by ZHANG, TONG-YI; ZHAO, MING-HAO; GAO, CUN-FA

This paper reports on the analysis of the strip dielectric breakdown (DB) model for an electrically impermeable crack in a piezoelectric medium based on the general linear constitutive equations. The DB model assumes that the electric field in a strip ahead of the crack tip is equal to the dielectric breakdown strength, which is in analogy with the classical Dugdale model for plastic yielding. Using the Stroh formalism and the dislocation modeling of a crack, we derived the relationship between the DB strip size and applied mechanical and electrical loads, the intensity factors of stresses and electric displacement, and the local energy release rate. Based on the results, we discussed the effect of electric fields on fracture of a transversely isotropic piezoelectric ceramic by applying the local energy release rate as a failure criterion. It is shown that for an impermeable crack perpendicular to the poling direction, a positive electric field will assist an applied mechanical stress to propagate the crack, while a negative electric field will retard crack propagation. However, for an impermeable crack parallel to the poling direction, it is found that the applied electric field does not change the mode I stress intensity factor and the local energy release rate, i.e., the applied electric field has no effect on the crack growth.

DOI: 10.1007/s10704-005-2054-8
Print publication date: 4/1/2005
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by POCHIRAJU, K. V.; TANDON, G. P.

The stress distributions near the points of singularity in a single-fiber micromechanics model as obtained by local asymptotic methods and global (numerical solutions to full-field boundary value problem) methods are described. While the numerical/analytical solutions (without special treatment of the singularity) can capture higher order terms and are sufficiently accurate away from points of singularity, the solutions are approximate in the neighborhood of the singularity due to the inherent assumptions (single-valued at the point of singularity) about the nature of the stress fields. The study focuses on a methodology for accurate determination of generalized stress intensity factors from the “approximate” methods of stress analysis with relatively coarse discretizations and without any special modeling of the singularity. The approach adopted entails the comparison of the angular distribution of the stress components at varying radial distances near the point of singularity and identifying a region in which the numerical/analytical solutions have the best ability to determine the stress intensity factor. Determination of the generalized stress intensity factors is illustrated for a penny-shaped crack in a homogeneous medium and for a crack in fiber terminating at the fiber-matrix interface (fiber-break problem).

DOI: 10.1007/s10704-005-1891-9
Print publication date: 4/1/2005
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by GIANNOPOULOS, G. I.; ANIFANTIS, N. K.

Thermal loading of fractured structures is associated with the development of differential deformations along crack surfaces which result in the closure of the crack. Inherent non-linearities demand application of numerical procedures to resolve this problem. In this paper, a boundary element procedure is formulated to treat crack surface interference imposed under thermal steady-state or transient loadings. An iterative-incremental procedure is developed to deal with the non-linearity produced by the frictional contact of the crack surfaces. The open, adhesion and slip contact conditions are modeled through the utilization of the multi-domain technique. Two approaches are followed regarding the thermal boundary contact conditions along the crack region. In the first, crack surfaces are assumed to be thermally insulated. This assumption simplifies the formulation significantly. In the second, the crack surfaces are assumed to provide perfect thermal contact. Thermal stress intensity factors are evaluated from traction nodal results that adopt singular elements in the crack tip region. Numerical examples are illustrated, discussed and compared with analytical solutions, where possible. Fracture characteristics are predicted in terms of the involved parameters. As a general conclusion, peak values of thermal stress intensity factors depend on the friction conditions existing between crack faces.

DOI: 10.1007/s10704-005-1890-x
Print publication date: 4/1/2005
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by LE, JUN; SONG, LIXIN; PENG, XIAOFENG; HU, XINFANG

This paper presents a fracture mechanics analysis of a thermally tempered glass plate. The fracture is induced by an embedded penny-shaped crack. The analysis shows that the existence of a penny-shaped crack will reduce the strength of tempered glass. The impact and fatigue resistance of the glass is related to the position and size of the penny-shaped crack. When the tempering intensity reached to a certain level, thermally tempered glass with a penny-shaped crack could experience spontaneous fracture. The damage of a central crack on glass is more severe than a surface crack. With surface compression, thermal tempering will increase the critical applied stress of the glass if the surface penny-shaped crack size is in the range of 0 < a/d < 0.27, where a is the crack size, d is the half thickness of the glass plate. For a small surface crack with the size of a/d ≤ 0.09, the tempering can hinder its extension. However, if there is a central penny-shaped crack, the critical applied stress of the tempered glass will decrease with the intensity of tempering.

DOI: 10.1007/s10704-005-1889-3
Print publication date: 4/1/2005
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by CHEN, Y. Z.; LIN, X. Y.

In this paper, numerical solutions of a hypersingular integral equation for curved cracks in circular regions are presented. The boundary of the circular regions is assumed to be traction free or fixed. The suggested complex potential is composed of two parts, the principle part and the complementary part. The principle part can model the property of a curved crack in an infinite plate. For the case of the traction free boundary, the complementary part can compensate the traction on the circular boundary caused by the principle part. Physically, the proposed idea is similar to the image method in electrostatics. By using the crack opening displacement (COD) as the unknown function and traction as right hand term in the equation, a hypersingular integral equation for the curved crack problems in the circular regions is obtained. The equation is solved by using the curve length coordinate method. In order to prove that the suggested method can be used to solve more complicated cases of the curved cracks, several numerical examples are given.

DOI: 10.1007/s10704-005-0990-y
Print publication date: 4/1/2005
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by KORSUNSKY, Alexander M.; KIM, Kyungmok

The energy (or work) characterizing the resistance of a structure to ductile fracture is important for many applications, from structural design to impact protection. Essential work of fracture (EWF) is one such measure traditionally associated with the specific energy, per unit cross sectional area, consumed during ductile fracture in a double edge notched tensile (DENT) specimen. This energy is referred to as ’essential’ in order to distinguish it from the non-essential energy consumed on distributed plastic deformation accompanying fracture, but not required for material separation. The present article describes how the essential work of tearing can be determined from a single tensile test on an unnotched specimen. Tensile tests were performed on unnotched dog-bone (DB) tensile specimens carrying large numbers of markers, with continuous measurement of elongation between any two markers using a laser scanning extensometer. From such single test it is then possible to obtain multiple load-elongation curves for a large number of tensile specimens. This data is analyzed by separating contributions to specimen elongation made by distributed (pre-softening) and localized (post-softening) plastic deformation. Essential and non-essential work of necking and tearing is determined for an aluminum alloy subjected to different heat treatments, and results compared with those obtained from conventional DENT tests.

DOI: 10.1007/s10704-005-4483-9
Print publication date: 4/1/2005
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by Kotousov, Andrei

Stress singularities at angular corners of plates of arbitrary thickness with free boundaries subjected to in-plane loading are studied within the first order plate theory. By adapting a stress resultant function approach a characteristic equation for determining the structure and orders of the singularities near the vertex is developed. This equation differs from that obtained within the classical plane theory of elasticity (Williams’ solution) and includes singularities of the out-off-plane shear stress resultants.

DOI: 10.1007/s10704-005-4481-y
Print publication date: 4/1/2005
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by RITCHIE, R. O.

The Paris power law, which relates fatigue-crack growth rates to the applied stress-intensity range, is an example of a scaling law with the inherent property of incomplete similarity. Previous considerations of dimensions and self-similarity have suggested that the assumed ‘materials constants’ in this law are also a function of specimen size. In this note, the question of the size-dependence of the Paris law is re-examined, and through comparison to a larger body of fatigue-crack growth data in steels, physical explanations why such scaling effects may exist are deduced.

DOI: 10.1007/s10704-005-2266-y
Print publication date: 4/1/2005
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by Shterenlikht, Anton; Hashemi, Sayyed H.; Yates, John R.; Howard, Ian C.; Andrews, Robert M.

DOI: 10.1007/s10704-005-4480-z
Print publication date: 4/1/2005
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by ESTEVEZ, R.; BASU, S.; GIESSEN, E. VAN DER.

A previous isothermal study (Estevez et al., Journal of Mechanics and Physics of Solids 48, 2585–2617, 2000) has shown that the toughness of glassy polymers is governed by the competition between shear yielding and crazing. The present work aims at investigating loading rates for which thermal effects need to be accounted for. The influence of the heat coming from the viscoplastic shear yielding and from crazing on their competition and on the toughness is examined. Crazing is shown to be the dominant heat source, and the dependence of the craze properties on temperature appears to be key in controlling the toughness of the material.

DOI: 10.1007/s10704-005-2182-1
Print publication date: 4/1/2005
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