Coble creep in heterogeneous materials: The role of grain boundary engineering

Grain boundary engineering methods improve materials properties by modifying the composition and connectivity of grain boundary networks. A quantitative understanding of grain boundary network characteristics and their impact on materials properties is therefore desirable for both scientific and practical purposes. In this paper, we focus on the case of Coble creep, a viscous deformation mechanism prevailing at intermediate to high temperatures. Using computer simulations, we characterize the creep viscosity as a function of the fraction of slow-diffusing "special" grain boundaries in a two-dimensional honeycomb grain boundary network. This basically defines a new class of percolation problem where mass diffusion and force equilibrium are coupled in a complex way. The percolation threshold and scaling exponents are extracted from the simulation data and analyzed in the context of correlations and energy balance on the network. We also explore stress concentrations induced by the grain boundary character distribution, the effect of crystallographic constraints, and an empirical effective-medium equation that may be used with classical creep constitutive laws in order to predict the viscosity of a heterogeneous material.