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.

An exact theory of interfacial debonding in layered elastic composites

“…Brittle behavior has the defect behaving in an almost stationary manner, opening a small amount but not extending much until a critical P precipitates an abrupt unzipping behavior. This phenomenon has been described elsewhere in different contexts (Needleman, 1990a,b;Xie and Levy, 2007). Note that when both layers have identical material and geometric properties, the results (not shown) are virtually the same as that of elementary beam theory.…”

“…This kind of bifurcation behavior, in the brittle case akin to snap buckling, can be difficult to capture using FEA. (For a study of interface behavior of this kind in a circular inclusion/matrix system see Xie and Levy, 2007.) An analysis of the three slab system will be the subject of a future publication.…”

Mechanics of interface failure in the trilayer elastic composite

“…Furthermore, the defect behaves in an almost stationary manner, opening a small amount but not extending much until a critical P precipitates an abrupt unzipping behavior. This phenomenon has been described elsewhere in different contexts (Needleman, 1990a,b;Xie and Levy, 2007).…”

A linear elastic-brittle interface model: application for the onset and propagation of a fibre-matrix interface crack under biaxial transverse loads

“…Levy and co-workers in a series of studies, see Xie and Levy (2007) and references therein, carried out parametric studies on the stability of the phenomenon of circular-inclusion decohesion under biaxial loading applying a CZM. Carpinteri et al (2005) used a CZM to study the instability phenomena in fibrous metal matrix composites through FEM.…”