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. Stress-intensity factors for a semi-elliptical surface crack located at the center of a semicircular edge notch in a plate subjected to remote tensile loadings were calculated using the improved models. A wide range in configuration parameters was considered. The ratio of crack depth to crack length ranged from 0.4 to 2; of crack depth to plate thickness from 0.2 to 0.8; and of notch radius to plate thickness from 1 to 3. The finite-element or nonsingular elements models employed in the parametric study had singularity elements all along the crack front and linear-strain (eight-noded) elements elsewhere. The models had about 15 000 degrees of freedom. Stress-intensity factors were calculated by using the nodal-force or virtual-crack-closure method.

An extensive research program was conducted by the Boeing Company under the funding of the Federal Aviation Administration (FAA), National Aeronautics and Space Administration (NASA), and the United States Air Force Research Laboratory (USAF/RL) to investigate the effects of multiple-site damage (MSD) on the residual strength of several types of fuselage splice joints. Under this program, a series of experiments were conducted for validation of the analytical tools. The test specimens consisted of large flat panels, curved panels, and an aft pressure bulkhead. The flat panel specimens included three types of typical fuselage longitudinal splice joints and one type of circumferential splice joint. The curved panels were tested under simulated loads of combined cabin pressure and fuselage down bending. Two fuselage skin splice types were tested. A section of an aft fuselage containing a large lead crack and MSD in the pressure dome was also tested to demonstrate the capabilities of the methodologies in analyzing actual aircraft structures. This paper presents the analytical approaches using Crack-Tip-Opening-Angle (CTOA) fracture criterion and the comparison of predictions with the experimental results in terms of crack linkup stress and residual strength.

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The Boundary Force Method (BFM) was formulated for the two-dimensional stress analysis of complex crack configurations. In this method, only the boundaries of the region of interest are modeled. The boundaries are divided into a finite number of straight-line segments; at the center of each segment, concentrated forces and a moment are applied. This set of unknown forces and moments is calculated to satisfy the prescribed boundary conditions of the problem. The elasticity solution for the stress distribution due to concentrated forces and a moment applied at an arbitrary point in a cracked infinite plate is used as the fundamental solution. Thus, the crack need not be modeled as part of the boundary. The formulation of the BFM is described, and the accuracy of the method is established by analyzing several crack configurations for which accepted stress-intensity factor solutions are known. The crack configurations investigated include Mode I and mixed-mode (Modes I and II) problems. The results obtained are, in general, within ±0.5% of accurate numerical solutions. The versatility of the method is demonstrated through the analysis of complex crack configurations for which limited or no solutions are known.

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