Ασυμπτωτική ανάλυση διεπιφανειακών ρωγμών

Abstract

One of the most significant sources of failure in adhesive joints, thin films and composite materials is the propagation of interfacial cracks between the constituent materials. In the last few decades significant progress has been made towards the understanding of the mechanics of the interface crack within the framework of linear elasticity. The oscillatory character of the singular elastic crack-tip stress field and the coupling of the opening and shearing modes are important features that distinguish fracture mechanics from the mechanics of cracks in homogeneous media. The elasto-plastic analysis of the interface cracks has also attracted a lot of attention recently. In the context of this thesis an elastic-plastic asymptotic solution of the problem of a plane strain crack lying along the interface between an incompressible elastic-plastic powerlaw hardening material and a rigid substrate is developed. The elastoplastic asymptotic stress field expansion which is assumed to be separable in r and#, where (r,#) are polar coordinates at the crack tip, consists of two terms and is of the general form. The leading and second order terms in the stress and displacement field expansions are derived from the solution of two eigenvalue problems, non-linear and linear respectively. The elastoplastic asymptotic solution of the interfacial crack problem is studied via a perturbation of the elastic solution, i.e., for η = \ + ε where ε is a small parameter and n the strain hardening exponent. It is shown that both the leading and second order terms in the stress expansion are singular and branch from the mode-I and mode-II of the linear elastic solution respectively.