by Bao, Y. G.; Wang, X. D.

The current paper presents a theoretical study of the identification of cracks in an elastic medium based on optimization methods using harmonic elastic waves. A generalized crack model was used to determine the elastodynamic behaviour of an arbitrarily located and oriented crack subjected to a plane harmonic wave. Sensitivity analysis was conduced to evaluate the variation of stress and strain fields with various crack parameters using the direct differential method (DDM). These general results were then used to identify an unknown crack from known strain components at discrete locations. The BFGS optimization scheme based on the sensitivity analysis was used to determine the length, the orientation and the position of the crack. Numerical simulation was conducted and the results were presented to show the effectiveness of the sensitivity analysis and the optimization method. It was observed that starting from a set of arbitrarily determined initial values, the length, position and the orientation of the crack can be accurately determined.

DOI: 10.1007/s10704-009-9394-8
Online Date: 9/30/2009
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by Travaš, V.; Ožbolt, J.; Kožar, I.

In the paper, the results of numerical failure analysis of plain concrete beams loaded by impact three-point bending load are presented and discussed. The theoretical framework for the numerical analysis is continuum mechanics and irreversible thermodynamics. The spatial discretization is performed by the finite element method using update Lagrange formulation. Green–Lagrange stain tensor is used as a strain measure. To account for cracking and damage of concrete, the beam is modeled by the rate sensitive microplane model with the use of the so-called co-rotational stress tensor. Damage and cracking phenomena are modeled within the concept of smeared cracks. To assure objectivity of the analysis with respect to the size of the finite elements, crack band method is used. The contact-impact analysis is based on the mechanical interaction between two bodies—concrete beam (master) and dropping hammer (slave) falling on the mid span of the beam. The contact constrains are satisfied by Lagrange multiplier method, which is adapted for the explicit time integration scheme. To investigate the influence of loading rate on the failure mode of the beam parametric study is carried out. The numerical results are evaluated, discussed and compared with test results known from the literature. It is shown that the beam resistance and failure mode strongly depend on loading rate. For lower loading rates beam fails in bending (mode-I fracture). However, with increasing loading rate there is a transition of the failure mechanism from bending to shear. The results are in good agreement with theoretical and experimental results known from the literature.

DOI: 10.1007/s10704-009-9400-1
Online Date: 9/26/2009
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by Gommerstadt, B. Y.

The energetics of two unequal-length collinear cracks for modes- I, II, III is considered. The analysis is performed for remote uniform load normal to the plane of cracks by applying the J and M path-independent integrals and the relationship between them. The material forces for each crack as well as the total crack energy of the system are evaluated. The exact closed form solution to this interaction problem is expressed as a function of cracks’ dimensions and spacing between them. The expression derived for the energy of interaction between a main crack and a nearby microcrack can be used for an estimate of the toughness degradation due to microcracks. Another application of the two-crack energy solution is related to the elastic compliance of cracked solids relevant for the cases when crack faces are in contact along certain areas.

DOI: 10.1007/s10704-009-9401-0
Online Date: 9/25/2009
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by Zohdi, T. I.

In many materials, strong electrical fields can cause highly conductive pathways to occur due to
dielectric breakdown, which can cause the material to “jump” to a higher permittivity state. This effect is often undesirable and can lead to electrically-induced failure of a device, for example due to overheating. The overall goal of this work is to estimate the volume fraction and properties of the particulate additives needed to reduce the electrical load carried by a bulk material, in order to avoid dielectric breakdown.

DOI: 10.1007/s10704-009-9403-y
Online Date: 9/24/2009
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by Rokach, Ihor V.; Łabędzki, Paweł

A simple method for determination of the dynamic stress intensity factor (DSIF) variation with time during a four-point impact bend test has been proposed. A formula for DSIF calculation from the recorded loading has been obtained using modal superposition method. Results of calculations for different specimens have been compared with the experimental data and the results of the direct finite element analysis.

DOI: 10.1007/s10704-009-9404-x
Online Date: 9/23/2009
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by Aliha, M. R. M.; Ayatollahi, M. R.; Kharazi, B.

The four-point bend specimen subjected to anti-symmetric loading (ASFPB) is frequently used for determining pure mode II fracture resistance of rock materials. It is shown in this paper that, when the applied loads are close to the crack plane, the ASFPB specimen does not provide pure mode II condition, since the effect of mode I also appears in crack tip deformation. A set of fracture test were also conducted on a type of marble using ASFPB configuration. The test results showed that fracture resistance is strongly dependent on the loading distance from the crack plane. The effective fracture toughness increases when the distance between the loading points and the crack plane decreases. It is shown that the enhanced fracture resistance of marble samples could be mainly because of very large negative T-stresses that exist for the mentioned loading situations.

DOI: 10.1007/s10704-009-9402-z
Online Date: 9/23/2009
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by Li, Xian-Fang; Liu, Guang-Lian; Lee, Kang Yong

This paper studies crack extension resulting from a closed crack in compression. The crack-tip field of such a crack contains a singular field relative to K
_II and non-singular T-stresses T

_x
and T

_y
parallel and perpendicular to the crack plane, respectively. Using a modified maximum tensile stress criterion with the singular and non-singular terms, the kinking angle at the onset of crack growth is determined by a two parameter field involving the mode-II stress intensity factors and T-stresses, and at fracture initiation a wing crack may be created at an arbitrary angle from 0° to 90°. A compressive T

_y
increases the kinking angle and reinforces apparent mode-II fracture toughness, while a compressive T

_x
decreases the kinking angle and enhances apparent mode-II fracture toughness. The direction and resistance of fracture onset is strongly affected by T-stresses as well as frictional stress. The von Mises effective stress is determined for small-scale yielding near the crack tip. The effective stress contour shape exhibits a marked asymmetrical behavior unless 2T

_x
 = T

_y
 ≤ 0 for plane stress state. Coulomb friction between two crack faces generally increases the kinking angle, shrinks the size enclosed by the effective stress contour and enhances apparent fracture toughness. Field evidence and experimental observations of many phenomena involving the growth of closed cracks in compression agree well with theoretical predictions of the present model.

DOI: 10.1007/s10704-009-9397-5
Online Date: 9/23/2009
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by Shifrin, Efim I.

The reciprocity gap functional for a linear elastic body with an embedded defect is considered. The functional is a bilinear functional depending on two stress states—in an elastic body with a defect and without it. It is shown that for various types of boundary conditions the functional is a symmetric one in a certain sense. Some corollaries of the symmetry properties of the functional are obtained.

DOI: 10.1007/s10704-009-9395-7
Online Date: 9/19/2009
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by Doquet, V.; Abbadi, M.; Bui, Q. H.; Pons, A.

Fatigue crack growth tests were performed under various mixed-mode loading paths, on maraging steel. The effective loading paths were computed by finite element simulations, in which asperity-induced crack closure and friction were modelled. Application of fatigue criteria for tension or shear-dominated failure after elastic–plastic computations of stresses and strains, ahead of the crack tip, yielded predictions of the crack paths, assuming that the crack would propagate in the direction which maximises its growth rate. This approach appears successful in most cases considered herein.

DOI: 10.1007/s10704-009-9396-6
Online Date: 9/19/2009
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by Gómez, F. J.; Elices, M.; Berto, F.; Lazzarin, P.

The purpose of this research is threefold. First, to provide experimental results of fracture loads for V-notched beams loaded under mixed mode. Second, to check the suitability of fracture criteria based on the cohesive zone model and strain energy density when applied to those samples. And, third, to suggest a very simple fracture criterion, based on the dominance of the local mode I, for notched samples (with different V-notch angles and notch root radii) loaded under mixed (I + II) mode. This proposal unifies predictions for the experimental results obtained under mode I and mixed mode loading. To this end, 36 fracture tests on V-notched beams were performed and reported: three V-notched angles were investigated (90°, 60°, 30°, four different loadings (mixed modes I and II) were selected and three samples were tested for each configuration.

DOI: 10.1007/s10704-009-9387-7
Online Date: 9/13/2009
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