Stress intensity factors around a crack parallel to a free surface of a half-plane

Abstract

In this paper, stress intensity factors for a crack in a half-plane are considered. The crack is parallel to the stress-free surface of the half-plane and subjected to internal gas pressure. By using Fourier transforms, the mixed boundary value problem is reduced to the solution of a pair of dual integral equations. To solve the equations, the crack surface displacements are expanded in a series of functions which are zero outside the crack. The unknown coefficients in that series are solved with the aid of the Schmidt method. The stress intensity factors are calculated numerically and the results are compared with those given in other papers.

Finite element analysis of a subsurface crack

“…In view of this, we [7] solved this problem once more using a dislocation model. Our analytical results agreed with Chen et al [2], Higashida and Kamada [3], and Itou [6] for tensile loading. However, for shear loading the crack faces were found to overlap each other for the stress-free boundary condition over the crack faces.…”

“…The problem of determining the stress distribution in the neighborhood of a crack parallel to the surface of a semi-infinite medium has been studied for tensile, compressive or concentrated force loadings [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15]. For a brief review, see [7].…”

“…However this correction was missed by several subsequent publications [3][4][5][6] which caused some confusion. For example recently Itou [6] reconsidered this problem under tensile loading and was puzzled by the difference between his results and those of Erdogan [1] so he concluded without proof that perhaps the boundary condition inside the crack failed to be satisfied in his case. In view of this, we [7] solved this problem once more using a dislocation model.…”

The G2 constant displacement discontinuity method – Part II: Solution of half-plane crack problems

“…3 presents the variation of the dimensionless mode I and II SIFs ðK i =ðp ffiffiffi a p Þ; i ¼ I; IIÞ on the relative crack distance (h/a) from the stress-free surface (y = 0) as they are predicted by the G2CDD, and CDD methods, while the crack was discretized by 50 mode I dislocation elements. The continuous and dashed curves present the semi-analytical solution referring to the mode I and II SIF's, respectively, proposed by Itou (1994). This author solved quite accurately this specific problem by using the Fourier transform technique and the theory of dual integral eqns.…”

A new boundary integral equation method for analysis of cracked linear elastic bodies

“…Figure 3 shows an internal horizontal crack of length 2a under a uniform pressure p in an isotropic half-plane x 2 ≥0. The distance from the crack to the free surface is h. The problem was solved by Ito (1994). The SIFs for several ratios of h/a are given in Table 1 and compared to those obtained by Ito (1994).…”