Full–field analysis of a planar anisotropic layered half–plane for concentrated forces and edge dislocations

Abstract

The problem of a planar anisotropic elastic layered half-plane subjected to concentrated forces and edge dislocations applied either in the layer or in the half-plane is analysed. One of the objectives of this study is to develop an effective analytical methodology to construct the exact full-field solution for this problem. By using the Lekhnitskii formalism for anisotropic elastic material with the Fourier-transformation technique, the explicit closed-form solutions for stresses in the layer and the halfplane are obtained. The solutions are suitable for loadings that are acting on the free surface or at the interface. The complete solutions for this problem consist only of the simplest solutions obtained from an infinite homogeneous medium with concentrated forces and edge dislocations. The solutions include Green's function for applied loadings in an infinite medium and an infinite number of image singularities that are induced to satisfy the boundary and interface conditions. It is shown that the physical meaning of the solution is the image method. The magnitudes and locations of image singularities are determined automatically from the mathematical method presented in this study. Numerical results for the full-field stress distribution in the layered half-plane medium subjected to concentrated forces or edge dislocations are discussed in detail.

On screw dislocation in a multiphase lamellar inclusion

“…His classical solution for the force on a screw dislocation in an isotropic half space on which there is a surface film paved the way for similar investigations for a variety of configurations of layered materials (see, for example, [3][4][5]). More recently, variants of the image method have been used to study the interaction of dislocations with boundaries for some two-dimensional anti-plane configurations (see, for example, [6][7][8][9][10]). In [7], the technique of Mellin transform was used in conjunction with the image method to analyze the problem of two-dimensional dissimilar isotropic composite annular wedges subjected to anti-plane concentrated forces and screw dislocations.…”

Three-dimensional solution of concentrated forces in semi-infinite coating materials

“…Wu et al [14] derived the exact solutions for interfacial edge dislocations in an anisotropic bicrystal under plane strain by the image dislocation approach. Lately Ma and Lee [15,16] considered 2-D semi-infinite coating problems for anisotropic and magnetoelectroelastic materials based on the image method.…”

The degeneration of image singularities from anisotropic materials to isotropic materials for an elastic half-plane

“…The concept of image method has been further extended to solve more complicated problems of layered half-plane medium by Ma and Lin (2002) and Ma and Lee (2009) for anisotropic material and magnetoelectroelastic material, respectively. The mathematical approach used by them provided an automatic determination for the locations and magnitudes of all image singularities.…”