# Stress Intensity Factors for Crack Problems in Bonded Dissimilar Materials

## DOI:

https://doi.org/10.5614/j.eng.technol.sci.2020.52.5.5## Keywords:

complex variable function, bonded dissimilar materials, hypersingular integral equation, stress intensity factor## Abstract

The inclined crack problem in bonded dissimilar materials was considered in this study. The system of hypersingular integral equations (HSIEs) was formulated using the modified complex potentials (MCP) function method, where the continuity conditions of the resultant force and the displacement are applied. In the equations, the crack opening displacement (COD) serves as the unknown function and the traction along the cracks as the right-hand terms. By applying the curved length coordinate method and the appropriate quadrature formulas, the HSIEs are reduced to the system of linear equations. It was found that the nondimensional stress intensity factors (SIF) at the crack tips depend on the ratio of elastic constants, the crack geometries and the distance between the crack and the boundary.### Downloads

## References

Nik Long, N.M.A. & Eshkuvatov, Z.K., Hypersingular Integral Equation for Multiple Curved Cracks Problem in Plane Elasticity, International Journal of Solids and Structure, 46, pp. 2611-2617, 2009.

Denda, M. & Dong, Y.F., Complex Variable Approach to the BEM for Multiple Crack Problems, Computer Methods in Applied Mechanics and Engineering, 141, pp. 247-264, 1997.

Chen, Y.Z., Ling, X.Y. & Wang, X.Z., Numerical Solution for Curved Crack Problem in Elastic Half-plane using Hypersingular Integral Equation, Philosophical Magazine, 89(26), pp. 2239-2253, 2009.

Elfakhakhre, N.R.F., Nik Long, N.M.A. & Eshkuvatov, Z.K., Stress Intensity Factor for an Elastic Half Plane Weakened by Multiple Curved Cracks, Applied Mathematical Modelling, 60, pp. 540-551, 2018.

Chen, Y.Z., Multiple Crack Problems for Two Bonded Half Planes in Plane and Antiplane Elasticity, Engineering Fracture Mechanics, 25(1), pp. 1-9, 1986.

Isida, M. & Noguchi, H., Arbitrary Array of Cracks in Bonded Half Planes Subjected to Various Loadings, Engineering Fracture Mechanics, 46(3), pp. 365-380, 1993.

Lan, X., Ji, S., Noda, N.A. & Cheng, Y., Stress Intensity Factor Solutions for Several Crack Problems using the Proportional Crack Opening Displacement, Engineering Fracture Mechanics, 171, pp. 35-49, 2017.

Hamzah, K.B., Nik Long, N.M.A., Senu, N. & Eshkuvatov, Z.K., Stress Intensity Factor for Multiple Cracks in Bonded Dissimilar Materials using Hypersingular Integral Equations, Applied Mathematical Modelling, 73, pp. 95-108, 2019.

Huang, K., Guo, L. & Yu, H., Investigation on Mixed-mode Dynamic Stress Intensity Factors of an Interface Crack in Bi-materials with an Inclusion, Composite Structures, 202, pp. 491-499, 2018.

Itou, S., Stress Intensity Factors for Four Interface-close Cracks between a Nonhomogeneous Bonding Layer and One of Two Dissimilar Elastic Half-planes, European Journal of Mechanics A/Solids, 59, pp. 242-251, 2016.

Muskhelishvili, N.I., Some Basic Problems of the Mathematical Theory of Elasticity. Leyden: Noordhoff International Publishing, 1953.