by Maiti, S. K.; Wathare, S. M.

A method to estimate fatigue crack extension in three point bend (TPB) testing based on changes in transverse natural frequency is presented. The theoretical formulation for the transverse free vibration of the specimen is given to relate natural frequency to the specimen dimensions and crack size employing the Timoshenko beam theory and representing crack as a rotational spring. Experimental studies are presented considering three steels, viz. SA333, 20Mn and En47, to demonstrate the accuracy of the proposed method and compare it with the conventional compliance method. The results clearly indicate that the vibration method can be an alternative to the compliance method. The Paris law constants for the materials are presented.

DOI: 10.1007/s10704-006-8476-0
Print publication date: 9/1/2006
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by Zhu, X. K.; Zhou, C. B.

A mixed-mode fatigue crack growth model with taking account of fracture surface contact and friction was developed recently by Bian et al. (2006), in reference to the general three-dimensional tensile stress solution for an elastic elliptical crack that was given by Kassir and Sih (1975). However, this general stress solution contains an error, and thus all equations for the fatigue crack growth model proposed by Bian et al. (2006) involve the error. The correct three-dimensional stress field for the elastic elliptical crack is then presented, and three fatigue crack growth models are corrected and expressed as simple functions in this paper.

DOI: 10.1007/s10704-006-8475-1
Print publication date: 9/1/2006
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by Papadopoulos, G. A.; Moscos, N.

The optical evaluation of the stress intensity factors and the distribution of the principal stresses from isochromatic and isopachic fringes is presented. The stress intensity factors and the principal stresses at the bi-material interface crack-tip are experimentally determined using the comparison photoelastic and isopachic measurements. 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 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. The size of the two branches mainly depends on the elastic modulus and the Poisson’ s ratio of the two materials.

DOI: 10.1007/s10704-006-8474-2
Print publication date: 9/1/2006
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by Ravi-Chandar, Krishnaswamy

DOI: 10.1007/s10704-006-8417-y
Print publication date: 9/1/2006
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by Kotowski, Piotr

In this study, a complete method of determination of the fractal dimension for fracture surfaces of ferrous alloys has been proposed. This dimension is determined for the vertical profile obtained by the profile technique cross-section. The image of the profile, seen through the microscope coupled with a camera, is recorded in a computer, where numerical processing is performed. For calculation of the same fractal dimension, the fd3 program has been used, which is available through the Internet. The essential element of the method is optimisation concerning microscopic magnification (scale of a length), resolution of the recorded image and selection of the grey level threshold at binarization. The tests for the stability of discretization, which enable minimization of the error of the measurement, have also been carried out. These tests consist in checking the difference in fractal dimensions for the same profile obtained in two different methods of contouring as well as the difference between capacitive, informative and correlative dimensions. In both cases, too big difference suggests that the determined dimension is not reliable. This method allows determination of the fractal dimension with an absolute accuracy of 0.05 in non-dimensional units. The method has been employed in many studies. In this paper the following tests have been presented: a “fractal map” of the fracture surface was made, an influence of the mechanical notch radius in a compact specimen on the fractal dimension of the fracture surface, an influence of the distortion rate on the fractal dimension, an effect of fatigue crack propagation rate on the fractal dimension and influence of the stress-intensity factor on the fractal dimension of the fracture surface. The following materials were examined: Armco iron, P355N steel and 41Cr4 steel in different states after the heat treatment. The measurements have been made for the specimens of the compact type. There was considered an influence of location of the place of measurement on the fractal dimension being determined. The dimension was determined on the profiles lying longwise and crosswise the crack propagation direction. It has been found that the fractal dimension of the fracture surface does not depend on a place of measurement. This suggests, among other things, that a distinction between the places, which were created under conditions of the plane stress, and the places, which were created under conditions of the plane strain state, cannot be made with the help of the fractal dimension. When testing an influence of the radius of the mechanical tip notch on the fractal dimension of a fracture surface, this dimension was determined in the places located at different distances from the tip of the mechanical notch. With respect to the radii up to 1.0 mm, no significant differences in fractal dimensions have been found. The fractal dimensions of the fracture surface for all examined materials were practically the same and they ranged from 2.02 to 2.10. However in some ranges of da/dN rate the dimension was changing inversely proportional to da/dN. Obtained results confirm that fractal dimension do not depend on the investigated material.

DOI: 10.1007/s10704-006-8264-x
Print publication date: 9/1/2006
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by Tada, N.

Electric field analysis for multiple circular cracks with different radii and angles subjected to direct electric current was carried out by the crack- current modification method (CCMM). It was found from the analysis that the increase in the potential difference normalized by the value in the case of no crack, ΔV/V
0, is in proportion to the product of the volumetric density of the cracks and the mean of the cubed crack radius and the squared cosine of the crack angle to the current direction, n

v
[r
3 cos2 θ]m. This relationship held for any crack distribution conditions discussed in this study. Using the relationship, a method for non-destructive evaluation of the distribution of circular cracks by means of direct-current potential difference method (DC-PDM) was proposed. The validity was numerically examined for two example cases.

DOI: 10.1007/s10704-006-7763-0
Print publication date: 9/1/2006
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by Tian, W. Y.; Rajapakse, R. K. N. D.

A penny-shaped crack at the interface of a piezoelectric bi-material system is considered. Analytical general solutions based on Hankel integral transforms are used to formulate the mixed-boundary value problem corresponding to an interfacial crack and the problem is reduced to a system of singular integral equations. The integral equations are further reduced to two systems of algebraic equations with the aid of Jacobi polynomials and Chebyshev polynomials. Thereafter, the exact expressions for the stress intensity factors and the electric displacement intensity factor at the tip of a crack are obtained. Selected numerical results are presented for various bi-material systems to portray the significant features of crack tip fracture parameters and their dependence on material properties, poling orientation and electric loading.

DOI: 10.1007/s10704-006-7634-8
Print publication date: 9/1/2006
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by Banks-Sills, Leslie; Freed, Yuval; Eliasi, Rami; Fourman, Victor

Experiments are carried out to determine the delamination toughness for a crack along the interface between two transversely isotropic materials. The material chosen for study consists of carbon fibers embedded within an epoxy matrix. A crack is introduced between two layers of this material, with fibers in the upper layer along the  + 45°-direction and those in the lower layer along the  − 45°-direction both with respect to the crack plane. The Brazilian disk specimen is employed in the testing. To calibrate the specimens, stress intensity factors are obtained which result from the applied load, as well as residual curing stresses. It may be noted that all three modes are coupled, leading to a three-dimensional problem. The finite element method and a mechanical M-integral are employed to determine the stress intensity factors arising from the applied load. For the residual stresses, a three-dimensional conservative thermal M-integral is presented for stress intensity factor determination. The stress intensity factors found for the applied load and residual stresses are superposed to obtain a local energy release rate, together with two phase angles. From the load at fracture, the critical interface energy release rate or interface toughness $${{\mathcal G}_{ic}}$$ as a function of phase angles ψ and ϕ is determined. Results are compared to a fracture criterion.

DOI: 10.1007/s10704-006-0084-5
Print publication date: 9/1/2006
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by Yosibash, Zohar; Priel, Elad; Leguillon, Dominique

The failure criterion of Leguillon at reentrant corners in brittle elastic materials (Leguillon 2002, Eur J Mech A/Solids 21: 61–72; Leguillon et al. (2003), Eur J Mech A—Solids 22(4): 509–524) validated in (Yosibash et al. 2004, Int J Fract 125(3–4): 307–333) for mode I loading is being extended to mixed mode loading and is being validated by experimental observations. We present an explicit derivation of all quantities involved in the computation of the failure criterion. The failure criterion is validated by predicting the critical load and crack initiation angle of specimens under mixed mode loading and comparison to experimental observations on PMMA (polymer) and Macor (ceramic) V-notched specimens.

DOI: 10.1007/s10704-006-0083-6
Print publication date: 9/1/2006
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by Pugno, Nicola

In this paper new quantized failure criteria are proposed, also for nanoscale applications. The main theories in the context of the strength of solids, i.e., of brittle fracture, dynamic fracture, fatigue and Weibull Statistics are reconsidered according to the proposed “quantization rules”. The “corresponding principle” is verified and thus the classical theories are found to be the limit cases of the quantized counterparts. As an example, our treatment is applied to very recent experimental results on carbon or WS2 nanotubes and to futurist ultra-nanocrystalline diamond nanowires, for which the tensile, bending and ideal strength are estimated.

DOI: 10.1007/s10704-006-0082-7
Print publication date: 9/1/2006
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