FFT-based investigation of the shear stress distribution in face-centered cubic polycrystals. (October 2022)

• Record Type: Journal Article
• Authors: Gehrig, Flavia; Wicht, Daniel; Krause, Maximilian; Böhlke, Thomas
• Is Part Of: International journal of plasticity. Volume 157(2022)
• Publication Date: 2022-10
• Subjects: Crystal plasticity -- Grain boundaries -- Spatial stress distribution -- Elastic anisotropy -- Fast Fourier transformation -- Maximum entropy method; Plasticity -- Periodicals; Plasticité -- Périodiques; Plasticity; Periodicals; 620.11233
• DOI: 10.1016/j.ijplas.2022.103369
• Languages: English
• ISSNs: 0749-6419

Abstract

Abstract: The onset of nonlinear effects in metals, such as plasticity and damage, is strongly influenced by the heterogeneous stress distribution at the grain level. This work is devoted to studying the local stress distribution in fcc polycrystals using FFT-based solvers. In particular, we focus on the distribution of shear stresses resolved in the slip systems as the critical driving force for plastic deformations. Specific grain orientations with respect to load direction are investigated in the linear elastic regime and at incipient plastic deformations based on a large ensemble of microstructures. The elastic anisotropy of the single crystal is found to have a crucial influence on the scatter of the stress distribution, whereas the Young's modulus in the respective crystal direction governs the mean stress in the grain. It is further demonstrated that, for higher anisotropy, the shear stresses deviate from the normal distribution and are better approximated by a log-normal fit. Comparing the full-field simulations to the Maximum Entropy Method (MEM), reveals that the MEM provides an excellent prediction up to the second statistical moment in the linear elastic range. In a study on the spatial distribution of shear stresses, the grain boundary is identified as a region of pronounced stress fluctuations and as the starting point of yielding during the elastic–plastic transition. Highlights: Large-scale (200 realizations) FFT-based investigation of local stress distribution. Statistical variance of stresses in a grain increases for higher anisotropy. Local shear stress distributions are not exact Gaussian normal distributions. Elastic MEM predicts grain stress means and covariances close to full-field results. Plastification starts close to the grain boundary, expanding inwards from there.