by Ballarini, Roberto; Villaggio, Piero

In the above referenced paper, misinterpretations led Martin to claim that there are errors in certain equations derived in our paper on the use of Frobenius’ method to solve curved crack problems. This note identifies the misinterpretations and shows that our results are the same as those derived by Martin.

DOI: 10.1007/s10704-008-9186-6
Online Date: 2/28/2008
Print publication date: 11/1/2007
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by Kanaun, S. K.

An isolated elliptical crack in an infinite orthotropic elastic medium is considered. An efficient numerical algorithm of the solution of the problem for a crack subjected to a constant external field is proposed. The calculation of the crack opening vector and the stress intensity factors on the crack edge is reduced to regular 2D-integrals. These integrals may be simply calculated numerically for an arbitrary orientation of the crack plane with respect to the principal axes of the anisotropy of the medium. Examples of the calculation of the crack opening vector and stress intensity factors are presented.

DOI: 10.1007/s10704-008-9187-5
Online Date: 2/26/2008
Print publication date: 11/1/2007
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by Livieri, Paolo; Segala, Fausto

In the present work the J-integral (indicated here as J_Vρ
because two parallel flanks are not present) was calculated by using, along the free border, the exact analytical stress distribution for the ellipse and the asymptotic one for parabolic notches. The material was assumed as homogeneous isotropic and linear elastic. First, for an ellipse under remote tensile loading, the expression of J_Vρ
has been analytically calculated on the basis of Inglis’ equations. The equations have been used to prove that, in terms of J-integral, the crack is the limit case of an equivalent elliptic notch. Furthermore, by distinguishing the symmetric and skew-symmetric terms, the well-known Stress Intensity Factors (SIF) of mode I and II for a crack in a wide plate under tension are obtained by adding a limiting condition. Second, by means of Creager–Paris’ equations, J_Vρ
has been analytically calculated for a parabolic notch of assigned tip notch radius ρ. The asymptotic value of J_Vρ
and the relationship between the peak stress and the relative SIF are the same as the ellipse. Finally, as an engineering application, we provide an accurate formula for the evaluation of the Notch Stress Intensity Factors of a crack, mainly subjected to tensile stress, from the peak stress of the equivalent ellipse under the same loading.

DOI: 10.1007/s10704-008-9178-6
Online Date: 2/26/2008
Print publication date: 11/1/2007
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by Katsaga, Tatyana; Sherwood, Edward G.; Collins, Michael P.; Young, R. Paul

In this study acoustic emission (AE) techniques were employed to investigate the process of fracture formation in large, shear-critical, reinforced concrete beams and to gain improved insight into the mechanisms of shear failure. Large sensor arrays were specially designed to study various aspects of failure by observing the fracturing processes throughout the load history of the beams. Smaller, more concentrated sensor arrays revealed complex spatial and temporal fracture development at the slow quasi-static and spontaneous dynamic stages of propagation. When AE events are related to the micro-structure of concrete through computed tomography images and surface fracture measurements they show that coarse aggregates play important roles in shear fracture propagation in reinforced concrete.

DOI: 10.1007/s10704-008-9174-x
Online Date: 2/19/2008
Print publication date: 11/1/2007
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by Grechka, Vladimir

We establish an exact equivalence of the non-interaction approximation (NIA) and Gassmann theory in describing the changes in effective elasticity due to variations in the bulk modulus of fluid infill of isolated inclusions that have identical shapes and orientations. If the sizes of inclusions (pores or fractures) are equal, the fluid pressures in all inclusionsare equal too regardless of their hydraulic connectivity. This fact makes Gassmann theory rigorous; therefore, other effective media schemes should comply with it when applied to such microstructures. While the NIA satisfies this requirement, other effective media schemes (e.g., self-consistent and differential) do not.

DOI: 10.1007/s10704-008-9188-4
Online Date: 2/14/2008
Print publication date: 11/1/2007
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by Marsavina, Liviu; Sadowski, Tomasz

The paper investigates the effect of the biaxial loading on crack deflection/penetration at a bi-material ceramic interface. A biaxially loaded geometry was numerically investigated using Finite Element Analysis in order to determine the energy release rate. The obtained results could be used in conjunction with a fracture criteria at interface for estimating the path of the crack after the interface was reached.

DOI: 10.1007/s10704-008-9181-y
Online Date: 2/8/2008
Print publication date: 11/1/2007
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by Papadopoulos, G. A.; Kravaritis, J.; Badalouka, B.

An experimental method of the principal stresses estimation which is based on photoelasticity and isopachic methods is presented. The principal stresses at the bi-material interface crack-tip are theoretically determined using the combination photoelastic and isopachic fringes. The size and the shape of crack-tip isochromatic and isopachic fringes, at a bi-material interface under static load, are studied. When the crack-tip, which is perpendicular to interface, is placed at the interface of the bi-material, the isochromatic and the isopachic fringes depend on the properties of the two materials. Thus, the isochromatic and the isopachic fringes are divided into two branches, which present a jump of values at the interface. The size of the two branches mainly depends on the elastic modulus and the Poisson’ s ratio of the two materials. From the combination of the isochromatic and the isopachic fringes, the principal stresses σ₁ and σ₂ can be estimated and the contour curves around the crack-tip can be plotted.

DOI: 10.1007/s10704-008-9180-z
Online Date: 2/8/2008
Print publication date: 11/1/2007
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by Levin, Valery M.; Alvarez-Tostado, Juan M.

A two-component poroelastic composite material is considered. This material consists of a homogeneous transversely isotropic poroelastic matrix and aligned spheroidal inclusions filled with material having different poroelastic properties. The effective poroelastic characteristics are obtained by the effective field method. All the formulas are presented in explicit ready-to-use form.

DOI: 10.1007/s10704-008-9182-x
Online Date: 2/8/2008
Print publication date: 11/1/2007
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by Chen, Xiaohong

A coupled hygro-thermo-viscoelastic fracture theory is developed for quasi-static and dynamic crack propagation in viscoelastic materials subject to combined mechanical loading and hygrothermal environmental exposure based on fundamental principles of thermodynamics. The Helmholtz free energy is taken to be a functional of the histories of strain, temperature and fluid concentration with the crack parameter being introduced as an internal state variable. A thermodynamically consistent time-dependent fracture criterion for crack propagation in the presence of thermally and mechanically assisted fluid transport is obtained from the global energy balance equation and the requirement of non-negativity of the global energy dissipation rate, which is generally applicable to both quasi-static and dynamic loading and both isothermal/isohumidity and non-isothermal/non-isohumidity conditions with classic fracture criteria as special cases. On the basis of the developed theory, the generalized energy release rate method, the generalized contour integral method and the extended essential work of fracture method are proposed for fracture characterization of load-carrying viscoelastic materials in hygrothermal environments, and the interrelation of these methods and their correlation with conventional methods and existing models, simulations and experiments are discussed.

DOI: 10.1007/s10704-008-9176-8
Online Date: 2/8/2008
Print publication date: 11/1/2007
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