by Pati, Prasanta Kumar; Shrivastava, S. K.; Basu, Sumit

In this work we study the initiation and growth of a semi-elliptical internal axial crack in the wall of an internally pressurised cylinder. We show that small diameter structures, which we may call ‘tubes’, are more likely to undergo noticable yield before a small internal flaw starts to grow. However, when growth starts, it is likely to be catastrophic. On the other hand, large diameter structures, called ‘pipes’, can fail by cracking at reasonable design pressures. We have also shown that a small semi-elliptical crack attains a particular (almost circular) shape during growth irrespective of its initial aspect ratio.

DOI: 10.1007/s10704-008-9202-x
Online Date: 5/29/2008
Print publication date: 12/1/2007
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by Cravero, Sebastian; Ruggieri, Claudio

Laboratory testing of fracture specimens to measure resistance curves (J − Δa) have focused primarily on the unloading compliance method using a single specimen. Current estimation procedures (which form the basis of ASTM E1820 standard) employ load line displacement (LLD) records to measure fracture toughness resistance data incorporating a crack growth correction for J. An alternative method which potentially simplifies the test procedure involves the use of crack mouth opening displacement (CMOD) to determine both crack growth and J. However, while the J-correction for crack growth effects adopted by ASTM standard holds true for resistance curves measured using load line displacement (LLD) data, it becomes unsuitable for J-resistance measurements based upon the specimen response defined in terms of load-crack mouth opening displacement (CMOD). Consequently, direct application of the evaluation procedure for J derived from LLD records in laboratory measurements of resistance curves using CMOD data becomes questionable. This study provides further developments of the evaluation procedure for J in cracked bodies that experience ductile crack growth based upon the eta-method and CMOD data. The introduction of a constant relationship between the plastic components of LLD (Δ
_p
) and CMOD (V

_p
) drives the development of a convenient crack growth correction for J with increased loading when using laboratory measurements of P-CMOD data. The methodology broadens the applicability of current standards adopting the unloading compliance technique in laboratory measurements of fracture toughness resistance data (J resistance curves). The developed J evaluation formulation for growing cracks based on CMOD data provides a viable and simpler test technique to measure crack growth resistance data for ductile materials.

DOI: 10.1007/s10704-008-9211-9
Online Date: 5/27/2008
Print publication date: 12/1/2007
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by Berto, F.; Lazzarin, P.; Gómez, F. J.; Elices, M.

Two fracture criteria are proposed and applied to blunt-notched components made of brittle materials loaded under mixed mode; the former is based on the averaged strain energy density over a given control volume, the latter on the cohesive crack zone model. In both instances use of the equivalent local mode I hypothesis is made. Only two material properties are needed: the ultimate tensile strength and the fracture toughness. Numerical predictions of rupture loads from the two criteria are compared with experimental measurements from more than 160 static tests with notched beams. The samples are made of PMMA and tested at  − 60°C to assure a bulk behaviour almost linear elastic up to rupture. Notch root radii range from 0.2 to 4.0 mm and load mixicity varies from pure mode I to a prevailing mode II. The good agreement between theory and experimental results adds further confidence to the proposed fracture criteria.

DOI: 10.1007/s10704-008-9213-7
Online Date: 5/23/2008
Print publication date: 12/1/2007
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by Kanaun, S. K.

A planar crack of an arbitrary shape in a homogeneous elastic medium is considered. The problem is reduced to integral equation for the crack opening vector. Its numerical solution utilizes Gaussian approximating functions that drastically simplify construction of the matrix of a linear algebraic system of the discretized problem. For regular grids of approximating nodes, this matrix turns out to have the Teoplitz structure. It allows one to use the Fast Fourier Transform algorithms for calculation of the matrix-vector products in the process of iterative solution of the discretized problem. The method is applied to a crack bounded by the curve $${x^{2p}_{1} + x^{2p}_{2}\leq 1}$$ for 0.2 ≤ p ≤ 4. The contribution of a crack to the overall effective elastic constants is calculated.

DOI: 10.1007/s10704-008-9208-4
Online Date: 5/20/2008
Print publication date: 12/1/2007
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by Kotousov, Andrei; Harding, Steven

The paper investigates the buckling mode of failure of long interfacial cracks subjected to shear loading. A criterion which describes the transition from fracture to buckling instability failure modes is derived.

DOI: 10.1007/s10704-008-9216-4
Online Date: 5/20/2008
Print publication date: 12/1/2007
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by Panigrahi, S. K.; Pradhan, B.

Three-dimensional non-linear finite ele- ment analyses have been carried out to evaluate the out-of-plane stresses in the adhesive layer existing between the lap and the strap adherends of the Lap Shear Joint (LSJ) in laminated FRP composites for varied delamination lengths. The delaminations are presumed to be pre-embedded in the thin resin rich layer existing between the first and second plies of the strap adherend. Sublaminate technique has been used to model the LSJ with the delamination. Contact finite element analyses have been performed in order to avoid interpenetration of delaminated surfaces. The effects of varied delamination lengths on the peel and interlaminar shear stresses and the individual modes of Energy Release Rate (ERR) in the delamination zones are highlighted in this paper. It is seen that three-dimensional effects exist near the free edges of the overlap end of the joint. The delamination propagation significantly affects the stress distributions in the adhesive layer existing between the lap and the strap adherends of the LSJ. The variations of interlaminar stresses and ERRs on both the delamination fronts are found to be significantly different and thus, indicate that the propagation of delamination does not occur at same rate at the two delamination fronts. This may throw some light to the evaluation of structural integrity of the LSJ in the presence of pre-embedded delaminations.

DOI: 10.1007/s10704-008-9210-x
Online Date: 5/16/2008
Print publication date: 12/1/2007
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by Christopher, C. J.; James, M. N.; Patterson, E. A.; Tee, K. F.

This work introduces a novel mathematical model of the stresses around the tip of a fatigue crack, which considers the effects of plasticity through an analysis of their shielding effects on the applied elastic field. The ability of the model to characterize plasticity-induced effects of cyclic loading on the elastic stress fields is assessed and demonstrated using full-field photoelasticity. The focus is on determining the form of the shielding stress components (induced by compatibility requirements at the elastic–plastic interface along the crack flank and via the crack tip plastic zone) and how they influence the crack tip elastic stress fields during a load cycle. The model is successfully applied to the analysis of a fatigue crack growing in a polycarbonate CT specimen.

DOI: 10.1007/s10704-008-9209-3
Online Date: 5/16/2008
Print publication date: 12/1/2007
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by Alderliesten, René C.

Previous numerical work on crack tunnelling and plane-strain delamination in layered solids is evaluated with static and fatigue experiments and analysis. It is concluded that the translation of the theory derived for static fracture to fatigue loading is not as straightforward as initially assumed. Details such as delamination location, stress state, plasticity and mode-mixity need further consideration to obtain a theory that is sufficiently adequate to describe the static and fatigue phenomena observed in practice.

DOI: 10.1007/s10704-008-9212-8
Online Date: 5/16/2008
Print publication date: 12/1/2007
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by Mei, Haixia; Pang, Yaoyu; Huang, Rui

Channeling cracks in brittle thin films have been observed to be a key reliability issue for advanced interconnects and other integrated structures. Most theoretical studies to date have assumed no delamination at the interface, while experiments have observed channel cracks both with and without interfacial delamination. This paper analyzes the effect of interfacial delamination on the fracture condition of brittle thin films on elastic substrates. It is found that, depending on the elastic mismatch and interface toughness, a channel crack may grow with no delamination, with a stable delamination, or with unstable delamination. For a film on a relatively compliant substrate, a critical interface toughness is predicted, which separates stable and unstable delamination. For a film on a relatively stiff substrate, however, a channel crack grows with no delamination when the interface toughness is greater than a critical value, while stable delamination along with the channel crack is possible only in a small range of interface toughness for a specific elastic mismatch. An effective energy release rate for the steady-state growth of a channel crack is defined to account for the influence of interfacial delamination on both the fracture driving force and the resistance, which can be significantly higher than the energy release rate assuming no delamination.

DOI: 10.1007/s10704-008-9205-7
Online Date: 5/6/2008
Print publication date: 12/1/2007
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by Hasebe, Norio; Keer, Leon M.

A semi-infinite body with a rigid stiffener on a part of the surface under uniform anti-plane shear stress is considered. This is a mixed boundary value problem, and a closed and exact solution is obtained. Stress concentration occurs at the ends of the stiffener; therefore a crack or a debonding may occur at the end of the stiffener. This paper investigates the competition between a crack or a debonding occurrence. It also investigates how far the debonding will extend. The maximum strain energy release rate is used as criterion for detecting a crack and a debonding initiation. Also the strain energy release rate just after crack initiation is investigated and the crack initiation angle is 140.8°. As the applied load, the following three kind of loading conditions are considered; constant loading, increasing loading and small cyclic loading.

DOI: 10.1007/s10704-008-9203-9
Online Date: 5/6/2008
Print publication date: 12/1/2007
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