Hypersingular integral equation for triple inclined cracks problems in half plane elasticity

Hypersingular integral equation associated with the modified complex potential is formulated to solve the three inclined cracks problems in an elastic half-plane with free traction boundary condition. The modified complex potential possesses two parts; the principal and the complementary parts. The principal part is derived from the original complex potential of the crack problem in an infinite plate. The complementary part eliminates the traction along boundary of half-plane caused by the principal part. The crack opening displacements (COD) is the unknown function and the traction is the right hand terms. The appropriate quadrature formula is adapted to solve the integral equation numerically and the stress intensity factor (SIF)is computed. The behaviour of SIF at crack tips is analysed. Numerical examples show that the SIF increases as the angle of inclined cracks and the distance of cracks from the boundary of half-plane increase. Our results are agreeable with the previous works

Hypersingular integral equation for triple circular arc cracks in an elastic half-plane

Triple circular arc cracks problems subjected to shear stress in half-plane elasticity is investigated. Modified complex potentials (MCP) with the free traction boundary condition are applied to formulate the hypersingular integral equation (HSIE) for the problems. The unknown crack opening displacements (COD) of the HSIE are solved numerically by using the appropriate quadrature formulas. Mode I and Mode II of nondimensional stress intensity factor (SIF) at all cracks tips are presented for the problems of three adjacent circular arc cracks, three circular arc cracks with dissimilar radius and three circular arc cracks in series in a half-plane. The results exhibit that as the crack opening angle increases and the distance of cracks closer to the boundary of half-plane, the nondimensional SIF increases. This indicates that the strength of material becomes weaker and the tendency of material to fail is higher

Hypersingular integral equations for triple Griffith cracks problems in an elastic half-plane

In this thesis, the triple Griffith cracks problems subjected to shear stress in an elastic half-plane with free traction boundary condition are formulated into hypersingular integral equation (HSIE) associated with the modified complex potential. Curved length coordinate method is utilized to transform the HSIEs for the various cracks configurations into the HSIEs for a straight crack on the real axis which requires less collocation points. With the suitable choices of collocation points on the cracks, the HSIEs is reduced to a system of linear equations. The system of HSIEs is solved numerically by adapting the appropriate quadrature rules and the unknown coefficients with M+1 collocation points are obtained. The obtained unknown coefficients will later be used in computing the stress intensity factors (SIFs). The nondimensional SIFs at all cracks tips for straight, inclined and circular arc cracks of various cracks configurations are analyzed. For the test problems, our results give good agreements with the existence results. Numerical results presented that the nondimensional SIFs are influenced by the inclined angle, crack opening angle and the distance of cracks to the boundary of half-plane. The influence vary for different cracks configurations. The higher the value of SIFs the weaker the material