Defect propagation at a circular interface

Abstract

In this paper a nonlinear, nonuniform cohesive zone is employed to study the detailed features of quasi-static defect evolution in a simple, planar elastic system consisting of a circular inclusion embedded in an unbounded matrix subject to different remote loading configurations. The inclusion–matrix interface is assumed to be described by Needleman-type force-separation relations characterized by an interface strength, a characteristic force length and a shear stiffness parameter. Interface defects are modeled by an interface strength which varies with interface coordinate. Infinitesimal strain equilibrium solutions, which allow for rigid body inclusion displacement, are sought by eigenfunction approximation of the solution of the governing interfacial integral equations. For equibiaxial tension, quasi-static defect initiation and propagation occur under increasing remote load. For decreasing characteristic force length, a transition occurs from more or less uniform decohesion along the bond line to propagation of a crack-like defect. In the later case a critical failure load is well defined and interface failure is shown to be defect dominated (brittle decohesion). For interfaces with large characteristic force length, the matrix “lifts off” the inclusion accompanied by a delay in defect propagation (ductile decohesion). The decohesion modes ultimately give rise to a cavity with the inclusion situated within it on the side opposite to the original defect. Results for small characteristic force length show consistency with England’s results for the sharp arc crack on a circular interface (England AH (1966) ASME J Appl Mech 33:637–640) Stress oscillation and contact at the tip of the defect are observed primarily for small characteristic force lengths under extremely small loading. Results for remote tension, compression and pure shear loading are discussed as well. In the final section of the paper the results obtained in the first part are utilized to estimate the plane effective bulk response of a composite containing a dilute distribution of inclusions with randomly oriented interface defects.