Boundary Element Analysis for Piezoelectric Cracks by an Interaction Integral

In this paper, an interaction integral is applied to evaluate the crack-tip field intensity factors for piezoelectric cracks by using BEM. Based on this, the fracture parameters for different crack configurations and loading conditions are analyzed in details for both the center crack and edge crack problem. According to the present results, the path-independent behavior of the interaction integral is verified. The comparison of the I-integral results with those by the J-integral and the displacement interpolating methods shows a good agreement.

PARAMETER AND INTERACTION STUDY OF EDGE CRACK PROBLEM USING MESHFREE METHOD

In this work, element free Galerkin method (EFGM) has been used to obtain the solution of edge crack problem under mechanical loads as it provides a versatile technique to model static as well as moving crack problems without any requirement of remeshing. At first, some techniques are presented for enriching the EFG approximations near the crack tip such as extrinsic and intrinsic enrichment. Extrinsic enrichment involves the addition of solution form to the trial function, whereas the EFG basis is expanded to include few terms from crack tip solution in intrinsic enrichment. Apart from enrichment techniques, four basic techniques of smoothing meshless approximations near nonconvex boundaries are also presented such as diffraction, transparency, see through and wedge model. These techniques are then used for the parameteric analysis of an edge crack problem under mode-1 loading and results obtained using different approaches are compared with each other as well as with exact solution. Among these techniques, the extrinsic PU enrichment technique was found to be more accurate as compared to other approaches. Extrinsic PU enrichment technique has also been used for the analysis of a shear edge crack problem. In all these techniques, the value of mode-1 stress intensity factor and mode-2 stress intensity factor has been evaluated by interaction integral approach. Effect of crack orientation is also studied for different cases.

SINGULAR INTEGRAL EQUATION METHOD FOR MULTIPLE CURVED EDGE CRACKS EMANATING FROM BOUNDARY OF HALF-PLANE

This paper provides, an elastic solution for multiple curved edge cracks emanating from the boundary of the half-plane. After placing the distributed dislocations at the prospective sites of cracks in an infinite plate, the principal part of the complex potentials is obtained. By using the concept of the modified complex potentials, the complementary part of the complex potentials can be derived. The whole complex potentials satisfy the traction free condition along the boundary of half-plane automatically. This is a particular advantage of the suggested method. This concept or method of the modified complex potentials is a counterpart of the Green's function method, which is universal in mathematical physics. The direct usage of this method cannot provide a solution in detail. Comparing with the line edge crack case, the following points are significant in the presented study. The relevant kernels in the integral equation are more complicated than in the line edge crack case and the relevant integrations in the problem should be completed on curves. This paper solves a rather complicated problem, the multiple curved edge crack problem, and gives the final solution. A singular integral equation is formulated with the dislocation distribution being unknown function and the traction being the right hand term. The singular integral equation is solved by using the curve length method in conjunction with the semiopening quadrature rule. Periodic curved edge crack problem is also addressed. Finally, several numerical examples are given to illustrate the efficiency of the method presented.