by Fett, T.; Njiwa, A. B. Kounga; Rödel, J.

Crack opening displacements (COD) were obtained on fully developed cracks in compact tension specimens manufactured from a commercial, soft lead zirconate titanate (PZT). The data were evaluated using the weight function method to provide crack closures stresses as a function of distance to the crack tip. As ferroelastic toughening in PZT shows time-dependent effects, data were taken at different stages of unloading. The peak closure stress was determined as 20 MPa.

DOI: 10.1007/s10704-005-8547-7
Print publication date: 7/1/2005
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by Zafošnik, Boštjan; Ren, Zoran; Flašker, Jože; Mishuris, Gennady

The paper describes modelling approach to computational simulation of surface crack growth subjected to lubricated rolling–sliding contact conditions. The model considers the size and orientation of the initial crack, normal and tangential loading due to rolling–sliding contact and the influence of fluid trapped inside the crack by a hydraulic pressure mechanism. The motion of the contact sliding load is simulated with different load cases. The strain energy density (SED) and maximum tangential stress (MTS) crack propagation criteria are modified to account for the influence of internal pressure along the crack surfaces due to trapped fluid. The developed model is used to simulate surface crack growth on a gear tooth flank, which has been also experimentally tested. It is shown that the crack growth path, determined with modified crack propagation criteria, is more accurately predicted than by using the criteria in its classical form.

DOI: 10.1007/s10704-005-8546-8
Print publication date: 7/1/2005
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by Jin, Z. -H.; Sun, C. T.

A linear hardening model together with a linear elastic background material is first used to discuss some aspects of the mathematical and physical limitations and constraints on cohesive laws. Using an integral equation approach together with the cohesive crack assumption, it is found that in order to remove the stress singularity at the tip of the cohesive zone, the cohesive law must have a nonzero traction at the initial zero opening displacement. A cohesive zone model for ductile metals is then derived based on necking in thin cracked sheets. With this model, the cohesive behavior including peak cohesive traction, cohesive energy density and shape of the cohesive traction–separation curve is discussed. The peak cohesive traction is found to vary from 1.15 times the yield stress for perfectly plastic materials to about 2.5 times the yield stress for modest hardening materials (power hardening exponent of 0.2). The cohesive energy density depends on the critical relative plate thickness reduction at the root of the neck at crack initiation, which needs to be determined by experiments. Finally, an elastic background medium with a center crack is employed to re-examine the shape effect of cohesive traction–separation curve, and the relation between the linear elastic fracture mechanics (LEFM) and cohesive zone models by considering the cohesive zone development and crack growth in the infinite elastic medium. It is shown that the shape of the cohesive curve does affect the cohesive zone size and the apparent energy release rate of LEFM for the crack growth in the elastic background material. The apparent energy release rate of LEFM approaches the cohesive energy density when the crack extends significantly longer than the characteristic length of the cohesive zone.

DOI: 10.1007/s10704-005-7864-1
Print publication date: 7/1/2005
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by Labeas, G.; Diamantakos, J.

An analytical methodology for predicting the condition when interacting cracks coalesce and estimate the residual strength under Multiple Site Damage situations is proposed. Dominating magnitudes of the criterion are the changes in elastic and plastic strain energy due to crack ligament fracture. The strain energy magnitudes of interest are calculated using analytical formulations, such that the methodology is efficiently applicable in the design of real aircraft panels. Link-up stress predictions using the present methodology are in very good correlation to the experiments and in most cases better, as compared to the alternative crack link-up prediction models.

DOI: 10.1007/s10704-005-0155-z
Print publication date: 7/1/2005
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by Miyazaki, Tatsujiro; Noguchi, Hiroshi; Kage, Masaharu

In this paper, push–pull fatigue tests of notched specimens under R=−1, 0 and 0.5 are carried out on annealed 0.1 % carbon steel and quenched-tempered 0.5 % carbon steel with Hrm B simeq 600. The fatigue limit of a long crack, sigmaw2, is obtained from that of a notched specimen with a sharp and deep notch whose radius is smaller than the branch point rho0. Using the present and past sigmaw2 data, the effect of the positive mean stress on the dKw of the long crack is evaluated using 3.2 Hrm B (simeq sigmarm B) and sigmarm S(3.2 Hrm B), where dKw is the stress intensity factor range for predicting the fatigue limit of a metal with an arbitrary crack, sigmarm S is the lower yield stress or 0.2% proof stress, sigmarm B is the ultimate tensile strength and Hrm B is the Brinell hardness. Although the sigmaw2 decreases with the mean stress, sigmaw2 is cut off by the threshold stress sigmawe of the plastic deformation at the crack tip. For the quantitative prediction of the fatigue limit of a cracked steel with an arbitrary crack length under a positive mean stress, the sigmaw2 and sigmawe values are approximated by simple formulae.

DOI: 10.1007/s10704-005-7268-2
Print publication date: 7/1/2005
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by Bunger, Andrew P.; Detournay, Emmanuel; Garagash, Dmitry I.

This paper considers the problem of a hydraulic fracture in which an incompressible Newtonian fluid is injected at a constant rate to drive a fracture in a permeable, infinite, brittle elastic solid. The two cases of a plane strain and a penny-shaped fracture are considered. The fluid pressure is assumed to be uniform and thus the lag between the fracture front and the fluid is taken to be zero. The validity of these assumptions is shown to depend on a parameter, which has the physical interpretation of a dimensionless fluid viscosity. It is shown that when the dimensionless viscosity is negligibly small, the problem depends only on a single parameter, a dimensionless time. Small and large time asymptotic solutions are derived which correspond to regimes dominated by storage of fluid in the fracture and infiltration of fluid into the rock, respectively. Evolution from the small to the large time asymptotic solution is obtained using a fourth order Runge–Kutta method.

DOI: 10.1007/s10704-005-0154-0
Print publication date: 7/1/2005
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by Dobroskok, Anastasia; Ghassemi, Ahmad; Linkov, Alexander

A method is developed for tracing crack propagation in a blocky medium subjected to thermoelastic and poroelastic stresses arising due to the porous pressure of liquid or gas. It is based on extension of the CV-BEM methodology to include body forces. The model considers tensile, shear and mixed mode propagation, as well as crack coalescence. Examples illustrate the accuracy and efficiency of the method.

DOI: 10.1007/s10704-005-1369-9
Print publication date: 7/1/2005
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by Mokross, B. J.

Crack propagation is hypothesized as being a discontinuous process and by decoupling in time the (macroscopic) dynamic energy release rate, Gd, from the (microscopic) J-integral a discrete non-linear equation is obtained having the form of a logistic map. Applying this equation to fracture in amorphous brittle materials (in particular PMMA) it shows that for an accelerating crack, propagation changes from a continuous process in time to a discontinuous one concomitant with instabilities in velocity related to macroscopic branching.

DOI: 10.1007/s10704-005-1368-x
Print publication date: 7/1/2005
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by Chapman, D. J.; Radford, D. D.; Reynolds, M.; Church, P. D.

Taylor impact experiments in the classic and symmetric configurations were used to study the plastic deformation and void nucleation in Al-6082-T6 rods. Deformation histories during impact were recorded using high-speed photography. X-ray computed tomography was used to visualize the extent of damage in recovered specimens. Above threshold velocities, void nucleation was observed along the central axis of the specimens, and reconstructed images from the tomography provide a 3-D mapping of the damaged region. The use of X-ray tomography is the first step in developing a method to characterise the damage process during impact using in-situ flash X-rays, which is also attempted in this study. Finite element simulations of these experiments are in good agreement with the experimental measurements, and confirm that void nucleation is due to the coalescence of lateral release waves at the centre of the specimen. The simulations also revealed that the time to failure is velocity dependent, and that the threshold velocity for void nucleation is sensitive to the properties and geometry of the target.

DOI: 10.1007/s10704-005-7151-1
Print publication date: 7/1/2005
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by Alegre, J. M.; Gutiérrez-Solana, F.

In this paper, the local approach model developed by Gurson–Tvergaard has been applied to simulate both the crack initiation and the crack growth of aged duplex stainless steel. The parameters of the Gurson–Tvergaard model have been obtained, from axisymmetric notched specimen testing, as a function of the ageing time at 400°C, the ferrite content of the steel and the stress triaxiality. After that, to simulate the fracture of CT specimens, finite element (FE) calculations have been effected in order to obtain the stress triaxiality value at each point on the process zone ahead of the crack tip of these specimens. The adequate damage parameters concerning triaxiality are determined from the ones obtained at the notched specimens, in order to be used in FE simulations of fracture behaviour. With them, the corresponding J−Δa curves have been simulated as representative of both the crack initiation and crack propagation stages, and compared with experimental results in order to validate the methodology proposed.

DOI: 10.1007/s10704-005-7150-2
Print publication date: 7/1/2005
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