On the computation of stress intensity factors for three-dimensional geometries by means of the stiffness derivative and J-integral methods

Two methods are examined for accurately calculating stress intensity factors in two and three dimensions: the stiffness derivative technique and the J-integral method. In two dimensions the J-integral is expressed as an area integral, whereas in three dimensions it is a volume integral. With both techniques, a virtual crack extension is introduced. Although the expressions employed for each method are quite different, it is proven that when written analytically for finite element calculation, they reduce to identical expressions. Numerical calculations are carried out in both two and three dimensions. As a result of the equivalence of the two methods, close numerical agreement is expected. For two-dimensional geometries and a penny shaped crack in a finite height cylinder, there is at least five significant figure agreement between solutions determined by both methods. For an elliptical crack embedded in a plate, the agreement is generally to four significant figures.