A closed-form solution to the equivalent through-crack model for surface cracks

Theocaris, PS; Wu, DL

dc.contributor.author	Theocaris, PS	en
dc.contributor.author	Wu, DL	en
dc.date.accessioned	2014-03-01T01:06:31Z
dc.date.available	2014-03-01T01:06:31Z
dc.date.issued	1986	en
dc.identifier.issn	00015970	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/9434
dc.subject	Closed Form Solution	en
dc.subject	Singular Integral Equation	en
dc.subject	Three Dimensional	en
dc.title	A closed-form solution to the equivalent through-crack model for surface cracks	en
heal.type	journalArticle	en
heal.identifier.primary	10.1007/BF01176597	en
heal.identifier.secondary	http://dx.doi.org/10.1007/BF01176597	en
heal.publicationDate	1986	en
heal.abstract	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 forces N(x, 0) and moments M(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. © 1986 Springer-Verlag.	en
heal.publisher	Springer-Verlag	en
heal.journalName	Acta Mechanica	en
dc.identifier.doi	10.1007/BF01176597	en
dc.identifier.volume	58	en
dc.identifier.issue	3-4	en
dc.identifier.spage	153	en
dc.identifier.epage	173	en