Graphs of the Three-Dimensional State of Stress at the Vertex of a Quarter-Infinite Crack in a Half-Space

摘要

Spherical coordinates are R, theta, phi. The half space extends in theta pi/2. The crack occurs along phi = 0. States of stress were previously considered in terms of the Cartesian displacement and stress components which leave the half space surface and crack surfaces traction free. Only a discrete spectrum of eigenvalues s is possible and the most important s value is that closest to the limiting value Re s - 1/2. To each eigenvalue s belongs an eigenfunction, i.e., a state of displacement and stress which may be described (taking R = 1) with the aid of only two of the spherical coordinates (theta and phi). For 5 Poisson's ratios, computer plotted graphs are given for these displacements and stresses which belong to the most important eigenvalues.