Criteria for Crack Extension and Arrest in Residual, Localized Stress Fields Associated with Second Phase Particles

Abstract

An energy balance approach is taken to determine the conditions in which crack extension will occur within the highly-localized, residual stress field associated with second phase particles embedded within a matrix phase. The unique result of this analysis is that the particle size R is one of the factors that governs the criterion of crack instability. The maximum stress (σ), the elastic properties of the two phases, the fracture energy of the cracked phase, and the size of the pre-existing crack are the other factors. It is shown that for a given material, crack extension will not occur unless σ² R ≥ a constant, regardless of the pre-existing crack size. Once this condition is satisfied, the size of the pre-existing crack will then govern the stress required to extend the crack. It is also shown that crack arrest will occur once the above conditions are satisfied and that the length of the stable crack depends on the particle size. The implications of these results are briefly discussed in relation to observed phenomena.