# On a crack tip interacting with a bimaterial interface

Abstract (Summary)

Because of its relevance to fracture of composite materials, the problem of calculating the stress field at the tip of a crack perpendicular to the perfectly bonded interface between two isotropic half-planes has been addressed by several authors. However, to date a sound propagation criterion for cracks terminating at a bimaterial interface has not been proposed. The main purpose of this work is to provide such propagation criterion in terms of the physical parameters that control the inelastic deformation near the crack tip (critical crack tip opening displacement, ?c, and yield stress, ?o). The plane elastostatics analysis of a crack tip impinging on the interface is presented first. This fundamental problem is used as a reference configuration for the analysis of a crack tip very close to the interface. The stress intensity factor (s.i.f.) and crack opening displacement (COD) of a semi-infinite crack approaching or penetrating the interface are calculated by means of a singular integral equation formulation as functions of the distance of the crack tip to the interface, ?, the Dundurs parameters ? and ?, and the s.i.f., k, associated with the reference problem of the same crack touching the interface. The calculated universal results provide a powerful tool for the asymptotic analysis of the s.i.f. and COD of cracks of finite length 2l with one tip at a distance ?ll l from the interface. Results for a crack loaded by a uniform far-field tension in each half-plane show that as ? ? 0 the s.i.f. approaches its limits (zero or infinity, depending on the relative stiffness of the bonded materials) at a relatively slow rate. The problem of a crack terminating at the interface between an elastic and a yielding material is addressed next. A first estimate of the location of the elastic-plastic boundary in the ductile component of the bimaterial system is obtained by means of the Von Mises yield criterion applied to the elastic asymptotic stress field. These results show qualitatively that the size of the yielded region is a strong function of the elastic mismatch. A cohesive crack model is then proposed, which provides a general propagation criterion for both small and large crack tip deformation in terms of the non-dimensional ratio ?2/L, where the parameter ?2 is proportional to the small scale yielding (SSY) critical cohesive zone length and L is a characteristic length of the problem. This criterion, which represents a generalization of the Dugdale-Barenblatt model for a homogeneous medium, is used to analyze the effective toughening resulting from the presence of the interface in selected material combinations. It is shown that the critical stress at incipient crack propagation does not change significantly for a relatively wide range of ?-? and ?2/L combinations
Bibliographical Information:

Advisor:

School:Case Western Reserve University

School Location:USA - Ohio

Source Type:Master's Thesis

Keywords:crack tip bimaterial interface

ISBN:

Date of Publication:01/01/1995