Stress Singularities at the Apex of a Dissimilar Anisotropic Wedge

Abstract

The complex form of the characteristic equation for the stress singularities of the order rλ-1(0<Re[λ]<1) for the dissimilar anisotropic wedges is derived. Special attention is then focused on the problems that are composed by two orthotropic materials. For such problems the characteristic equation is expressed in real forms from which the dependence of the singularities on the material parameters and wedge angles is investigated. The case of a single free-fixed wedge problem is particularly studied in detail. Numerical results for several special wedge geometries are also presented.

Singular stress field near interface edge in orthotropic/isotropic bi-materials

“…In this paper, however, the asymptotic fields near the interface edge can be directly calculated only by using the eigenvalues determined from the eigenequation and the stress intensity factors obtained by the numerical or experimental method. By contrast to the known solutions (for example, Delale, 1984;Lin and Sung, 1998;Labossiere and Dunn, 1999;Shin et al, 2004Shin et al, , 2007, the eigenvector is no longer required in this solution. Therefore, the solution proposed in this paper is more convenient and effective for the analysis of the singular stresses near the interface edge in the orthotropic/isotropic bi-material.…”

“…The Stroh formalism (Eshelby et al, 1953;Stroh, 1958) is an effective tool in the investigation of anisotropic problems. By adopting this formalism the asymptotic solution near the anisotropic interface edge was treated by Ting (1996) and Lin and Sung (1998), where the eigenequation obtained was expressed in terms of 3 Â 3 determinant having usually complex elements. Lately, Dunn (1999, 2002) used a combination of the Stroh formalism and the Williams eigenfunction expansion method to calculate the displacement and singular stress fields near an anisotropic bi-material interface edge, and the path independent H-integral was developed to compute the stress intensity factors.…”

The Plane Wedge Problem Loaded at Its Apex ? the Self-similarity Property and the Characteristic Vector

“…In addition, Pageau et al [13], Joseph and Zhang [14], Horgan [15] and Gdoutos and Theocaris [16] have studied multi-material wedges whereas Dundurs and Markenscoff [17] presented the anomalies due to a concentrated couple. On the other hand, the Stroh formalism [18] in anisotropic homogeneous elasticity has already been applied by Ting [4,19], Chen [20], Lin and Sung [21], Poonsawat et al [22] in order to study the singular stress state at the singular multimaterial corners. Recently Yin [23] in the case of non-degenerate (anisotropic), degenerate (isotropic) and extra-degenerate materials and Barroso et al [24], in the case of non-degenerate and degenerate materials, have studied explicitly, the anisotropic multi-sector wedge eigensolutions.…”

Asymptotic fields near an interface corner in orthotropic bi-materials

“…Using Lekhnitskii's general formulation and Williams' method, Delale (1984) studied stress singularities in bonded anisotropic materials. Lin and Sung (1998) used the Stroh formalism to deduce the eigenequation for the anisotropic bi-material wedge. Labossiere and Dunn (1999) used a combination of the Stroh formalism and the Williams eigenfunction expansion method to calculate the displacement and singular stress fields near an anisotropic bi-material interface edge, and the path independent H -integral was developed and implemented to compute the stress intensity factors.…”