Experimental Measurement of Residual Stress Field around Sharp Indentation in Glass

A new technique is developed to measure the residual stress field around Vickers indentations in glass and ceramics. This technique uses a small indentation as a microprobe to measure the residual stress at a specific position near a large indentation. The approach is based on the observation that the crack lengths of the small indentation are changed under the influence of the residual stress field created by the large indentation. A simple fracture mechanics model is derived to calculate the residual stress from the measurement of the changes of the crack lengths of the small indentation. The results show that the residual stress around Vickers indentations is a nonequal biaxial field; both tensile and compressive stresses exist around a sharp indentation and decrease as the distance from the center of indentation increases. This technique can be easily extended to many other cases of residual stress in ceramics and composites.     

Nanoindentation in elastoplastic materials: insights from numerical simulations

Finite element simulations of nanoindentation were performed on an elastoplastic material using Berkovich and conical indenters to investigate the effects of geometry on the load–displacement response of the material. The Berkovich indenter, widely used in nanoindentation experiments, is typically simplified to a theoretically equivalent 70.3° conical indenter for numerical simulations, which allows for a less computationally intensive two-dimensional (2D) axisymmetric analysis. Previous studies into the validity of this equivalence assumption for indentations in elastoplastic materials have varying conclusions. Using 2D and 3D finite element simulations, the present study investigates the response of elastoplastic materials, obeying a combined isotropic and kinematic hardening, to indentation with conical and Berkovich indenters. Simulations show that there is a clear difference in the load–displacement response of the selected material to the two indenters. The Berkovich geometry is found to produce a more localized pattern of contact stresses and plastic strains, leading to a smaller mobilized force for the same magnitude of displacement. To further validate the numerical simulations, experimental results of nanoindentation into an aluminium specimen were compared to elastoplastic finite element simulation results. Comparisons suggest that machining-induced residual stresses have likely affected the experimental results.     

In Situ Cube-Corner Indentation of Soda–Lime Glass and Fused Silica

Indentation fracture with a cube-corner diamond pyramid on soda–lime silicate glass and fused silica is investigated during the entire indentation cycle in both silicone oil and ambient-air environments. Radial cracks form immediately on loading in all cases. The two-component, elastic-contact + elastic-plastic mismatch (residual) stress field model that has been used successfully to describe radial crack evolution at Vickers indentations fails to describe the fracture response with the cube-corner. The amplitudes of both elastic-contact and residual stress-intensity factors as deduced from these cube-corner experiments are up to a factor of 10 greater than have been previously observed.     

Temperature dependence of indentation size effect,dislocation pile‐ups,and lattice friction in (001) strontium titanate

Nanoindentations with a Berkovich type indenter were performed on (001) strontium titanate (STO) single crystal at 25°C and 350°C, analyzing the influence of temperature on the indentation size effect (ISE) and dislocation structure around the residual impression. It is found that the STO exhibits an ISE, which is strongly reduced at 350°C compared to 25°C. The dislocation structure around the residual impression has been resolved using an etch‐pit technique. At 25°C, the extension of the dislocation pile‐ups were found to be shorter as compared to 350°C. This also correlates with the smaller size effects at 350°C. Peach‐Koehler forces and the elastic‐plastic indentation stress field were used to model the influence of the lattice frictional stress on the dislocation pile‐ups. Based on an equilibrium position of the outermost dislocations, the average lattice frictional stresses were calculated to be 89 MPa and 46 MPa at 25°C and 350°C, respectively.     

真空平板玻璃封边残余应力的研究

 以实验室制样的真空平板玻璃为基础，用电测法对真空平板玻璃封边结构进行了残余应力场研究，成功测试 出了封边残余应力场的分布。采用数值分析法对真空平板玻璃封边残余应力场进行了分析，采用有限元法分析已建 立的数学模型，得出了其应力分布规律，并得出理论计算与试验结果基本一致的结果。探讨封边料的线膨胀系数对 真空玻璃残余应力的影响，同时分析封边应力耦合对真空玻璃残余应力分布的影响，以残余应力作为评估真空玻璃 失效的基本参量，揭示残余应力强度与弹性模量之间的关系，创立一种基于残余应力的真空平板玻璃失效计算新方 法，为真空玻璃封边残余应力的许容值分析提供理论基础。     

Spherical instrumented indentation of porous nanocrystalline zirconia

Nanoindentation tests with a spherical tip were performed to analyze the stress-strain response on 3-mol%-yttria-doped tetragonal zirconia polycrystals produced by spark plasma sintering (SPS) with porosities in the range 2-21% and nanometric average grain sizes in the range 65-120 nm. Indentation stress-strain curves were obtained by using load (P)-displacement (h) data. Onset of elasto-plastic transition was determined by Hertz fits on P-h curves. Elastic modulus obtained from spherical indentation was similar to the values obtained by Berkovich indentation, with a slight difference with increasing porosity. Microstructural characterisation shows no cracks around and beneath the indentations. Raman spectroscopic analysis of the residual indentation imprints reveals tetragonal to monoclinic phase transformation in the most porous material, whereas no phase transformation was detected in the dense material in spite of its larger grain size. The results are discussed in terms of porosity, grain size and tetragonal-monoclinic transformability.     

A technique for measuring stresses in small spatial regions using cube-corner indentation: Application to tempered glass plates

Vickers indentation cracks have been used to estimate residual stress in materials; however, a high threshold load for cracking limits the smallest spatial region for stress measurement. Cube-corner indenters have a lower included angle, and their sharpness leads to lowered cracking thresholds enabling stress measurement in small spatial regions. Cube-corner indentations on tempered glass plate and on annealed soda-lime-silica glass revealed that crack surface traces on the tempered material were significantly smaller. Cracks were found to be quarter-penny shaped as opposed to half-penny/radial for Vickers indentation. Using an appropriate stress-intensity factor and a stress-intensity factor superposition approach, surface stresses in the tempered plate were calculated. The stresses were in good agreement with those determined using well-established Vickers indentation approach; however, the spatial region sampled is 6–10 times smaller. An estimate of the smallest spatial region at which a particular stress may be measured using this technique is presented.     

Analytical Approaches to Stress Intensity Factor Evaluation for Indentation Cracks

In the present paper, an analytical solution for the stress intensity factor in the case of cracks produced by Vickers indenters has been extended to the cases of triangular indenters, i.e., Berkovich and cube-corner. According to the adopted approach, median/radial cracks produced by indentations are modeled as loaded by either a point-force or a symmetric disk-shaped wedge. The wedge diameter is assumed to be equal to the plastic zone size whereas the wedge thickness is evaluated by comparing the wedge volume with the hardness-impression volume. The point-force and the disk-shaped wedge analyses produce an upper and a lower bound, respectively, of the geometry-dependent parameter appearing in the expression for the fracture toughness. The predictions of the present analysis are in good agreement with similar experimental and numerical results.     

Simulation of crack propagation in Alumina particle-dispersed SiC composites

Addition of alumina particles to silicon carbide results in strongly improved toughness values. In order to come to a better understanding of this phenomenon, crack propagation is simulated for a 20 vol% alumina particles-dispersed silicon carbide composite material using the Body Force Method. Special emphasis is paid to the influence of graded compositions. Numerically obtained crack paths are compared to crack paths generated experimentally by Vickers indentations. Moreover, mechanical properties of the investigated material were measured experimentally. Microstructural toughness variations as well as the direction of crack propagation are found to be strongly influenced by residual stresses due to the mismatch between thermal expansion coefficients of alumina and silicon carbide and by the actual crack location. According to tensile residual stresses in the radial direction cracks approaching a particle are deviated circumferentially in the matrix around the particle. Moreover, the failure behavior of cracks propagating into a zone of increasing or decreasing volume fraction of alumina particles is found to behave differently as residual stress fields superimpose in the case of particle clustering. ©.     

Mesoscopic Nonlinear Elastic Modulus of Thermal Barrier Coatings Determined by Cylindrical Punch Indentation

Cylindrical punch indentations are performed to determine the effective modulus of a plasma-sprayed ZrO₂–8 wt% Y₂O₃ thermal barrier coating (TBC) as a function of coating depth. Cylindrical punch indentations offer significant advantages over pointed (Vickers, Berkovich, or Knoop) indentations for materials that do not exhibit linear elastic behavior. Cyclic loading with a cylindrical punch clearly shows the TBCs to exhibit nonlinear elastic behavior with significant hysteresis that is related to the compaction and internal sliding within the plasma-spray splat microstructure. Also, the effect of a high-heat-flux laser treatment is shown to produce a gradient both in the effective TBC modulus and degree of loading/unloading hysteresis with depth.     

Amorphization‐induced volume change and residual stresses in boron carbide

The residual pressure surrounding quasistatic and dynamic Vickers indentations in boron carbide was quantitatively mapped in 3 dimensions using Raman spectroscopy. These maps were compared against similar maps of amorphization intensity and optical micrographs of deformed regions to determine the roles of amorphization and damage upon indentation‐induced residual stress. Stress relaxation was observed near radial cracks, spalled regions, and graphitic inclusions. A positive correlation was found between high levels of residual stress and the number of amorphized sites detected. Finite element simulations were conducted to model the indentation‐induced residual stress fields in the absence of amorphization and cracking. The simulations underpredicted the average residual pressure observed through Raman spectroscopy, implying that amorphization contributes to increased pressure in the material. This pressure is interpreted as potential evidence of volumetric expansion of the amorphized material which is less ordered and hence exerts compressive forces on the surrounding crystalline matrix.     

孔洞平板玻璃钢化及承载仿真模拟

用非线性有限元分析方法,建立了玻璃的热粘弹性应力松弛数学模型、Narayanaswamy结构松弛数学模型,对带孔洞平板玻璃钢化过程进行三维仿真模拟,得到玻璃孔洞周围的应力分布。再把孔洞玻璃板的钢化应力场的最后结果作为初始应力状态导入拉伸模型中,进行孔洞玻璃承载仿真模拟,结果表明孔洞为最先破裂部位。模拟结果有助于在实际钢化生产中采取相应针对性工艺措施,提高玻璃孔周围的残余压应力,增强玻璃强度。     

Residual Stress Analysis of Commercial Float Glass Using Digital Photoelasticity

Residual stresses are generated in float glass at the time of manufacturing due to thermal gradients created during the cooling process. The quantification of these residual stresses is important in glass industries as they affect their cutting quality. Photoelasticity can be used for residual stress analysis of glasses, as glass exhibits stress-induced birefringence. In this study, a methodology involving carrier fringes in conjunction with digital photoelasticity is used to quantify the residual stress in float glass. The results are verified by six-step phase-shifting technique (a subset of ten-step phase-shifting method) using an automatic polariscope. Finally, to demonstrate the utility of the proposed method, the residual stress is measured in float glasses of different thicknesses. A method for approximate estimation of residual stress which does not require sophisticated digital image acquisition and processing systems is also reported.     

Determination of Surface Residual Stresses in Brittle Materials by Hertzian Indentation: Theory and Experiment

Hertzian indentation has been used to determine the surface residual stress levels in brittle materials. In this method, a hard sphere is pressed into the surface of the material: at a critical load a preexisting surface-breaking crack in the neighborhood of the contact will propagate. There is a threshold load below which no such crack, of whatever size, can be propagated. The presence of a residual stress in the surface will lead to a shift in this threshold load. The effects of residual stresses on the minimum load to produce Hertzian fracture are predicted for alumina and glass, assuming that the variation of the residual stress over the length of the crack is small. Two methods of analysis (one approximate, one more general) are presented that enable the residual stress to be calculated from the shift in threshold load; the only further information required is a knowledge of the radius of the sphere, the elastic constants of the sphere and substrate, and also the fracture toughness of the substrate (or use of a stress-free specimen as a reference). No measurement of any crack length is necessary. Experimental results are presented for the residual stress levels determined in glass strengthened by ion exchange. Indenting balls of a variety of materials with a range of elastic mismatch to the glass substrate were used, so as to evaluate the effects of elastic mismatch and interfacial frictional tractions on the results obtained. The results obtained by Hertzian indentation are consistent with residual stress levels determined by differential surface refractometry. We also present results on alumina specimens with induced surface stresses.     

Electric field-assisted ion exchange strengthening of borosilicate and soda lime silicate glass

In this study, we investigate the effects of electric field-assisted ion exchange (EF-IE) on potassium for sodium ion exchanges of soda borosilicate and soda lime silicate glasses. The results show that applying an electric field (E-field) with the intensity of 1000 V cm⁻¹ for few minutes produces an exchanged layer with a thickness comparable to the conventional chemical strengthening for 4 hours. There is a critical E-field that increases the mobility and, therefore, the diffusion coefficient of the potassium ions in the glasses. The increase is, perhaps, related to the evolution of the glass structure due to the penetration of potassium ions under an E-field. Vickers indentations showed that strong compression is generated in the glass by EF-IE; however, the bending strength improvement is limited because of the presence of large surface defects and the stress distribution inhomogeneity.     

Comparisons of Static and Impact Loading Damage in Zinc Sulfide

Contact damage was induced in CVD zinc sulfide by static and impact loading using glass spheres. Calculations based on the relation between the residual depth of the indentation and the ratio of the hardness to Young's modulus were used to estimate the dynamic hardness and impact load. Comparisons of applied loads, threshold loads for crack formation, and crack lengths for static and impact indentations at equal indentation radii show that predictions of impact damage using data from static loading are inadequate.     

The Effect of Tempering and Wall Thickness on the Fracture of Pint Glasses

This study presents a comprehensive analysis of the effect of tempering and wall thickness on the fracture of tempered drinking glasses typically used in bars and pubs in the United Kingdom. The fracture patterns are related to the manufacturing process, the glass geometry, and the level of residual stress. The bulk of experimentation was split into two categories: Firstly, an assessment of the residual stress was conducted, followed by an assessment of the fracture response of the glass in practical applications. Drinking glasses have a variable wall thickness as a consequence of their design and manufacture. This has a direct effect on the level of residual stress in the article, which in turn produces glasses that break to give fragments of variable sizes, with large sharp-edged fragments nearer the glass rim. It is also shown that tempered glasses broken by impact have a characteristic fracture pattern. The results show that to control the fracture of glasses to produce small fragments similar to those in tempered flat glass, the wall thickness and resulting level of residual stress need to be optimized.     

Precision Glass Molding: Validation of an FE Model for Thermo-Mechanical Simulation

In precision glass molding process, the required accuracy for the final size and shape of the molded lenses as well as the complexity of this technology calls for a numerical simulation. The current paper addresses the development of an FE model for thermo-mechanical simulation of the precision glass molding process including heating, pressing, and cooling stages. Temperature-dependent viscoelastic and structural relaxation behavior of the glass material are implemented through a FORTRAN material subroutine (UMAT) into the commercial FEM program ABAQUS, and the FE model is validated with a sandwich seal test. Subsequently, precision molding of several glass rings is performed at three different pressing temperatures, and the experimental deformation of the glass rings at the end of the molding is compared with the predicted ones from FE simulation. Furthermore, the transient and residual stress distribution inside the glass rings are calculated by the developed FE model, and the effects of some important process parameters such as interface friction and mold temperature on the FE results are assessed. The developed FE model can be employed to predict the deformation behavior, final size/shape, and the residual stress state inside the glass lenses in a precision glass molding process.     

Effect of angled indentation on mechanical properties

Indentation on a smooth surface, perpendicular to the indenter tip, is critical to obtaining accurate mechanical property values with nanoindentation. However, for some materials, achieving such a scenario may not always be feasible. To investigate the effect this may have, angled indentations were made on flat, sintered hydroxyapatite samples individually mounted so as to produce indentation angles of 10°, 20°, 30°, 40° and 50°, as well as leading contact with either the face or edge of the Berkovich tip used. While significant scatter in results reinforced the importance of perpendicular penetration, two phenomena were found to serve as potential indicators of angled indentation, and hence unreliable data. It is recommended that topographical profiles are obtained on any material of uncertain roughness prior to indentation.     

Oxidation-Induced Toughening and Strengthening of Y2O3/SiC Nanocomposites

Effects of oxidation on mechanical properties have been investigated for Y₂O₃/5 vol% SiC nanocomposite. The roomtemperature fracture strength and toughness substantially increased after oxidation around 900–1000°C for 5 h. On the other hand, little improvement was identified for specimens treated in an inert atmosphere under the same conditions. A TEM study of the oxidized specimen surfaces revealed formation of extensive residual strain contours around SiC nanoparticles. The improved strength and toughness could be caused by compressive surface stress, which was generated by volume expansion of the nanoparticles due to oxidation.