by Lucon, Enrico

The most commonly used test standards for performing Charpy impact tests (ISO 148 and ASTM E 23) envisage the use of strikers having different radii of the striking edge, i.e. 2 mm (ISO) and 8 mm (ASTM). The effect of striker geometry on Charpy results was extensively studied in the past in terms of absorbed energy measured by the machine encoder, but few investigations are available on the influence of striker configuration on the results of instrumented Charpy tests (characteristic forces, displacements and integrated energy). In this paper, these effects are investigated based on the analysis of published results from three interlaboratory studies and some unpublished Charpy data obtained at SCK·CEN. The t-test was used for establishing the statistical significance of the observed effects. The instrumented variables which are the most sensitive to the radius of the striking edge are the maximum force and its corresponding displacement, with 8 mm-strikers providing systematically higher values. The effect on general yield forces, on the other hand, is less consistent and more difficult to rationalize, although 2 mm-strikers generally tend to deliver higher values. Absorbed energies, obtained both from the instrumented trace and from the pendulum encoder, are almost insensitive to the type of striker up to 200 J. For higher energy levels, the values obtained from 8 mm-strikers become progressively larger. Data scatter is generally higher for 2 mm-strikers.

DOI: 10.1007/s10704-008-9283-6
Online Date: 11/27/2008
Print publication date: 9/1/2008
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by Aliha, M. R. M.; Ayatollahi, M. R.; Pakzad, R.

A ring shaped specimen is used for studying mixed mode fracture in brittle materials. The ring specimen is subjected to a compressive diametral load and contains two angled central cracks. A series of fracture tests are conducted under various mode mixities using the ring specimen. It is shown that the obtained experimental results are in a very good agreement with theoretical predictions of the modified maximum tangential stress criterion.

DOI: 10.1007/s10704-008-9280-9
Online Date: 11/20/2008
Print publication date: 9/1/2008
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by Chen, Chih-Hao; Wang, Chein-Lee

A particular weight function method is used in this study to determine the stress intensity factors (SIFs) and T-stresses for offset double edge-cracked plates (ODECPs). By using reference loading conditions prescribed on the crack flanks for finite element analyses, the coefficients of weight functions are derived and compiled in the form of tables. With the weight functions, the SIFs and T-stresses for several loading cases are calculated. The results compare well with those obtained using the displacement method. Applying the derived weight functions, the SIFs and T-stresses for ODECPs under several loading conditions are determined. The results can be used as references for related applications.

DOI: 10.1007/s10704-008-9276-5
Online Date: 11/19/2008
Print publication date: 8/1/2008
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by Ru, C. Q.

In many practical applications, piezoelectric ceramics are bonded to non-piezoelectric and insulating isotropic elastic materials such as polymer. Since the conventional form of Stroh’s formulation, on which almost all of existing works on interfacial cracks in piezoelectric media have been based, breaks down or becomes complicated for isotropic elastic materials, many solutions available in the literature cannot be directly applied to interfacial cracks between a piezoelectric material and an isotropic elastic material. The present paper is devoted to a hybrid complex-variable method which combines the Stroh’s method of piezoelectric materials with the well-known Muskhelishvili’s method of isotropic elastic materials. This method is illustrated in detail for an insulating interfacial crack between a piezoelectric half-plane and an isotropic elastic half-plane, although interface cracks between piezoelectric and isotropic elastic conductor can be analyzed in a similar way. The solution obtained generally exhibits oscillatory singularity, in agreement with a previous known result based on the Stroh’s formulation. A simple explicit condition is obtained for the bimaterial constants under which the oscillatory singularity disappears. It is expected that the hybrid complex-variable method could more conveniently handle other possible complications (such as a hole or an inclusion) inside the isotropic elastic material, because it offers explicit solutions of a single complex variable rather than several different complex-variables associated with the Stroh’s formulation.

DOI: 10.1007/s10704-008-9279-2
Online Date: 11/19/2008
Print publication date: 8/1/2008
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by Lalegname, A.; Sändig, A. -M.; Sewell, G.

We discuss the propagation of a running crack in a bounded linear elastic body under shear waves for a simplified 2D-model. This model is described by two coupled equations in the actual configuration: a two-dimensional scalar wave equation in a cracked, bounded domain and an ordinary differential equation derived from an energy balance law. The unknowns are the displacement fields u  =  u(y, t) and the one-dimensional crack tip trajectory h  =  h(t). We assume that the crack grows straight. Based on a paper of Nicaise-Sändig, we derive an improved formula for the ordinary differential equation of motion for the crack tip, where the dynamical stress intensity factor occurs. The numerical simulation is an iterative procedure starting from the wave field at time t  =  t

_i
. The dynamic stress intensity factor will be extracted at t  =  t

_i
. Its knowledge allows us to compute the crack-tip motion h(t

_i+1) with corresponding nonuniform crack speed assuming (t

_i+1 − t

_i
) is small. Now, we start from the cracked configuration at time t  =  t

_i+1 and repeat the steps. The wave displacements are computed with the FEM-package PDE2D. Some numerical examples demonstrate the proposed method. The influence of finite length of the crack and finite size of the sample on the dynamic stress intensity factor will be discussed in detail.

DOI: 10.1007/s10704-008-9274-7
Online Date: 11/19/2008
Print publication date: 8/1/2008
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by Kumar, Shailendra; Barai, S. V.

Comparative study for determining the K

_R
-curves associated with the cohesive stress distribution for complete fracture process for two standard specimen geometries i.e., three-point bending test and compact tension test specimen geometries of concrete using analytical method and weight function approach is reported in the paper. The laboratory size specimen (100 ≤  D  ≤  400 mm) with initial-notch length/depth ratios 0.3 and 0.5 are considered in the investigation. The load-crack opening displacement curves for these specimens are obtained using well known version of Fictitious Crack Model (FCM). It is found from the numerical results that the weight function method improves computational efficiency without any appreciable error. The stability analysis on the K

_R
-curves and the influence of specimen geometry and the size-effect on the K

_R
-curves, the CTOD-curves and the process zone length during crack propagation of complete fracture process are also described.

DOI: 10.1007/s10704-008-9275-6
Online Date: 11/19/2008
Print publication date: 8/1/2008
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by Li, Yong-Dong; Lee, Kang Yong

Anti-plane fracture analysis is performed for a micropolar material. The crack problem is reduced as Cauchy singular integral equations by Fourier integral transform. Numerical solutions of the stress intensity factors are obtained by the Lobatto–Chebyshev collocation method. Parametric studies indicate that the fracture behavior of the micropolar material depends on the coupling factor and the internal length scale. Larger coupling factor and internal length scale lead to stronger micropolar effect. The micropolarity is beneficial to reducing the driving force of a micro-crack, however, it may also prompt the propagation of a macro-crack.

DOI: 10.1007/s10704-008-9277-4
Online Date: 11/19/2008
Print publication date: 8/1/2008
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by Ramesh, M.; Simha, K. R. Y.

Fibrous materials often contain cylindrical cracks due to delamination along the matrix-fiber interface. It is instructive to analyse a cylindrical crack of length 2a and diameter 2h in a homogeneous medium and compare the results with those for a pair of parallel cracks of length 2a and spacing 2h. The pair of parallel cracks mutually shielding each other is examined here with regard to the variation of stress intensity factors and energetics including the asymptotic limit of a pair of nearly coalescing parallel cracks. A unified formulation for parallel cracks/cylindrical crack based on crack opening displacement (COD) in terms of Chebyshev polynomials is developed. The characteristic variation of stress intensity factors as the cracks approach each other (h → 0) shows that the stress intensity factors vanish for the case of a vanishingly small cylindrical crack but not for the 2D parallel pair of cracks. The 2D case of a pair of collapsing parallel cracks ensures a finite energy release rate asymptoting to that of a single crack. Further research is needed to establish definitive asymptotic bounds for the case of extremely closely spaced cracks on the lines of Hutchinson and Suo (Adv Appl Mech 29:377–384, 1992), Kachanov (1993) and Gorbatikh et al. (Int J Fract (Lett Fract Micromech) 143:377–384, 2007). Results are presented for different values of Poisson’s ratio.

DOI: 10.1007/s10704-008-9273-8
Online Date: 11/14/2008
Print publication date: 8/1/2008
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by Chen, D. H.; Ozaki, S.

In this study, a method of evaluating the static strength of a V-shaped notch based on the singular stress field at the notch tip is studied. The singular stress fields is defined by two parameters, $${K_{I, \lambda_1}}$$ and $${K_{II,\lambda_2}}$$ , which correspond to the intensities of symmetric stress field and the skew-symmetric field, respectively. Four kinds of fracture criteria are considered; two of them are based on the tensile strength σ

_B
and the other two are based on the fracture toughness K

_IC
. The usefulness of the criteria is investigated through the experimental results carried out on plane specimens of acrylic resin having a sharp notch for various notch configurations such as the opening angle, the inclined angle and the notch depth. It is shown that the criteria using stress intensity factor and the energy release rate not sensitive to the length of the virtual crack $${\varepsilon}$$ .

DOI: 10.1007/s10704-008-9272-9
Online Date: 11/14/2008
Print publication date: 8/1/2008
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