Integrating the Chaboche Hardening Model into Phase Field Frameworks: A Numerical Study of Fatigue Crack Growth in S275 Mild Steel

Abstract

In this research work, we present an implementation of the Chaboche hardening law within a phase field model to predict fatigue crack growth under cyclic plasticity in metals. The Chaboche model is particularly advantageous due to its ability to capture both isotropic and kinematic hardening behaviors, making it suitable for materials subjected to complex loading conditions. Our approach is based on a variational formulation of fracture, wherein we resolve an energy minimization problem that governs the evolution of cracks in materials. Consequently, we derive a coupled system of equations for both displacement and phase field variables, which is integrated into a nonlinear finite element procedure using a user element subroutine with the finite element software Abaqus. To validate our computational framework, we analyze several cyclic tests of mild steel S275 using the SAC 2000 loading protocol. The results demonstrate that the Chaboche hardening model effectively captures the material’s response to cyclic loading, revealing insights into the mechanisms of damage accumulation and crack propagation. We also explore the influence of varying hardening parameters on the stress-strain behavior during cyclic loading. This study not only enhances our understanding of fatigue crack growth in metals but also provides a robust computational tool for engineers and researchers working with materials subjected to cyclic loading conditions.