# Mixed‐mode stress intensity factors of a three‐dimensional crack in a bonded bimaterial

T.Y. Qin (College of Science, China Agricultural University, Beijing, People's Republic of China)
B.J. Zhu (College of Science, China Agricultural University, Beijing, People's Republic of China College of Mechatronic and Information Engineering, Hainan University, Haikou, People's Republic of China)
N.A. Noda (Department of Mechanical Engineering, Kyushu Institute of Technology, Kitakyushu, Japan)

ISSN: 0264-4401

Article publication date: 4 April 2008

406

## Abstract

### Purpose

This paper aims to calculate the mixed‐mode stress intensity factors (SIFs) of a 3D crack meeting the interface in a bimaterial under shear loading by a hypersingular integral equation (HIE) method, And further to assess the accuracy of numerical solutions for the mixed mode SIFs along the crack front.

### Design/methodology/approach

A 3D crack modeling is reduced to solving a set of HIEs. Based on the analytical solutions of the singular stress field around the crack front, a numerical method for the HIEs is proposed by a finite‐part integral method, where the displacement discontinuities of the crack surface are approximated by the product of basic density functions and polynomials. Using FORTRAN program, numerical solutions of the mixed‐mode SIFs of some examples are presented.

### Findings

The numerical method is proved to be an effective construction technique. The numerical results show that this numerical technique is successful, and the solution precision is satisfied.

### Research limitations/implications

This work takes further steps to improve the fundamental systems of HIE for its application in the fields of arbitrary shape crack problems. Propose several techniques for numerical implementation, which could increase the efficiency and accuracy of computation.

### Practical implications

Whenever there is a structure containing the 3D crack, the analysis method described in this paper can be utilized to find the critical configurations under which the structure may be most vulnerable. In such cases, the strength predictions would be safer if the crack could be taken into account.

### Originality/value

This paper is the first to apply HIE method to analyzing the mixed‐mode crack meeting the interface in 3D dissimilar materials. Numerical solutions of the mixed‐mode SIFs can give the satisfied solution precision.

## Citation

Qin, T.Y., Zhu, B.J. and Noda, N.A. (2008), "Mixed‐mode stress intensity factors of a three‐dimensional crack in a bonded bimaterial", Engineering Computations, Vol. 25 No. 3, pp. 251-267. https://doi.org/10.1108/02644400810857083

## Publisher

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Emerald Group Publishing Limited