Stress intensity factor for multiple inclined or curved cracks problem in circular positions in plane elasticity

Abstract

The problems of multiple inclined or curved cracks in circular positions is treated by using the hypersingular integral equation method. The cracks center are placed at the edge of a virtual circle with radius R. The first crack is fixed on the x-axis while the second crack is located on the boundary of a circle with the varying angle, θ. A system of hypersingular integral equations is formulated and solved numerically for the stress intensity factor (SIF). Numerical examples demonstrate the effect of interaction between two cracks in circular positions are given. It is found that, the severity at the second crack tips are significant when the ratio length of the second to the first crack is small and it is placed at a small angle of θ .

Analytical study on stress intensity factor due to the propagation of Griffith crack in a crystalline monoclinic layer subjected to punch pressure

“…Numerous researchers deal the problems of moving crack in various elastic solids having distinct anisotropy and obtained the expressions of SIF with the impact of several dynamic loading conditions. [28][29][30][31][32][33] As per the authors' knowledge, no mathematical investigation has been made till date to examine the propagation of Griffith crack influenced by plane waves in a monoclinic crystalline layer. The present mathematical model is a novel investigation for SIF at the tip of moving Griffith crack associated with plane wave propagation in a crystalline monoclinic layer with moving parallel punch pressure acting on the boundaries of the layer under the impact of mechanical point loading.…”

Mode Stresses for the Interaction between Two Inclined Cracks in Bonded Two Half Planes

“…These problems will affect the engineering structures which related to the stability and safety of the materials. A number of works have been discussed to investigate the characteristics of stress intensity factors (SIFs) at all crack tips for the crack problems in an infinite plane [1,2], half plane [3,4] and bonded two half planes [5,6,7]. The nondimensional SIFs for the crack problems in bonded two half planes subjected to the various stresses was calculated by using the body force method with continuous distributions along cracks [5].…”

Water Wave Scattering by a Thin Vertical Submerged Permeable Plate

“…Hypersingular integral equations of order 2 and 3 arise as a consequence of the reduction of boundary value problems associated with Laplace equation when the boundary conditions involving normal derivatives are enforced. The applications of the hypersingular integral equation of the first kind (HSIE I) of orders 2 and 3 are widely available in the literature of fluid mechanics [6,15,16], acoustic waves [14], fracture mechanics [2], crack problem [24] etc. However, involvement of hypersingular integral equations of the second kind (HSIE II) is not so frequent, especially in the literature of linear water waves.…”