by Chattopadhyay, J.; Acharyya, S.; Kushwaha, H. S.

Leak-before-break (LBB) assessment of primary heat transport piping of nuclear reactors involves detailed fracture assessment of pipes and elbows with postulated throughwall cracks. Fracture assessment requires the calculation of elastic–plastic J-integral and crack opening displacement (COD)¹ for these piping components. Analytical estimation schemes to evaluate elastic–plastic J-integral and COD simplify the calculations. These types of estimation schemes are available for pipes with various crack configurations subjected to different types of loading. However, such schemes for elbow (or pipe bend), which is one of the important components for LBB analyses, is very meager. Recently, elastic–plastic J and COD estimation scheme has been developed for throughwall circumferentially cracked elbow subjected to closing bending moment. However, it is well known that the elbow deformation characteristics are distinctly different for closing and opening bending modes because the ovalisation patterns of elbow cross section are different under these two modes. Development of elastic–plastic J and COD estimation scheme for an elbow with throughwall circumferential crack at intrados subjected to opening bending moment forms the objective of the present paper. Experimental validation of proposed J-estimation scheme has been provided by comparing the crack initiation, unstable ductile tearing loads and crack extension at instability with the test data. The COD estimation scheme has been validated by comparing the COD of test data with the predictions of the proposed scheme.

DOI: 10.1007/s10704-007-9097-y
Online Date: 7/25/2007
Print publication date: 4/1/2007
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by Priel, Elad; Bussiba, Arie; Gilad, Ilan; Yosibash, Zohar

Three mixed mode failure initiation criteria at reentrant corners in brittle elastic materials are examined. Prediction of failure load and crack initiation angle are compared to experimental observations carried out on PMMA (polymer) and MACOR (glass ceramic) V-notched specimens. Since the mode mixity ratio influences greatly both the failure load and crack initiation angle, a detailed experimental procedure has been followed, focusing on obtaining a wide range of mode mixity ratios. It is demonstrated that by assuming a sharp V-notch tip some failure criteria predict reasonably well both the crack initiation angle and failure load.

DOI: 10.1007/s10704-007-9098-x
Online Date: 7/24/2007
Print publication date: 4/1/2007
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by Yan, J. -H.; Sutton, M. A.; Deng, X.; Cheng, C. -S.

Cracks in thin structures often are subjected to combined in-plane and out-of-plane loading conditions leading to complex mixed mode conditions in the crack tip region. When applied to ductile materials, large out-of-plane displacements make both experimentation and modeling difficult. In this work, the mixed-mode behavior of thin, ductile materials containing cracks undergoing combined in-plane tension (mode I) and out-of-plane shear (mode III) deformation is investigated experimentally. Mixed-mode fracture experiments are performed and full, three-dimensional (3D) surface deformations of thin-sheet specimens from aluminum alloy and steel are acquired using 3D digital image correlation. General characteristics of the fracture process are described and quantitative results are presented, including (a) the fracture surface, (b) crack path, (c) load-displacement response, (d) 3D full-field surface displacement and strain fields prior to crack growth, (e) radial and angular distributions of the crack-tip strain fields prior to crack growth and (f) singularity analysis of the crack-tip strains prior to crack growth. Results indicate that the introduction of a mode III component to the loading process (a) alters the crack tip fields relative to those measured during nominally mode I loading and (b) significantly increases the initial and stable critical crack-opening-displacement. The data on strain fields in both AL6061-T6 aluminum and GM6208 steel consistently show that for a given strain component, the normalized angular and radial strains at all load levels can be reasonably represented by a single functional form over the range of loading considered, confirming that the strain fields in highly ductile, thin-sheet material undergoing combined in-plane tension and out-of-plane shear loading can be expressed in terms of separable angular and radial functions. For both materials, the displacement and strain fields are (a) similar for both mixed-mode loading angles Φ = 30° and Φ = 60° and (b) different from the fields measured for Mode I loading angle Φ = 0°. Relative to the radial distribution, results indicate that the in-plane strain components do not uniformly exhibit the singularity trends implicit in the HRR theory.

DOI: 10.1007/s10704-007-9101-6
Online Date: 7/24/2007
Print publication date: 4/1/2007
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by Eriksson, K.

Vanishing divergence of Eshelby’s (energy momentum) tensor allows formulation of path or domain independent integral expressions of the crack extension force. In this work, a decomposition scheme of this tensor is presented, which results in zero divergence decomposed parts that allow formulation of expressions yielding the Mode I, II and III crack tip parameters J and K, with particular emphasis on Mode III, at present. By using the Mode III decomposed part of Eshelby’s tensor and the virtual crack extension method, a path and a domain independent integral, both new, for the crack extension force of a plane circular crack in axi-symmetric Mode III loading, are derived as examples of application.

DOI: 10.1007/s10704-007-9096-z
Online Date: 7/24/2007
Print publication date: 4/1/2007
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by Codrington, John; Kotousov, Andrei

An analytical method for calculating plasticity-induced fatigue crack closure in plates of finite thickness is presented. The developed method utilizes the distributed dislocation technique (DDT) and Gauss-Chebyshev quadrature. Crack tip plasticity is incorporated by adopting a Dugdale type strip yield model. The finite plate thickness effects are taken into account by using a recently obtained three-dimensional solution for an edge dislocation in an infinite plate. Numerical results for the ratio of the size of the crack tip plasticity zones are presented for the cases of uniform thickness wake and linearly increasing wake for a range of plate thickness to crack length ratios and applied load ratios. The results show a very good agreement with previous analytical solutions in the limiting cases of very thick and very thin plates. Further results for the opening stress to maximum stress ratio are also provided and are compared with known three-dimensional finite element (FE) solutions. A good agreement is observed. The developed method is shown to be an effective and very powerful tool in modeling the crack closure phenomenon.

DOI: 10.1007/s10704-007-9100-7
Online Date: 7/20/2007
Print publication date: 4/1/2007
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by Alfredsson, K. S.; Högberg, J. L.

Fracture behaviour of adhesive joints under mixed mode loading is analysed by using the beam/adhesive-layer (b/a) model, in which, the adherends are beamlike and the adhesive is constrained to a thin flexible layer between the adherends. The adhesive layer deforms in peel (mode I), in shear (mode II) or in a combination of peel and shear (mixed mode). Macroscopically, the ends of the bonded part of the joints can be considered as crack tips. The energy release rate of a single-layer adhesive joint is then formulated as a function of the crack tip deformation and the mode-mixity is defined by the shear portion of the total energy release rate. The effects of transversal forces and the flexibility of the adhesive layer are included in the b/a-model, which can be applied to joints with short crack length as well as short bonding length. The commonly used end-loaded unsymmetric semi-infinite joints are examined and closed-form solutions are given. In comparison to the singular-field model in the context of linear elastic fracture mechanics, the b/a-model replaces the singularity at the crack tip with a stress concentration zone. It is shown that the b/a-model and the singular-field model yield fundamentally different mode-mixities for unsymmetric systems. The presented closed-form b/a-model solutions facilitates parametric studies of the influence of unbalance in loading, unsymmetry of the adherends, as well as the flexibility of the adhesive layer, on the mode mixity of an adhesive joint.

DOI: 10.1007/s10704-007-9099-9
Online Date: 7/19/2007
Print publication date: 4/1/2007
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by Cherepanov, Genady. P.; Esparragoza, Ivan E.

The breakage of a tiny tail on a head of solid glass just removed from a glass bath and treated by fluoric acid (a “Batavian tear”) makes the tear explode into a cloud of dust with the sound like that of a shot. This explosion reminds that of TNT but TNT disintegrates into molecules of the order of 10⁻⁹ m while the glass particles of dust are of the order of 10⁻⁶ m and have the same chemical composition as the solid glass. Rock bursts in deep mines of South Africa and Russia represent another example of the sudden, explosive self-destruction. To explain this phenomenon the theory of self-sustaining fracture waves was suggested earlier by Galin and Cherepanov (1966). This theory was based on the analogy with detonation waves later criticized as insufficiently substantiated. The approach presented below is based only on the conservation laws and does not use any analogies. It proves that the self-sustaining fracture wave can propagate only in compressed structures at the speed of longitudinal elastic waves.

DOI: 10.1007/s10704-007-9090-5
Online Date: 7/12/2007
Print publication date: 4/1/2007
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by Toribio, J.; González, B.; Matos, J. C.

Cold-drawn prestressing steel wires exhibit strength anisotropy in the form of fracture path deflection towards a direction approaching the wire axis, or cold drawing line, as a consequence of the pearlitic microstructure orientation induced by the manufacturing procedure. Such a crack path deflection is initiated at certain nuclei (fracture origins) at which axial cracking appears in the cold drawing direction (or wire axis) in the form of micro-cleavage units that produce in the load-displacement curve a macroscopic phenomenon of pop-in. This paper shows that such fracture initiators appear at a certain distance from the fatigue pre-crack tip at which a local maximum of the cleavage stress is located.

DOI: 10.1007/s10704-007-9087-0
Online Date: 7/11/2007
Print publication date: 4/1/2007
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by Lazghab, Tarek; Ayari, Fayza; Chelbi, Lotfi

The occurrence of cracks in aging aircraft fuselage is major problem in the airline industry. The remaining life of the aircraft is strongly dependent on the residual strength of its structure. Residual strength is affected by crack sizes and their growth rates. In the case of a longitudinal crack in a pressurized cylinder (as in the case of an aircraft fuselage), the geometry and loading conditions cause the edges of the crack to bulge out generating a complex stress field around the crack tips; this is known as the ‘bulging effect’. The geometry of the shell, crack size and pressure contribute to this phenomenon. A proposed solution to reduce the effect of bulging for this type of crack is to apply a layer of polyisocyanurate (PIR) foam to the inner side of the fuselage near the crack site. This layer will bond to the shell and has the effect of reducing the bulge and consequently, the Stress Intensity Factor (SIF) at the crack tips. PIR foam is a lightweight material that adheres well to the shell and provides additional stiffness around the crack area. In the present study the effect of applying a PIR foam layer to a longitudinal crack in a pressurized cylindrical shell is assessed. Nonlinear Finite Element Analysis (FEA) is used in conjunction with the Modified Crack Closure Integral technique (MCCI) in order to evaluate the effect of bulging on the crack’s SIF. Parameters considered in this study include shell radius, shell thickness, crack length, foam thickness and pressure. Numerical results are compared with existing experimental data and the effect of foam thickness for several shell configurations is presented. Results indicate that the bulge factor (BF) could be reduced by as much as 45% depending on shell configuration, foam thickness and pressure.

DOI: 10.1007/s10704-007-9093-2
Online Date: 7/11/2007
Print publication date: 4/1/2007
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by Xiang, Yong; McKinnell, James; Ang, Wie-Ming; Vlassak, Joost J.

An experimental technique is presented for measuring the fracture toughness of brittle thin films. In this technique, long rectangular membranes are fabricated from the film of interest using standard silicon micromachining techniques. A focused ion beam is then used to introduce pre-cracks of different lengths along the centerline of the membranes and the membranes are pressurized until rupture. The fracture stress of the membrane is measured as a function of pre-crack length and the fracture toughness of the film is determined from a simple fracture mechanics analysis. The technique is applicable to a wide range of materials and is especially suited for ultra-thin films. We have demonstrated the experimental procedure for a 150 nm AlTa intermetallic film and obtained a room-temperature fracture toughness of K
_1c
 = 4.44 ± 0.21 MPam^1/2.

DOI: 10.1007/s10704-007-9095-0
Online Date: 7/6/2007
Print publication date: 4/1/2007
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