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Abstract

Fatigue is a process occurring on different length scales, from atomic rearrangements leading to delamination and nucleation of nanovoids, over the microstructural length scale on which damage accumulates and finally leads to a mechanically short crack whose growth can be described by fracture mechanical concepts on the macroscale. Although multiple continuum fatigue models exist, most of them are concerned with the growth of a preexisting crack under cyclic loading, i.e. those models neglect the crack initiation phase. However, under high-cycle fatigue (HCF) conditions the mechanisms of crack initiation can be dominating the lifetime, even in technical materials where a finite density of microcracks can be expected. However, the growth of such microcracks can not be described by fracture mechanical concepts. Therefore, pure crack growth models cannot be applied to determine fatigue liftetimes under HCF conditions.

To account for accumulation of plastic strains during cyclic loading and the connected evolution of internal stresses, we implement different constitutive relations for cyclic plasticity in a finite element model on the microstructural scale. It is assumed that the accumulation of irreversible strains that strongly dependents on local stress amplifiers, like inclusions, microcracks, or grain boundaries, governs the length in time of the crack initiation phase. On the microscale we study a heterogeneous material consisting of a matrix with cyclic plasticity and stiff or compliant elastic inclusions. The accumulation of plastic strains in the vicinity of such inclusions is calculated with conventional von Mises plasticity as well as crystal plasticity models. Both constitutive relations take into account isotropic as well as kinematic hardening. However, the crystal plasticity model additionally is sensitive to anisotropy due to plastic slip and cyclic accumulation of plastic deformation on crystallographic slip systems. A simple failure hypothesis on the basis of accumulation of equivalent plastic strain during cyclic loading is proposed and applied to calculate the number of cycles for crack initiation and hence the fatigue lifetime. The shape of the inclusions is varied to cover several realistic scenarios and to determine the most severe defect under HCF conditions. The results of conventional plasticity and crystal plasticity are compared and thus the importance of considering the crystallographic nature of plastic slip for fatigue simulations on the microstructural scale is analyzed.