Analytical stress intensity factors for edge-cracked cylinder

Abstract

We use the Hamiltonian formalism in elasticity to analyze edge-cracked cylinder under various three-dimensional loading conditions. The Hamiltonian form enables the successful separation of the independent variables in polar coordinates so that symplectic eigenfunctions can be analytically determined. The displacements and stresses are proved to be conjugating to each other and can be expanded in series of the symplectic eigenfunctions. The coefficients of the series are determined from the lateral boundary conditions along the crack faces and the outer boundary conditions along the finite geometric domain. The stress intensity factors and T-stresses near the crack-tip are found analytically. Three modes of stress intensity factors can be obtained simultaneously. The result indicates that the stress intensity factors depend directly on the respective first few coefficients of the general eigenvalue solutions. Examples for mixed boundary conditions, e.g., partly clamped and partly forced, are included. The influence of various parameters on the stress intensity factors is discussed. Since the method is analytic, the results can be considered as benchmark for numerical methods in determining singularities.