Closed‐form solution for an orthotropic elastic strip with a crack perpendicular to the edges under arbitrary anti‐plane shear

Abstract

A cracked orthotropic elastic strip of finite width is analyzed under antiplane shear loading. For four frequently encountered constraint edges, i.e. free-free, clamped-clamped, free-clamped, or clamped-free edges, the Fourier series method is used to reduce triple series equations, and then to a mixed boundary value problem associated with a mode-III crack for each case to a singular integral equation. Closed-form solutions are derived for the resulting equations, and formulae for calculating stress intensity factors are obtained for an internal crack and edge cracks subjected to arbitrarily varying loading. Numerical results of the stress intensity factors for an eccentric, central, and edge crack are shown graphically for the case of uniform loading at the crack faces. Obtained formulae for determining stress intensity factors can be taken as a benchmark of numerical evaluations. The derived results are also applicable to an isotropic elastic strip with an anti-plane shear crack normal to the edges.

Effect of boundary conditions on the interfacial fracture behavior: Circular arc antiplane crack model for an annular sector bilayer plate

“…In addition, the similar phenomenon can also be found from the internal crack problem with various boundary conditions (see Fig. 3 of Li and Lee [27]). As observed, for the FF and CC radial edges, the crack tip A and B…”

“…(27). By adding and subtracting this asymptotic value to and from 5 () Qn, one can obtain a Cauchy singular integral equation…”

“…Besides, other correlative studies for rectangular strip can confirm this suspicion. For example, Li and Lee [27] discussed the effect of constraint edges on singular elastic behavior of a crack, in which an rectangular strip with an internal or edge crack was performed and the crack was assumed normal to the edges and subjected to arbitrary anti-plane shear loading. Here the strip edges are assumed either 4 traction-free or clamped.…”

The Yoffe-type moving tubular interface crack in a hollow composite cylinder with finite length

“…In addition, the similar phenomenon can also be found from the internal crack problem with various boundary conditions (see Fig. 3 of Li and Lee [22]). There only exist the different boundary conditions on the inner surfaces between the F-F and C-F edges (or C-C and F-C edges), but they have the same boundary conditions on the outer surfaces.…”

“…Li and Lee [22] discussed the effect of constraint edges on singular elastic behavior of crack, in which an orthotropic elastic strip with an internal or edge crack is performed and the crack is assumed normal to the edges and subjected to arbitrary anti-plane shear loading. The strip edges are assumed either traction-free or clamped in their work.…”