Assessment of J-Integral for Three-Dimensional Surface Crack at Notch Root.

Abstract

The contour J-integral values were calculated using the three-dimensional elastic-plastic finite element method for semielliptical surface cracks originated at notch roots under tensile loading. Then these were compared with the J-integral values calculated using the conventional equation we proposed in earlier papers, which we refer to as J hereafter. The difference between the two was quite small at the deepest point A in the semielliptical surface crack, but was fairly large at the edge of a crack on the specimen surface, C. The conventional equation was modified by considering stress/strain gradients developed in the cross section at the notch root. The J-integral value calculated using the proposed equation, J′ was in quite good agreement with the contour J-integral value at both points, A and C in a semielliptical surface crack. The difference between the ratio J/J′ and 1.0 increased with increase in crack depth, depending upon the aspect ratio of the surface crack, magnitude of the applied stress and notch root radius. The parameter RW was proposed, so that J/J′ could be expressed by a unique curve as a function of RW over quite wide ranges of notch root radius, surface-crack shape and magnitude of stress. The application limit of the simple J-integral estimation proposed earlier was assessed using this curve. The crack growth rates obtained from fatigue tests of notched specimen were successfully plotted against J-integral range calculated using the modified conventional equation.