Numerical simulation of low cycle fatigue behavior, combining the phase-field method and the Armstrong-Frederick model

Abstract

The present work couples the phase field method of fracture to the Armstrong-Frederick model of plasticity with the kinematic hardening. The chosen approach inherits the advantages of both techniques and is aimed at the study of low cycle fatigue effects in ductile materials. However, the numerical implementation of this promising concept brings with it several challenges, such as the definition of a unique framework for both setups, the derivation of coupled evolution equations, the distinction between tension and compression mode and the development of a computationally efficient algorithm. In the approach developed, the derivation of evolution equations uses the minimum principle of the dissipation potential. This step requires the expression of the dissipation potential of the classic Armstrong-Frederick model in terms of the internal variable rates by using the Legendre transformation. The model is eventually implemented in the FE-program and applied in order to investigate the life-time of the cold-formed carbon steel and the cold-formed stainless steel.