Eur. J. Mech. ASolids 18 1999 465–479
Elsevier, Paris
Analysis of interfacial cracks emanating from a hole in a bi-material plate
J.S. Kuang
a
, Y.H. Wang
b
a
Department of Civil Engineering, Hong Kong University of Science Technology, Kowloon, Hong Kong
b
Department of Civil Engineering, Huazhong University of Science Technology, Wuhan, China Received 12 July 1997; revised and accepted 10 August 1998
Abstract – In this paper the boundary collocation method has been used successfully to analyse the interfacial cracks emanating from a hole in a
bi-material plate. The stress functions are assumed such that they can satisfy a series of governing conditions, such as the equilibrium equations in the domain, the boundary conditions on the crack surfaces, and the stress and displacement conditions on the crack surfaces and across the interface.
Moreover, they can also represent the stress singularity at the crack tips. Thus, only the boundary conditions on the hole and the external boundary of the plate are necessarily to be considered, and they can be approximately satisfied by the collocation method and least square technique. Numerical
investigations for two cases, two-equal-crack and one crack, are carried out. It is shown that the proposed method is effective and gives satisfactory results. In addition, the proposed approach shows many advantages compared to other methods and can be used for investigating more general cases of
cracks emanating from a hole in a bi-material plate.
Elsevier, Paris
1. Introduction
It is well recognised that cracks originate most frequently from stress concentration areas developed around holes. In engineering practice of “stress relief”, holes may be drilled at the end of a thin slot to reduce the
stress concentration. When holes are drilled at the interface of two different metals which are bound or welded together, cracks could grow from these holes. Similar phenomena occur in composite interfaces. For example,
concrete is made as a two-phase composite consisting of mortar and aggregate inclusions. At the interface, air froth or voids could exist, and cracks may emanate from these regions. In the analysis of rock fracture, it is
important to investigate the interaction and coalescence of pressurised fracture proceeding from the boreholes. Therefore, the study of interfacial cracks emanating from holes in a bi-material structural element has its
practical significance.
The boundary collocation method BCM Sawyer and Anderson, 1972 has been shown as an effective method for a variety of crack problems for plates of finite geometry with isotropic and homogeneous materials.
For the bi-material interfacial crack problem, the analysis is different from that in isotropic and homogeneous bodies, since a special stress singularity at the crack tips exists Erdogan, 1963, 1965; Rice and Sih, 1965.
A series of assumed complex stress functions for the central or edge interfacial crack in a bi-material plate have been proposed, and the BCM is used to calculate the stress intensity factors Woo et al., 1992.
In this paper, the BCM is used further to analyse the behavior of interfacial cracks emanating from a hole in a bi-material plate. A set of complex stress functions are assumed with r
−12∓iε
stress singularity at the crack tips. They can satisfy a series of governing conditions, such as the equilibrium equations in the domain, the
boundary conditions on the crack surfaces, and the stress and displacement conditions on the crack surfaces and across the interface, as well as the single-value displacement conditions. Only the boundary conditions on
the hole and the external boundary of the plate are necessarily to be considered, and they can be approximately
466 J.S. Kuang, Y.H. Wang
satisfied by the BCM and least square technique. Numerical investigations for two cracking cases, two-equal- cracks and one crack, under biaxial or uniaxial loading are given and the results are presented in the related
figures and discussed.
2. Basic formulation
