Interaction Between a Circular Inclusion and an Arbitrarily Oriented Crack

Abstract

The plane interaction problem for a circular elastic inclusion embedded into an elastic matrix which contains an arbitrarily oriented crack is considered. Using the existing solutions for the edge dislocations [6] as Green’s functions, first the general problem of a through crack in the form of an arbitrary smooth arc located in the matrix in the vicinity of the inclusion is formulated. The integral equations for the line crack are then obtained as a system of singular integral equations with simple Cauchy kernels. The singular behavior of the stresses around the crack tips is examined and the expressions for the stress-intensity factors representing the strength of the stress singularities are obtained in terms of the asymtotic values of the density functions of the integral equations. The problem is solved for various typical crack orientations and the corresponding stress-intensity factors are given.

Mode I Strain Energy Release Rate in composite laminates in the presence of voids

“…However, it seems that analytical tools describing the crack-void interaction are available only for isotropic plate loaded in tension (see [22][23][24][25] for some examples) and, to the best of authors' knowledge, no solutions have been developed so far for composite DCBs.…”

On the Accuracy of Benchmark Tables and Graphical Results in the Applied Mechanics Literature1

“…In order to illustrate the points made above we consider an example involving two papers presenting results for normalized stress intensity factors of a matrix crack in the presence of an elastic cylinder: one classic paper by Erdogan, Gupta, and Ratwani [1], and a recent paper by Cheeseman and Santare [2]. In the latter paper the authors validate their algorithm by comparing with results from the former paper.…”

“…We simply recompute some results of Erdogan, Gupta, and Ratwani [1] and Cheeseman and Santare [2] using an algorithm based on a pair of integral equations for the crack and inclusion problem developed by Helsing and Peters [3]. The integral equations, number (48) and number (49) in Helsing and Peters, are of Fredholm's second kind with compact operators.…”

“…Figure 1: Left, a straight crack outside an inclusion under uniaxial tension. This is the setup of Erdogan, Gupta and Ratwani [1] corresponding to their Table 3. Right, an arc-shaped crack outside a circular inclusion under biaxial tension.…”

Crack extension near an auxetic particle using symmetric Galerkin boundary elements

“…The general problem of a crack interacting with a particle has been studied analytically both for isotropic materials (see, for example, [11][12][13]) and for anisotropic problems (see, for example, [14]). The most relevant to the study reported here is the paper by [15] where the problem of a crack approaching either a coated or uncoated inclusion was studied.…”