Anti-Plane Interaction between a Crack and an Elliptically Cylindrical Layered Media

Abstract

Anti-plane interaction of an elliptically cylindrical layered media with an arbitrarily oriented crack embedded in an infinite matrix, intermediate layer, or inner inclusion under a remote uniform shear load is considered in this paper. Based on the technique of conformal mapping and the method of analytical continuation in conjunction with the alternating technique, the solution for a screw dislocation in the inclusions and the matrix is first derived in a series form. The integral equations with logarithmic singular kernels for a line crack can easily be obtained by using the screw dislocation solutions as the Green's function together with the principle superposition. The stress intensity factors, which can properly reflect the interaction between a crack and an elliptically cylindrical layered media, are then obtained numerically in terms of the values of the dislocation density functions of the integral equations. The effects of material property combinations and geometric parameters on the normalized mode-III stress intensity factors are discussed in detail and shown in graphic form.

Complex Potential Methods for a Crack and Three-phase Circular Composite in Anti-plane Elasticity

“…where, Meanwhile, the complex potential functions of the other case in which the screw dislocation is located in core inclusion can be expressed in Equation 5 where recurrence formula for Θn(z) is expressed in Equation 6 and Equation 7. A crack can be modeled by place a dislocation distribution along the prospective site of the crack.…”

“…The merit of this technique is that allows us to easily deal with the interface continuity conditions of multi-layered composites. The studies that has been done using those techiques including an anti-plane crack interacting with reinforced elliptic hole [6], elliptically layered media [7], eccentric circular inclusion [8], and tri-material media [9]. To our knowledge, an anti-plane crack interacting with multi layered circular media has not been recorded in the literature.…”

Computation of Stress Intensity Factors Using Wavelet-Based Element

“…Chen et al developed a multilayer hybrid-stress finite element model together with two types of composite multilayer elements to analyze the influence of various crack parameters (position, length, thickness and fiber orientation) on the estimation of SIFs of composite laminates [4]. Different boundary element methods were applied by a number of researchers (e.g., Miyazaki et al [5], Lu et al [6], Lu and Cheng [7], Chao and Wikarta [8] and Chao and Lu [9]) to analyze two-dimensional crack problems including biomaterial interface crack problems, dynamic propagation problem concerning Mode I crack, Asymmetrical dynamic propagation problem concerning Mode III crack, layered structures, respectively. Giner et al proposed an Extended Finite Element Method (X-FEM) for the numerical analysis of crack problems and implemented it in the finite element code Abaqus [10].…”

Anti-Plane Interaction of a Coated Circular Inclusion with a Crack Located in Matrix

“…Indeed, a number of investigations concerning the crack problem in multi-layered composite have appeared in the literature, these include the work of [4][5]. However, the aforementioned works focused on problems with elliptic and straight boundaries.…”