Plane strain mixed mode crack-tip stress fields characterized by a triaxial stress parameter and a plastic deformation extent based characteristic length

Abstract

Using physical observations from controlled crack growth experiments in ductile materials as a guide, a series of numerical and theoretical studies were performed. Results from these studies demonstrate that a self-similar family of mixed mode crack-tip stress fields exist in the crack-tip region that are characterized in terms of (a) a stress triaxiality parameter, A m, based on the ratio between the mean stress and effective stress, and (b) a characteristic length scale, L p, based on the spatial extent of crack-tip plastic deformation. Finite element models used to demonstrate this include; small-scale yielding with a modified boundary layer formulation (SSY); slant cracked tension bar (TB); and an asymmetric three point bend (TPB) bar. Since experimental evidence has shown that crack growth occurs along local directions that are predominantly either mode I or mode II, special emphasis is placed on radial variations in stress components along these directions. Results for all cases indicate that, for the full range of mode mixity and constraint conditions present in the SSY, TB and TPB models, the proposed, self-similar family of mixed mode crack-tip fields accurately represents the stress fields for both SSY and all fracture specimens considered. Specifically, the crack-tip stress fields are shown to belong to a family of solutions parameterized by A m and L p when the distance from crack tip, r, is measured in terms of its normalized value by the characteristic length scale, r/ L p.