Surface effects on image stresses and dislocation pile-ups in anisotropic bi-crystals

Abstract

A new bi-crystal surface layer configuration with stiff layer adjacent to the free surface is modeled based on the image decomposition method.• The numerically computed dislocation image stress is different from purely free or rigid surface.• Size effects on the dislocation image stress are found in presence of two parallel free surfaces or two grain boundaries.• The equilibrium dislocation positions are computed for a double-ended dislocation pile-up considering surface conditions, grain boundary and critical stress.

Energy variation and stress fields of spherical inclusions with eigenstrain in three-dimensional anisotropic bi-materials

“…However, certain cubic materials can ex-hibit much higher values of A, like lithium metal with A ≈ 8 (Aspinall et al, 2022), a crucial component in batteries, or some shape memory alloys like CuAlBe with A ≈ 13 (Rios-Jara et al, 1991). Nevertheless, the image effect is expected to increase asymptotically with A since the maximum image effect should occur in presence of free or rigid surfaces as it was computed for dislocations (Chen et al, 2021).…”

“…Secondly, grain boundaries possess small, albeit finite, width (of the order of the nanometer), unlike the singular interface examined in this study. Therefore, it is certainly worthwhile to consider a specific elastic stiffness tensor over the grain boundary width, as done in previous studies (Chen et al, 2019(Chen et al, , 2020(Chen et al, , 2021. For the symmetrical 1, as well as the two symmetrical tilt boundaries defined by their tilt angle θ.…”

Nonsingular Stress Distribution of Edge Dislocations near Zero-Traction Boundary

“…Here, the contribution from the image dislocation cancels out the contribution from the real dislocation at every point along . This technique of canceling the stress component at a given boundary is called the image force method [ 47 , 48 ], which is a mechanical analog of the image charge construction employed in electromagnetism [ 49 ].…”

Analytic formulation of elastic field around edge dislocation adjacent to slanted free surface

“…In addition to the attraction force, the torque acting on dislocations due to the free surface has also been discussed [ 6 , 7 ]. Moreover, other interesting consequences of the surface effects have also been suggested for elastic media with voids [ 8 , 9 ] or cracks [ 2 , 10 , 11 ], multilayered media [ 12 ], and the interplay between the elasticity and dynamic motion of dislocations [ 13 , 14 ]. For micro-sized materials, the ratio of surface area to sample volume is so high that the aforementioned free-surface-driven phenomena are expected to be more prominent than those observed in macroscale samples [ 15 , 16 ].…”