Incompatibility Stresses and Lattice Rotations Due to Grain Boundary Sliding in Heterogeneous Anisotropic Elasticity

Thiebaud Richeton

doi:10.3390/cryst7070203

Abstract

Non-uniform grain boundary sliding can induce strain and rotation incompatibilities at perfectly planar interfaces. Explicit analytic expressions of stress and lattice rotation jumps are thus derived at a planar interface in the general framework of heterogeneous anisotropic thermo-elasticity with plasticity and grain boundary sliding. Both elastic fields are directly dependent on in-plane gradients of grain boundary sliding. It is also shown that grain boundary sliding is a mechanism that may relax incompatibility stresses of elastic, plastic and thermal origin although the latter are not resolved on the grain boundary plane. This relaxation may be a driving force for grain boundary sliding in addition to the traditionally considered local shears on the grain boundary plane. Moreover, the obtained analytic expressions are checked by different kinds of bicrystal shearing finite element simulations allowing grain boundary sliding and where a pinned line in the interface plane aims at representing the effect of a triple junction. A very good agreement is found between the analytic solutions and the finite element results. The performed simulations particularly emphasize the role of grain boundary sliding as a possible strong stress generator around the grain boundary close to the triple line because of the presence of pronounced gradients of sliding.

Highlights

Grain boundary sliding (GBS) is a specific deformation mechanism of polycrystals which is especially important during creep [1,2,3,4,5,6]
While GBS can act as a stress relaxation mechanism able to lead to superplasticity, it may induce cavities at triple points and causes intergranular fracture initiation [3,6,7,8]
GBS generally needs relatively high homologous temperature and/or relatively small grain sizes [1,2,3,4]. It is sometimes observed with coarse grain sizes at room temperature, in metals with hexagonal close-packed (HCP) structure [5,6,7,9,10]

Summary

Introduction

Grain boundary sliding (GBS) is a specific deformation mechanism of polycrystals which is especially important during creep [1,2,3,4,5,6]. Due to the low symmetry of the hexagonal lattice, HCP materials are known to be strongly anisotropic and to exihbit significant strain incompatibilities between adjacent grains In those materials, the origin of GBS might be the need for an additional mechanism that can accommodate grain incompatibilities [6,7,9]. In the grain boundary plane, a line is pinned in order to mimic the effect of a triple junction Based on both the obtained theoretical expressions and numerical results, the dual role of grain boundary sliding, as a stress generator and as a stress relaxation mechanism, is discussed. Where σi are stresses, εei elastic strains and sij components of the elastic compliances tensor that include the multiplying factors of 2 and 4 [11]

Compatibility Relations

Stress Jumps

Lattice Rotation Jumps

Validation by FE Simulations

Discussion