Three-dimensional Stress Distribution Near a Sharp Crack in a Plate of Finite Thickness

Book excerpt: An attempt has been made to investigate the three-dimensional stress distribution near the tip of a semi-infinite crack embedded in an infinite plate of arbitrary thickness. The problem is formulated by means of three biharmonic functions in the classical theory of elasticity as developed by Galerkin. The eigenfunction expansion technique of Williams for solving two-dimensional crack problems is incorporated into the three-dimensional crack analysis. It is found that the stresses rr, theta theta, zz, r theta are singular of the order of r( -1/2), r being the distance measured from the crack point, but the transverse shear components rz, theta z are bounded everywhere in the plate. Determined in an approximate manner is the intensity of the crack-edge stress field which depends on the thickness coordinate of the plate. The results provide an improved understanding of the three-dimensional aspects of fracture theories, particularly on the effect of plate thickness.