A generalised phase field model for fatigue crack growth in elastic-plastic solids with an efficient monolithic solver

TL;DR

This paper introduces a comprehensive phase field model for fatigue crack growth in elastic-plastic metals, featuring various degradation functions, multiple constitutive theories, and an efficient monolithic solver, validated through diverse 2D and 3D simulations.

Contribution

It develops a versatile phase field framework for fatigue crack prediction, integrating multiple material models and an efficient solver, with open-source implementation.

Findings

The monolithic solver outperforms staggered approaches.

Different fatigue degradation functions influence crack growth predictions.

The framework accurately models complex geometries and cyclic deformation behaviors.

Abstract

We present a generalised phase field-based formulation for predicting fatigue crack growth in metals. The theoretical framework aims at covering a wide range of material behaviour. Different fatigue degradation functions are considered and their influence is benchmarked against experiments. The phase field constitutive theory accommodates the so-called AT1, AT2 and phase field-cohesive zone (PF-CZM) models. In regards to material deformation, both non-linear kinematic and isotropic hardening are considered, as well as the combination of the two. Moreover, a monolithic solution scheme based on quasi-Newton algorithms is presented and shown to significantly outperform staggered approaches. The potential of the computational framework is demonstrated by investigating several 2D and 3D boundary value problems of particular interest. Constitutive and numerical choices are compared and insight is gained into their differences and similarities. The framework enables predicting fatigue crack growth in arbitrary geometries and for materials exhibiting complex (cyclic) deformation and damage responses. The finite element code developed is made freely available at www.empaneda.com/codes.