Analytical verification of FFT-based micromechanical simulations near an elliptical crack tip by using composite voxels

Abstract

In this paper, we make use of composite voxels in elasto-viscoplastic formulations based on fast Fourier transforms (EVPFFT) to calculate the stress field around an elliptical crack. The predicted stress field at the vicinity of the crack is verified against recently developed analytical solutions. The representation of an elliptical crack in the image-based method is stair-stepped, resulting in oscillations that are mitigated by the use of partially-filled, i.e. composite voxels. Dependencies of the oscillations in the predicted stress fields based on minor changes in the crack size crack size and aspect ratio are discussed and quantified. New understanding is gained of the factors that affect the oscillations, such as the aspect ratio of the ellipse, and the effect of minor changes in the crack interface location. The results show that the use of composite voxels significantly reduces the spurious oscillations in predicted stress fields, and consequently improves the agreement between the EVPFFT simulations and analytical solutions.