Summary
A closed-form solution for plates containing surface cracks is obtained by using an equivalent through-crack model, which reduces the three-dimensional problem of the surface cracked plates to a two-dimensional Hilbert problem. The effect of surface crack is replaced by a continuous distribution of forcesN(x, 0) and momentsM(x, 0) applied along the crack face of the equivalent through-crack model. A convenient form of expressing these forces and moments is by using power polynomials. Then the singular integral equation, expressing the solution of the Hilbert problem can be readily integrated.
According to this model we assumed that the crack depth at extremities, where the crack intersects the free surface of the plate, is not zero. This assumption, corroborated by experimental evidence, means that a singularity exists at the extremities of the crack. The experimental evidence was achieved by using the method of caustics and photoelasticity. The results of the evaluation of the stress intensity factor for elliptical cracks were compared well with the solutions of the respective 3-D problem solved by applying the finite-element method, the line-spring model based on the Reissner plate theory, the finite-element alternating method and the benchmark estimate. The distribution of the stress intensity factor along the crack lips, as calculated in this paper, was dropping off rapidly in the surface layer and it was very close to the results given by the approximate 3-D theory.
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Theocaris, P.S., Wu, D.L. A closed-form solution to the equivalent through-crack model for surface cracks. Acta Mechanica 58, 153–173 (1986). https://doi.org/10.1007/BF01176597
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DOI: https://doi.org/10.1007/BF01176597