The influence of the shape and curvature of crack fronts on the values of the order of singularity and the stress intensity factor

Summary

The forms of cracks which are created in various cases and especially during stress-corrosion cracking need for their description the knowledge of the ratio of their total opening and their length, their maximum curvatures at the crack tip zones as well as the geometry describing the regions near their curved regions around the crack tips. These factors are studied in the paper and the values of stress intensity factors and the orders of singularity existing at the effective point of singularity of stresses, so that the stress field in the cracked plate to be described with satisfactory accuracy. For this purpose convenient functions mapping the various shapes of the deformed cracks are defined by using the Schwarz-Christoffel mapping technique from the crack shapes to the unit circle. Then the potential function φ(ζ) of Muskhelishvili is defined in closed form.

The form and size of the initial curve and the caustic or caustics created at the crack tip vicinity are established by the analysis based on the form of the φ(ζ)-function. The order of singularity and the respective stress intensity factors at the position of the singular point are evaluated. A comparison of the values of the first stress invariant derived from the closed form solution, the present one, as well as from the singular one-term solution assuming that the singular point is placed at mid-distance from the apex of the crack and the center of curvature of the crack tip indicates the accuracy of the method.