Intergranular fracture in model polycrystals with correlated distribution of low-angle grain boundaries

Abstract

Grain boundary engineering of materials is intended to increase the fraction of ``special'' boundaries that possess preferred properties. These may be low-angle boundaries with good mechanical and corrosion resistance properties. In this case, the distribution of special boundaries is spatially correlated rather than random, due to crystallographic constraints. Such a correlated distribution, in addition to the density of special boundaries, will likely affect the progression of damage and failure of a polycrystalline material under load or applied strain. This is demonstrated for a two-dimensional model polycrystal, which is an array of hexagonal grains defining a ``honeycomb'' network of grain boundary facets. The facets are assigned a high or low elasticity modulus in accordance with their ``special'' or ``nonspecial'' designation, respectively. Then damage evolution due to an increasing strain is monitored as the following sequence of two steps is repeated until material failure: (1) calculation of the stress and strain fields by use of a scalar Hooke's law and (2) rupture of the facet with greatest strain energy. For polycrystals with a high fraction of special facets, damage proceeds by a series of ``bursts'' (``avalanches'') of single-facet failures distributed over the polycrystal. These failures occur at special facets that connect two clusters of nonspecial facets, thereby creating larger clusters of ``weak'' (nonspecial plus ruptured) facets oriented roughly perpendicular to the applied strain. Eventually a weak cluster grows to a critical size such that sufficient stress is diverted through the nonspecial facets (which have served as ligaments preventing a crack from nucleating on the weak cluster) to cause those facets to fail. This crack growth leads to catastrophic failure of the model polycrystal.