Stress Concentration Induced by Variation of Surface Energy in Half-Anisotropic Materials

Abstract

The author has performed the analyses of stress and deformation taking into account a surface energy, which exists at the surface and interface dividing phases. In the present paper, the equilibrium formulation considering the surface energy previously deduced by author is used for calculating the stress and deformation. The problem that the surface energy in a half region of a half-infinite anisotropic materials varies is analyzed by using the theory of elasticity. This problem relates with the surface of contaminating, oxidizing or polluting by other materials. Hilbert transform techniques was used for solving an integral equation with respect to an unknown Fourier transform function in the analysis. Consequently, all stress components and displacements were deduced in a closed form. The shear components of bulk stress become infinite at the edge of discontinuity of the surface energy, and then the free suface deforms alike a step. This result may be suggest that cracking occurs easier in a chemically contaminated surface than in a clean one.