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 [1, 2] 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.

A microstructure-based model is presented to predict the fatigue life of polycrystalline metallic alloys which present a bilinear Coffin-Manson relationship. The model is based in the determination of the maximum value of a fatigue indicator parameter obtained from the plastic energy dissipated by cycle in the microstructure. The fatigue indicator parameter was obtained by means of the computational homogenization of a representative volume element of the microstructure using a crystal-plasticity finite element model. The microstructure-based model was applied to predict the low cyclic fatigue behavior of IN718 alloy at 400• C which exhibits a bilinear Coffin-Manson relationship under the assumption that this behavior is triggered by a transition from highly localized plasticity at low cyclic strain ranges to more homogeneous deformation at high cyclic strain ranges. The model predictions were in very good agreement with the experimental results for a wide range of cyclic strain ranges and two strain ratios (R ε = 0 and -1) and corroborated the initial hypothesis. Moreover, they provided a micromechanical explanation for the influence of the strain ratio on the fatigue life at low cyclic strain

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Summary A new algorithm is proposed to impose a macroscopic stress or mixed stress/deformation gradient history in the context of nonlinear Galerkin‐based fast Fourier transform homogenization. The method proposed is based on the definition of a modified projection operator in which the null frequencies enforce the type of control (stress or strain) for each component of either the macroscopic first Piola stress or the deformation gradient. The resulting problem is solved exactly as the original variational method, and it does not require additional iterations compared to the strain control version, neither in the linear iterative solver nor in the Newton scheme. The efficiency of the proposed method is demonstrated with a series of numerical examples, including a polycrystal and a particle‐reinforced hyperelastic material.