Abstract
The modified complex variable function method with the continuity conditions of the resultant force and displacement function are used to formulate the hypersingular integral equations (HSIE) for an inclined crack and a circular arc crack lies in the upper part of bonded dissimilar materials subjected to various remote stresses. The curve length coordinate method and appropriate quadrature formulas are used to solve numerically the unknown crack opening displacement (COD) function and the traction along the crack as the right hand term of HSIE. The obtained COD is then used to compute the stress intensity factors (SIF), which control the stability behavior of bodies or materials containing cracks or flaws. Numerical results showed the behavior of the nondimensional SIF at the crack tips. It is observed that the nondimensional SIF at the crack tips depend on the various remote stresses, the elastic constants ratio, the crack geometries and the distance between the crack and the boundary.
Highlights
A number of papers have been publish to analyze the behaviour of stress intensity factors (SIF) at the crack tips subjected to specific remote stress for the crack problems in an infinite plane [1,2], finite plane [3,4], half plane [5,6] or bonded dissimilar materials [7,8,9]
It is observed that the nondimensional SIF at F1A1 and F2A1 are equals to negative of F1A2 and F2A2, respectively
The nondimensional SIF increases subjected to shear stress σ=x1 σ=x2 p and tearing stress σ= x1y1 σ= x2 y2 p, SIF decreases subjected to normal stress σ=y1 σ=y2 p and mixed stress σ=x1 σ=x2 σ=y1 σ=y2 p as α increases at crack tip A1
Summary
A number of papers have been publish to analyze the behaviour of stress intensity factors (SIF) at the crack tips subjected to specific remote stress for the crack problems in an infinite plane [1,2], finite plane [3,4], half plane [5,6] or bonded dissimilar materials [7,8,9]. The logarithmic singular integral equations were used to solve the nondimensional SIF for a circular arc crack lie in the upper part of bonded dissimilar materials [9]. The combinations of Chebyshev polynomials and collocation methods were utilized to solve the nondimensional SIF of a perpendicular crack to the interface of bonded dissimilar materials [10]. The objectives of this paper is to formulate the HSIE and analyze the behavior of nondimensional SIF by using the modified complex variable function method for an inclined and a curved crack lie in the upper part of bonded dissimilar materials subjected to the various remote stresses such as shear stress σ=x1 σ=x2 p , normal stress σ=y1 σ=y2 p , tearing stress σ= x1y1 σ= x2 y2 p or mixed stress σ=x1 σ=x2 σ=y1 σ=y2 p
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