Large plastic deformation of voids in crystals

TL;DR

The paper addresses void growth and coalescence in single crystals under large deformations by developing an Eulerian rigid-viscoplastic crystal plasticity framework with ALE to capture evolving void shapes in 2-D. It employs a 3-slip-system, plane-strain model to simulate radial and uniaxial loading, illustrating how slip bands, kink bands, and lattice rotations drive void morphology. Key findings include fractal slip/kink-band networks forming around voids under hydrostatic tension, evolution to hexagonal void shapes accompanied by lattice rotations, and strong orientation-dependent void evolution under uniaxial loading. The work advances predictive understanding of ductile fracture in crystalline materials by linking microstructural slip patterns and rotations to macro-scale void coalescence tendencies.

Abstract

The mechanisms of void growth and coalescence are key contributors to the ductile failure of crystalline materials. At the grain scale, single crystal plastic anisotropy induces large strain localization leading to complex shape evolutions. In this study, an Arbitrary Lagrangian-Eulerian (ALE) framework for 2D crystal plasticity combined with dynamic remeshing is used to study the 2D shape evolution of cylindrical voids in single crystals. The large deformation and shape evolution of the voids under two types of loading are considered: (i) radial and (ii) uni-axial loadings. In both cases, the voids undergo complex shape evolutions induced by the interactions between slip bands, lattice rotations and large strain phenomena. In case (i), the onset of the deformation revealed the formation of a complex fractal network of slip bands around the voids. Then, large deformations unearth an unexpected evolution of the slip bands network associated with significant lattice rotations, leading to a final hexagonal shape for the void. In case (ii), we obtain shear bands with very large accumulated plastic strain (> 200%) compared to the macroscopic engineering strains (< 15%). A high dependence between crystalline orientations, slip band localization and therefore shape evolution was observed, concluding in a high dependency between crystalline orientation and void shape elongation, which is of prime importance regarding coalescence of the voids, thus to the formation of macro-cracks.

Figures (13)

• Figure 1: Two dimensional model with three slip systems.
• Figure 2: Schematic representation (not to scale) of a porous single-crystal disc unit cell with a single circular void at its center.
• Figure 3: Onset of the deformation: qualitative comparison using two different approaches. Left: equivalent strain obtained under small strain hypothesis, as reported in paux2022. Right: zoom of the equivalent strain rate at a low deformation level ($\epsilon^{eng}_{vol}=0.0033\%$) obtained with the Eulerian model.
• Figure 4: Onset of the deformation. The three slip systems of HCP crystal based on finite element simulation results : (left) $s=1$, (middle) $s=2$, and (right) $s=3$. Top: slip deformation rates computed with the presented Eulerian model. Bottom: slips deformation computed with a strain gradient crystal plasticity model without hardening from BORG20076382.
• Figure 5: Evolution of equivalent deformation strain rate and void morphology at different stages of the deformation: $\epsilon^{eng}=0.2475\%$, $\epsilon^{eng}=0.66\%$, $\epsilon^{eng}=0.99\%$ and $\epsilon^{eng}=1.32\%$.