by Martin, E.; Poitou, B.; Leguillon, D.; Gatt, J. M.

The mechanisms which govern crack deflection and crack penetration at interfaces must be understood in order to design composites and layered materials. Experimental observations have shown that a realistic description of crack deflection must take into account the initiation of fracture mechanisms by the stress field of an approaching matrix crack. Fracture mechanisms which include interfacial debonding and penetration are thus analysed in the vicinity of a main crack. For this purpose, a unit cell consisting of a single fibre surrounded by a cylindrical tube of matrix is studied with the help of a finite element model. Initiation stress and nucleation length are determined for both mechanisms by using an initiation criterion which requires to fulfil an energy and a stress condition. Investigating the competition between the initiation of the two mechanisms provides decohesion/penetration maps which depend on the strength and toughness of interface and fibre. It is shown that the debonding or penetration condition can be reduced to an energy or a stress condition depending on the relative value of some characteristic fracture lengths of interface and fibre. Finally it is noted that a low toughness interface is not systematically a sufficient condition to promote the initiation of deflection.

DOI: 10.1007/s10704-008-9228-0
Online Date: 8/21/2008
Print publication date: 6/1/2008
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by Kulkarni, D. M.; Chaudhari, Vikas; Prakash, Ravi; Kumar, A. N.

In this research work, the effect of thickness on fracture criterion is studied for extra deep drawn (EDD) steel sheets. Experimental results are generated on fracture toughness of EDD steel sheets using compact tension specimens and a ‘maximum load’ as a fracture criterion. Critical crack tip opening displacement (CTOD) is found with the help of three methods: plastic hinge model (PHM), crack flank opening angle (CFOA) and finite element model (FEM). The fracture toughness is found to increase with increase in thickness of specimens. The fracture behaviour exhibited characteristics of general yielding fracture mechanics.

DOI: 10.1007/s10704-008-9253-z
Online Date: 8/19/2008
Print publication date: 6/1/2008
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by Shirazi, Alireza; Varvani-Farahani, Ahmad; Lu, Hua

The present study attempts to evaluate the stress-strain hysteresis responses of SAC solder joints in Resistor and FleXBGA144 packages subjected to thermal cyclic loading using several constitutive models. The total deformation of the solder material consists of elastic, rate-independent plastic and rate-dependent creep components. The constitutive models discussed in this study each weighted elastic, plastic and creep deformations differently. At low stresses SAC solder alloys were found to be creep resistant, where at higher stresses, the influence of different microstructures disappears as matrix-creep dominates in this region. Thus, the proper constitutive model requires all the three ingredients of the elastic, the creep, and the time-independent plastic data for different stress levels to effectively predict the hysteresis behavior of the SAC solder alloys. The hysteresis loops predicted by constitutive models were also found in close agreement with the loops generated by FEM for the SAC solder joint subjected to thermal cycling.

DOI: 10.1007/s10704-008-9254-y
Online Date: 8/15/2008
Print publication date: 6/1/2008
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by Maeng, Wan Young

Stress Corrosion Cracking (SCC) tests (pH: 3 ~ 5) and Corrosion Fatigue (CF) tests (R = 0.2, 0.1 Hz) were conducted to evaluate the effect of acetic acid on the corrosion crack growth behavior in high temperature water at 150°C. Acetic acid significantly influenced the corrosion fatigue cracking behavior of turbine disc steels in high temperature water. The CF crack growth rates of turbine disc steels increase until the organic acid concentration reaches a critical saturation value (between pH 4 and pH 3) because of the crack tip sharpening. Below the critical value of pH, the CF crack growth rates decreases because of the crack tip blunting. The corrosion fatigue crack growth rate is accelerated by the interaction of the fatigue and the stress corrosion in the test environment. The synergistic interaction should be accounted for in the realistic prediction of the corrosion fatigue life of turbine steel (3.5NiCrMoV steels) in high temperature water of acetic acid solution. With the high temperature corrosion fatigue data obtained in this study, it is possible to assess the life of turbine components in high temperature and high pressure.

DOI: 10.1007/s10704-008-9256-9
Online Date: 8/15/2008
Print publication date: 6/1/2008
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by Şimşir, Mehmet

In this experimental study, fracture toughness of heat-treated metal matrix composite was investigated. The gray cast iron was reinforced with steel wire of volume fraction of V_r = 0.05 and three-point bend specimens were manufactured to determine fracture toughness. Heat treatment was applied to the specimens at the normalization temperatures of 850°C and then cooled in three distinct environments (water, air, and furnace). Fracture toughness of the metal matrix composite was calculated by unloading compliance method. The study shows that the fracture toughness of the steel-wire-reinforced gray cast iron increases with the increase in cooling rate. Scanning electron microcopy (SEM) analyses were used to examine the microstructure and fracture surface. It is observed that the carbon diffuses from the gray cast iron to the steel wire and transition region having partially dissolved graphite was observed due to carbon diffusion, and it plays an important role in the fracture toughness depending on the cooling media.

DOI: 10.1007/s10704-008-9255-x
Online Date: 8/15/2008
Print publication date: 6/1/2008
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by Fang, F.; Yang, W.; Zhang, F. C.; Qing, H.

In-situ observation of the electrically induced fatigue crack growth is carried out for $${\langle001\rangle}$$-oriented (Pb(Mg_1/3Nb_2/3)O₃)_0.72–(PbTiO₃)_0.28 (PMN-28PT) ferroelectric single crystals under alternating electric field. It is found that apparent crack growth takes place even though the peak value of the applied electric field is below E
_c. The crack propagation is a repeated process of advancement in small increments, followed by a sudden increase in the crack length. When the crack tip pops-in, there is a tendency for branching. The test data suggest that the variation of the crack boundary condition may contribute to the observed electrically induced crack growth behavior.

DOI: 10.1007/s10704-008-9248-9
Online Date: 8/12/2008
Print publication date: 6/1/2008
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by Wang, Zhao-Xi; Lu, Jian; Shi, Hui-Ji; Li, Dong-Feng; Ma, Xianfeng

In the Ductile–Brittle Transition Temperature (DBTT) region, it is not realistic to take unique fracture stress or fracture strain as the fracture criterion to investigate the fracture properties. In this paper, an updated continuum damage model was proposed, in which the fracture energy density, a function of the stress triaxiality, temperature and strain rate in the transition region was taken as the critical damage factor. Uniaxial tension tests were carried out to get the basic material properties at different temperatures, to calibrate the fracture model constants and verify the validity of the damage model. The fracture behaviour of pipes with penetrating cracks under the internal pressure was experimentally investigated with the load–deflection curves and the crack propagation length captured from tests. The J–R curves were obtained from the testing results for different temperatures. Based on the Finite Element Analyses (FEA) with the proposed fracture criterion of the updated continuum damage model, the loading level of pipes with penetrating cracks were estimated and compared with the experimental results. Meanwhile the fracture processes of the pipeline structures in the transition region were reproduced. The experimental and numerical results agreed very well in present calculations. It has been shown that the fracture process in the transition region strongly depends on both the stress and strain states, and could be effectively predicted using the continuum damage model.

DOI: 10.1007/s10704-008-9250-2
Online Date: 8/12/2008
Print publication date: 6/1/2008
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by Mao, W. G.; Dai, C. Y.; Yang, L.; Zhou, Y. C.

Thermal barrier coatings (TBCs) have been extensively used in aircraft engines for improved durability and performance for more than fifteen years. In this paper, thermal barrier coating system with plasma sprayed zirconia bonded by a MCrAlY layer to SUS304 stainless steel substrate was performed under tensile tests at 1000°C. The crack nucleation, propagation behavior of the ceramic coatings in as received and oxidized conditions were observed by high-performance camera and discussed in detail. The relationship of the transverse crack numbers in the ceramic coating and tensile strain was recorded and used to describe crack propagation mechanism of thermal barrier coatings. It was found that the fracture/spallation locations of air plasma sprayed (APS) thermal barrier coating system mainly located within the ceramic coating close to the bond coat interface by scanning electron microscope (SEM) and energy dispersive X-Ray (EDX). The energy release rate and interface fracture toughness of APS TBCs system were evaluated by the aid of Suo–Hutchinson model. The calculations revealed that the energy release rate and fracture toughness ranged, respectively, from 22.15 J m⁻² to 37.8 J m⁻² and from 0.9 MPa m^1/2 to 1.5 MPa m^1/2. The results agree well with other experimental results.

DOI: 10.1007/s10704-008-9246-y
Online Date: 8/8/2008
Print publication date: 6/1/2008
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by Li, Dong-Feng; Li, Chen-Feng; Shu, Si-Qi; Wang, Zhao-Xi; Lu, Jian

This paper presents a fast and accurate solution for crack interaction problems in infinite- and half- plane solids. The new solution is based on the method of complex potentials developed by Muskhelishvili for the analysis of plane linear elasticity, and it is formulated through three steps. First, the problem is decomposed into a set of basic problems, and for each sub-problem, there is only one crack in the solid. Next, after a crack-dependent conformal mapping, the modified complex potentials associated with the sub-problems are expanded into Laurent’s series with unknown coefficients, which in turn provides a mechanism to exactly implement in the form of Fourier series the boundary condition in each sub-problem. Finally, taking into account the crack interaction via a perturbation approach, an iterative algorithm based on fast Fourier transforms (FFT) is developed to solve the unknown Fourier coefficients, and the solution of the whole problem is readily obtained with the superposition of the complex potentials in each sub-problem. The performance of the proposed method is fully investigated by comparing with benchmark results in the literatures, and superb accuracy and efficiency is observed in all situations including patterns where cracks are closely spaced. Also, the new method is able to cope with interactions among a large number of cracks, and this capability is demonstrated by a calculation of effective moduli of an elastic solid with thousands of randomly-spaced cracks.

DOI: 10.1007/s10704-008-9249-8
Online Date: 8/6/2008
Print publication date: 6/1/2008
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by Fu, X. L.; Wang, G. F.; Feng, X. Q.

On the physical nature, most crack tips are not ideally sharp but have a small curvature radius. Both surface energy and crack-root curvature affect the stress and displacement fields in the vicinity of the crack tip. In the present paper, a numerical method, which incorporates the effect of surface elasticity into the finite element method, is employed to study the surface effects on the mode-II crack tip fields. It is found that when the curvature radius of the crack root decreases to micro-/nanometers, surface elasticity has a significant influence on the stresses near the crack tip. For a mode-II crack, surface effects alter both the magnitude and position of the maximum stresses, as is different from a mode-I crack, in which case only the stress magnitude is influence by surface stresses.

DOI: 10.1007/s10704-008-9245-z
Online Date: 8/6/2008
Print publication date: 6/1/2008
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