by Jiang, Fengchun; Rohatgi, Aashish; Vecchio, Kenneth S.; Cheney, Justin L.

The following response to the discussion of the above mentioned paper is divided into two parts: (1) a response to the issue of our comparison of the ‘apparent period of specimen oscillation’, τ, and the natural vibration period of a cracked specimen, T, and (2) a verification of the applicability of our model to ‘short time-to-fracture’ tests, which Rokach has questioned, due to a lack of knowledge of Hopkinson bar techniques.

DOI: 10.1007/s10704-004-7140-9
Print publication date: 2/1/2005
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by Rokach, I. V.

DOI: 10.1007/s10704-004-7139-2
Print publication date: 2/1/2005
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by Esparragoza, Ivan E.

Debonding of two different solids made of power law hardening materials is studied for the case of anti-plane shear loading mode by using an interface crack model. The stresses and the stress intensity factor at the interface crack are determined analytically. Using these analytical results, the constitutive equations by Hencky–Ilyushin and the general equation of energy in the neighborhood of the crack tip, the adhesion energy for the loading mode under consideration is found analytically. It can be observed that for the particular case of two linearly elastic materials and a homogeneous linearly elastic material the solution found here is in excellent agreement with the solutions found in the literature.

DOI: 10.1007/s10704-004-7137-4
Print publication date: 2/1/2005
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by Matvienko, Yu G.

DOI: 10.1007/s10704-004-5300-6
Print publication date: 2/1/2005
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by Saha, T. K.; Ganguly, S.

The problem of interaction between equal coplanar elliptic cracks embedded in a homogeneous isotropic elastic medium and subjected to shear loading was solved analytically by Saha et al. (1999) International Journal of Solids and Structures 36, 619–637, using an integral equation method. In the present study the same integral equation method has been used to solve the title problem. Analytical expression for the two tangential crack opening displacement potentials have been obtained as series in terms of the crack separation parameter βi up to the order βi5,(i=1,2) for both the elliptic as well as penny-shaped crack. Expressions for modes II and III stress intensity factors have been given for both the cracks. The present solution may be treated as benchmark to solutions of similar problems obtained by various numerical methods developed recently. The analytical results may be used to obtain solutions for interaction between macro elliptic crack and micro penny-shaped crack or vice-versa when the cracks are subjected to shear loading and are not too close. Numerical results of the stress-intensity magnification factor has been illustrated graphically for different aspect ratios, crack sizes, crack separations, Poisson ratios and loading angles. Also the present results have been compared with the existing results of Kachanov and Laures (1989) International Journal of Fracture 41, 289–313, for equal penny-shaped cracks and illustrations have been given also for the special case of interaction between unequal penny-shaped cracks subjected to uniform shear loading.

DOI: 10.1007/s10704-004-5104-8
Print publication date: 2/1/2005
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by Kato, Tetsuji; Nishioka, Toshihisa

The existence of numerous microcracks causes changes in the stiffness or fracture toughness of materials. In this paper, the manifestations of mechanical properties in the damaged materials caused by the microcracks are evaluated by the present homogenization method based on the superposition method together with the VNA solution. Moreover, it is known that the stress concentration at the macrocrack tip decreases due to the stress relaxation effect caused by the existence of the microcracks. In order to evaluate the manifestations of mechanical behavior, the mechanical effects of the existence of the microcracks on the macrocrack, the component separation method for mixed-mode stress intensity factors of the macrocrack in the damaged materials is newly developed in this paper. Various numerical analyses are successfully conducted for the two topics, the mechanical properties of the damaged materials and the mechanical behavior of the macrocrack in the damaged materials.

DOI: 10.1007/s10704-004-4558-z
Print publication date: 2/1/2005
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by Gorbatikh, Larissa; Lomov, Stepan; Verpoest, Ignace

In the present work, we predict contribution of a partially debonded circular inhomogeneity into the material overall elastic compliance. Debonding at the matrix/inclusion boundary is modeled as interfacial arc cracks. The change in the elastic compliance caused by interface cracking is estimated through the accompanying energy change that is related to the mode I and mode II stress intensity factors at the crack tips. The sum of the crack compliance and the inhomogeneity compliance (with perfect bonding) gives the total compliance of the debonded inhomogeneity. The latter is obtained in terms of the material properties and crack length. Additional analysis shows that the replacement of an interface crack with a crack in a homogenized medium is an inadequate approach when seeking approximate solutions. The paper also provides guidelines how to determine properties of a fictitious perfectly bonded orthotropic inhomogeneity that has the same contribution into the material compliance as the debonded isotropic one. This problem is of practical importance when modeling damage accumulation in composite materials by means of homogenization schemes.

DOI: 10.1007/s10704-004-4271-y
Print publication date: 2/1/2005
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by Chen, W. Q.; Lim, C. W.

This paper considers the non-axisymmetric three-dimensional problem of a penny-shaped crack with permeable electric conditions imposed on the crack surfaces, subjected to a pair of point normal forces applied symmetrically with respect to the crack plane. The crack is embedded in an infinite transversely isotropic piezoelectric body with the crack face perpendicular to the axis of material symmetry. Applying the symmetry of the problem under consideration then leads to a mixed–mixed boundary value problem of a half-space, for which potential theory method is employed for the purpose of analysis. The cases of equal eigenvalues are also discussed. Although the treatment differs from that for an impermeable crack reported in literature, the resulting governing equation still has a familiar structure. For the case of a point force, exact expressions for the full-space electro-elastic field are derived in terms of elementary functions with explicit stress and electric displacement intensity factors presented. The exact solution for a uniform loading is also given.

DOI: 10.1007/s10704-004-4195-6
Print publication date: 2/1/2005
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