FFT-based simulations of slip and kink bands formation in 3D polycrystals: Influence of strain gradient crystal plasticity

Abstract

The ability of softening strain gradient plasticity to simulate intragranular plastic slip localization modes called slip and kink bands, at is investigated at incipient plasticity. A strain gradient crystal plasticity model based on a quadratic energy contribution of the Nye tensor has been implemented within the massively parallel FFT-based solver AMITEX FFTP. It is shown that a classical evaluation of the double curl operator does not properly account for the backstress induced by GNDs in slip and kink bands. Consequently, a better suited differentiation operator is proposed for this purpose. Besides, four practical implementations of interface conditions at grain boundaries are implemented and discussed. It is demonstrated that these conditions have a strong influence on GND induced hardening but weakly affect the formation of slip localization patterns.A theoretical and numerical study of an idealized kink band shows that this modeling framework, contrary to classical crystal plasticity models, is able to capture their essential physical features. A quantitative analysis of high resolution 3D polycrystalline simulations, based on imaged processing and a peak detection on plastic slip profiles, is applied to show that gradient effects strongly influence the mechanisms of selection between slip and kink banding, to the favor of the first. In particular, some kink bands are shown to decompose into an homogeneous distribution of parallel slip bands of finite length. Finally, the competition between structural effects and energetic cost of lattice curvature in the formation of localized slip bands networks in polycrystals is discussed. The present results demonstrate the relevance of softening crystal plasticity modeling including an energetic contribution of GND density to accurately capture slip localization in polycrystals.

Slip localization in Inconel 718: A three-dimensional and statistical perspective

“…It is likely these differing band origins produce characteristic features in local slip activity evolution, this presents a limitation of the classical CPFE model used in this study and a possible source of deviation with experimental results. Higher-order gradient crystal plasticity models with additional microscopic boundary conditions that account for slip transfer across grain boundaries could potentially shed light on these interactions [52][53][54][55][56][57]. The implication from the present slip activity calculations is that planar slip and high-lattice-rotation zones are two opposing states of slip activity.…”

Modeling size effects in microwire torsion: A comparison between a Lagrange multiplier-based and aCurlFpgradient crystal plasticity model

“…The full gradient and reduced-order models could further be compared in the case of localization phenomena in crystalline materials as recently explored by Marano et al (2021). Regularization of strain localization phenomena in single crystals such as slip, kink and shear bands was demonstrated in (Ling et al, 2018).…”

A simple and fast algorithm for computing discrete Voronoi, Johnson-Mehl or Laguerre diagrams of points

“…A special attention is given, in the present paper, to the case of large images with a high number of grains. Indeed, it is not uncommon nowadays to apply FFT-based homogenisation methods on microstructures discretised with hundreds of millions of voxels (Müller et al (2015), Boittin et al (2017), Chen et al (2019), , Marano et al (2021) ) and, in the case of polycrystalline materials, composed of hundreds of thousands of grains (Wojtacki et al (2020)). The generation of such microstructures can lead to non negligible computation times.…”