钢化真空玻璃球形支撑的玻璃压痕应力场理论及分析

针对钢化真空玻璃球形支撑物对玻璃压痕的应力场分布问题,采用接触力学,对Hertzian压痕方程进行了修正,推导了三维应力场方程,同时,对完全发展的锥形裂纹的应力强度因子进行了数值求解。结果表明,在球体与玻璃接触区域内,所有的主应力都是压应力,主应力σ₁导致了裂纹的萌生,而主应力σ₂形成了环形裂纹。与玻璃表面正交的最小主应力从接触边缘向外偏离,形成的近似平行的曲线即为锥形裂纹的形状,而最大拉应力总是垂直于这些曲线。因此,在最大主拉应力的作用下,球体加载后裂纹遵循最小主应力的轨迹。裂纹尖端的应力强度因子决定了断裂韧性,随着裂纹的扩展,应力强度因子减小,在离表面一定距离后,应力强度因子达到临界值,裂纹停止。不同压痕载荷下的归一化应力强度因子是一组具有相似形状的曲线。     

Photoelastic Measurement of Residual Thermomechanical Stress in SiC-Reinforced Glass Composites

Residual thermomechanical stresses in a Nicalon® SiC/7740 glass composite system were measured directly. Residual stresses for both single-tow and two-dimensional cloth-reinforced samples were completely described via a digital microphotoelastic technique. Normal stresses approaching 4 MPa were observed in this composite system that had a thermal expansion coefficient mismatch of only 1.8%. The advantages of using this direct, full-field technique over other theoretical and composite model approaches are also discussed.     

Hertzian Indentation Stress Field Equations

Indentation with hard spherical indenters (so called Hertzian indentation) is a well‐known technique to probe the mechanical properties of ceramics and other brittle materials. Using contact mechanics, it is possible to calculate the stress distribution in the sample and use it to express maximum tensile or compressive stresses as a function of load and contact radius. The equations describing the full stress distribution are not usually mentioned in the literature, and surprisingly most of the classical references disclosing them are either mistaken or incomplete. We recovered the full and detailed equations for the stress field distribution and numerically implemented them using the computer language Python. We point out the relationships between the different expressions that have been published, check the consistency with existing results, and discuss the sources of confusion.     

Residual Stress in Singly and Doubly Ion-Exchanged Glass

Photoelastic measurement on rings sliced from soda-lime glass tubes, ion-exchanged with electric field assistance, were used to calculate the residual stress in this material. Account was taken of the effect of sample distortion due to slicing. Well below the glass transition the measured surface stresses were independent of time of exchange but increased markedly with decreasing temperature of exchange for both singly and doubly exchanged specimens.     

Residual Stress in Siliceous Glass Between Mullite Crystals

A birefringence of siliceous glass, which is coexisting with mullite crystals, was studied by an optical polarizing microscope. The cause of the birefringence was assumed to be the residual stress induced by a large contraction difference between the mullite and glass on cooling. The stress has been evaluated to be as high as—0.3 GPa, and to correspond to the elastic one which began to develop at the glass transition point.     

残余应力测试及压入试验模拟研究进展

回顾了残余应力测试的钻孔法、环芯法、X射线衍射法和中子衍射法4种传统方法的发展历程,并介绍了其应用现状;介绍及展望了较为新型的压痕应变法;由于现有方法均无法测试压痕凹坑的残余应力,最后综述了压入试验研究中凹坑残余应力的二维、三维有限元模拟情况。     

Residual Stress Fields at the Surface of Sharp Pyramid Indentations

This paper describes an experimental measurement of the residual stress field around Berkovich and Knoop indentations on the surface of soda-lime glass. The isostress contours of both the residual tensile and compressive stress are presented. The results are compared with similar measurements around Vickers indentations on the same glass. The residual stress field around all three different shapes of indentations is clearly nonequal biaxial, with characteristic differences in the form of the stress contours that relate to each specific shape. The results for Berkovich indentation are compared with finite element (FEM) numerical calculations. Some general conclusions related to the sharp indentations are deduced from this study.     

Measurement of Residual Stresses in Coatings on Brittle Substrati by Indentation Fracture

A method for evaluating stresses in coatings on brittle substrates by indentation is described. The basis for evaluations is fracture mechanics model of the radial crack system in the Vickers geometary, incorpeorating the effects of a thin surface demonstrate the methodology. The crack size on these coated specimens are found to be considerebly small than those on uncoated controls, indicating substantial (∼50 MPa) in-plane expansions observed after applying the coatings to already indented sufaces, are found to make an unexpectedly large contribution to the fracture susceptibility. The procedure offers a simple means for quantifying the mechanical integrity of coating configuration for ceramic components.     

Measurement of Indentation Residual Stresses in Materials Susceptible to Slow Crack Growth

Knowledge of the size and distribution of the indentation residual stress field is important when interpreting slow crack growth data for indented ceramic materials. A technique based on compressively loading indentation cracks has been used to measure the wedging residual stresses at radial indentation cracks. The method also gives information on the fatigue limit and can be applied on any ceramic material susceptible to slow crack growth. Soda–lime glass specimens were indented and the resulting residual stresses, wedging the radial cracks, were measured as a function of indentation load. Calculations of K ₀, the fatigue limit, were made for both virgin indentation cracks and cracks aged until saturation. The magnitude of closing stress needed to prevent slow crack growth was found to depend linearly on the indentation load. For example, for indentation loads of 20 and 60 N, the corresponding closing stresses were 14 and 26 MPa, respectively.     

Indentation Strength of Glass

The tensile strength of plate and sheet glasses was investigated by means of indentation experiments with small spherical indenters. In agreement with earlier experiments by Powell and Preston, tensile strengths were observed about 10 to 100 times higher than those found in tensile or bending tests, the highest values being about one-half the greatest strength of thin fibers or freshly drawn rods. It did not seem that any further reduction of the diameter of the indenting sphere below 1 mm. would lead to a significant increase of the highest strength values. The highest values of the indentation strength of freshly cleaved surfaces were not above those of ordinary surfaces, although the average was considerably higher. This indicates that, unless the use of the Hertz stress distribution involves a significant inaccuracy, the upper limit of about 300,000 lb. per sq. in. of the tensile stress may represent the order of magnitude of the tensile strength of bulk glass in the absence of surface defects. This value is within a factor of two to five of the probable molecular tensile cohesion of a glass of maximum homogeneity. Fracture stress histograms and maximum endured stress histograms are given for a variety of flat glasses.     

Measurement of Internal Stress in Glass Articles

We have developed a method for measurement of internal stress in glass articles. The method uses Rayleigh-scattered light from a properly polarized laser beam propagating through glass at an oblique angle. This light is imaged with an electronic focal plane array camera. The method is similar to earlier published methods except for the inclusion of an externally controlled phase retarder. The phase retarder allows for the success of the method. The method is suitable for use on flat or curved glass and is applicable over a broad range of residual stresses. Experimental results are provided showing the in-plane stress throughout the thickness of a television glass sample.     

Kinetics of Indentation Cracking in Glass

The propagation of indentation radial cracks in soda—lime silicate glass is measured as a function of time after indentation. Rapid lift-off of the indenter from the specimen surface causes a step-function perturbation in the radial crack mechanical energy release rate, thus providing access to a large range of observable crack velocities in the indentation stress field. Analysis of the data shows distinct threshold, reaction-limited, and transport-limited behavior in the crack velocity responses, in agreement with measurements made using macroscopic crack geometries. Atomistic models of fracture kinetics in reactive environments are fit to the data and are deconvoluted to yield the underlying atomic-scale, bond-rupture parameters. These latter are used to calculate potential functions for activated fracture and predict crack velocity responses as a function of temperature and pressure.     

Residual Stress Measurement Using Acoustic Emission

An analysis is presented which shows how acoustic emission caused by microcracking is expected to vary during an elastically reversible load cycle. The acoustic emission rate during unloading can be predicted directly from the acoustic emission rates observed during the loading and holding periods of a test cycle. Any discrepancy between the measured and predicted rates during unloading indicates irreversible behavior. A measure of the severity of the residual stress that results from irreversibility can be determined from the measured acoustic emission.     

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.     

Indentation Damage and Residual Stress Field in Alumina-Y2O3-Stabilized Zirconia Composites

Fracture features, residual stresses, and zirconia transformation are studied in indentation strength specimens of alumina-Y₂O₃-stabilized zirconia (3% mol of Y₂O₃, 3YTZP) ceramics in order to analyze the extension of the indentation damage in the bulk of the specimens. Two compositions, 5 vol% 3YTZP (A5) and 40 vol% 3YTZP (A40), have been prepared by stacking tape-casted tapes and sintering. After indentation with loads ranging from 50 to 300 N, samples were fractured in four-point bending and the fracture surfaces were characterized by scanning electron microscopy. Raman and piezospectroscopic techniques were used to determine the monoclinic zirconia fraction and the residual stresses through the fracture surfaces. In the A5 composition, the indentation damage morphology was clearly half-penny, whereas the A40 composition presented Palmqvist crack formation. Zirconia transformation was only observed in the plastically deformed zones underneath the imprints whereas there were significant residual compressive stresses outside the plastic zones due to the indentation damage. The intensity of this residual compressive field was dependent on the level of zirconia transformation due to indentation damage because zirconia transformation induced tensile stress fields superimposed on the compressive stresses.     

Photoelastic Measurement of High Stress Profiles in Ion-Exchanged Glass

Photoelastic fringes were directly measured to fully characterize high magnitude, steep compressive stress gradients in an ion-exchanged glass, trade named Ion-Armor™. Initially, using a thick (9.9 mm) rectangular bar and circular polariscope arrangement the overall residual stress profile in a bulk specimen was determined. However, due to the relatively large thickness of the specimen, the high density of fringes (steep stress gradient) close to the edge of the specimen became too diffused to allow an accurate count of fringe order. A thinner (0.71 mm) specimen was then used along with a polarizing light microscope to enhance the fringe contrast. This arrangement yielded approximately four isochromatic fringes, representing a maximum surface compressive stress of 984 MPa, which rapidly decreased to ~300 MPa within 25 μm depth from the strengthened surface. Also, the case-depth of the ion-exchange process was found to be 0.8 mm. Thus, the technique was able to directly capture the extremely high residual compressive stresses generated in an ion-exchanged glass. The current technique utilized for residual stress measurement is more objective and straightforward to implement than what is specified in ASTM standard C-1422, particularly for those specimens having steep stress gradients just below the strengthened surface.     

微晶玻璃应力测量与退火实验研究

应力大小是玻璃光学性能的重要指标之一。介绍了玻璃应力的分类、计算方法、测量方法和先进测试设备。退火是消除应力的有效手段。采用最高575℃的温度曲线对微晶玻璃块(40mm×50 mm×30 mm)进行退火实验,退火前后采用高精度数字应力仪进行应力测量。退火前实验件的应力分布不均匀,应力最小值0.85 nm/cm,最大值25.06 nm/cm;退火后实验件的应力分布均匀,应力最小值为0.75 nm/cm,最大值2.39 nm/cm。实验结果表明此退火能够明显减小微晶玻璃应力值并大幅提高应力分布均匀性。