformation and fracture in viscoplastic materials

In recent years, the phase-field method has attracted a lot of attention and has emerged as one of the most efficient tools for modeling fracture and phase transformation. The phase-field method is based on the regularization of discontinuities which allows the resolution of complex problems using classical numerical methods. A multiphase-field model which is essential for describing crack propagation in non-static heterogeneous materials is still missing. In this work, we fill this gap by combining the fracture phase-field approach based on Griffith's theory with the phase-field approach for diffusive phase transformation in viscoplastic materials. Several benchmark examples of increasing complexity demonstrate, the effect of viscoplasticity and diffusive phase transformation on fracture behavior based on the critical loading, energy density until failure and crack topology. We show that viscoplastic activity at the crack tip mitigates the effect of pre-existing defects on mechanical strength. In a heterogeneous case, it is shown that viscoplastic activity introduces an intermediate fracture response between the reference behavior, which does not take into consideration the phase transformation-induced residual stresses, and the elastic behavior, which integrates these residual stresses by taking into account only the elasticity. The interaction between the heterogeneities and the crack topology is also highlighted.

Automated summary

The phase-field method is an efficient tool for modeling fracture and phase transformation. This study combines fracture phase-field approach with phase-field approach for diffusive phase transformation to describe crack propagation in non-static heterogeneous materials. The effects of viscoplasticity and diffusive phase transformation on fracture behavior are demonstrated using benchmark examples, including critical loading, energy density, and crack topology. The mitigation of pre-existing defects by viscoplastic activity at the crack tip is shown, as well as the intermediate fracture response introduced by viscoplastic activity in a heterogeneous case.