The stress field and energy of a three-dimensional dislocation loop at a crack tip
The self stress field and self energy are estimated for a planar three- dimensional dislocation loop emanating from a half-plane crack tip. While the problem is of greatest interest for analysis of shear loops nucleating from the crack tip in the concentrated stress field there due to applied loadings, it is addressed here in the interest of tractability for three-dimensional prismatic loops lying in the same plane as the crack. Exact elastic calculations for that case are based on recent developments of three-dimensional crack weight function theory and specific results are given for induced stress fields, intensity factors and energy of semicircular and rectangular prismatic dislocation loops. Also, self stresses and energy expressions are derived for the two- dimensional case of a line dislocation lying parallel to the crack for arbitrary Burgers vector type and general orientation of the dislocated plane relative to the crack plane, and those results are used together with the three-dimensional prismatic loop results to estimate approximately the self energy for three-dimensional shear dislocation loops emanating from the tip on planes inclined to the crack plane.
approximate estimate of energy correction factor
planar three-dimensional dislocation loop
scientific article; zbMATH DE number 4043390