Path-independent H integrals for three-dimensional fracture mechanics

In fracture mechanics, a number of real applications have intrinsically three-dimensional crack geometries, thereby requiring a means of extracting stress intensity factors under such circumstances. Two approaches to this end are examined here: one, a three-dimensional J-integral; the other, three-dimensional H integrals for each mode. The first integral is well accepted by the fracture mechanics community; the second integrals are newly developed herein. The two are compared on three-dimensional test problems with closed-form solutions that are constructed for this purpose. Analysis is via quarter-point elements on two successively refined grids for each test problem. The results demonstrate that both types of path-independent integral can furnish estimates of stress intensity factors which converge to good levels of accuracy in return for reasonable levels of computational effort.