Fatigue as a process of cyclic brittle microfracture

While fatigue crack growth in vacuum may occur by slip alone, environmental fatigue including crack growth in air is strongly influenced by crack‐tip surface chemistry that adversely affects ductility. Cumulative diffusion, combined with adsorption and chemisorption in the loading half‐cycle may promote instantaneous crack extension by brittle microfracture (BMF). Unlike slip, the BMF component will be sensitive to parameters that affect near‐tip stresses, such as load history and constraint. BMF dominates near‐threshold environmental fatigue. Being a surface phenomenon, it loses its significance with increasing growth rate, as slip‐driven crack extension gains momentum and growth becomes less sensitive to environment. The BMF model provides for the first time, a scientific rationale for the residual stress effect as well as the related connection between stress–strain hysteresis and load‐sequence sensitivity of metal fatigue including notch response. Experimental evidence obtained on a variety of materials under different loading conditions in air and vacuum appears to support the proposed model and its implications.     

Simulation of crack propagation resistance in brittle media of high porosity

Summary The crack propagation resistance through a porous or microstructurally heterogeneous brittle solid with local variability in strength and stiffness has been simulated. Specifically, the simulation probes the behavior of porous brittle materials in the range of porosity less than those of cellular materials and greater than those of microstructures that are in the category of dilute porosity. The simulation plane consists of a triangular network of points interacting with each other through both linear central force springs and bond angle springs, incorporating an appropriate element of a noncentral force contribution. Explicit microstructural details were incorporated into the model and the simulation was first carried out under conditions of uniaxial tensile strain in order to investigate the mechanisms of subcritical damage evolution, leading to quasi-homogeneous fracture. In order to investigate material strength and stiffness variability on the scale of a representative volume element for coherent fracture events in a crack tip stress gradient, the explicit microstructural results were incorporated into a simulation with boundary conditions characteristic of the displacement field of an infinite Mode I crack. To impart some 3D realism to the primarily 2D simulations a special 2D super-element was devised, which incorporated variability information as might be sampled by a crack front in three dimensions. For a given porosity, in general, only small differences were found between nominally diverse microstructures in terms of their tensile toughness, maximum strength and elastic moduli. The strongest dependence of the overall fracture toughness was found to come from the average porosity. The variability in local element strength and stiffness on the scale of the porosity produced highly tortuous crack paths, roughly on the scale of the chosen representative volume element. The tortuosity of the crack was largest where local variability of strength and stiffness was uncorrelated. Examples of microcrack toughening and crack bridging were observed.     

Dynamic crack propagation and unloading behavior of brittle polymers

The method of caustics in combination with a Cranz–Schardin high-speed camera was utilized to study dynamic crack propagation and unloading behavior of epoxy, PMMA and Homalite-100 specimens. Dynamic stress intensity factor K _ID and crack velocity were evaluated in the course of crack propagation. Caustic patterns at the loading points were also recorded to estimate load P applied to the specimen. Unloading rate , the time derivative of P, was determined as a function of time t, and its time correlation with K _ID or was examined. The findings showed that the change in was qualitatively in accord with the change in K _ID or . However, there existed slight differences among the values of t giving the maximum , and K _ID, so that their order was , and K _ID. This revised version was published online in July 2006 with corrections to the Cover Date.     

High speed fracture in brittle materials: Supersonic crack propagation

Microcircuit resistance grids were deposited on the surface of glass and glass-ceramic single edge notched beam (SENB) specimens. The individual strips were as small as ~ 10 μm in width. The specimens were broken in bending and the signal from the grids was captured using a waveform recorder. It was observed that the crack began to propagate with a nonzero initial velocity provided the initial notch was blunt. With continued crack propagation, the crack velocity decreased. In specimens with sharp notches, the crack began propagating with a near zero velocity and the velocity increased with increasing crack length. In some glass specimens with blunt notches, the initial crack velocity was found to be considerably greater than the sound velocity thereby showing that supersonic crack propagation can occur.     

Numerical simulation of intergranular and transgranular crack propagation in ferroelectric polycrystals

We present a phase-field model to simulate intergranular and transgranular crack propagation in ferroelectric polycrystals. The proposed model couples three phase-fields describing (1) the polycrystalline structure, (2) the location of the cracks, and (3) the ferroelectric domain microstructure. Different polycrystalline microstructures are obtained from computer simulations of grain growth. Then, a phase-field model for fracture in ferroelectric single-crystals is extended to polycrystals by incorporating the differential fracture toughness of the bulk and the grain boundaries, and the different crystal orientations of the grains. Our simulation results show intergranular crack propagation in fine-grain microstructures, while transgranular crack propagation is observed in coarse grains. Crack deflection is shown as the main toughening mechanism in the fine-grain structure. Due to the ferroelectric domain switching mechanism, noticeable fracture toughness enhancement is also obtained for transgranular crack propagation. These observations agree with experiment.     

Computer simulation of fast crack propagation in brittle material

A method is presented to simulate the behavior of a rapidly running crack by employing the finite element method with a singular element. The crack-tip is assumed to move so as to satisfy a dynamic fracture criterion that the dynamic energy release rate be equal to a specific fracture energy during failure. Simulation is carried out for a crack in a rectangular plate subjected to a suddenly applied load, and it has indicated that the dynamic behavior of a crack, such as onset of crack propagation, bifurcation, or stopping, is deeply influenced by the magnitude and the time duration of the applied load.

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Résumé On présente une méthode pour simuler le comportement d'une fissure en propagation rapide, utilisant la méthode des éléments finis avec un élément singulier. On suppose que l'extrémité de la fissure se meut de telle sorte que soit satisfait un critère de rupture dynamique selon lequel la vitesse de relaxation de l'énergie dynamique est égale à une énergie de rupture spécifique au cours du processus de dégradation. Une simulation est effectuée dans le cas d'une fissure dans une plaque rectangulaire sujette à une charge appliquée de manière soudaine; cette simulation indique que le comportement dynamique d'une fissure tel qu'il se présente au moment du démarrage d'une propagation de fissure, d'une bifurcation ou d'un arrêt d'une fissure, est influencé de manière profonde par l'amplitude et par la durée en fonction du temps de la charge appliquée.

     

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.     

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.     

An analysis of slow crack propagation data in PMMA and brittle materials

Slow crack propagation data in PMMA previously published by Atkins et al. are reanalyzed in terms of a thermodynamic model in which the activation area is inversely proportional to the crack extension force. Important thermodynamic activation parameters are derived from the data. A correlation between the activation area and the crack extension force is observed in many brittle materials; it is compared to Li's general correlation for activation areas in creep.

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Résumé Les résultats expérimentaux sur la propagation lente d'une fissure dans le polyméthacrylate de méthyle, publiés préalablement par Atkins et col, sont analysés de nouveau en fonction d'un modèle thermodynamique dans lequel l'aire d'activation est inversement proportionnelle à la force d'extension de la fissure. Les importants paramètres thermodynamiques d'activation sont derivés à partir des données expérimentales. Pour de nombreux matériaux fragiles, on observe une corrélation entre l'aire d'activation et la force d'extension de la fissure; cette corrélation est comparée à celle de Li pour les aires d'activation en fluage.

     

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.     

Simulation of crack propagation and failure of concrete

First of all the heterogeneous structure of concrete is described in terms of a multi-level system. To take different effects of crack propagation and crack arresting into consideration, four different levels have been introduced. Conditions for crack propagation in the porous structure of hardened cement paste and in a matrix with inclusions are studied analytically. By using the derived formulae crack formation and failure of lightweight, normal, and high strength concrete are discussed. Computer experiments are described. It is shown that crack propagation and final degradation of composite structures can be simulated realistically. Finally some supplementing experiments are mentioned. Experimental results are in reasonable agreement with theoretical predictions.     

Arrest and propagation of a brittle crack in structural steels. Report 1

The results are presented of determining the fracture toughness of three structural steels 11.373, 11.483.1, and 15.313.5 in the stage of crack arrest at different temperatures. Microstructural and fractographic special features of the propagation and arrest of the brittle crack are analyzed.     

Correction and extension of Broberg's results on brittle crack propagation

The solution to the problem posed by Broberg is deduced as a special case of the problem of a line crack with ends moving at different speeds. This latter problem is solved using the similarity method recently developed by the author. The generality of the method allows for a unified treatment and extension of several problems which have been considered individually by other authors. The similarity method is used in conjunction with the techniques introduced by Muskhelishvili for static elasticity and is proposed as an alternative to the Wiener-Hopf method.     

Arrest and propagation of a brittle crack in structural steels. Report 2

The authors describe a laboratory method of determining the fracture toughness of structural steel in the crack propagation stage K_ID. The K_ID — a dependences were obtained for three structural ferritic-pearlitic and bainitic steels at different temperatures. The K_ID — a dependences are analyzed from the viewpoint of microstructural features of failure of these materials.     

A probabilistic nonlocal model for crack initiation and propagation in heterogeneous brittle materials

A probabilistic damage model is developed to study crack initiation and growth in quasi‐brittle materials. Two different thresholds are considered to describe these mechanisms. A Weibull model is used to account for the randomness of crack initiation(s) and then a fracture mechanics based threshold is considered to model crack propagation. The model is integrated in a finite element code via a nonlocal damage approach. A regularization operator based on a stress regularization is introduced. Both damage thresholds are checked using the ‘regularized’ stress field to avoid mesh dependence. The interaction between propagating cracks and potential initiation sites is accounted for. Copyright © 2012 John Wiley & Sons, Ltd.     

Secondary cracking process during fatigue crack propagation

Using the scanning electron microscope, fatigue striations in secondary microcracks normal to the main fatigue cracks have been observed on fracture surfaces of fatigue specimens made from 2024 and 2618 aluminium alloys, a Ti-6A1-V titanium alloy, and an Incolloy 901 nickel-base refractory alloy. Tentative explanations of these observations are presented in the paper together with a short discussion.