Small-Scale Yielding Analysis of Mixed Mode Plane-Strain Crack Problems

The small-scale yielding analysis of an elastic-plastic body with a line crack under plane-strain conditions subject to combinations of Mode I and II loadings is examined. The analysis of the near-tip field follows the works of Hutchinson and Rice and Rosengren. Dominant singularity solutions governing the asymptotic behavior of the stresses and strains at the crack tip are obtained for the complete range of loadings between Mode I and II. The results of an accurate finite element technique, which imbeds the dominant singularity solutions, directly relates the near-tip behavior to the elastic stress intensity factors K(I) and K(II). Implications of this study to mixed mode fracture mechanics is also discussed, particularly with respect to the direction of crack initiation and the relation of fracture toughness under mixed modes to that in Mode I. Details of the mixed mode plastic zone sizes and shapes are also given.