On the Determination of Stresses, Displacements, and Stress-Intensity Factors in Edge-Cracked Sheets With Mixed Boundary Conditions

The stresses and displacements in a finite, isotropic, elastic sheet containing a single edge crack are considered. Solutions are constructed through superposition of the solutions due to Williams. Variational principles are used to obtain solutions for mixed boundary conditions on the edge of a sheet containing a single, straight, unloaded edge crack. Trial solutions are constructed by expanding stresses and displacements in series of Williams’ solutions and a procedure for determining the coefficients for the best finite expansion is developed through the use of Reissner’s principle. The method is applicable to any combination of prescribed displacements and prescribed tractions on the boundary. The method is used to determine the stress-intensity factor for a rectangular edge-cracked sheet with two edges free of traction and a prescribed extension of the ends. Values of KI and compliance are given for various aspect ratios and crack lengths.