Similarities in the fracture surface features of borosilicate and polymer glasses

Considerable similarity exists between the features on the fracture surfaces of a borosilicate glass and those on the fracture surfaces of polymer thermoset glasses like epoxies and vinyl esters. These features include the steps and welts of the hackle, the arrays of skewed cracks, and the basic longitudinal texture. It was the latter, the basic longitudinal texture, that was the most surprising find on the fracture surfaces of borosilicate glass. On the fracture surfaces of polymer thermoset glasses, the basic longitudinal texture has been interpreted as a remnant from the fracturing process, arising from an instability in the meniscus between air and a polymer layer softened or “liquified” by the stresses of cracking. The meniscus instability results in an array of crack fingers preceding the nominal crack front. By analogy, it is suggested that the borosilicate glass fractures by a similar process, including the softening of the glass ahead of the crack front. The basic longitudinal texture is usually visible only at high magnification and often requires (a necessity for the borosilicate glass fracture surface) the tilting of the normal to the fracture surface toward the detector. The steps, welts and arrays of skewed cracks are simply explained with the crack fingering hypothesis.     

Influence of surface modification of porous glasses on their surface free energy

Investigations of zeta-potential changes of initial and thermally treated controlled-porosity glasses (CPGs), whose surfaces were covered with different amounts of n-octane and/or nitromethane, are presented. The dispersive ( _s ^d ) and non-dispersive ( _s ⁿ ) components of the surface free energy were then calculated using the relationships obtained. _s ^d was found to be practically independent of the treatment time (a small increase in the range of 4 mJ m^–2 can be seen), but a considerable decrease in _s ⁿ was observed (from 76.95 to 27.2 4 mJ m^–2). In the case of CPG modified with -aminopropyltriethoxysilane an increased hydrophobic character of the surface was found. This was reflected in increased _s ^d and decreased _s ⁿ values.     

Mechanical property and structural changes by thermal cycling in phase-separated metallic glasses

Nondestructive cryogenically thermal cycling has been a simple but effective treatment to enhance mechanical properties of glassy materials.However,how the structural heterogeneities on nanometer scales are affected by thermal cycling is still an issue.Here,we report the response of spatial hetero-geneities in three selected Ti41Zr25Be28Fe6,Zr56Co14Cu14Al16 and Zr42Y14Co22Al22(at.％)metallic glasses(MGs)with different compositions to the thermal cycling,which show significantly different structure and properties after the same treatments and could be ascribed to the joint contribution of relaxation and rejuvenation induced by thermal cycling.The rejuvenation is initially prevailed in a Zr-Y-containing MG,whereas the relaxation is dominant in a Cu-Co-containing MG,both eventually entering into a dynamic equilibrium state.By employing nanometer-scale structural models,the intrinsic correlation between the spatial heterogeneity and thermal cycling is proposed.The discovery could provide the fundamental understanding of the role of spatial heterogeneity in influencing the macroscopic properties of MGs via thermal cycling and help design high-performance glassy materials by tailoring their atomic structures with suitable thermal treatments.     

Internal friction,crack length of fracture origin and fracture surface energy in alumina-zirconia composites

Two series of alumina-zirconia composites, i.e. alumina-unstabilized zirconia and alumina-partially stabilized zirconia with 3 mol % Y₂O₃, with different zirconia content were slip casted and fired at 1550°C for 3 h. Elastic constant, bending strength and fracture toughness were measured. Internal friction was determined to follow the formation of cracks, nondestructively, which could be one of the fracture origins. The crack length of the fracture origin and the fracture surface energy were calculated by applying Griffith's fracture theory. Microstructures of the fracture surfaces were observed using a scanning electron microscope. For the unstabilized zirconia system, the increase in the internal friction of the order from 10⁻⁴ to 10⁻³ was a guide to find the formation of cracks which lead to the fracture. The increase in the cracks becoming a fracture origin lead to the increase inK _lc and also to the apparent increase in the fracture surface energy. For the partially stabilized zirconia system, the increase in the fracture surface energy with an increase in zirconia content, keeping low internal frictions of the order of 10⁻⁴, indicates the intrinsic strengthening of the grain boundaries in comparison to the unstabilized zirconia system. Internal friction is the most suitable nondestructive physical quantity to find the microcracks which leads to the fracture.     

A theoretical estimate of the surface energy in ductile fracture

An estimate of the surface energy for the coalescence of cavities by internal microscopic necking is derived from a rigid-plastic model [1] for ductile fracture. The. results suggest that the surface energy for coalescence will be a function of the mean-free-path between the cavities or second phase particles. The theoretical surface energy for coalescence of cavities in steels was found to be about an order of magnitude less than experimental estimates of the total surface energy for ductile crack propagation. Since the surface energy measured in experiments includes a contribution from pre-coalescence straining ahead of the advancing crack, it is concluded that the theoretical surface energy for coalescence is of the right order and that the theoretical model for ductile fracture by internal necking of cavities may be closely related to the true mechanism of ductile fracture in real materials.

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Zusammenfassung Ausgehend von einem steiff-plastischen Modell für die Untersuchung des Dehnbruchverhaltens, konnte die Oberflächenenergie geschätzt werden, welche nötig ist um das Zusammenfließen von Lücken durch mikroskopische Verengungen zu bewirken.Die Ergebnisse führen zu der Vermutung, daß die Oberflächenenergie für das Zusammenfließen eine Funktion des mittleren freien Weges zwischen den Lücken oder den Partikeln der zweiten Phase ist.Es wurde für die Koaleszens von Hohlraumen eine theoretische Oberflächenenergie bestimmt, welche um eine Größenordnung unterhalb den für die gesamte Oberflächenenergie einer duktilen Rißfortpflanzung experimentell ermittelten Schätzungen liegt.Letztere enthält jedoch auch den Beitrag der dem Zusammenfließen vorlaufenden Verformung an der fortschreitenden Rißspitze. Man gelangt also zum Schluß, daß die für die Koaleszenz ermittelte theoretische Oberflächenenergie größenordnungsmäßig zufriedenstellend ist und, daß das theoretische Modell welches das Bruchdehnverhalten durch interne. Verengungen von Hohlraumen beschreibt, mit dem wirklichen Mechanisrnus des Dehnbruchverhaltens der Werkstoffe in einem engen Zusammenhang steht.

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Résumé En partant d'un modèle à plasticité rigide destiné à l'étude de la rupture ductile, on a pu estimer l'énergie de surface nécessaire pour engendrer la coalescence de cavités par des strictions internes microscopiques. Les résultats suggèrent que cette énergie de surface est une fonction du libre parcours moyen entre les cavités ou les particules de seconde phase. On a trouvé que l'énergie théorique de surface pour engendrer la coalescence de cavités dans l'acier était environ d'un ordre de grandeur inférieure aux estimations expérimentales de l'énergie totale de surface associée à la propagation de fissures dans des conditions ductiles.Toutefois, une partie de l'énergie de surface mesurée en cours d'expérience résulte de déformations préalables à la coalescence, qui prennent naissance deviant le front de fissure en propagation. On en conclut done que l'énergie de surface théorique associée à la coalescence est d'un ordre de grandeur satisfaisant, et que le modèle théorique décrivant la rupture ductile par des strictions internes de. cavités peut être étroitement associé au mécanisme véritable de la rupture ductile de matériaux réels.

     

Fracture II. A theoretical estimation of fracture surface energy

In the discussion of the form taken by the expression for the energy for a crack of finite width, an energy term analogous to the plastic work of fracture was introduced. This term is shown to account for the normally observed relation between failure stress and crack length for brittle materials, and methods of estimating it are discussed. It is shown that the fracture surface energy of homogeneous materials such as glass can be derived approximately from an atomistic model. Metals, however, require consideration of larger scale non-uniformities such as those observed in the electron microscope, and it is shown that a modified expression derived for the toughness of fibre reinforced composites gives toughness values of the correct order of magnitude for metals.

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Résumé Lors d'une discussion sur la forme que prend l'expression décrivant l'énergie associée à une fissure de largeur fine, on a introduit un terme énergétique analogue au travail de déformation plastique lors de la rupture. On montre que ce terme tient compte des relations que l'on observe généralement entre la tension à la rupture et la longueur de fissure, dans le cas des matériaux fragiles, et on discute les méthodes pour en estimer la valeur. On montre que l'énergie superficielle de rupture de matériaux homogènes tels que le verre peut-être à peu près déduite d'un modèle atomistique. Les métaux, toutefois, exigent que l'on tienne compte d'hétérogénéités à plus grande échelle, telles que celles que l'on observe au microscope électronique, et l'on montre qu'une expression modifiée propre à décrire la tenacité de composites renforcés de fibres fournit des valeurs de la ténacité des métaux avec un ordre de grandeur correct.

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Part I is published in Vol. 11, No. 3 (1975) 479–488.     

Estimation of fracture energy from the work of fracture and fracture surface area: I. Stable crack growth

Past attempts to determine fracture energy by the work of fracture (γ _WOF) technique, in most cases, have resulted in greater estimates due to the use of the cross-sectional area rather than the actual area of the fracture surface in calculations. The actual fracture surface area A _F of soda-lime-silica glass chevron-notch flexure specimens was estimated using atomic force microscopy. An equation for A _F was developed using the data from these tests. The use of A _F in the equation for γ _WOF resulted in γ _WOF values less than values reported from traditional fracture mechanics tests and from those obtained using the cross-sectional area. The implication is that the tortuosity of the fracture surface contributes to the energy expended during fracture and should be accounted for in the calculation of the fracture energy. These calculations provide an estimate for the minimum energy required to break bonds in the fracture process.     

Strength and fracture of grasses

The strength of leaves from six grasses of sclerenchyma content from 2% to 30% has been measured. The strength of sclerenchyma is 144 M Pa. As long as the sclerenchyma fibres are mechanically separated laterally, they toughen the leaf by reducing its sensitivity to damage. At high sclerenchyma contents the fibres tend to be laterally joined and the leaf, although stronger, becomes more brittle.     

The fracture topography of metallic glasses

This paper discusses the way in which the features found on some tensile fracture surfaces of amorphous metals are formed. The relevance of the strongly inhomogeneous plastic flow present in these solids to the formation of the particular fracture topography discussed is pointed out, as well as features common to the well-known fracture micromechanisms, cleavage and dimpled rupture.     

The fracture of bulk metallic glasses

The fracture of metallic glasses has received relatively little attention until recently. The development of bulk metallic glasses (BMGs) with more compositions, large sample sizes and diverse fracture behaviors provides a series of ideal model systems for the study of fracture in glassy materials. The fracture toughness of different BMGs varies significantly from approaching ideally brittle to the highest known damage tolerance. Diverse fracture patterns on the fracture surface, fracture modes and dynamic propagation of cracks have been observed in different BMGs. In this review paper, we present a comprehensive view of the state-of-the-art research on various aspects of the fracture of BMGs, including fracture behavior and characteristics, fracture mode, fracture criterion, fracture toughness, and fracture morphology. Accumulated experimental data on BMG fracture are presented and their possible theoretical connections with continuum fracture mechanics and the atomic-scale process are introduced and discussed. Modeling studies of the fracture of BMGs by various computational methods are also reviewed. The review also presents a number of perspectives, including the relation of BMG fracture study to other topics, and unsolved issues for future investigation.     

Macroscopic fracture surface energy of unidirectional metal matrix composites: experiment and theory

A method of measuring the macroscopic frature surface energyγ _F is studied and its verification is made compared with the theoretical prediction. Metal matrix composites used in the experiment are unidirectional graphite fibre-reinforced 6061 aluminium. A good agreement between the experimental and theoretical results is obtained.     

Subcritical crack growth,surface energy,fracture toughness,stick-slip and embrittlement

It is proposed that the difficulties encountered with the meaning of subcritical crack growth arose from a misunderstanding of the Griffith equation. This equation is G=2γ for an equilibrium crack (stable or unstable) where γ is the intrinsic surface energy. When G>2γ the crack has a velocity v depending on the crack extension force G−2γ, even in a vacuum, and the following equation, well verified for adherence of elastomers, G−2γ=2γφ _T(v) where φ _T(v) is related to viscoelastic losses or internal friction at the crack tip, is generalized to other materials. At a critical speed v _c, dφ/dv becomes negative; as a negative branch cannot be observed the velocity jumps to high values on a second positive branch, so that G=G _c is a criterion for crack speed discontinuity, not the Griffith criterion. The multiplicative factor 2γ on the right-hand side accounts for the shift of the v-K curves with environment. No stress corrosion is needed to explain subcritical crack growth. Subcritical crack growth in glasses and ceramics and velocity jump in brittle polymers are shown to agree with this proposal. This model can also explain stick-slip motion when a mean velocity is imposed in the negative branch. Occurrence of velocity jump or stick-slip depends on the geometry tested and the stiffness of the apparatus. A second kind of stick-slip associated with cavitation in liquid-filled cracks is discussed. When the surrounding medium can reach the crack tip and reduce the surface energy, even at the critical speed v _c, the critical strain energy release rate G _c is reduced in the same proportion as γ, and a loading which would have given subcritical growth will give a catastrophic failure. Reduction of surface energy in the Rehbinder effect and in embrittlement by segregation is discussed. Finally, the evolution of ideas concerning the Irwin-Orowan formula and fracture toughness is examined.     

Strength and fracture mechanisms in beta-alumina

The fracture stress, fracture initiation energy and work of fracture have been measured for a fine grained beta-alumina ceramic. The fracture stress has been shown to be naturally distributed and can be described by the Weibull distribution function. Values of the fracture initiation energy and work of fracture were found to be similar, 25 J m^–2.The microstructure of beta-alumina has been examined using transmission electron microscopy. In thin foils of the fine grained material cleavage cracks were invariably found to occur in the basal layers. The phenomena has been explained empirically in terms of atomic bonding of the mirror plane. Contributing terms to the fracture energy t have been discussed and it is suggested that lamination and deformation at the crack tip by generation and movement of dislocations along basal planes is a significant factor.