by Mishnaevsky, Leon; Brøndsted, Povl

On the basis of the kinetic theory of strength, a new approach to the modeling of material degradation in cyclic loading has been suggested. Assuming that not stress changes, but acting stresses cause the damage growth in materials under fatigue conditions, we applied the kinetic theory of strength to model the material degradation. The damage growth per cycle, the effect of the loading frequency on the lifetime and on the stiffness reduction in composites were determined analytically. It has been shown that the number of cycles to failure increases almost linearly and the damage growth per cycle decreases with increasing the loading frequency.

DOI: 10.1007/s10704-007-9086-1
Online Date: 6/19/2007
Print publication date: 4/1/2007
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by Belnoue, Jonathan P.; Nguyen, Giang D.; Korsunsky, Alexander M.

This paper presents a new 1-D non-local damage-plasticity deformation model for ductile materials. It uses the thermodynamic framework described in Houlsby and Puzrin (2000) and holds, nevertheless, some similarities with Lemaitre’s (1971) approach. A 1D finite element (FE) model of a bar fixed at one end and loaded in tension at the other end is introduced. This simple model demonstrates how the approach can be implemented within the finite element framework, and that it is capable of capturing both the pre-peak hardening and post-peak softening (generally responsible for models instability) due to damage-induced stiffness and strength reduction characteristic of ductile materials. It is also shown that the approach has further advantages of achieving some degree of mesh independence, and of being able to capture deformation size effects. Finally, it is illustrated how the model permits the calculation of essential work of rupture (EWR), i.e. the specific energy per unit cross-sectional area that is needed to cause tensile failure of a specimen.

DOI: 10.1007/s10704-007-9075-4
Online Date: 6/8/2007
Print publication date: 3/1/2007
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by Xie, Mayue; Levy, Alan J.

In this paper a nonlinear, nonuniform cohesive zone is employed to study the detailed features of quasi-static defect evolution in a simple, planar elastic system consisting of a circular inclusion embedded in an unbounded matrix subject to different remote loading configurations. The inclusion–matrix interface is assumed to be described by Needleman-type force-separation relations characterized by an interface strength, a characteristic force length and a shear stiffness parameter. Interface defects are modeled by an interface strength which varies with interface coordinate. Infinitesimal strain equilibrium solutions, which allow for rigid body inclusion displacement, are sought by eigenfunction approximation of the solution of the governing interfacial integral equations. For equibiaxial tension, quasi-static defect initiation and propagation occur under increasing remote load. For decreasing characteristic force length, a transition occurs from more or less uniform decohesion along the bond line to propagation of a crack-like defect. In the later case a critical failure load is well defined and interface failure is shown to be defect dominated (brittle decohesion). For interfaces with large characteristic force length, the matrix “lifts off” the inclusion accompanied by a delay in defect propagation (ductile decohesion). The decohesion modes ultimately give rise to a cavity with the inclusion situated within it on the side opposite to the original defect. Results for small characteristic force length show consistency with England’s results for the sharp arc crack on a circular interface (England AH (1966) ASME J Appl Mech 33:637–640) Stress oscillation and contact at the tip of the defect are observed primarily for small characteristic force lengths under extremely small loading. Results for remote tension, compression and pure shear loading are discussed as well. In the final section of the paper the results obtained in the first part are utilized to estimate the plane effective bulk response of a composite containing a dilute distribution of inclusions with randomly oriented interface defects.

DOI: 10.1007/s10704-007-9071-8
Online Date: 6/6/2007
Print publication date: 3/1/2007
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by Li, Tianlei; Li, Zhonghua

The stress field around the tip of an elliptically blunted crack induced by an edge dislocation has been obtained in closed form, from which the mode I and mode II stress intensity factors induced by the edge dislocation are obtained. The solutions apply to the edge dislocation either emitted from crack-tip surface or originated elsewhere, and for the dislocation located anywhere around the crack tip. The effects of the crack length, the crack-tip bluntness, the origination and position of the dislocation on the stress intensity factors are examined.

DOI: 10.1007/s10704-007-9074-5
Online Date: 6/5/2007
Print publication date: 3/1/2007
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by Block, G.; Rubin, M. B.; Morris, J.; Berryman, J. G.

Experimental data indicates that the limiting crack speed in brittle materials is less than the Rayleigh wave speed. One reason for this is that dynamic instabilities produce surface roughness and microcracks that branch from the main crack. These processes increase dissipation near the crack tip over a range of crack speeds. When the scale of observation (or mesh resolution) becomes much larger than the typical sizes of these features, effective-medium theories are required to predict the coarse-grained fracture dynamics. Two approaches to modeling these phenomena are described and used in numerical simulations. The first approach is based on cohesive elements that utilize a rate-dependent weakening law for the nodal cohesive forces. The second approach uses a continuum damage model which has a weakening effect that lowers the effective Rayleigh wave speed in the material surrounding the crack tip. Simulations in this paper show that while both models are capable of increasing the energy dissipated during fracture when the mesh size is larger than the process zone size, only the continuum damage model is able to limit the crack speed over a range of applied loads. Numerical simulations of straight-running cracks demonstrate good agreement between the theoretical predictions of the combined models and experimental data on dynamic crack propagation in brittle materials. Simulations that model crack branching are also presented.

DOI: 10.1007/s10704-007-9085-2
Online Date: 6/1/2007
Print publication date: 4/1/2007
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by Kumar, A.; Roberts, S. G.; Wilkinson, A. J.

The micromechanisms of fracture of a spheroidised A533B reactor pressure vessel steel over the temperature range of −190°C to + 60°C were investigated by performing uniaxial tensile tests on double-notched cylindrical specimens. Failure was by quasi-cleavage at temperatures between −190°C and −145°C. Quasi-cleavage fracture surfaces are characterised by clusters of planar facets that are separated from other facets either by large voids or by clusters of microvoids. At temperatures between −145°C and −25°C failure was by mixed microvoid coalescence and cleavage while complete microvoid coalescence was observed at temperatures higher than −25°C. Over the whole temperature range studied, fracture nucleation was either from large single voids or localised regions of microvoids.

DOI: 10.1007/s10704-007-9084-3
Online Date: 6/1/2007
Print publication date: 4/1/2007
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by Moon, Seong-In; Chang, Yoon-Suk; Kim, Young-Jin; Lee, Jin-Ho; Song, Myung-Ho; Choi, Young-Hwan

The 40% of wall thickness criterion which has been used as a plugging rule is applicable only to a single cracked steam generator tubes. In the previous studies performed by authors, several failure prediction models were introduced to estimate the plastic collapse pressures of steam generator tubes containing two adjacent collinear or parallel axial through-wall cracks. The objective of this study is to examine the failure prediction models and propose optimum ones for two non-aligned axial through-wall cracks in steam generator tubes. In order to determine the optimum ones, a series of plastic collapse tests and finite element analyses were carried out for steam generator tubes with two machined non-aligned axial through-wall cracks. Thereby, either the plastic zone contact model or COD based model was selected as the optimum one according to axial distance between two cracks. Finally, the optimum failure prediction model was used to demonstrate the conservatism of flaw characterization rules for multiple cracks having equal lengths according to ASME code.

DOI: 10.1007/s10704-007-9082-5
Online Date: 6/1/2007
Print publication date: 3/1/2007
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by Winiarski, Bartlomiej; Guz, Igor

The current paper addresses the problem of 2-D modelling of the onset of failure process in a layered composite with periodic array of interfacial cracks under static compression along layers. The statement of the problem is based on the most accurate approach, the model of piecewise-homogenous medium. The condition of plane strain state is considered. The shear and the extensional buckling modes are examined. The laminae are modelled by transversally isotropic material (a matrix reinforced by continuous parallel fibres). The complex non-classical failure mechanics problem is solved utilizing finite element analysis. It is found that the 0°-plies volume fraction, the crack length and the mutual position of cracks influence the critical strain in the composite.

DOI: 10.1007/s10704-007-9076-3
Online Date: 6/1/2007
Print publication date: 3/1/2007
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by Hamdi, A.; Hocine, N. Aït; Abdelaziz, M. Naït; Benseddiq, N.

This work deals with the fracture of rubbers under a mixed mode loading (I + II) and it is an extension of our previous papers on that subject [Aït Hocine N, Naït Abdelaziz M, Imad A (2002) Int J Fract 117:1–23; Aït Hocine N, Naït Abdelaziz M (2004) In: Sih GC, Kermanidis B, Pantelakis G (eds) 6th international conference for mesomechanics. Patras (Greece), May 31–June 4, pp 381–385]. An experimental and a numerical analysis were carried out using a Styrene Butadiene Rubber (SBR) filled with 20 and 30% of carbon black. Sheets with an initial central crack (CCT specimens) inclined with a given angle compared to the loading direction were used. The J-integral and its critical values J
_c (fracture surface energy) were determined by combining experimental data and finite element results. These critical values, determined at the onset of crack growth, were found to be quite constant for each elastomer tested, which suggests that J
_c represents a reasonable fracture criterion of such materials. Then, the strain–stress field and the strain-energy-density factor S, earlier introduced by Sih [Sih GC (1974) Int J Fract 10(3):305–321; Sih GC (1991) Mechanics of fracture initiation and propagation. Kluwer Academic Publishers, Dordrecht, 428 pp] were numerically calculated around the crack tip. According to the experimental observations, the plan of crack propagation is perpendicular to the direction of the maximum principal stretch. Moreover, as suggested by Sih in the framework of linear elastic fracture mechanics (LEFM), the minimum values S
^min of the factor S are reached at the points corresponding to the crack propagation direction. These results suggest that the concept of the maximum principal stretch and the one of the strain-energy-density factor can be used as indicators of the crack propagation direction.

DOI: 10.1007/s10704-007-9080-7
Online Date: 6/1/2007
Print publication date: 3/1/2007
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by Zhao, Haifeng; Wei, Yueguang

Peel test measurements have been performed to estimate both the interface toughness and the separation strength between copper thin film and Al₂O₃ substrate with film thicknesses ranging between 1 and 15 μm. An inverse analysis based on the artificial neural network method is adopted to determine the interface parameters. The interface parameters are characterized by the cohesive zone (CZ) model. The results of finite element simulations based on the strain gradient plasticity theory are used to train the artificial neural network. Using both the trained neural network and the experimental measurements for one test result, both the interface toughness and the separation strength are determined. Finally, the finite element predictions adopting the determined interface parameters are performed for the other film thickness cases, and are in agreement with the experimental results.

DOI: 10.1007/s10704-007-9083-4
Online Date: 6/1/2007
Print publication date: 3/1/2007
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