Mode Stresses for the Interaction between an Inclined Crack and a Curved Crack in Plane Elasticity

2020

KEM

The various mode of stresses for the interaction between two inclined cracks in the upper part of bonded two half planes which are normal stress (Mode I), shear stress (Mode II), tearing stress (Mode III) and mixed stress was studied. For this problem, the modified complex potentials (MCPs) method was used to develop the new system of hypersingular integral equations (HSIEs) by applying the conditions for continuity of resultant force and displacement functions with the unknown variable of crack opening displacement (COD) function and the right hand terms are the tractions along the crack. The curve length coordinate method and Gauss quadrature rules were used to solve numerically the obtained HSIEs to compute the stress intensity factors (SIFs) in order to determine the strength of the materials containing cracks. Numerical solutions presented the characteristic of nondimensional SIFs at the cracks tips. It is obtained that the various stresses and the elastic constants ratio are influences to the value of nondimensional SIFs at the crack tips.

Section: Introductionmentioning

confidence: 99%

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

Hamzah

2020

KEM

Straight cracks in circular positions in plane elasticity

Rafar

AIP Conference Proceedings

Senu

2016

A system of hypersingular integral equation for the multiple straight cracks in a circular position in plane elasticity is formulated and presented. The center of the cracks are placed at the edge of a circle with radius R. The second crack in this problem is located in a different position based on the varying angle, θ. The sraight cracks problem is reduced to a system of hypersingular integral equations by using the method of complex potential. With the help of particular quadrature rules, the unknown coefficients are solved numerically from the resulting system of hypersingular integral equations. The obtained unknown coefficients are then can be used for determining the stress intensity factor (SIF). To prove that the suggested method can be used to solve more complicated model cases of the cracks in circular positions, examples are given to demonstrate the behaviour of SIF for different crack positions.

Stress intensity factor for multiple cracks in half plane elasticity

Elfakhakhre

AIP Conference Proceedings

Eshkuvatov

2017

Self Cite

Abstract. The multiple cracks problem in an elastic half-plane is formulated into singular integral equation using the modified complex potential with free traction boundary condition. A system of singular integral equations is obtained with the distribution dislocation function as unknown, and the traction applied on the crack faces as the right hand terms. With the help of the curved length coordinate method and Gauss quadrature rule, the resulting system is solved numerically. The stress intensity factor (SIF) can be obtained from the unknown coefficients. Numerical examples exhibit that our results are in good agreement with the previous works, and it is found that the SIF increase as the cracks approaches the boundary of half plane.