On the accuracy of spectral solvers for micromechanics based fatigue modeling

TL;DR

This paper introduces a FFT-based micromechanical fatigue modeling framework that offers comparable accuracy to FEM while significantly reducing computational costs, enabling efficient prediction of fatigue life in polycrystals.

Contribution

The paper develops a variational FFT approach with a novel projection operator for improved microfield fidelity, providing an efficient alternative to FEM for fatigue modeling.

Findings

FFT framework achieves similar macroscopic fatigue predictions as FEM.

Microfield differences decrease with a discrete projection operator.

Fatigue life estimates differ by around 15% from FEM.

Abstract

A framework based on FFT is proposed for micromechanical fatigue modeling of polycrystals as alternative to the Finite Element method (FEM). The variational FFT approach is used with a crystal plasticity model for the cyclic behavior of the grains introduced through a FEM material subroutine, in particular an Abaqus umat. The framework also includes an alternative projection operator based on discrete differentiation to improve the microfield fidelity allowing to include second phases. The accuracy and efficiency of the FFT framework for microstructure sensitive fatigue prediction are assessed by comparing with FEM. The macroscopic cyclic response of a polycrystal obtained with both methods were indistinguishable, irrespective of the number of cycles. The microscopic fields presented small differences that decrease when using the discrete projection operator, which indeed allowed simulating accurately microstructures containing very stiff particles. Finally, the maximum differences in the fatigue life estimation from the microfields respect FEM were around 15% . In summary, this framework allows predicting fatigue life with a similar accuracy than using FEM but strongly reducing the computational cost.