Stress Intensity Factors at the Top of the Central Semi-Infinite Crack in an Arbitraly Loaded Isotropic Strip

A two-dimensional problem of elasticity theory on an isotropic strip with a central semi-infinite crack is considered. The load in the form of a concentrated force is assumed to be applied at an arbitrary point of the strip. Using invariant mutual integrals and solutions for a strip loaded with bending moments and longitudinal forces applied at infinity, expressions for stress intensity factors (SIF) for the problem under consideration are obtained. The cases of forces applied at the crack faces, at the strip boundaries and at the internal points of the strip are considered. Asymptotic expressions are obtained for the cases of application of forces far from the crack tip and forces applied at the crack faces near its tip. The obtained solutions are shown to coincide with known solutions for special cases: loads in the form of a pair of normal forces applied to the crack faces and forces applied far from the crack tip.