Boundary element method for fracture mechanics analysis of 3d non-planar cracks in anisotropic solids

Abstract

Among the numerical approaches to fracture mechanics analysis of cracked anisotropic solids, the boundary element method is notable for high accuracy and performance due to its semi-analytical nature and the use of only boundary mesh. Various boundary element techniques were proposed for 3D fracture mechanics analysis. However, the main problem of these approaches is the treatment of singular and hypersingular integrals, which can demand analytic evaluation of coefficient at kernel singularity at singular point in local curvilinear coordinates, which produce cumbersome equations in the case of non-planar geometries. Therefore, the paper presents novel formulation of the boundary element method for 3D fracture mechanics analysis of anisotropic solids with non-planar cracks. Pan’s single domain boundary element formulation is extended with several novelties, which allow accurate analysis of non-planar geometries. These are modified Kutt’s numerical quadratures with Chebyshev nodes for accurate evaluation of singular and hypersingular integrals; polynomial mappings for smoothing the integrand at the crack front line; and special shape functions, which account for a square-root stress singularity at crack front and allow accurate determination of stress intensity factors. The kernels of boundary integral equations are evaluated using the exponentially convergent quadrature, which allows derivation of fast boundary element technique. The procedure for accurate numerical determination of stress intensity factors at arbitrary point of the crack front is also developed. Numerical examples are presented, which show high accuracy of the proposed boundary element method. It is shown that non-planar cracks exhibit shearing mode opening along with normal one due to its geometry and direction of the applied loading. Present approach can be combined with Sih’s strain energy density criterion to study 3D cracks propagation in anisotropic elastic solids under fatigue loading, which is the direction of future research.