Fracture mechanics description of fracture mirror formation in single crystals

The formation of microbranching and macrobranching in brittle materials has been proposed to occur at a constant stress intensity and strain intensity. The strain intensity and stress intensity criteria are basically the same in their approach and have been shown to be predictive for isotropic materials. A fracture energy criterion can be proposed based on the energy balance approach of Griffith and related to those two criteria. This latter approach is also valid to describe the formation of branching in isotropic materials. The critical test for determining the validity of a criterion for branching is in anisotropic materials. In order to distinguish between the criteria, single crystal Si was fractured and the fracture surfaces were analyzed. In this study, the fracture energy criterion is shown to best describe the formation of microbranching and macrobranching in anisotropic materials. The energy of formation of the mirror-mist boundary is the same in two different orientations: {100} and {110} tensile surface on the {110} fracture plane.     

Dynamics of brittle fracture

The equation of motion and the stability conditions of surface cracks which are subjected to stress waves are derived from an energy balance and the law of angular momentum conservation. From the resulting differential equation the terminal crack velocity and dynamic threshold conditions can be derived. It will be shown that not only a critical stress (amplitude of the wave) but also a critical time (duration of the wave) are necessary to move the crack. These two critical quantities can be combined to a critical action. The specific action of the wave must exceed a certain minimal value for crack propagation to occur. Quantum considerations allow us to generalize this criterion further. Some simple applications of the least action law are mentioned. Supercritical stress pulses are also treated briefly. This leads to the concept of the cross section of a stress wave. Crack stability can also be treated as an eigenvalue problem.     

Thermal stress fracture of wire glass

The phenomenon of thermal stress fracture of wire glass panes used as shower screens in bathrooms is studied in this paper. It is found that both membrane and bending stresses are generated at the edges of the glass pane due to temperature gradients across the planform and in the thickness direction. These thermal stresses alone are lower than the nominal glass strength and cannot cause thermal fracture. However, circular flaws with small edge cracks are shown to exist in postitions near where the steel wires protrude. Using fracture mechanics concepts, it is shown that these stresses together with the edge cracks have exceeded the fracture toughness of the glass pane thus causing thermal stress fracture.

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Résumé Cette étude porte sur la rupture par contrainte thermique de carreaux de verre armés utilisés dans les panneaux paredouche. On établit que contrainte de membrane et contrainte de flexion aux bords des panneaux sont occasionnées par des gradients de température qui se développent sur tout le champ du panneau et dans son épaisseur. Les contraintes thermiques seules ont une valeur inférieure à la résistance nominale du verre et ne peuvent déterminer de rupture. Néanmoins, des hétérogénéités circulaires accompagnées de petites fissures sur les bords se révèlent à proximité des endroits où les fils métalliques sont saillie. En appliquant les concepts de la mécanique de la rupture, on montre que la présence de fissures fait que les contraintes dépassent la résistance du carreau de verre et déterminent l'effet de rupture par contrainte thermique.

     

Nanoscale damage during fracture in silica glass

We report here atomic force microscopy experiments designed to uncover the nature of failure mechanisms occuring within the process zone at the tip of a crack propagating into a silica glass specimen under stress corrosion. The crack propagates through the growth and coalescence of nanoscale damage spots. This cavitation process is shown to be the key mechanism responsible for damage spreading within the process zone. The possible origin of the nucleation of cavities, as well as the implications on the selection of both the cavity size at coalescence and the process zone extension are finally discussed.     

The fracture stress of float glass

A fracture test [1] which uses concentrically loaded square plates supported near their corners has been used to measure the fracture stress of float glass. The plates were 102mm square and 5.98mm thick. The maximum displacement at fracture was less than 0.4mm. Under these circumstances it has been shown that use of a linear finite element solution for the stress distribution and the plate deflections is justified. The glass plates had greater edge damage than had the alumina plates tested in an earlier investigation. In order to secure an adequate proportion of failures in the central plate region, it was necessary to move the supports inwards towards the centre of the plate. This reduced the ratio of the maximum edge stress to the maximum stress in the plate. Batches of plates were tested with loading circle diameters of 7.5 and 25mm, to measure volume effects, with the side of the plate that had been in contact with the liquid tin in tension. Median ranking was used in the statistical analysis and edge failures were treated as suspensions, it being assumed that the minimum fracture stress of the central region of the edge-fractured plates was the plate centre stress at the fracture load. The Weibull modulus was determined by a linear regression in which extreme members of the population were given reduced weighting using the relationship of Faucher and Tyson [3]. The average fracture stresses were 147.2 and 107.3 N mm^–2 for the 7.5 and 25 mm loading circles, respectively, and the Weibull moduli were 4.49 and 5.44. These data are shown to agree well with Weibull statistics. Tests using a 7.5 mm diameter loading circle on plates with the non-tin side in tension gave a significantly higher average fracture stress of 242.1 N mm^–2, confirming the fact that the non-tin side has a higher strength.     

Thermal forming of glass microsheets for x-ray telescope mirror segments

We describe a technology to mass-produce ultrathin mirror substrates for x-ray telescopes of near Wolter-I geometry. Thermal glass forming is a low-cost method to produce high-throughput, spaceborne x-ray mirrors for the 0.1-200-keV energy band. These substrates can provide the collecting area envisioned for future x-ray observatories. The glass microsheets are shaped into mirror segments at high temperature by use of a guiding mandrel, without polishing. We determine the physical properties and mechanisms that elucidate the formation process and that are crucial to improve surface quality. We develop a viscodynamic model for the glass strain as the forming proceeds to find the conditions for repeatability. Thermal forming preserves the x-ray reflectance and scattering properties of the raw glass. The imaging resolution is driven by a large wavelength figure. We discuss the sources of figure errors, and we calculate the relaxation time of surface ripples.     

Sliding fracture of soda-lime glass in liquid environments

The critical load required to form a hertzian fracture in sliding is markedly influenced by the liquid environment in which sliding takes place. The presence of an active environment (water and phosphoric acid) reduces the critical load by 65 to 70%, while the presence of a less-active environment (liquid paraffin) reduces the friction and increases the critical load. It is shown that the critical load in some environments can be predicted in agreement with experimental results provided that the critical load in a certain environment is known.     

Analysis of symmetric fracture mirrors in glass bottles

Fracture conditions which defined the mirror fracture that developed from random flaws were characterized in glass bottles. A constant ratio of the mirror constant to the critical stress intensity factor (A/K _IC) equal to 2.35 with a scatter of 12% was found. The sharp transition between the flaw and the mirror plane signifies an abrupt transition to rapid fracture propagation. The model implied by Shand that the mirror boundary is the loci of all points occurring at different times when conditions for bifurcation are reached, is confirmed. For this purpose both changes of stress with the thickness of glass wall and edge effects on the stress intensity factor were considered.

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Résumé Les conditions de rupture qui définissent la fracture en lentille que se développe à partir de défauts aléatoires ont été caractérisées dans le cas de bouteilles de verre. On a trouvé un rapport constant entre la constante de lentille et le facteur d'intensité de contrainte critique (A/K _IC) égale à 2.35, ceci avec une dispersion de 12%. La transition brutale entre le plan du défaut et le plan de lentille signifie une transition abrupte lors du passage en propagation rapide de la rupture. Le modèle inspiré par Shand suivant lequel le bord de la lentille est le lieu de tous les points qui se trouvent à des moments différents dans les conditions où la bifurcation est atteinte, se voit confirmé. A cet effet, on a considéré à la fois les changements de contrainte avec l'épaisseur de la paroi de verre et les effets de bord sur le facteur d'intensité de contrainte.

     

Transition of hertzian fracture to flexure fracture produced in glass plates by impact

The strength and fracture of a glass plate in a three-dimensional state of stress produced by the transverse impact of a spherical body is investigated. The plate is supported by a ring foundation whose radius is comparable to the thickness of the plate. A general impact theory is developed to determine the critical stresses in the plate as a function of impact velocity, plate thickness, and support span.

Impact experiments were carried out to measure the impact velocity required to fracture a glass plate specimen as a function of support span. Hertzian fracture was observed at a short span of support whereas flexure fracture was observed at a larger support span. The impact velocity of fracture was measured to be increasing with increasing support span and its corresponding critical stress of fracture was also determined.     

The fracture energy of carbon-fibre reinforced glass

The fracture energy of carbon-fibre reinforced glass has been measured by the work of fracture technique, using specimens of varied geometry, Meaningful material properties were obtained only when crack propagation was controlled throughout failure. The work of fracture ( _F) depended on strain-rate and fibre volume fraction, and was typically 3 kJm^–2 for a 40 vol % specimen. Variations of work of fracture due to strain-rates have been related to the microstructure of the fracture surfaces and estimates have been obtained of the fibre-matrix interfacial shear stress during pull-out. Approximate estimates have been made of the fracture initiation energy ( _I) by fracture mechanics analyses, _I was less than _F and no strain-rate sensitivity was detected. An attempt has been made to explain _I in terms of the initial rate of release of strain energy during fibre fracture.     

Mechanisms of fatigue fracture in short glass fibre-reinforced polymers

Fatigue-crack profiles and fracture surfaces of several short glass fibre-reinforced polymers were examined to gain insight into the mechanisms of cyclic damage and fatigue-crack propagation in these materials. Several distinctly different features were noted between fracture surfaces generated by stable fatigue crack growth and those produced by monotonic or unstable fracture. Among the most significant differences were the higher degree of single and multiple fibre fracture generally observed on stable fatigue-crack growth fracture surfaces, and the variations in the interfacial failure site in well-bonded systems. While the former effect is attributed to the occurrence of crack closure and the build-up of compressive stresses in the crack-tip damage zone during unloading, the differences in the interfacial failure mode are related to the adverse effect of fatigue loading on the interfacial bond strength. No features could be identified that would allow a quantitative correlation between the applied stress intensity factor level or the crack growth rates and characteristic fracture surface details.     

Easy glass formation in magnesium-based Mg-Ni-Nd alloys

A number of magnesium-based alloys containing up to 20 at % Ni and 15 at % Nd were cast directly into a wedge shaped mould and also rapidly solidified by chill-block melt-spinning to produce ribbons between 30 and 100 m in thickness. The formation of the amorphous state in the wedge and ribbons was confirmed by X-ray diffraction and differential scanning calorimetry. The measured tensile fracture strength and microhardness of these ribbons were found to be in the range 330–630 MPa and 190–250 kg mm^–2, respectively, which are significantly higher than for conventional magnesium alloys. Critical cooling rates for the glass formation of these alloys were obtained from wedge section thickness, Bridgman growth, thermal analysis data by differential thermal analysis and computational methods. The significance of several parameters for the glass-forming ability of these alloys is discussed.     

Bulk glass formation in the Zr--Ti--Al--Cu--Ni system

Abstracts are not published in this journal This revised version was published online in November 2006 with corrections to the Cover Date.