Phase-field models for ductile fatigue fracture

Abstract

Fatigue fracture is one of the main causes of failure in structures. However, the simulation of fatigue crack growth is computationally demanding due to the large number of load cycles involved. Metals in the low cycle fatigue range often show significant plastic zones at the crack tip, calling for elastic–plastic material models, which increase the computation time even further. In pursuit of a more efficient model, we propose a simplified phase-field model for ductile fatigue fracture, which indirectly accounts for plasticity within the fatigue damage accumulation. Additionally, a cycle-skipping approach is inherent to the concept, reducing computation time by up to several orders of magnitude. We show that the proposed model is in fact a direct simplification of a phase-field model with elastic–plastic material behavior.

We validate this simplified model in two ways: First, we show that it can reproduce the main characteristics of fatigue crack growth. Secondly, we compare it to a reference phase-field model with a conventional elastic–plastic material routine, nonlinear hardening and a fatigue variable based on the strain energy density. The comparison shows that for moderate load amplitudes, the simplified model approximates the stress state at the crack tip well. The same is true for size and shape of the plastic zone and the approximation of the crack driving force. The model’s limitations lie in the modeling of the stress redistribution due to plasticity. Both model variants are parametrized with experimentally determined values for elastic, plastic, fracture and fatigue properties of AA2024 T351 aluminum sheet material.