Asymptotic approximations to crack problems

Complex variable methods are applied to the plane elastic problem of a rectangular tensile sheet with symmetric edge cracks. A mapping function is used which is sufficiently flexible to account for both variations of crack length and length/width ratios of the sheet on the stresses local to the crack tips. The stress-intensity factors are determined numerically for varying crack lengths in sheet with 1 × 1 and 3 × 1 length/width ratios and compared with Irwin’s earlier approximation derived from Westergaard’s collinear crack solution. The results indicate that the approximation is valid for deep cracks but in error by 13 percent for small crack depths.