The effects of heterogeneity and anisotropy on the size effect in cracked polycrystalline films

A model is developed for quantifying the size effect due to heterogeneity and anisotropy in polycrystalline films. The Monte Carlo finite element calculations predict the average and standard deviation of the microscopic (local) stress intensity factors and energy release rate of a crack in a columnar aggregate of randomly orientated, perfectly bonded, orthotropic crystals (grains) under plane deformation. The boundary of the near-tip region is subjected to displacement boundary conditions associated with a macroscopic (far field or nominal) Mode-I stress intensity factor and average elastic constants calculated for the uncracked film with a large number of grains. The average and standard deviation of the microscopic stress intensity factors and energy release rate, normalized with respect to the macroscopic parameters, are presented as functions of the number of grains within the near-tip region, and the parameters that quantify the level of crystalline anisotropy. It is shown that for a given level of anisotropy, as long as the crack tip is surrounded by at least ten grains, then the expected value and standard deviation of the crack tip parameters are insensitive to the number of crystals. For selected values of crystalline anisotropy, the probability distributions of Mode-I stress intensity factor and stress ahead of the crack are also presented. The results suggest that the size effect due to heterogeneity and anisotropy is weak; crack initiation load and direction are governed only by the details of the grains in the immediate vicinity of the crack tip.