Parameters and micromechanisms of fatigue crack growth in sheet magnesium alloy samples

Growth rates of part-through and through fatigue cracks have been measured for two magnesium alloys — MA12 and IMV6 — and the micromechanisms of fatigue fracture were studied at all stages of growth. Conclusions about the peculiarities of the kinetics and micromechanisms of part-through and through crack growth, depending on the applied stress amplitudes and alloy structure, are made from a comparison of the results obtained.     

Mechanics of two-stage crack growth in fretting fatigue

Motivated by experimental observations, we carry out a numerical analysis of the two-stage crack growth under fretting fatigue by using an efficient and accurate boundary element method. To start with, the variation of stress field during a loading cycle is analyzed. Various values of friction coefficient in the contact zone are considered, which is shown to considerably affect the stress field. Then, by assuming crack initiation to occur in the shear mode, a surface-breaking crack is introduced to the specimen at the location of highest shear-stress amplitude. The crack-tip stress intensity factors (SIFs) are calculated for various crack lengths and at various crack angles ranging from 25° to 45° about the contact surface. It is shown that, for a loading ratio of 0.5, the cyclic mode-II SIF amplitude decreases with increasing crack length, whilst its mean value increases. It suggests that the (first-stage) shear crack would sooner or later become dormant, or switch to another mode that can provide continuous support of growth. Then, the first-stage shear crack is manually kinked into a second-stage opening crack, and the follow-on driving force is analyzed. It is shown that the kinking event is only favored after the first-stage crack has grown to a certain length. The present study thus provides insights in the mechanics of two-stage crack growth that has been frequently observed in a typical dovetail joint under fretting fatigue. It also suggests an improved experimental setup to quantitatively investigate the fretting fatigue in dovetail joints.     

Dynamic crack branching in brittle solids

A state-of-the-art review of recent and on-going analytical and numerical research on dynamic crack branching in brittle solids is presented. First, fundamental experimental evidence concerning the physics of the branching mechanism is reviewed. Next, elastostatic work dealing with crack branching under an arbitrary angle and crack branching fracture criteria is summarized. The idealizations inherent in the mathematical models under investigation are emphasized. The analytical and numerical schemes that have recently yielded several much needed dynamic self-similar crack branching solutions are discussed. A perturbation-type approximation to the initial-boundary conditions whereby the artificial constraint of self-similarity is removed and variable velocity crack branching can be treated is discussed also. Finally, new directions and the needs of future research are identified.

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Résumé On présente un état de la question relatif aux recherches analytiques et numériques récemment effectuées ou en cours sur le phénomène d'arborescence de fissures dynamiques dans des solides fragiles. On passe d'abord en revue les constatations expérimentales de base concernant la physique du mécanisme de l'arborescence. Ensuite, est résumé un travail élastostatique relatif à l'arborescence d'une fissure sous un angle arbitraire et les critères de rupture d'une fissure en arborescence. On met l'accent sur les idéalisations auxquelles conduisent les modèles mathématiques étudiés. On discute les schémas analytiques et numériques qui ont récemment conduit à des solutions au phénomène de branchment d'une fissue dynamique dans des conditions comparables. On discute également une approximation de type perturbation applicable aux conditions initiales aux limites et par laquelle la contrainte artificielle d'auto-similarité peut être éliminée et le phénomène d'arborescence d'une fissure sous vélocité variable peut être traité. Finalement, on identifie de nouvelles directions et les besoins pour des recherches futures.

     

Probabilistic description of fatigue crack growth in polycrystalline solids

A stochastic model describing the crack evolution and scatter associated with the crack propagation process has been built on the basis of the discontinuous Markovian process. The evolution and scatter are identified in terms of constant probability curves whose equation is derived as In P_r(i) = B(e^KI₀ − e^Ki), i ≥ I₀, where i is the number of cycles, B and K are crack-length-dependent variables, P_r(i) is the probabiliity of the crack being at position r along the fracture surface after i cycles elapse and I₀ is the minimum number of cycles required for the crack to advance from one position on the fracture surface to the next. The validity of the model is established by comparing the crack growth curves generated for Al 2024-T3 at a specific loading condition with those experimentally obtained.     

Mechanics of mixed mode small fatigue crack growth

An elastic-plastic analysis of a mixed mode crack was conducted under general yielding conditions using a finite element method. Based on the finite element analysis, a formula of the J-integral was developed, and the behavior of the crack opening or sliding displacement was investigated. Crack growth mechanics was discussed to explain mixed mode growth. A model expressed by the J-integral was proposed assuming that the crack growth is determined by the linear summation of relations of pure Mode I and II crack-tip deformation. The crack growth rate obtained using Inconel 718 thin-wall tubular specimens was correlated with the range of ΔJ evaluated from the proposed formula. The crack growth equations in terms of ΔJ for three different biaxial strain ratios were compared with the relations expected from the proposed crack growth model. The difference between the experimental results and the estimation was discussed from the viewpoint of crack closure and the geometry of the surface crack.     

An investigation of the micromechanisms of fatigue crack growth in structural gas turbine engine alloys

This paper presents an overview of fatigue fracture modes in selected structural alloys employed in gas turbine engines. These include the mechanisms of fatigue crack growth in the near-threshold, Paris and high-K regimes obtained from Ti-6Al-4V, Inconel 718 and PWA 1472 (a single crystal nickel-based superalloy of similar chemical composition to Inconel 718). Fatigue fracture modes in these materials are shown to be strong functions of the stress intensity factor range, K, and the maximum stress intensity factor, K _max. Fatigue mechanism maps are also presented to show the parametric ranges of K and K _max corresponding to the different fatigue fracture modes.     

Mechanics and synergetics of the selfsimilar growth of a fatigue crack

As was shown by T. Yokobori, it is important to combine the fracture mechanics approach with analysis of the fracture mechanism. Analyses parameters controlling boundaries of the selfsimilar growth of a fatigue crack and the relation between threshold characteristics of fracture toughness, corresponding to the change of fracture mechanism (bifurcation points) were carried. The analysis conducted on steels, titanium and aluminium alloys shows that bifurcation points in the fatigue crack growth are highly informative. Their recognition can be instrumental in establishing the relationship between characteristics of cyclic and static fracture toughness.     

Experimental investigations of crack trapping in brittle heterogeneous solids

Over the past two decades many mechanisms of toughening have been considered for brittle solids. Some of the most prominent ones, applicable to either monolithic materials or fiber-reinforced composites, include deformation-induced local transformations, microcracking, crack trapping, crack bridging, and fiber pull-out. Few, if any, of these have been studied in the past in a manner which permitted evaluation of the effects of individual mechanisms in the absence of other interacting mechanisms. Here, we present an experimental study of toughening by the process of crack trapping by second-phase particles (spheres and fibers) of such toughness that make them impenetrable by probing cracks, forcing the cracks to bow around the obstacles with increasing applied load.

The model fracture specimens employed here were wedge-loaded double cantilever beams, cast of a brittle epoxy, containing macroscopic (3 mm diameter) inclusions of Nylon or polycarbonate, having elastic properties similar to the matrix. The tests were performed at −60°C to achieve controlled, stable crack propagation. Images of the crack fronts, advancing at velocities of about 10⁻⁴m/s, were recorded with good resolution, providing a continuous record of crack-front shapes during the evolution of the crack-trapping process — from the initial pinning configuration through the transition to crack-flank bridging. Remarkable agreement between these images and crack-front shapes predicted by the numerical simulation of Bower and Ortiz is demonstrated. A parametric approach was adopted to study the influence of obstacle spacing, surface adhesion, and thermally induced residual stresses upon the observed crack-front behavior and enhanced stress intensity required to propagate the cracks past these obstacles. Analysis of the quantitative data has demonstrated that in brittle matrices containing particle volume fractions of approximately 0.2, toughness enhancement by over a factor of 2, relative to neat matrix values, may be achieved through the crack-trapping mechanism alone, provided that a high level of adhesion can be maintained between the matrix and the tough reinforcing particles.     

Boundary element analysis of fatigue crack propagation micromechanisms in austempered ductile iron

The Dual Boundary Element Method (DBEM) is used in this work to model the micro mechanics of fatigue crack propagation in austempered ductile iron (ADI). Emphasis is put in devising accurate procedures for the evaluation of the interaction effects between very close crack–microcrack arrays. Fracture parameters are computed via the so-called one-point displacement formula using special crack-tip elements. Crack propagation is modelled using an incremental crack extension analysis; with crack extensions calculated using a propagation law that accounts for the near-threshold regime. Obtained results are in agreement with experimental observations, providing evidence to fracture mechanics models proposed in the literature.     

To the theory of crack propagation in deformed brittle solids

We present elements of the theory of propagation of cracks in a deformed brittle body. The problem of propagation of cracks is formulated with regard for the forces of interaction between the opposite lips of the crack in the vicinity of its ends. The basic equations of the problem are obtained and their solutions are given for some special cases. Karpenko Physicomechanical Institute, Ukrainian Academy of Sciences, L'viv. Published is Fizko-Khimichna Mekhanika Materialiv, Vol. 32, No. 4, pp. 119–122, July–August, 1996.     

Creep crack growth in brittle materials

During steady state crack growth by diffusive cavitation at grain boundaries, crack tip fields are relaxed due to the presence of a cavitation zone. In the present analysis, analytic solutions for the actual crack tip stress fields and the crack velocity in the presence of cavitation zone consisting of continuously distributed cavities ahead of the crack tip are derived using the smeared volume concept. Results indicate that the r ^–1/2 singularity is now attenuated to r ^{–1/2 +} (0<<1/2) singularity. The singularity attenuation parameter is a function of the crack velocity and material parameters. The crack growth rate is related to the mode I stress intensity factor K by K ² at relatively high load, K ⁿ at intermediate load, and approaches zero at small load near K _th. Meanwhile, the cavitation zone extends further into the material due to the stress relaxation at the crack tip and the subsequent stress redistribution. Such relaxation effects become very distinct at low crack velocity and low applied load. Key words: Creep crack growth, brittle material, diffusive cavity growth, sintering stress, crack tip stress field.     

Crack propagation in brittle heterogeneous solids: Material disorder and crack dynamics

Crack propagation in a linear elastic material with weakly inhomogeneous failure properties is analyzed. An equation of motion for the crack is derived in the limit of slow velocity. Predictions of this equation on both the average crack growth velocity and its fluctuations are compared with recent experimental results performed on brittle heterogeneous materials (Ponson in Phys Rev Lett, 103, 055501; Måløy et al. in Phys Rev Lett, 96, 045501). They are found to reproduce quantitatively the main features of crack propagation in disordered systems. This theoretical framework provides new tools to predict life time and fracture energy of materials from their properties at the micro-scale.     

Effect of porosity and stress concentration associated with pores on elastic creep by crack growth in brittle solids

The solution for the creep rate of a porous solid as a function of pore volume fraction, pore size and the radial or annular flaw size, is presented. The analysis is based on the concept of crack opening displacement which assumes that the displacement of a solid under stress is solely due to the opening of all radial or annular cracks emanating from the surface of the cavities. It is shown that the strain rate by crack growth is a strong function of pore size and preexisting flaw size. A linear relationship was found to exist between the strain rate by crack growth and the porosity volume fraction.     

Steady-state crack growth in rubber-like solids

The fracture toughness of rubber-like materials depends on several factors. First there is the surface energy required to create new crack surface at the crack tip. Second, a significant amount of energy is dissipated through viscoelastic processes in the bulk material around the crack tip. Third, if the crack propagates very rapidly, inertia effects will come into play and contribute to the fracture toughness. In the present study, a computational framework for studying high-speed crack growth in rubber-like solids under conditions of steady-state is proposed. Effects of inertia, viscoelasticity and finite strains are included. The main purpose of the study is to study the contribution of viscoelastic dissipation to the total work of fracture required to propagate a crack in a rubber-like solid. The model was fully able to predict experimental results in terms of the local surface energy at the crack tip and the total energy release rate at different crack speeds. In addition, the predicted distributions of stress and dissipation around the propagating crack tip are presented.     

Delay in fatigue crack growth

The importance of delay, or retardation in the rate of fatigue crack growth, produced by load interactions in variable amplitude loading on the accurate prediction of fatigue lives of engineering structures has been well recognized for some time. Heretofore, only a few simple loading combinations or spectra have been examined systematically. In this investigation the effects of a broad range of loading variables on delay in fatigue crack growth at room temperature are examined for a mill annealed Ti-6A1-4V alloy. The results are used to estimate crack growth behavior under programmed loads.

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Zusammenfassung Die Wichtigkeit des Einflusses des Aufschiebung oder Verspätung der Ausdehnungsgeschwindigkeit eines Müdigkeitrisses, unter Belastung mit wechselnder Amplitude, durch gegenseitige Beeinflussung der Lasten, auf die genaue Voraussagung der Müdigkeitslebensdauer von Bauelementen ist seit einer gewissen Zeit gut bekannt.Bis jetzt wurden nur einige einfachen Belastungsfälle oder Kollektive systematisch untersucht. In diesem Bericht wird der Einfluss von einer grossen Anzahl Belastungsveränderlichen auf die Verspätung der Ausdehnungsge-schwindigkeit eines Müdigkeitrisses bei Zimmertemperatur untersucht, für einen geglühten Ti-6A1-4V legierten Stahl. Die Ergebnisse werden gebraucht um die Rissausdehnung unter einem Belastungskollektiv vorauszusagen.

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Résumé On a reconnu depuis quelque temps l'importance que revêt, pour une prédiction fiable de l'endurance en fatigue des éléments de construction, le ralentissement dans la vitesse de propagation des fissures de fatigue, résultant d'interaction des charges lorsque celles-ci sont d'amplitudes variables.Jusqu'à présent, seul un petit nombre de combinaisons de charges ou de spectres ont fait l'objet d'un examen systématique. Dans la présente étude, on a étudié les effets d'une gamme étendue de variations de la charge sur le retard à la propagation des fissures de fatigue à température ambiante, dans le cas d'un alliage Ti-6A1-4V recuit.Les résultats de cette étude sont appliqués à l'estimation de l'extension des fissures de fatigue sous des programmes collectifs de charges.

     

Analysis of smooth crack growth in brittle materials

When a fault in the crust extends, earthquake faults appear as a set of displacement discontinuities on the ground surface and cause strong motion and large deformation. For the prediction of such earthquake faults, one needs to analyze the propagation of smoothly growing cracks. This paper develops an analysis method based on a new formulation of growing crack problems. In this method, the change in the stress intensity factors due to a small extension is explicitly related to the curvature and length of the extension, and these geometrical parameters can be determined from assumed fracture criteria, without taking any trial-and-error routes of the extension geometry. The validity of the proposed method is numerically examined; in particular, the predicted stress intensity factor changes coincide with numerically computed ones. The proposed method is applied to reproduce two experimental observations. It is shown that in both cases, the configuration of the simulated crack is in good agreement with the observed one.