Stress intensity factors for cracks at or close to and parallel to an interface

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Stress intensity factors for cracks at or close to and parallel to an interface


Author: So, Wai-man Grace
Title: Stress intensity factors for cracks at or close to and parallel to an interface
Degree: M.Phil.
Year: 2002
Subject: Hong Kong Polytechnic University -- Dissertations
Strains and stresses
Fracture mechanics
Department: Dept. of Mechanical Engineering
Pages: xix, 118, 43 p. : ill. ; 30 cm
Language: English
InnoPac Record:
Abstract: The problems concerning cracks at or close to the interface of two dissimilar materials are gaining importance for their applications in the use of advanced and composite materials, and in electronic packaging. In this work, methods for determining the complex stress intensity factors for cracks on an interface were examined and improved, while conventional stress intensity factors for cracks close to and parallel to an interface are also determined, with a view of designing a test specimen for studying such cracks. In the case of interfacial cracks, plates and beams of various thickness and modulus ratios are modeled for finite element analysis and the complex stress intensity factors of interfacial cracks are obtained by a new modified stiffness derivative method. This new method made use of the strain energies of near-crack-tip elements before and after a virtual crack extension: The cumbersome need for computing element stiffnesses in the originally and commonly adopted procedure is removed. Accuracy of the method was verified for central cracks, edge cracks and the four-point bending specimen configuration. In the case of cracks close and parallel to the interface, a bimaterial four point bending specimen is developed. Finite element analysis is employed to determine specimen configurations that produce constant strain energy release rates. A crack surface displacement method is employed to find the stress intensity factors for beams of different thickness ratios and modulus ratios, different crack lengths and for cracks at various distances from the interface. Displacements on the crack surface are then used in conjunction with a semi-infinite-crack crack model to solve for the opening mode and the shearing mode stress intensity factors. Basing on the strain energy release rate and stress intensity factor plots, recommendations for support spacing and specimen heights are made. Due to the large number of parameters involved, a special way for normalizing the stress intensity factor values is implemented by using values from a beam of the same dimension but consisting of one material only. These normalized values are curve-fitted using a combination of power and polynomial terms in the distance between the crack and the interface. The use of these curves is demonstrated by an application to cracks near solder/copper, Ni/MgO, and Si/Cu interfaces. Finally the relationship between the conventional stress intensity factors for a crack close to and parallel to the interface and the complex stress intensity factors of a corresponding interfacial crack is studied. The validity of a closed-form relationship is established within a certain range of crack-interface separation distance.

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