On the accuracy of spectral solvers for micromechanics based fatigue modeling

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 (de Geus et al. in Comput Methods Appl Mech Eng 318:412–430, 2017; Zeman et al. in Int J Numer Methods Eng 110:903–926, 2017) is used with a crystal plasticity model for the cyclic behavior of the grains that is 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.