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

Abstract

We present a generalised phase field-based formulation for predicting fatigue\ncrack growth in metals. The theoretical framework aims at covering a wide range\nof material behaviour. Different fatigue degradation functions are considered\nand their influence is benchmarked against experiments. The phase field\nconstitutive theory accommodates the so-called AT1, AT2 and phase\nfield-cohesive zone (PF-CZM) models. In regards to material deformation, both\nnon-linear kinematic and isotropic hardening are considered, as well as the\ncombination of the two. Moreover, a monolithic solution scheme based on\nquasi-Newton algorithms is presented and shown to significantly outperform\nstaggered approaches. The potential of the computational framework is\ndemonstrated by investigating several 2D and 3D boundary value problems of\nparticular interest. Constitutive and numerical choices are compared and\ninsight is gained into their differences and similarities. The framework\nenables predicting fatigue crack growth in arbitrary geometries and for\nmaterials exhibiting complex (cyclic) deformation and damage responses. The\nfinite element code developed is made freely available at\nwww.empaneda.com/codes.\n