# An efficient phase-field model for fatigue fracture in ductile materials

## TL;DR

This paper introduces a computationally efficient phase-field model for fatigue fracture in ductile materials, combining phenomenological and durability concepts to simulate crack initiation and growth under cyclic loading.

## Contribution

It presents a novel, low-cost phase-field model that captures fatigue crack behavior in ductile materials using a simplified, phenomenological approach.

## Key findings

- Model accurately predicts fatigue crack initiation and growth.
- Reproduces Paris law behavior in fatigue crack propagation.
- Requires only one load cycle increment, reducing computational effort.

## Abstract

Fatigue fracture in ductile materials, e. g. metals, is caused by cyclic plasticity. Especially regarding the high numbers of load cycles, plastic material models resolving the full loading path are computationally very demanding. Herein, a model with particularly small computational effort is presented. It provides a macroscopic, phenomenological description of fatigue fracture by combining the phase-field method for brittle fracture with a classic durability concept. A local lifetime variable is obtained, which degrades the fracture resistance progressively. By deriving the stress-strain path from cyclic material characteristics, only one increment per load cycle is needed at maximum. The model allows to describe fatigue crack initiation, propagation and residual fracture and can reproduce Paris behaviour.