by Ding, Sheng-Hu; Li, Xing

In this paper, the interface cracking between a functionally graded material (FGM) and an elastic substrate is analyzed under antiplane shear loads. Two crack configurations are considered, namely a FGM bonded to an elastic substrate containing a single crack and a periodic array of interface cracks, respectively. Standard integral-transform techniques are employed to reduce the single crack problem to the solution of an integral equation with a Cauchy-type singular kernel. However, for the periodic cracks problem, application of finite Fourier transform techniques reduces the solution of the mixed-boundary value problem for a typical strip to triple series equations, then to a singular integral equation with a Hilbert-type singular kernel. The resulting singular integral equation is solved numerically. The results for the cases of single crack and periodic cracks are presented and compared. Effects of crack spacing, material properties and FGM nonhomogeneity on stress intensity factors are investigated in detail.

DOI: 10.1007/s10704-008-9302-7
Online Date: 12/31/2008
Print publication date: 9/1/2008
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by Bian, Lichun; Taheri, Farid

In the present investigation, the G
_max criterion, which is based on the elastic strain energy principle, is extended to study the fatigue crack growth characteristics of mixed mode cracks. A modification has been made to this criterion to implement the plastic strain energy and, hence, a new elasto-plastic energy-based model is presented. Subsequently, the proposed model is employed to predict fatigue crack growth in rectangular steel plates under complex stress states. The results obtained using the elasto-plastic energy model proposed are compared with those obtained using the commonly used Paris law and our experimental data.

DOI: 10.1007/s10704-008-9301-8
Online Date: 12/25/2008
Print publication date: 10/1/2008
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by Yin, H. M.; Paulino, G. H.; Buttlar, W. G.

A two-dimensional explicit elastic solution is derived for a brittle film bonded to a ductile substrate through either a frictional interface or a fully bonded interface, in which periodically distributed discontinuities are formed within the film due to the applied tensile stress in the substrate and consideration of a “weak form stress boundary condition” at the crack surface. This solution is applied to calculate the energy release rate of three-dimensional channeling cracks. Fracture toughness and nominal tensile strength of the film are obtained through the relation between crack spacing and tensile strain in the substrate. Comparisons of this solution with finite element simulations show that the proposed model provides an accurate solution for the film/substrate system with a frictional interface; whereas for a fully bonded interface it produces a good prediction only when the substrate is not overly compliant or when the crack spacing is large compared with the thickness of the film. If the section is idealized as infinitely long, this solution in terms of the energy release rate recovers Beuth’s exact solution for a fully cracked film bonded to a semi-infinite substrate. Interfacial shear stress and the edge effect on the energy release rate of an asymmetric crack are analyzed. Fracture toughness and crack spacing are calculated and are in good agreement with available experiments.

DOI: 10.1007/s10704-008-9286-3
Online Date: 12/16/2008
Print publication date: 9/1/2008
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by Fett, Theo; Creek, Dominic; Wagner, Susanne; Rizzi, Gabriele; Volkert, Cynthia A.

The validity of fracture toughness data obtained from tests with V-notched bending bars is affected by the notch root radius and the presence of R-curve behavior. A macroscopic test specimen has been developed that contains a notch introduced by focused ion beam machining. This produces a notch root radius of less than 0.1 μm, so that notch effects can be ignored for most ceramics. Also, due to the very small notch depths the influence of a rising R-curve should be very close to that of natural cracks. First tests, carried out on a Ce-doped zirconia ceramic resulted in a toughness of K
_Ic ≈ 5.9 MPa√m.

DOI: 10.1007/s10704-008-9288-1
Online Date: 12/5/2008
Print publication date: 9/1/2008
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by Fett, Theo; Fünfschilling, Stefan; Hoffmann, Michael J.; Oberacker, Rainer

R-curves caused by crack face interactions are important for the strength assessment of components with small cracks. Whereas an influence of the initial crack length on the R-curve is well understood on the basis of fracture mechanics, it will be shown here that also the type of the crack affects the crack growth resistance. For a given crack-bridging relation it can be shown that 3-dimensional cracks as circular internal cracks and semi-circular surface cracks must exhibit a lower R-curve than obtainable from 2-dimensional edge cracks.

DOI: 10.1007/s10704-008-9289-0
Online Date: 12/4/2008
Print publication date: 10/1/2008
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by Menshykov, Oleksandr V.; Guz, Igor A.

The paper is devoted to the solution of the three-dimensional elastodynamic problem for linearly elastic, homogeneous and isotropic solid with two penny-shaped in-plane cracks under normally incident harmonic tension-compression wave with allowance for the contact interaction of crack faces. The effect of the distance between cracks on the stress intensity factor (opening mode) is studied for different wave numbers. The results are compared with those obtained neglecting the cracks’ closure.

DOI: 10.1007/s10704-008-9282-7
Online Date: 12/2/2008
Print publication date: 9/1/2008
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by Das, S.; Chakraborty, S.; Srikanth, N.; Gupta, M.

The problem of two edge cracks of finite length, situated symmetrically in an orthotropic infinite strip of finite thickness 2 h, under normal point loading has been discussed. The displacements and stresses in plane strain conditions are expressed in terms of two harmonic functions. The problem is addressed by seeking the solution of a pair of simultaneous integral equations with Cauchy type singularities solved by finite Hilbert Transform technique. For large h, analytical expression for the stress intensity factor at the crack tip is obtained.

DOI: 10.1007/s10704-008-9284-5
Online Date: 12/2/2008
Print publication date: 9/1/2008
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