Elastic Yield Zone Around an Interfacial Crack Tip

Abstract

A closed-form approximate solution for a small-scale yielding (SSY) plastic zone around a planar interfacial crack tip, occurring between two dissimilar ideally-bonded elastic half spaces, is obtained by equating the elastically-calculated Mises equivalent stress with the material yield strength, σys. The dimensionless parameter ζ(θ), which is defined as ζ(θ) = ∠K + εlnrp (θ), where ∠K is the phase angle of the complex stress intensity factor K, ε is the bimaterial constant, and rp (θ), is the polar representation of the plastic zone radius, naturally arises. The SSY interfacial load angle (ILPA), defined as ζ0 = ∠K + εln(KK/σ2ysπcosh2(πε)), leads to periodic zone growth. The ILPA characterizes the overall applied load phase by combining the oscillatory radial phase shift, attributable to the increase in zone size due to increased loading, with ∠K. At a particular angle θ0 from the uncracked interface, the plastic zone radius thus calculated is independent of ∠K, proportional to KK, and has no oscillatory radial phase dependence. The derived plastic zone expression reproduces the shape characteristics, and it modestly reproduces the zone size when compared with solutions for an elastic/perfectly-plastic solid adjoint to an elastic solid. As the strain-hardening exponent in the plastically deforming medium decreases, agreement between the approximation and various accurate numerical solutions improves. In the limiting case when ε = 0, the well-known homogeneous elastic solutions for pure Mode I and Mode II are recovered, as well as all possible mixed-mode combinations. Approximate validity conditions for the existence of Williams-type asymptotic fields (traction-free crack faces) are presented.