by

DOI: 10.1007/s10704-005-0832-y
Print publication date: 6/1/2005
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DOI: 10.1007/s10704-005-0831-z
Print publication date: 6/1/2005
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by Xiao, Z. M.; Zhao, J. F.; Fan, H.

A Zener–Stroh (Z–S) crack can be nucleated on the interface of a multi-layered structure when a dislocation pileup is stopped by the interface which works as an obstacle. During the entire fracture of a crack, Z–S crack mechanism controls the initial stage, or the first phase of crack initiation and propagation. In our current research, investigation on a Z–S crack at the interface of a multi-layered structure is carried out. The problem is formulated into a set of singular integral equations by applying the distributed dislocation based fracture mechanics. The obtained integral equations are then solved with numerical method after the singularities at crack tips are carefully checked. In the solution procedure, the contact zone model is adopted to cease the oscillation behavior. The contact zone length, the stress field near the crack tips and the stress intensity factors (SIFs) of the crack are discussed based on the numerical results of two typical structures. It was found that the contact zone length could be very large and was determined by the properties of all the three materials and loading conditions. Our analysis also shows that the thickness of the middle thin layer plays a critical role for the fracture behavior of the crack when it is comparable to the crack length.

DOI: 10.1007/s10704-005-6701-x
Print publication date: 6/1/2005
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by Berdichevsky, Victor; Le, Khanh Chau

A theory of microcracks nucleation in brittle solids is proposed. Theoretical predictions are compared with the experimental data for silica glass.

DOI: 10.1007/s10704-005-0632-4
Print publication date: 6/1/2005
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by MA, Lifeng; Korsunsky, Alexander M.

In this paper the criterion for crack-growth in solids is investigated on the basis of the concept of potential energy release rate. The expressions for path-independent vector integral Ji (i = 1,2) are derived for brittle crack growth. The relationship is then established between the value of the path-independent vector integral Ji and the potential energy release rate for crack growth in an arbitrary orientation. This allows the prediction of crack re-orientation angles on the basis of the maximum energy release rate (MERR) criterion. The crack growth angle is determined analytically as a function of (). This result is compared with other theoretical formulations of crack growth criteria, as well as with experimental results reported in the literature, and good agreement is found. The formulation provides a rigorous basis for numerical modelling of the processes of crack initiation and propagation.

DOI: 10.1007/s10704-005-0631-5
Print publication date: 6/1/2005
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by Dong, C. Y.; Lee, Kang Yong

In this paper, the boundary integral equation approaches are used to study the doubly periodic array of cracks/rigid-line inclusions in an infinite isotropic plane medium. For the doubly periodic rigid-line inclusion problems, the special integral equation containing the axial and shear forces within the rigid-line inclusion is used. The doubly periodic crack problems are dealt with using the displacement discontinuous integral equation approach. Stress intensity factors, effective elastic properties for doubly periodic array of cracks/rigid-line inclusions are calculated and compared with the available numerical solutions.

DOI: 10.1007/s10704-005-5993-1
Print publication date: 6/1/2005
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by Mühlich, U.; Donoso, J. R.; Landes, J. D.

A new
$$\cal J$$ estimation scheme based on the Common Format Equation (CFE) is laid out for Compact Tension (C(T)) specimens. In this context, the CFE constraint factor Ω*, originally given only for the two limits plane stress, and plane strain, is discussed. A nonlinear finite element analysis of the behaviour of blunt notched C(T) specimens with varying crack length was performed. The specimen thickness B has been varied from 3.125 up to 25 mm. Furthermore the special cases plane stress and plane strain have been considered. Considering a linear elastic – ideal plastic material, a limit load analysis has been performed numerically from which Ω* has been obtained as a function of the ligament-to-thickness-ratio B/b. The
$$\cal J$$-integral as a function of the load line displacement v has been determined for isotropic, nonlinear hardening material, where
$${\cal J}$$ has been calculated using its definition as contour or surface integral, respectively. It is shown that if the obtained
$${\cal J}(v)$$ curves are normalized according to the Common Format Methodology, all curves fall approximately into one single curve. This allows to estimate J(v) curves for C(T) specimens using the CFE.

DOI: 10.1007/s10704-005-5825-3
Print publication date: 6/1/2005
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by Xiao, H. T.; Yue, Z. Q.; Tham, L. G.; Lee, C. F.

This paper presents a boundary element analysis of elliptical cracks in two joined transversely isotropic solids. The boundary element method is developed by incorporating the fundamental singular solution for a concentrated point load in a transversely isotropic bi-material solid of infinite space into the conventional displacement boundary integral equations. The multi-region method is used to analyze the crack problems. The traction-singular elements are employed to capture the singularity around the crack front. The values of stress intensity factors (SIFs) are obtained by using crack opening displacements. The results of the proposed method compare well with the existing exact solutions for an elliptical crack parallel to the isotropic plane of a transversely isotropic solid of infinite extent. Elliptical cracks perpendicular to the interface of transversely isotropic bi-material solids of either infinite extent or occupying a cubic region are further examined in detail. The crack surfaces are subject to the uniform normal tractions. The stress intensity factor values of the elliptical cracks of the two types are analyzed and compared. Numerical results have shown that the stress intensity factors are strongly affected by the anisotropy and the combination of the two joined solids.

DOI: 10.1007/s10704-005-4802-1
Print publication date: 6/1/2005
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by Chen, Jian

The thermal fracture problem of an interface crack between a graded orthotropic coating and the homogeneous substrate is investigated by two different approaches. For the case that most of the material properties in the graded orthotropic coating are assumed to vary as an exponential function, the integral transform and singular integral equation technique is used to obtain some analytical results. In order to analyze the case with more complex material distribution, an interaction integral is presented to evaluate the thermal stress intensity factors of cracked functionally graded materials (FGMs), and then the element-free Galerkin method (EFGM) is developed to obtain the final numerical results. The good agreement is obtained between the numerical results and the analytical ones. In addition, the influence of material gradient parameters and material distribution on the thermal fracture behavior is also presented.

DOI: 10.1007/s10704-005-4728-7
Print publication date: 6/1/2005
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by Zohdi, T.I.; Kachanov, M.

Experimental evidence suggests that, for materials exhibiting no appreciable work hardening and containing no more than approximately 20% volume fraction of pores, the macroscopic strain at which yield occurs is nearly constant, with a tendency to increase slightly as porosity increases. The present work shows that both observations – approximate constancy of strain at yield and its tendency to increase with porosity – have a relatively simple micromechanical explanation.

DOI: 10.1007/s10704-005-7143-1
Print publication date: 6/1/2005
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