An Analysis of Crack Trapping by Residual Stresses in Brittle Solids

The residual stress distribution in a brittle polycrystalline solid may have a significant influence on its toughness. Grains in a state of residual compression are less likely to be fractured by a growing crack and may trap the crack front or be left behind as bridging particles (Evans et al., 1977). This paper estimates the toughness enhancement due to intergranular residual stresses, using a three-dimensional model. The residual stress is approximated as a doubly sinusoidal distribution acting perpendicular to the plane of an initially straight semi-infinite crack. An incremental perturbation method developed by Bower and Ortiz (1990) for solving three-dimensional crack problems is extended here to cracks loaded by nonuniform remote stresses. It is used to calculate the shape of the semi-infinite crack as it propagates through the doubly sinusoidal residual stress. It is shown that the local regions of compression may trap the crack front and give rise to some transient toughening. In addition, if the residual stress exceeds a critical magnitude, pinning particles may be left in the crack wake. However, for practical values of residual stress and grain size, the predicted toughness enhancement is insignificant. Furthermore, the analysis cannot account for the large bridging zones observed in experiments. It is concluded that the R-curve behavior and bridging particles observed in monolithic ceramics are caused by mechanisms other than residual stresses acting perpendicular to the crack plane.