Fracture Analysis For Torsion Problem Of Isotropic Or Anisotropic Bar With Curvilinear Cracks

There have been many studies about the torsion problem of an isotropic bar with cracks, but most of them are available only to the special section geometry with special curvilinear cracks. And the examples within the scope of the boundary element method (BEM) are limited to the simple torsion problems. Moreover, some approaches have been satisfactorily applied to the torsion problem of an anisotropic bar without cracks, but for crack cases, techniques or approaches are difficult to be found.In this paper, the torsion fracture problem of an isotropic or anisotropic bar with curvilinear cracks is investigated. New boundary integral equations for the torsion problem of an isotropic bar with curvilinear cracks are derived by using integration by parts and other techniques to the traditional boundary integral formulations. And the boundary integral equations for the torsion problem of an anisotropic bar with curvilinear cracks are also derived by using the isotropicalized boundary element method. Then the anisotropic problem can be solved on the base of the boundary element method of isotropic problem.The new boundary integral equations can be directly applied to the torsion fracture analysis, in which the isotropic or anisotropic bar can be of arbitrary section and the cracks can be either straight or curvilinear. The present method eliminates the improperly posed problem of the traditionally boundary integral equations. And the new equations involve only singularity of order 1/r. The crack dislocation density shows the singularity of orderr1/2 near the crack tips. So the stress intensity factors can be obtained directly from the crack dislocation density. The boundary element numerical methods based on the new boundary integral equations are also established. The crack dislocation density and boundary displacement density are taken as unknowns. The torsion rigidity and stress intensity factors can be easily calculated by introducing interpolation models for bothsingular crack tip elements and other crack linear elements.Some typical torsion problems of isotropic or anisotropic bar with different sections, involving a straight, kinked or curvilinear crack are calculated. The numerical results demonstrate the validity and applicability of the present boundary element method.