Kinematics of polycrystal deformation by grain boundary sliding

We analyze the macroscopic deformation of a polycrystalline solid due to local deformation events in the core of grain boundaries. The central result is an equation that decomposes the effective macroscopic strain into contributions from three deformation modes, namely: (i) the elastic strain in the bulk of the crystallites; (ii) the results of dislocation glide and climb processes; and (iii) the deformation events in the grain boundary core. The latter process is represented by jumps in the displacement vector field that can be decomposed into tangential (“slip”) and normal (“stretch”) components. The relevant measure for the grain-boundary-mediated deformation is not the displacement jump vector but a grain-boundary discontinuity tensor that depends on the displacement jump and on the orientation of the grain boundary normal. Accommodation processes at triple junctions do not contribute significantly to the macroscopic strain. By means of example, the theory is applied to the effective elastic response of nanocrystalline materials with an excess slip compliance at grain boundaries. The predictions, specifically on the size dependence of the Poisson ratio, agree with recent experiments on nanocrystalline Pd. The value of the slip compliance for grain boundaries in Pd is obtained as 18 pm GPa−1.