Finite versus small strain discrete dislocation analysis of cantilever bending of single crystals

Abstract

Plastic size effects in single crystals are investigated by using finite strain and small strain discrete dislocation plasticity to analyse the response of cantilever beam specimens. Crystals with both one and two active slip systems are analysed, as well as specimens with different beam aspect ratios. Over the range of specimen sizes analysed here, the bending stress versus applied tip displacement response has a strong hardening plastic component. This hardening rate increases with decreasing specimen size. The hardening rates are slightly lower when the finite strain discrete dislocation plasticity (DDP) formulation is employed as curving of the slip planes is accounted for in the finite strain formulation. This relaxes the back-stresses in the dislocation pile-ups and thereby reduces the hardening rate. Our calculations show that in line with the pure bending case, the bending stress in cantilever bending displays a plastic size dependence. However, unlike pure bending, the bending flow strength of the larger aspect ratio cantilever beams is appreciably smaller. This is attributed to the fact that for the same applied bending stress, longer beams have lower shear forces acting upon them and this results in a lower density of statistically stored dislocations. B Vikram S. Deshpande

Modelling surface roughening during plastic deformation of metal crystals under contact shear loading

“…where Ω is the domain in its undeformed configuration. Finally, the constitutive relations for S ij andŜ ij are obtained analogous to conventional crystal plasticity (Irani et al, 2015(Irani et al, , 2017. The equation 19along with boundary conditions can be solved by a conventional finite element method.…”

“…The equation 19along with boundary conditions can be solved by a conventional finite element method. However, dissimilar to the small strain formulation, the (ˆ) field problem is nonlinear and therefore, it should be solved iteratively (Irani et al, 2015(Irani et al, , 2017. Here, traction free and displacement boundary conditions are prescribed on the same material points throughout the simulation.…”

“…All these numerical analyses were performed under the assumption of small strains and hence, effects of finite lattice rotations and shape changes due to deformation and dislocation slip were neglected. However, both these effects are expected to play a non-negligible role in the plastic response of the material and its surface roughening (Irani et al, 2017). In this paper, we present a finite strain analysis of the shearing of a metallic FCC single crystal by a rigid solid.…”

A new mechanism of strain transfer in polycrystals

“…However, unlike slip transfer, which can be detected at the early stage of plastic deformation as soon as dislocations piling up at the boundary appear to "transfer" past it, the mechanism of strain transfer described here would only be detectable after the density of GNDs reaches 10 13 -10 14 m −2 . As shown in DDD simulations of cantilever bending 44,45,65 , this occurs at relatively large imposed deformations that atomistic simulations cannot yet simulate because of prohibitive requirements of computational resources.…”