A re-evaluation of the 3-D finite-element models and methods used to analyze surface crack at stress concentrations is presented. Previous finite-element models used by Raju and Newman for surface and corner cracks at holes were shown to have ill-shaped elements at the intersection of the hole and crack boundaries. These ill-shaped elements tended to make the model too stiff and, hence, gave lower stress-intensity factors near the hole-crack intersection than models without these elements. Improved models, without these ill-shaped elements, were developed for a surface crack at a circular hole and at a semi-circular edge notch. Stress-intensity factors were calculated by both the nodal-force and virtual-crack-closure methods. Both methods and different models gave essentially the same results. Comparisons made between the previously developed stress-intensity factor equations and the results from the improved models agreed well except for configurations with large notch-radii-to-plate-thickness ratios. Stress-intensity factors for a semi-elliptical surface crack located at the center of a semi-circular edge notch in a plate subjected to remote tensile loadings were calculated using the improved models. The ratio of crack depth to crack length ranged form 0.4 to 2; the ratio of crack depth to plate thickness ranged from 0.2 to 0.8; and the ratio of notch radius to the plate thickness ranged from 1 to 3. The models had about 15,000 degrees-of-freedom. Stress-intensity factors were calculated by using the nodal-force method. Tan, P. W. and Raju, I. S. and Shivakumar, K. N. and Newman, J. C., Jr. Langley Research Center RTOP 505-63-01-05...

This paper presents an evaluation of the three-dimensional finite-element models and methods used to analyze surface cracks at stress concentrations. Previous finite-element models used by Raju and Newman for surface and corner cracks at holes were shown to have "ill-shaped" elements at the intersection of the hole and crack boundaries. These ill-shaped elements tended to make the model too stiff and, hence, gave lower stress-intensity factors near the hole-crack intersection than models without these elements. Improved models, without these ill-shaped elements, were developed for a surface crack at a circular hole and at a semicircular edge notch. Stress-intensity factors were calculated by both the nodal-force and virtual-crack-closure methods. Both methods and different models gave essentially the same results. Comparisons made between the previously developed stress-intensity factor equations and the results from the improved models agreed well except for configurations with large notch-radii-to-plate-thickness ratios.

This book provides a systematic and standardized approach based on the authors’ over 30 years of research experience with weight function methods, as well as the relevant literature. Fracture mechanics has become an indispensable tool for the design and safe operation of damage-tolerant structures in many important technical areas. The stress intensity factor—the characterizing parameter of the crack tip field—is the foundation of fracture mechanics analysis. The weight function method is a powerful technique for determining stress intensity factors and crack opening displacements for complex load conditions, with remarkable computational efficiency and high accuracy. The book presents the theoretical background of the weight function methods, together with a wealth of analytical weight functions and stress intensity factors for two- and three-dimensional crack geometries; many of these have been incorporated into national, international standards and industrial codes of practice. The accuracy of the results is rigorously verified, and various sample applications are provided. Accordingly, the book offers an ideal reference source for graduate students, researchers, and engineers whose work involves fracture and fatigue of materials and structures, who need not only stress intensity factors themselves but also efficient and reliable tools for obtaining them.