Strength Degradation of Brittle Surfaces: Blunt Indenters

Indentation fracture mechanics is used to develop a theoretical basis for predetermining the strength properties of brittle surfaces in prospective contact situations. Indenters are classified as blunt or sharp; only the first is considered in the present work. The classical Hertzian cone crack conveniently models the fracture damage incurred by the surface in this class of indentation event. Significant degradation is predicted at a critical contact load; when the load is increased beyond this critical level, further degradation occurs at a relatively slight rate. Bend tests on abraded glass slabs confirm the essential features of the theoretical predictions. The controlling variables in the degradation process, notably starting flaw size and in-denter radius, are investigated systematically. An indication is also given as to optimization of material parameters.     

Strength Degradation of Brittle Surfaces: Sharp Indenters

A theory of strength loss for brittle surfaces in contact situations, developed in a previous paper for "blunt" indenters, is extended to the case of "sharp" indenters. A prior fracture mechanics analysis of crack growth beneath ideal cone indenters serves as the basis for predetermining the prospective surface degradation of ceramic components in service. Compared to blunt indenters, sharp indenters can cause severe degradation at lower contact loads. However, at high loads, the extent of degradation becomes remarkably insensitive to details in the indenter geometry. Essential theoretical predictions are verified by bend tests on glass slabs. Effects of indenter "sharpness" and initial specimen surface flaw state are investigated systematically, along with some secondary rate effects in the contact process. The possibility of minimizing degradation via adjustment of material parameters (including hardness) or surface condition (e.g. residual stresses, frictional properties) is briefly discussed.     

Comparative Measurement of Indentation Fracture Toughness with Berkovich and Vickers Indenters

Measurements of the load dependence of the radial crack size with Vickers and Berkovich indenters are compared for a range of materials. It is found that the extent of radial cracks was slightly larger for the Berkovich than for the Vickers indenter. The observations reveal that cracks from a Berkovich indenter are best described by an expression developed by Laugier combined with a modification proposed by Ouchterlony to account for the number of radial cracks. It was also found that the Berkovich indenter, which offers advantages for ultramicroindentation, gave more consistent toughness values at lower loads than a Vickers indenter.     

Median Cracking of Brittle Solids Due to Scribing with Sharp Indenters

The process of moving a loaded hard indenter across the surface of a brittle solid to produce a median crack is referred to as "scribing." As a first step in predicting the depth of median cracking due to sharp indenters, an approximate plastic plane strain analysis is presented for the region under the indenter. This allows the horizontal force transverse to the scribing direction to be predicted. Taking this force and an approximate solution for the stress intensity factor for the crack geometry in scribing leads to a prediction for crack depth as a function of load. The residual stresses which arise on unloading are shown to be a strong function of indenter geometry and may act to extend or partially close the original median crack formed during loading. Reasonable agreement is found between prediction and experiment for six indenter configurations.     

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.     

硬脆材料加工用微乳化切削液的研究及应用

硬脆材料加工用微乳化切削液应用于精密陶瓷、光学玻璃、蓝宝石等硬脆材料的加工过程,由表面活性剂、基础油、润滑添加剂、极压剂、防锈剂和水等成份组成,配合金刚石工具应用于硬脆材料的切割、铣磨、精磨、磨边、倒角等加工过程,具有良好的润滑、极压、冷却、清洗和防锈等性能。     

Spherical Indentation and Fracture of Glass Plates

Spherical indentation of thick and thin glass plates was investigated numerically and experimentally. The energy release rate at the tip of a cone crack was calculated by using finite element techniques and used to investigate the applicability in thick plates of Roesler's law relating the cone crack radius to the indentation load. Indentations of thin glass specimens resting on different substrates were also studied numerically and experimentally. The stresses in the thin specimens were calculated and correlated with the observed failures. On the basis of these results, a crack initiation mechanism map was developed for glass specimens on different substrates.     

硬脆性泥页岩微裂缝模拟研究

针对硬脆性泥页岩微裂缝封堵实验中裂缝尺寸较大的问题,采用化学腐蚀的方法,系统研究了石英玻璃岩心对应力的敏感情况和化学腐蚀中HF浓度、酸液比例、温度和时间对制造出的缝宽影响。结果表明:石英玻璃半圆柱应力敏感性很弱,随着加泄压次数增多,应力敏感不存在;在腐蚀的单因素实验中,随着HF浓度、HF在酸液中比例、温度、反应时间的增加,制造的缝宽变大,电阻值减小,缝宽与电阻值有良好的拟合关系;正交试验中,在20℃时,5 wt%HF∶5%H2SO4=1∶2超声反应20 min后,缝宽为1.317μm,表面呈部分凹坑状,得到的微裂缝对进一步研究纳米材料的封堵性能具有重要意义。     

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.     

Crack-Growth Resistance of Microcracking Brittle Materials

A mechanics model of microcrack toughening is presented. The model predicts the magnitude of microcrack toughening as well as the existence of R -curve effects. The toughening is predicated on both the elastic modulus diminution in the microcrack process zone and the dilatation induced by microcracking. The modulus effect is relatively small and process-zone-size-independent. The dilatational effect is potentially more substantial, as well as being the primary source of the R curve. The dilatational contribution is also zone-size-dependent. The analysis demonstrates that microcrack toughening is less potent than transformation toughening.     

Mechanics of Transformation-Toughening in Brittle Materials

Particles which undergo a stress-induced martensitic transformation are known to toughen certain brittle materials. The enhanced toughness can be considered to originate from the residual strain fields which develop following transformation and tend to limit the crack opening. The increased toughness can estimated from the crack-tip stress-intensity change induced by the transformation of a volume of material near the crack tip. It is found that the initial zone, prior to crackgrowth, provides no change in stress intensity. As the crack grows, the zone (associated with a positive transformation strain) induces a stress-intensity reduction that rises to a maximum level after some crack propagation. The influence of particle-size distribution on the stress-intensity reduction is also discussed.     

Indentation Method for Determining the Macroscopic Fracture Energy of Brittle Bimaterial Interfaces

Based on the mechanics analysis of crack-interface interaction, a simple and direct micro-indentation technique has been developed to evaluate the fracture energy of a bimaterial interface. The technique, when applied to a pristine planar SiC-Si₃N₄ interface at various angles of attack, is shown to provide a reasonable estimate of the interfacial fracture resistance. The experimentally obtained fracture energy has been compared favorably with a proposed atomic model of bond breaking between SiC and Si₃N₄.     

Flexural Properties of Brittle Multilayer Materials: I, Modeling

Multilayer systems comprising brittle materials can exhibit substantially different behaviors under flexural and tensile loadings. The present article addresses the origins of such differences, with emphasis on the modeling of the flexural stress–strain response. Systems with both a deterministic tensile strength and a distribution in strengths (characterized by Weibull statistics) are considered. The model predictions show that both the ultimate strength and strain-to-failure in flexure exceed the corresponding values in uniaxial tension. In addition, systems comprising alternating layers of two different materials are examined, and disparities in the flexural and tensile behaviors addressed.     

Implications of Transformation Plasticity in ZrO2-Containing Ceramics: II, Elastic-Plastic Indentation

Indentation hardness of partially stabilized zirconia was found to be 8.2 times the uniaxial compressive yield stress. This ratio is anomalously high for ceramic materials and is attributed to pressure hardening in transformation plasticity. An analytic solution of elastic-plastic indentation using the spherical-hole model is given, based on a pressure-sensitive idealized yield criterion. The theory correctly predicts a higher hardness and a larger plastic zone, both in quantitative agreement with the experimental observations in Mg-PSZ. Data analysis further reveals a large disparity of yield stress and hardness values among cubic, tetragonal, and monoclinic zirconias, resulting from their different phase transformation and twinning capabilities. The broader implications of pressure sensitivity in elastic-plastic Indentation are rationalized.     

Statistics of Flaw Interaction in Brittle Materials

The problem of elastic interaction of an array of microcracks is considered. The solution is based on an efficient surface integral method using distribution of edge dislocations to represent the microcracks in the mathematical model. From the analysis of the interaction between two identical cracks, it is seen that interaction is most likely to produce a slight enhancement in the stress intensity factor. By performing computer experiments on a random array of microcracks, the effect of crack interaction is studied statistically as a function of the density of the microcracks. The significance of the interaction effects for fracture in ceramics is discussed.     

Uniaxial Strength Behavior of Brittle Cellular Materials

Two types of brittle reticulated materials were evaluated under uniaxial tensile and compressive loading and analyzed in terms of the Gibson and Ashby model for brittle open-cell solids. The samples consisted of an open-cell alumina–mullite material which was tested as a function of density at a constant cell size and a reticulated vitreous carbon tested at one density and two cell sizes. The samples were mounted such that only the loading direction was varied in the tests. A combination of video photography and acoustic emission was critical to interpreting the results. The model assumes that identical deformation modes, bending failure of the struts, are responsible for failure of the bulk foam in tension and compression. The results of this work indicate a significant difference between the density dependence in tension and compression. Tensile failure in both materials appeared to be characterized by the catastrophic propagation of a single crack. Compressive failure was significantly different between the alumina and glassy carbon foams. The alumina foam failed by a damage accumulation process, whereas the carbon foam failed by the catastrophic collapse of a band of cells perpendicular to the loading direction.     

Reliability of Brittle Materials in Thermal Shock

The fracture-of alumina disks subjected to thermal shock is predicted from Weibull parameters derived from isothermal three-point-bend tests. Both the shear-insensitive Batdorf model and the principle of independent action model are used to compare results from three-point-benr1 and isothermal biaxial strength tests to results from thermal fracture tests. It is found that the shear-insensitive Batdorf model gives good agreement between mechanical tests and fracture of the thermally shocked disks.     

Model for Strength of Brittle Porous Materials

Many porous bodies form by the growth and joining of individual solid particles into a network-like structure. Assuming that the distribution of particles in the porous body is random, the relation between strength and porosity was derived and compared with commonly used empirical relations.     

Rationalized Load and Lifetime of Brittle Materials

The design and testing of structural parts from materials which exhibit subcritical crack growth can be improved by introducing auxiliary quantities into the classical concepts of fracture mechanics. The equivalent static stress, equivalent loading time, standardized loading time, and standardized lifetime, as well as the decrease in lifetime and residual lifetime, are defined, with examples of their application.