Elastic Fracture Mechanics Concepts for Interfacial Cracks

TLDR

Elastic fracture mechanics concepts are reexamined for a crack on the interface between dissimilar solids. The study discusses the complex stress‑intensity factor K for elastic interface cracks, evaluating its validity as a crack‑tip characterizing parameter in cases of small‑scale nonlinear behavior or contact zones. A function‑theory derivation yields stress and displacement fields near the crack tip, equivalent to Williams expansions, and the authors discuss classical definitions of stress‑intensity factors KI and KII for interface cracks. The authors show that equal complex stress‑intensity factors K indicate similar crack‑tip states, enabling crack‑growth criteria to be expressed via a critical locus in the complex plane; maintaining such similarity with changing crack length requires adjusting both magnitude and phase of combined tension and shear loading, while the plastic‑zone size scales with the square of load and field dependences on distance and load phase angle are coupled.

Abstract

Elastic fracture mechanics concepts are reexamined for a crack on the interface between dissimilar solids. A derivation by function theory is given of the form of stress and displacement fields in the vicinity of the crack tip, equivalent to complete Williams expansions of both inner and outer (external to a nonlinear or contact zone) type. The complex stress intensity factor K associated with an elastic interface crack, for which contact is ignored, is discussed and, specifically, its validity as a crack tip characterizing parameter is noted for cases of small scale nonlinear material behavior and/or small scale contact zones at the crack tip. That is, similar values of K for two cracked bodies then imply similar states as the crack tip, so that conditions for crack growth can be phrased in terms of K reaching a critical failure locus in a complex plane. The maintenance of a similar state at a crack tip under change of crack length is shown to require alteration of both the magnitude and phase angle of a combined tension and shear loading. Some possible definitions of stress intensity factors KI and KII of classical type associated with interface cracks are discussed. Also, the scaling of interface crack tip plastic zone size with load under small scale yielding conditions is found to deviate from classical scaling, in proportion to the square of the applied load level, and dependences of the field on distance from the tip and on load phase angle are found to be linked together.