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 Very Slow Crack Growth in Glass

The rate of very slow crack growth in glass is measured by inducing small, controllable changes in the direction of propagation of Hertzian cone cracks at known times. After completion of a growth sequence, the sample is sectioned to reveal the fracture surface. The stress intensity factor at each stage of crack growth is calculated by using finite-element modeling of the stresses near the crack tip. Data are presented for crack growth velocities as low as 10⁻¹⁴ m/s in soda–lime glass. These data provide strong evidence for the existence of a subcritical limit for crack growth in this material.     

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.     

Direct Measurement of Crack Tip Stresses

Raman microprobe spectroscopy was used to measure the crack tip stress distribution in single-crystalline silicon using a wedge-loaded double cantilever beam (dcb) specimen. The wedge was advanced until the crack just propagated. After the crack arrested, the stresses were measured between 3 and 20 μm directly ahead of the crack. An average value of –0.43 was obtained for the slope of log stress vs log distance from the crack tip, rather than the theoretical value of –0.5. The value of K _I was determined from (1) the intercept of this curve and (2) the slope of stress against     . The values were in good agreement. The average experimental value of K _I was determined to be 0.71 MPa · m^1/2, compared to literature values for the K _IC ranging from silicon of 0.8 to 0.94 MPa · m^1/2. The value measured with the Raman is the arrest value of K _I and is expected to be lower from kinetic energy considerations associated with wedge-loaded dcb specimens.     

Slow Crack Growth in Cement Paste

The dependence of crack velocity on stress intensity was measured in hardened cement paste. Fracture toughness, modulus of rupture, and dynamic elastic modulus were also measured to permit calculation of the time-to-failure (life expectancy) of stressed cement paste. The double torsion method was used for slow crack growth studies and fracture toughness measurements. Fracture toughness was also measured by a notched-beam method; the agreement between the two methods was excellent. The crack-velocity-stress-intensity curve for cement paste resembles that of glass in water. The slope of the log V -log K _I curve is ∼35.     

Indentation Crack-Shape Evolution during Subcritical Crack Growth

Indentation crack-shape evolution during subcritical crack growth was examined in soda-lime glass. Crack-arrest markings were generated on the fracture surfaces by temporary unloading during subcritical crack growth. Crack shapes were determined from these crack-arrest markings by optical microscopy. The shapes were found to be semielliptical, but the ellipticity changed significantly with crack extension under an applied bending stress. Crack-shape evolution was predicted by using the stress intensity factor equation for a semielliptical crack for the applied stress distribution and the subcritical crack growth parameters for the material/environment system. Experimental results were found to be in excellent agreement with the predictions. The influence of the initial crack size and shape, the loading configuration, and the subcritical crack growth exponent n on crack-shape evolution was also investigated in the simulations. It was found that, for the particular loading configuration and material, there is an equilibrium shape associated with the subcritically growing crack. The variation in crack shape with its extension during subcritical crack growth was found to be an important factor in lifetime prediction.     

Indentation Determination of Crack Growth Parameters in Gallium Arsenide

Indentation measurements of the environmentally enhanced crack growth parameter, n , in GaAs have been made in water, acetonitrile, and methanol. Reasonable agreement with n values obtained from double-cantilever-beam tests was obtained. It is concluded that the range of n values which can be measured by the indentation technique is much wider than previously observed, and is strongly dependent upon the experimental configuration employed.     

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.     

Functionally Graded Zircon–Molybdenum Materials without Residual Stresses

A layered, zircon–molybdenum functionally graded material was obtained by starting from commercial powders of molybdenum (median particle size ( d ₅₀) of ∼3 μm) and zircon ( d ₅₀∼ 0.8 μm). Conventional processing led to a material that was free of internal residual stress. The sintering behavior of green compacts with compositions that corresponded to the different layers was studied via dynamic sintering. The thermal expansion coefficients of each layer were measured using conventional dilatometry. The presence of residual stresses was determined using Vickers indentations. Both thermal expansion mismatch and differential shrinkage between the layers were negligible.     

Fracture Toughness and High-Temperature Slow Crack Growth inSiC

The subcritical growth of macroscopic cracks in hot-pressed and in sintered SiC was examined at 900° to 1100°C in oxygen partial pressures of 10⁻⁴ and 10⁻⁸ atm. The K ₁-V data for the hot-pressed SiC were generated using the double torsion specimen in the incremental displacement rate mode. These data, in addition to earlier results, included three distinct regions in the plot of log V vs log K ₁,: a low slope region, N∼20, of substantial slow crack growth which was insensitive to testing temperature and environment; a plateau region which shifted to higher velocities with increasing temperature; and a region of very high slope with K values near K _IC The results may be described qualitatively by viscous flow of the gram-boundary phase. No slow crack growth could be detected in the sintered SiC when tested hi the environments described.     

Use of Crack Branching Data for Measuring Near-Surface Residual Stresses in Tempered Glass

An analytical procedure based on fracture mechanics is used to obtain the amount of residual stress in glass from measurements on the fracture surface. The technique utilizes the measurement of microcrack branching distances, known as the mirror — mist boundary, which occur at a critical crack branching stress intensity (K _m ) value. This procedurre shows that σ _A r _m ^1/2 Y _F (θ) =σ _R r ^1/2 _m +Ψ₀, where σ _A is the applied stress, r _m is the microcrack branching radius, σ _R is the residual stress, Y _F ( θ ) is the crack-border correction factor, and Ψ₀ is a material constant based on K _m . Thus, the equation is that of a straight line with the slope equal to the magnitude of the residual stress. Data for tempered glass from the literature are used to demonstrate the applicability of the technique.     

Use of Cube-Corner Nano-Indentation Crack Length Measurements to Estimate Residual Stresses Over Small Spatial Dimensions

Cube-corner indenters, by virtue of their acuity, possess a lowered threshold load for cracking. Shorter crack lengths allow the sampling of residual stresses in small spatial dimensions. We conducted cube-corner indentation on tempered and annealed glasses. Indentation crack geometry was found to be "quarter-penny." A stress-intensity factor for this geometry, and crack length decrements on tempered materials were used in a stress-intensity superposition to provide reasonable estimates of residual stress. Stresses ∼100 MPa over a length scale of 10 μm, and 30 MPa over 20 μm were measured accurately, indicating that cube-corner indentation is a promising tool for materials characterization.     

Effects of Electric Fields on Slow Crack Growth in Glass

Electrical de fields applied through electrodes on either side of a slow-running crack in soda-lime-silica glass resulted in a deviation of the crack plane and in delayed deceleration, arrest, and healing. In some cases crack closure occurred while still under load. Resumption of propagation resumed gradually upon removal of the field. It is suggested that the effects involve displacement of the dilated negatively charged zone at the crack tip, while healing is effected by reformation of bonds between the crack surfaces.     

慢断裂试验仪的研制与应用

选择典型的具有不同分子链结构的４种聚乙烯为研究体系,利用慢断裂试验仪对４种材料进行不同温度、不同载荷以及不同切口深度分析的慢断裂生长失效实验。研究表明：４种材料中以Ｄ样品粘弹性最强,在实验条件下未观察到慢断裂失效过程;Ａ样品粘弹性最弱,材料断裂失效时间最短;Ｂ和Ｃ样品各项性能指数居中,该结果得到其他实验结果的支持。实验表明,慢断裂试验仪适用于对材料使用性能的失效评价测量。     

Water Entry into Silica Glass During Slow Crack Growth

Hydrogen concentration depth profiles on surfaces of SiO₂ glass fractured slowly in water and rapidly in oil were determined by nuclear reaction analysis. It was found that water enters SiO₂ glass during slow crack growth in water.     

温度梯度对聚乙烯耐慢速开裂性能的影响

通过调控温度梯度得到含取向球晶的聚乙烯(PE)试样,研究取向球晶结构对PE耐慢速开裂性能的影响。结果表明:在温度梯度作用下,PE球晶呈椭圆形,片晶沿温度梯度方向取向生长。当温度梯度下制备的试样受到轴向应力作用,取向晶片垂直于受力方向,易发生晶片层间破坏,导致其耐慢速裂纹开裂性能降低。随温度梯度增加,取向球晶增多,耐慢速开裂性能下降更明显。     

Comparison of Slow Crack Growth Behavior in Alumina and SiC-Whisker-Reinforced Alumina

Results of dynamic fatigue experiments in water at room temperature on an indented Al₂O₃/25 wt% SiC whisker composite material have shown that this composite has a high resistance to slow crack growth. Aging tests in water revealed that the residual stress due to the indentation does not play an important role, and interrupted fatigue tests showed that the crack starts to grow at very low stress intensities, but the velocity is very low. Detailed fractography indicated that the slow crack growth path is intergranular in the whisker composite. The slow crack growth behavior in the whisker composite is discussed in association with the indentation residual stress, the change of the crack shape during the bending test. These results are compared with a bio-grade Al₂O₃ with lower resistance to slow crack growth, and important differences are pointed out.     

Evaluation of Slow Crack Growth Resistance in Ceramics for High-Temperature Applications

The slow (subcritical) crack growth (SCG) resistance of Si₃N₄ and SiC ceramics has been evaluated by a stepwise loading test on bending bars precracked by Vickers indentation. Three highly refractory materials were selected for the evaluation: i.e., (1) high-purity Si₃N₄ sintered by hot isostatic pressing (HIP) without additives and (2,3) α - and β - SiC pressureless sintered with B and C addition. Under the hypothesis of linear elastic behavior at high temperature, which was found satisfied in the present materials, the SCG resistance was expressed in terms of initial stress intensity factor critical for SCG failure within a predetermined lifetime. The present method was found useful in shortening the testing time and consistent with other traditional fatigue tests (e.g., static-fatigue test): It is recommended as a screening test for materials under research and development. Among the materials tested in the present study, the highest SCG resistance up to 1440°C was found in the high-purity Si₃N₄ without additives.     

Relation Between Power and Exponential Laws of Slow Crack Growth

The coefficients ₀, and N of the power law of slow crack growth, =₀ exp [–/(RT)](K/K_C)^N, are evaluated in terms of the fundamental parameters V₀. Q₀. and B of the exponential law, V=V₀ exp [(-Q₀+BK)/(RT)]. It is shown that N =θ(BK_C)/(RT),=₀−θBK_C, and ₀=V₀θ^−N, where θ is a dimensionless coefficient with a value ranging from 0.2858 to 1.0, depending on the ratio of stress intensity at the fatigue limit to the critical stress intensity factor.     

Application of Load-Relaxation Techniques to Study Subcritical Crack Growth in Brittle Materials

The load relaxation technique was applied to double- cantilever-beam specimens for the determination of diagrams of the stress intensity factor (K₁ ) vs crack velocity (V) for soda-lime glass. The effect of machine compliance was explicitly incorporated into the velocity equation. The data were in good agreement with published data from different techniques. It was shown that a hard machine (small compliance) is best suited for the load-relaxation technique. The use of a soft machine (high compliance) will lead to catastrophic failure during load relaxation. A single-edge notched-beam specimen in bending is unsuitable for the relaxation technique since catastrophic failure will occur during relaxation regardless of machine compliance.