Finite element analysis of identation on glass(II)

The shapes of indentations made on Na₂O-SiO₂ glasses with differentalkali content were studied by using the finite element method to estimate the basic mechanical properties of the glasses. The yield stress Y, densification factor ¦α¦ and hardenining coefficient H′ of the glasses were successfully estimated, which cannot be determined by the usual methods. The densification factors ¦α¦ obtained for each glass at various temperatures did not change much, and it was considered that they were determined mainly by the structure of the glass. The value of ¦α¦ approached zero when the content of Na₂O exceeded 35 mol%, which corresponds to the stuffing effect of alkali ions in the glass network. The yield stress Y estimated by this method differed considerably from the tensile strength of the glass. The difference was especially large for the glass with low alkali content, i.e. the larger the value of ¦α¦ the larger the difference between Y from the hardness and the tensile strength. The reason for this could be partly attributed to the difference in the mode of deformation.     

Statistical analysis of fracture toughness of soda-lime glass determined by indentation

Vickers indentation tests were conducted on a commercial soda-lime glass to determine the fracture toughness. The resultant fracture toughness data were then analyzed statistically. It was found that there always exists a somewhat large scatter in the indentation toughness measured at each applied load level. The variability of the measured indentation toughness was modeled by the well-known Weibull statistics. For different sets of indentation toughness data measured at different load levels, the resultant Weibull moduli are nearly identical with each other, indicating that the statistical variability of the indentation toughness is load-independent.     

Finite element analysis of auxetic plate deformation

The paper deals with computer simulations of mechanical behavior of a thick elastic plate. The plate, made of isotropic material, has been clamped at two lateral surfaces, loaded at the front and back walls and left free at the upper and lower walls. Simulations have been done for Poisson’s ratio from interval ?1 < ν < 0.5 using the finite element method. An anomalous feature of the plate deformation for negative Poisson’s ratio values compared to classical positive values has been observed: at extremely negative Poisson’s ratios the displacement vector has components which are anti-parallel to the direction of loading.     

Crack-free high load Vickers indentation of silica glass

The surface of pure silica glass was prepared to be resistant to cracking from application of Vickers indentation loads of up to one kilogram force (1 kgf). Sample preparation, testing environment, and water content of the glass sample were found to be critical in producing crack-free indentations. Sample preparation consisted of a careful polishing and etching to remove the densified surface layer. Indentation was performed under a nitrogen environment which was also necessary to produce crack-free specimens. Water introduced into the silica glass sample mechanically as well as water introduced into the glass during melting or heat-treatment, were found to be detrimental to crack resistance.     

Effect of subsurface damage on indentation behavior of ground ULE™ glass

The subsurface damage in ground optical glasses was characterized using the ball-dimple technique. At the same lapping conditions, larger abrasive size introduced deeper subsurface damage, and the surface damage was proportional to the surface roughness. Surface degradation in the ground glasses due to the formation and propagation of the subsurface damage was evaluated using microindentation method. A two parameters empirical equation was used to describe the indentation behavior of the ground glasses. It was found that the nominal near-surface elastic constant decreases with the indentation load, suggesting the propagation and formation of surface cracks during the indentation.     

Influence of sol-gel coatings on crack initiation by vickers indentation in soda-lime glass

In this work an indentation technique was used to study the effect of the sol-gel coatings of soda-lime glasses on crack formation. The tendency of samples to develop radial cracks has been evaluated by measuring their number in correspondence with the Vickers impressions as a function of the applied load. Silica coatings of different thickness were obtained from alcoholic solutions of TEOS by the dipping technique on glass sheets with different degrees of surface hydration.

All the coated samples show a lower crackability compared with the uncoated ones. It was found that this parameter is influenced by layer thickness, heat treatment temperature and by the degree of galss surface hydration.     

Statistical analysis of threshold load for radial crack nucleation by Vickers indentation in commercial soda-lime silica glass

The threshold load for nucleation of primary radial cracks in commercial soda-lime silica glass was investigated at room temperature by using Vickers indentation. The Weibull statistics with three-parameters was employed to analyze the number of cracks nucleated around each indentation as function of the applied load. The used probability estimator was (n − 0.5)/N, where n is the total number of radial cracks nucleated at a specific load and N is the total number of possible cracks. The minimum applied load for radial crack nucleation that best fitted the experimental data was equal to 180 mN. Comparison between experimental data distribution and the binomial distribution was also performed. The results were interpreted according to the fracture mechanics models for sub-threshold indentation flaws of Lathabai et al. and for crack initiation in elastic/plastic indentation of Lawn and Marshall.     

IR investigation of density changes of silica glass and soda-lime silicate glass caused by microhardness indentation

Density changes of silica glass and soda-lime silicate glass caused by ball indentation and Vickers indentation were investigated. The IR reflection peak shift of the silica structural band was monitored to determine the extent of the fictive temperature change and the corresponding density change. Under the central portion of the ball indentation, the density of silica glass increased while a change in the soda-lime silicate glass structure was not clear. On the other hand, in the vicinity of the Vickers indentation, the opposite trend was observed. Namely, soda-lime silicate glass exhibited the structural change corresponding to the density decrease, while the structural change of the silica glass was uncertain. The initial density of the silica glass influenced the change of density under ball indentation in such a way that the initial density difference of the glass samples was reduced.     

Finite element analysis of the hyper-elastic contact problem in automotive door sealing

Specific problems regarding the sealing of doors and windows for the automotive industry will be considered in this work. Two main problems must be assessed for predicting sealing capabilities and close-up forces involved, firstly it is mandatory to identify the chemical and the mechanical properties for the rubber used on profiles. In addition, large deformation models with specific three dimensional constitutive equations are required for these problems. The work carried out will present and implement such a constitutive model in order to evaluate the capability for predicting the final geometric configuration and for simulating the closing process for measuring the required force. Specific efforts have been payed for evaluating the sensibility of forces against rubber’s mechanical parameters. Specific three dimensional constitutive equations are formulated and implemented as they are more convenient. These studies are relevant as they will allow for producing valid sections even during preproduction stages and reducing additional costs for section rebuilding and also additional costs for line reconfiguration. Finally real test results will be compared to simulated ones and specific conclusions will be formulated.     

Local strength evaluation and proof test of glass components via spherical indentation

Hertzian contact crack formation combined with acoustic emission was used to evaluate the local strength of glass in situ. The relationship between the critical load and the strength of the glass sample was established. Based on this model, a strength proof test was designed to examine the reliability of glass components in service. Moreover, a new testing device was designed and made for accomplishing this test. It has been demonstrated that this simple testing method is convenient and available for measuring or estimating the surface strength of a glass component in service, without using a standard specimen and a rupture test in laboratory.     

Finite element analysis of auxetic obstacle deformation and fluid flow in a channel

The influence of the Poisson’s ratio of a viscoelastic obstacle on the flow in a two-dimensional channel was studied by a finite element computer simulation. The arbitrary Lagrangian–Eulerian (ALE) formulation for deformed mesh was applied to handle the moving boundaries of the computational domain. An anomalous deformation of the obstacle was observed when the Poisson’s ratio was negative and close to its minimum value. It was also found that the maximum velocity of the fluid in the system decreased with the decreasing Poisson’s ratio.     

Viscosity of Ba-B-Si-Al-O glass measured by indentation creep test at operating temperature of IT-SOFC

Viscosity of a specific Ba-B-Si-Al-O glass used for intermediate-temperature solid oxide fuel cell was measured using indentation creep tests. Responses of shear strain to corresponding shear stress at the operating temperature of solid oxide fuel cell were analyzed, and the results revealed that the glass system possesses Newtonian flow behavior at 600-630 °C. In addition, the stress exponent and the activation energy for viscous flow at different temperatures and stresses were also determined. Finally, the absolute-rate theory was adopted to describe the viscous flow for the glass. The results were compared with other glass systems.     

Mechanical properties of thin silicon films deposited on glass and plastic substrates studied by depth sensing indentation technique

This work concerns the characterisation of mechanical properties of thin amorphous and microcrystalline silicon films deposited on glass and polyethylene terephthalate substrates. The film/substrate indentation response has been investigated from the near surface up to film/substrate interface using depth sensing indentation technique. The universal hardness, Vickers hardness, elastic modulus, fracture toughness and creep resistance of the studied films have been determined. Particular attention has been paid to the effects of the flexible viscoelastic-plastic substrate on the indentation response of the film/substrate system.     

Finite element analysis of dislocation density during bulk single crystal growth (effect of doping atoms in InP single crystal)

A computer code for simulation of dislocation density in a bulk single crystal during liquid encapsulated Czochralski (LEC) or Czochralski (CZ) growth process. In this computer code, the shape of crystal–melt interface and the temperature in a crystal at an arbitrary time were determined by linear interpolation of the results that were discretely obtained by heat conduction analysis of a CZ single crystal growth system. A dislocation kinetics model called Haasen–Sumino model was used as a constitutive equation. In this model, creep strain rate is related to dislocation density, and this model extended to multiaxial stress state was incorporated into a finite element elastic creep analysis program for axisymmetric bodies. Dislocation density simulations were performed using this computer code for InP bulk single crystals with about 8″ in diameter. In the analysis, the effect of dopant atoms on the dislocation density was examined. In the case of a low doped InP single crystal, dislocations are distributed in the whole of the crystal. On the other hand, in the case of a highly doped InP single crystal, dislocations are localized at both the central and peripheral regions of the crystal.     

Influence of impurity and indentation time on dislocation rosettes

It has been shown that the impurity type and indentation time affect appreciable on dislocation rosettes of NaCl single crystals. It was established that the growth of indentation diagonal was not practically followed by the increase of the dislocation zone size. This phenomenon connected with the cross slip processes, which are perhaps more intensive for prolonged indentation time and high temperatures. The assumption is made that the two mechanisms of responsible for indentation formation the movement of dislocations and their multiplication by the cross slip.     

Effect of temperature on hardness and indentation cracking of fused silica

The fracture behavior induced by Vickers indentations in fused silica was investigated as a function of temperature. Indentations were performed from room temperature to 400 °C in air. The indentations and the crack pattern formed were analyzed by optical and scanning electron microscopy. The hardness at room temperature was 7.3 ± 0.3 GPa and decreased to 4.2 ± 0.1 GPa at 400 °C. Cone and radial cracks were observed at all temperatures. The radial crack length increased with temperature for a constant load. Lateral and median cracks were present under the indenter, and their expansion was constrained by cone cracks nucleated during the loading-unloading cycle. The threshold loads for cone and radial crack nucleation increased with temperature. The results are discussed in terms of the elastic modulus/hardness ratio variation with temperature.     

Internal friction analysis of structural relaxation in Si-C-O glass

Forced torsional oscillations has been recorded in Si-C-O glass up to elevated temperatures (≈1900 K). An attempt is shown to extend the measurements into the transformation range where internal friction merely arises from a viscosity-related mechanism and is represented by a background curve, or network contribution (i.e., that component of the internal friction curve which remains after a peak caused by stress-induced anelastic phenomena has been subtracted). Below 2000 K, the internal friction background curve is affected by delayed elasticity. On the other hand, using an approximate expression which relates the tangent of the loss angle to the glass viscosity, it is shown that the frequency dependence of the background internal friction above 2000 K can be simply explained in terms of a Maxwell model. In other words, viscous flow simply represents the high-temperature limiting behavior for the silicon oxycarbide glass, but it is overlapped by an anelastic phenomenon which hampers the full stabilization of its network structure. Some details of the viscoplastic behavior of the material could be obtained by examining internal friction data collected upon cooling.     

Structure analysis of MgSiO3 glass

The structure of MgSiO₃ glass was investigated by a combination of radial distribution function (RDF) analysis with an intensity comparison method on the basis of X-ray diffraction data. There appeared five peaks at 1.63, 2.08, 2.58, 3.25 and 4.2 Å in the RDF curve. The short range structure was found to be similar to that observed in pyroxenes: single chains composed of SiO₄ tetrahedra are linked by Mg²⁺ ions laterally. The Mg²⁺ ion is surrounded by six oxygen atoms on average, four of which form MgO pairs with an average distance of 2.08 Å and the remainder Mg O pairs of 2.5 Å which contribute to the formation of the third peak at 2.58 Å in the RDF curve together with the OO pairs (2.66 Å) in SiO₄ tetrahedra. The calculated intensity curve based on this model was in good agreement with the observed one.     

Quantitative AFM analysis of phase separated borosilicate glass surfaces

Phase separated borosilicate glass samples were prepared by applying various heat treatments. Using selective chemical etching we performed AFM measurement on the phase separated glass surfaces. A quantitative roughness analysis allowed us to measure precisely the dependence of the characteristic size of the phase domains on heating time and temperature. The experimental measurements are very well described by the theoretically expected scaling laws. Interdiffusion coefficients and activation energy are estimated from this analysis and are consistent with literature data.     

Texture and surface analysis of thin-film GaAs on glass formed by pulsed-laser deposition

Thin-film GaAs on glass was formed by ablating n-type GaAs with nano-second pulses at 532 nm. The deposition was done in the most straightforward way without heating the substrate. The texture of films has been investigated with X-ray measurements, spatially resolved micro-Raman spectroscopy, and atomic force microscopy. The results reveal that the film texture is of multi-phase nature consisting of randomly oriented GaAs microcrystallites, amorphous parts, and (1 1 1) zincblende migrations in the nano-regime.