On the crack propagation with variable velocity

The plane problem of propagation of a straight crack in an elastic medium under arbitrary variable loading is considered. The locations of the edges of the crack are specified as arbitrary smooth functions of time under the only restriction that crack speed at any instant of time is less than the velocity of Rayleigh wave. Solution for the distribution of plane stress components near the crack tip is obtained. In particular, expressions for stress intensity factors at the crack are given, which thus makes it possible to deduce the crack motion under given loading conditions.

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Zusammenfassung Man untersucht das ebene Problem der Ausdehnung eines geraden Risses in einem elastischen Medium unter beliebig veränderlichen Belastung. Die Örter der Ränder des Risses werden als beliebige stetige Funktionen der Zeit angenommen mit der einzigen Einschränkung daß die Rißgeschwindigkeit zu jedem Zeitpunkt kleiner ist als die Geschwindigkeit der Rayleighwelle. Die Lösung der Verteilung der ebenen Spannungskomponenten an der Rißspitze wird aufgestellt. Insbesondere werden die Spannungsintensitätsfaktoren am Riß gegeben, was die Ableitung der Rißausdehnung unter gegebenen Belastungsbedingungen ermöglicht.

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Résumé On considère le problème plan de la propagation d'une fissure droite dans un milieu élastique soumis à une charge arbitraire et variable.On spécifie que les lieux des bords de la fissure sont des fonctions monotones du temps, sous la seule réserve que la vitesse de fissuration est à tout moment inférieure à la vitesse de propagation des ondes de Rayleigh. On obtient une solution pour la distribution des composantes de la contrainte plane au voisinage de la pointe de la fissure.En particulier, des expressions du facteur d'intensité des contraintes à l'extrémité de la fissure sont fournies, qui permettent de déduire le mouvement de la fissure sous des conditions de charge déterminées.

     

On interface crack propagation with variable velocity for longitudinal shear problems

The antiplane strain problem of straight interface crack propagation between two elastic half-spaces under arbitrary variable loading is considered. The crack edge is specified as an arbitrary smooth function of time. It is assumed that the crack speed is less than the smaller of the shear wave velocities of two media. An integral transform method and factorization technique are used to solve the problem. The solutions are worked out for semi-infinite crack and finite crack problems. The dynamic stress intensity factors at the crack tip of the moving interface crack are given and it is found that the stress intensity factor of the interface crack is slightly higher than that in the homogeneous medium with slower shear wave velocity.     

Coupling between the crack propagation velocity and the vapour diffusion in concrete

In this study, it is shown that the toughness of concrete calculated using the classical compliance method is not an intrinsic property of the material, since it depends on the loading rate even in the quasi-static condition. It would seem that this toughness is a decreasing linear function of the crack propagation velocity, at least in the range of crack propagation velocities obtained in the test presented. It is proposed that the propagation of a crack in concrete may be investigated from the standpoint of the propagation of a crack under conditions of confined viscoelasticity; a possible physical explanation of this confined viscoelasticity (this is an hypothesis) is coupling between the microcracking at the end of the propagating macrocrack and water vapour diffusion.     

On the crack propagation in micropolar elastic solids

This paper is concerned with the dynamic energy release rate for a sharp, straight crack in a micropolar elastic body.     

Process region influence on energy release rate and crack tip velocity during rapid crack propagation

A finite element model of a plate with an edge crack is investigated. A cell model of the material, with the cell size representing some characteristic intrinsic material length, is adopted. The size of the process region depends on the number of cells that have reached a state which is unstable at load control. The results show that the growth of the process region is a main factor responsible for the lack of a unique relation between the small scale yielding energy release rate and the crack tip velocity and also for the observed constant crack velocities that are significantly below the Rayleigh wave velocity. A rapidly propagating crack appears to meet an increase of the energy flow to the crack edge per unit of time by increasing the size of the process region rather than increasing its edge velocity.     

On the statistical characteristics of fatigue crack propagation

In order to investigate the governing factor which causes the statistical fluctuation in the fatigue crack growth process, various experimental and simulated results obtained based on the Paris-Erdogan equation of fatigue crack growth rate were surveyed. Then, the governing factors for the randomness in microscopic fatigue fracture process being reflected on the phenomenological crack growth characteristics were examined. As a result, the distribution of the resisting strength of material to crack propagation with a certain unit size US is considered to be important. Also, the significance of the restriction of crack plane, that it can not rotate remarkably around the crack growth direction axis, is also indicated.     

Experimental evaluation of brittle crack propagation velocity—an improved technique

A short review of experimental methods currently used in evaluating the velocity of fast crack extension is given. The technique of applying a surface deposited grid gauge has been innovated. This new technique involves a grid produced by a photo-chemical method and an electronic registration circuit based on integrated transistor-transistor logic. This new method has been applied to experimental studies of brittle crack extension in steel at temperatures between ?115 and +22°C.     

A mathematical model of fatigue crack propagation under variable amplitude loading

A mathematical model of fatigue crack propagation based on the crack closure concept is proposed. It allows prediction of fatigue crack growth under complex loading sequences on the basis of data obtained under constant amplitude and simple Low-High, High-Low loading sequences. The model explains the influence of single and multiple positive overloads and the interaction of positive and negative overloads. An algorithm for cycle-by-cycle calculation of crack growth is proposed.     

On statistical moments of fatigue crack propagation

A new statistical theory is proposed for the analysis of fatigue crack propagation, based on the concepts of fracture mechanics and random processes. Focus is centered on conceivably more useful information of the random time at which the crack size grows to any specific value. Given an initial crack size, recursive relationship is obtained for the statistical moments of this random time for a rather general class of material behaviors, and examples are given for the case where the crack propagation rate is governed by a power law. A procedure to estimate the parameters in the power-law model is also illustrated, using the experimental data of some 7475-T7351 aluminum fastener hole specimens subjected to the excitation of a certain bomber load spectrum.     

On computational homogenization of microscale crack propagation

The effective response of microstructures undergoing crack propagation is studied by homogenizing the response of statistical volume elements (SVEs). Because conventional boundary conditions (Dirichlet, Neumann and strong periodic) all are inaccurate when cracks intersect the SVE boundary, we herein use first order homogenization to compare the performance of these boundary conditions during the initial stage of crack propagation in the microstructure, prior to macroscopic localization. Using weakly periodic boundary conditions that lead to a mixed formulation with displacements and boundary tractions as unknowns, we can adapt the traction approximation to the problem at hand to obtain better convergence with increasing SVE size. In particular, we show that a piecewise constant traction approximation, which has previously been shown to be efficient for stationary cracks, is more efficient than the conventional boundary conditions in terms of convergence also when crack propagation occurs on the microscale. The performance of the method is demonstrated by examples involving grain boundary crack propagation modelled by conventional cohesive interface elements as well as crack propagation modelled by means of the extended finite element method in combination with the concept of material forces. © 2016 The Authors. International Journal for Numerical Methods in Engineering Published by John Wiley & Sons Ltd.     

On the intersonic crack propagation in an orthotropic medium

Motivaded by recent theoretical studies the elastodynamic response of an orthotropic material with a semi-infinite line crack, which propagates intersonically. is revisited through an approach which differs from those used in previous studies. The near tip stress and displacement fields are obtained for Mode I and Mode II of steady state crack propagation. The strain energy release rate analysis confirms that the Mode I is physically impossible due to the order of stress singularity, which is larger then one half. For Model II the order of stress is less than one half and it is shown that a steady state intersonic propagation is allowed only for a particular crack tip velocity which is a function of the material orthotropy.     

On the Hertzian fatigue cone crack propagation in ceramics

The Hertzian cone crack initiation and propagation in ceramics under cyclic fatigue loading with a spherical indenter is studied. Unlike the so-called quasi-static Hertzian cone crack, the fatigue Hertzian cone crack propagation eliminates the dynamic effect on unstable crack propagation. As such, the crack is found to propagate following the path of pure mode I type. We use an elasticity approach, a finite element analysis, and an empirical analysis to investigate the Hertzian cone crack in three stages: crack initiation, crack propagation, and crack kinking. The mechanism of the multiple concentric cone cracks is also explained. The purpose is to understand and predict the behavior of the formation of the Hertzian fatigue cone crack using available modeling tools.Zheng Chen is currently with Space Power Institute, Auburn University.     

Fatigue crack propagation under variable amplitude loading in PMMA and bone cement

Fatigue failure of PMMA bone cement is an important factor in the failure of cemented joint replacements. Although these devices experience widely varying loads within the body, there has been little or no study of the effects of variable amplitude loading (VAL) on fatigue damage development. Fatigue crack propagation tests were undertaken using CT specimens made from pure PMMA and Palacos R bone cement. In PMMA, constant amplitude loading tests were carried out at R- ratios ranging from 0.1 to 0.9, and VAL tests at R = 0.1 with 30% overloads every 100 cycles. Palacos R specimens were tested with and without overloads every 100 cycles and with a simplified load spectrum representing daily activities. The R- ratio had a pronounced effect on crack propagation in PMMA consistent with the effects of slow crack growth under constant load. Single overloads caused pronounced crack retardation, especially at low da/dN. In Palacos R, similar overloads had little effect, whilst individual overloads at low da/dN caused pronounced acceleration and spectrum loading retarded crack growth relative to Paris Law predictions. These results demonstrate that VAL can have dramatic effects on crack growth, which should be considered when testing bone cements.     

Effect of stress wave shape on the crack propagation velocity in cyclic delayed failure

Crack propagation velocity in delayed failure under superposed repeating load, ($\text{d}\text{a/}\text{d}\text{t)}{}_{\mathrm{R}}$, was compared with that under static load, ($\text{d}\text{a/}\text{d}\text{t)}{}_{\mathrm{S}}$Two peaks appear on the relation between decreasing rate of crack propagation velocity, $\text{1-β = 1 ? (}\text{d}\text{a/}\text{d}\text{t))}{}_{\mathrm{R}}\text{/(}\text{d}\text{a/}\text{d}\text{t)}{}_{\mathrm{S}}$ and frequency, ?, both under sinusoidal and square load. By changing the ratio of holding time at maximum stress intensity factor to that at minimum stress intensity factor in square load, it was deduced that the existence of two peaks on the 1 ? β vs $\text{f}$ curve was caused by an asymmetric interaction between hydrogen atoms and cyclic moving of the position with triaxial tensile stress at crack tip. Moreover, the relation between 1 ? β and $\text{f}$ under the positive or negative saw tooth load could be well explained by the interaction model.     

On the dynamic crack propagation in an interface with spatially varying elastic properties

This article provides a comprehensive theoretical treatment of a finite crack propagating in an interfacial layer with spatially varying elastic properties under antiplane loading condition. The theoretical formulations governing the steady state solution are based upon the use of an integral transform technique. The resulting dynamic stress intensity factor of the propagating cracks is obtained by solving the appropriate singular integral equations, using Chebyshev polynomials, for different inhomogeneous materials. Numerical examples are provided to verify the technique and to show the effect of the thickness of the interfacial layer and the material properties upon the dynamic stress intensity factor of the crack and the associated singularity transition.