Failure of brittle polymers by slow crack growth

The variation of crack velocity (V) with stress intensity factor (K _I) at the tip of a crack has been measured for an epoxy resin containing 42% by volume of irregularly-shaped silica particles. It has been found that at crack velocities above 10^–5 m sec^–1 the crack propagates primarily through the silica particles, whereas at velocities below this value, failure occurs primarily by particle pull-out. This variation in fracture mode is accompanied by a corresponding change in slope of the V(K) curve. Using data obtained from creep rupture experiments and the derived V(K) relationship, it has been possible to estimate the size of the inherent flaw in the composite. This was found to be approximately twice the average particle diameter which is also equal to the size of the largest particles (140 m). Fracture of the unfilled epoxy resin and the effect of environment upon slow crack growth in the composite have also been investigated.     

A simple method for evaluating slow crack growth in brittle materials

A simple method for evaluating stress intensity factor, crack velocity (K, V) diagrams is described. The method enables K and V to be obtained from the load relaxation at constant displacement. There are no additional requirements for monitoring crack growth. The method is evaluated for the glass/water system and is shown to generate data that is entirely consistent with data obtained on the same system using other techniques. The method is applied to the alumina/water system and the K, V diagrams are used to predict times to failure (). The calculated are in excellent agreement with available data.

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Zusammenfassung Eine einfache Methode zur Aufstellung der Diagramme Intensitätsfaktore Rißgeschwindigkeit (K.V.) wird beschrieben. Diese Methode ermöglicht die Ableitung von K und V von der Lastrelaxation bei konstanter Fortbewegung. Keine andere Mittel sind nötig zum Überwachen der Rissausbereitung. Die vorgeschlagene Methode wird für das Glasswassersystem erprobt und es ergibt sich dass die Resultate mit denen von anderen Methoden für das selbe System übereinstimmen.Die Methode wird auf das Aluminal Wasser System angewendet und die erhaltene K.V. Diagramme wurde ausgenützt um die Zeit bis zum Bruch () vorauszusagen. Die errechnete Werte von stimmen ganz gut mit denen zur Zeit zu Verfügung stehenden Resultate überein.

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Résumé On décrit une méthode simple pour déterminer les diagrammes facteurs d'intensité des contraintes/vitesse de fissuration (K. V.).Par cette méthode, on obtient K et V en mesurant la relaxation de la charge sous déplacement constant. Il n'est pas nécessaire de recourir à un moniteur de propagation de fissure.La méthode proposée est sujette à vérifications sur un système verre/eau et conduit à des données absolument identiques à celles obtenues sur le même système à l'aide d'autres techniques.On applique ensuite la méthode à un système alumine/eau, et on utilise les diagrammes K.V. obtenus à la prédiction des durées à la rupture ().Ces durées calculées sont en excellent accord avec les données actuellement disponibles.

     

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.     

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.     

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.     

Fatigue crack growth in polymers

A number of fatigue crack propagation laws applied in the study of polymers is described. Consideration of the stress field distribution at the crack tip leads to the application of fracture mechanics. It is shown that a simplified relationship of the form da/dN =F , where is a function ofK _IC,K _max,K _min andK _TH appears to be a convenient expression for cyclic crack growth. The effect of mean stress is more complicated than that in the field of metals, the compressive component of cyclic stress may delay the crack growth. Cyclic tests in tension performed on PMMA and PVC are dependent on K and its mean value,K _m . The threshold value,K _TH, is also influenced byK _m but a more complicated behaviour due to strain rate effects may be observed. Other differences, such as the position of upper and lower transition points and growth rate changes with frequence, are noted. The effect of biaxial cyclic loading of PMMA and PVC plates is compared and some differences highlighted. The results available so far indicate little effect of the crack curving on its growth. However, it is shown that, while the increasing biaxiality can substantially retard the crack growth in PMMA, no such effect was recorded in PVC. Finally, it is shown that at very high stress levels (region III), the cyclic crack growth consists of two propagation modes, namely, a pure cyclic propagation, together with slow growth. At lower stress levels, slow growth disappears and the crack propagates in pure fatigue (region II). In region I, the propagation is very slow, without the usual correspondence between cycles and striations. The results recently obtained on glass reinforced plastics (GRP) are also presented and differences highlighted.

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Résumé On décrit les diverses lois de propagation des fissures de fatigue appliquées a l'étude des polymères. En considérant la distribution de champs de contrainte a 1'extremité de la fissure, on est conduit á appliquer la mécanique de la rupture. On montre qu'une relation simplifiée de la forme da/dN =F ^a, où est une fonction deK _IC,K _max,K _min etKTH apparait être une expression convenable pour la croissance cyclique d'une fissure. L'effet de la contrainte moyenne est plus complexe que dans le domaine des métaux et la composante de compression du cycle de contraintes pent différer la croissance de la fissure. Des essais cycliques en traction exécutés sur du PMMA et du PVC dépendent de K et de la valeur moyenneK _m . La valeur de seuilK _TH est également influencée parK _m mais un comportement plus complexe associé aux effets de vitesses de déformation peut être observé aux effets de vitesees de déformation peut être observé. D'autres differénces, telles que la position des points de transition supérieurs et inférieurs ainsi que les changements de vitesse de croissance avec la fréquence ont été notées. L'effet d'une mise en charge cyclique biaxiale d'un PMMA ou d'un PVC sous forme de plaque est comparé et on met en avant certaines des différences observées. Les résultats disponibles jusqu'ici indiquent un effet modéré de la courbure de la fissure sur sa propagation. Cependant, on montre que si une biaxialité croissante pent retarder d'une manière substancielle la croissance d'une fissure dans du PMMA, aucun effet de ce genre n a été enregistré dans le cas d'un PVC. Enfin, on montre que pour des niveaux de contrainte très élevés (région III) la croissance cyclique d'une fissure consiste en deux modes de propagation, à savoir une propagation purement cyclique accompagnée d'une croissance lente. A des niveaux de contrainte plus faible, la phase de croissance lente disparait et la propagation de la fissure s'effectue en fatigue pure (région II). Dans la région I, la propagation est très lente sans que se présente la correspondance usuelle entre les cycles et les striures. Les résultats récemment obtenus sur des plastiques renforcés de verre (GRP) sont également présentés et les differences en sont mises en évidence.

     

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.

     

Some considerations on slow crack growth

Results are presented of a microscopical investigation on the initiation and growth of cracks in a ductile material under static load. Crack propagation appears to be primarily a slip mechanism. A similar conclusion can be drawn for fast fracture. The consequences of this conclusion for establishing a criterion for ductile fracture are briefly discussed.

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Zusammenfassung Ergebnisse einer mikroskopisehen Forschung zeigen dass dem Rissentstehen und der Rissfortpflanzung in einem zähen Material unter statischen Last ein Gleitmechanismus zu Grunde legt. In dieser Beziehung sind langsame and schnelle Rissfortpflanzung ähnlich. Die Diskussion gibt einige Bemerkungen über dem Bruchkriterium.

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Résumé L'article donne des resultats d'une recherche microscopique concernant l'initiation et la propagation des fissures dans les alliages d'aluminium sous tension statique. La propagation des fissures est un consequencé de fluage plastique. A cet égard les propagations lente et rapide sont similaires. La discussion concerne la critère pour la rupture.

     

Finite element analysis of slow crack growth

A finite element analysis of the process of slow crack growth is made for center-cracked specimens subjected to monotonically increasing load until the point of fast fracture is reached. The formulation is based on an incremental theory of plasticity with isotropic hardening. Numerical results and experimental data are compared. The need and the source of the governing equation for crack growth are discussed.     

Stable crack growth in ductile polymers

Growth of a crack in ductile polymers (polyarylate, PTFE, and PU/PMMA blends) was studied. The crack growth was described assuming that local yielding in the crack tip is similar to large-scale shear yielding in rigid-plastic materials. Crack growth was stable, and a wedge shaped crack tip was formed. The crack tip opening displacement and the crack extension in the initial stage of the crack growth were proportional to the square of the strain up to 11% elongation. Dugdale’s equation was modified to describe the magnitude of the crack tip opening. In PA, a yield subzone near the crack tip was observed. This revised version was published online in November 2006 with corrections to the Cover Date.     

Mechanics and micromechanisms of fatigue crack growth in brittle solids

This paper is concerned with the mechanics and micromechanisms of stable mode I crack growth in brittle solids subjected to compression-compression fatigue and tension-tension fatigue loads. Constitutive models, results of finite element analyses, and experimental observations are described for monolithic ceramics and ceramic-matrix composites, plain concrete, and a transformation-toughened ceramic in an attempt to deduce a general theory on the origin of mode I fracture in notched plates under uniaxial cyclic compression at room temperature. An analysis of the residual stress field which develops at elevated temperatures in response to power law creep and far-field compressive cyclic loads is also presented. The principal driving force for mode I fracture in cyclic compression is the generation of a near-tip zone of residual tension, when the deformation at the notch-tip leaves permanent strains upon unloading from the far-field compressive stress. The results indicated that materials with very different microscopic deformation mechanisms, i.e., microcracking, dislocation plasticity, martensitic transformation, interfacial debonding/slip, or creep, exhibit a macroscopically similar, stable fracture under far-field cyclic compression because the zone of residual tension is embedded in material which is elastically strained in compression. It is shown that cyclic compression loading offers a unique method for fatigue precracking notched specimens of brittle solids prior to tensile fracture testing, whereby an unambiguous interpretation of the critical stress intensity factors for crack initiation and growth can be achieved. Fatigue crack growth characteristics of a transformation-toughened ceramic and a creeping ceramic composite under tension-tension fatigue loads are also discussed.     

Cavity growth in ductile particles bridging a brittle matrix crack

The addition of a dispersed ductile phase in a brittle ceramic can result in an increased fracture toughness, mainly due to plastic dissipation during crack bridging. The large elastic-plastic deformations of a ductile particle intercepted by a brittle matrix crack are here analysed numerically with main focus on the effect of the growth of a single void in the particle centre, as has been observed experimentally. Particle-matrix debonding is incorporated in the numerical model, represented in terms of a cohesive zone formulation, and so is the effect of initial residual stresses induced by the thermal contraction mismatch during cooling from the processing temperature. The bridging behaviour is studied for different combinations of material parameters, and the void growth behaviour is related to previous results for cavitation instabilities in elastic-plastic solids.     

Slow crack growth in brittle materials under dynamic loading conditions

The failure of materials due to slow crack growth, under dynamic loading conditions, is analyzed in terms of crack velocity, stress intensity relationships. It is shown that this type of analysis can fully describe the failure characteristics for both constant strain-rate and constant stress-rate loading. The analysis is used to predict the variations of strength and subcritical crack growth with strain-rate and stress-rate. Application of the analysis to several ceramic systems give data which are entirely consistent with available experimental data.

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Zusammenfassung Der Bruch von Material durch langsame Rißausdehnung, unter dynamischer Beanspruchung wird in Hinsicht der Beziehung zwischen der Rißausdehnungsgeschwindigkeit und der Spannungsintensität untersucht. Man zeigt daß diese Form von Untersuchung die Bruchbegebenheiten vollständig beschreiben kann sowohl für eine Belastung, sowohl unter konstantem Verformungsgrad, als unter konstantem Spannungsgrad. Die Untersuchung wird zur Voraussagung der Änderungen der Festigkeit und des subkritischen Rißwachstums mit dem Verformungs- und dem Spannungsgard. Die Anwendung der Untersuchung auf verschiedene Keramiksysteme ergibt Ergebnisse die vorzüglich mit bestehenden Versuchsergebnissen übereinstimmen.

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Résumé La rupture des matériaux due à une propagation lente d'une fissure sous des charges dynamiques est analysée en termes de relations entre la vitesse de propagation et l'intensité des contraintes.On montre que le type d'analyse envisagé peut complètement décrire les caractéristiques d'une rupture sous charges caracterisées par une vitesse constante de déformation, ou par une vitesse constante de tension.On utilise l'analyse pour prédire les variations de la résistance et la propagation subcritique de la fissure en fonction de la vitesse de déformation ou de mise sous tension.L'application de l'analyse à divers systèmes céramiques fournit des données qui satisfont entièrement les données expérimentales disponibles.