Papers by Keyword: Matched Asymptotic Expansion

Abstract: The domain of the generalized stress intensity factors dominance ahead of the notch tip can be rather small with respect to the length of the perturbing cracks initiated from the tip of the notch. Thus the non-singular terms of the stress asymptotic expansion at the notch tip would play an important role in the notch tip stability. Following the procedures dealing with complex potential theory and path-independent two-state integrals developed for the singular stress analysis of the stress concentrators one can evaluate their magnitude and include them to the energy release rate of the preexisting crack initiated from the notch tip applying the matched asymptotic procedure. The presented analysis should lead to better understanding of the notch stability process and precising of the notch stability criteria.

Abstract: The methods based on the properties of the two-state integrals allow one to calculate the amplitude of singular and the other terms of the Williams’ asymptotic expansion. The paper is focused on the use of the Y-integral, whose application is conditioned by the knowledge of the so-called auxiliary solution of the solved problem. On the other hand, the Y-integral can be applied to the analysis of the problems with various geometries, e.g. the analysis of the bi-material notches. The application of the Y-integral can be also extended to the matched asymptotic procedure, which allows one to predict the behavior of the cracked notches or following crack growth near the bi-material interfaces.

Abstract: The evaluation of the stress singularities and generalised stress intensity factor (GSIF) for the case of an inclined surface crack terminating perpendicular to the interface between two orthotropic materials is considered. The knowledge of the regular and auxiliary solution allows evaluating the GSIF using the reciprocal theorem (Ψ-integral). A co-operating effect of a stronger and a weaker singular stress field for a crack impinging a bimaterial interface is investigated.

Abstract: Matched asymptotic procedure is used to analyze crack crossing a sharp interface between dissimilar elastic anisotropic materials. The link to the configurational forces approach is suggested.