Time-Dependent Strength Degradation of a Siliconized Silicon Carbide Determined by Dynamic Fatigue

Both fast-fracture strength and strength as a function of stressing rate at room temperature, 1100°, and 1400°C were measured for a siliconized SiC. The fast-fracture strength increased slightly from 386 MPa at room temperature to 424 MPa at 1100°C and then dropped to 308 MPa at 1400°C. The Weibull moduli at room temperature and 1100°C were 10.8 and 7.8, respectively, whereas, at 1400°C, the Weibull modulus was 2.8. The very low Weibull modulus at 1400°C was due to the existence of two exclusive flaw populations with very different characteristic strengths. The data were reanalyzed using two exclusive flaw populations. The ceramic showed no slow crack growth (SCG), as measured by dynamic fatigue at 1100°C, but, at 1400°C, an SCG parameter, n , of 15.5 was measured. Fractography showed SCG zones consisting of cracks grown out from silicon-rich areas. Time-to-failure predictions at given levels of failure probabilities were performed.     

Statistics of ceramic strength: Use ordinary Weibull distribution function or Weibull statistical fracture theory?

“Weibull statistics” for strength distribution analysis refers to either the ordinary Weibull distribution function or the Weibull statistical fracture theory. The ordinary Weibull distribution function is an empirical distribution function on an equal footing with other type of classical empirical distributions such as normal and log-normal distributions for fitting the statistical data of various random variables nonexclusive to materials strength. It has no explicit physical meaning and cannot be used for size scaling and prediction of strength. The Weibull statistical fracture theory is a weakest-link statistical fracture model for a solid with the strength distribution of an elemental volume being described by the ordinary Weibull distribution function. It has the capability of size scaling and prediction of strength for specimens with different geometries and different loading modes. The three-parameter Weibull statistical fracture theory in uniaxial flexure of prismatic beams is reformulated and validated by both numerical and real strength experiments of different ceramics.     

Dynamic fatigue behavior of lithium hydride at elevated temperatures

The fatigue properties of lithium hydride (LiH) are crucial to its application as neutron shielding and moderating at elevated temperatures. The dynamic fatigue tests of LiH were investigated with the notched 3-point bend (3 PB) specimens over ranges of loading rates at RT up to 400 °C. At RT, the results showed that slow crack growth (SCG) occurred prior to failure as the minor deviation from linearity to nonlinearity in the load-deflection curves. In addition, the fracture strength of LiH decreased with decreasing stress rate and the SCG zone gradually became smaller with higher stress rates, indicating evident dynamic fatigue phenomenon. However, the trends were quite different at 200, 300 and 400 °C due to accumulative creep damage for low stress rates at elevated temperatures. With increasing temperature and decreasing stress rate, there existed a transition of the dominated failure mechanism, from SCG to creep rupture. Evidence of very small SCG zone could also be detected at the notch for the failure dominated by creep rupture.     

Standardized Weibull statistics of ceramic strength

In order to estimate Weibull parameters in the Weibull statistical fracture theory as truly material properties independent of specimen geometry and loading mode, first the Weibull statistical fracture theory is transformed into the ordinary Weibull distribution function under certain approximation. Then the standardized format of ordinary Weibull distribution is introduced to enable Weibull modulus as the single parameter for estimation via the maximum likelihood method. The method of using standardized Weibull distribution for strength data synchronization and Weibull modulus estimation is validated by analyzing extensive strength data sets measured from uniaxial flexure, biaxial flexure and their combination, and from smooth and notched specimens. The technical path to estimate the scale parameter and threshold strength as material properties in the Weibull statistical fracture theory and effect of sample size on the estimation accuracy are also discussed.     

Analysis of Size Dependence of Ceramic Fiber and Whisker Strength

The strengths of ceramic fibers and whiskers have been observed to increase with decreasing fiber diameter and length. Typically, both surface flaws and volume flaws exist in ceramic fibers and whiskers, which makes it impossible to characterize the strength dependence of both the diameter and the length with a single-modal Weibull distribution function. Our data also show that the single-modal Weibull distribution is inadequate to characterize the strength of fibers with varying diameters even in the case of a constant fiber length. In addition, experimental data also show that, for sapphire whiskers whose surface flaws were removed by chemical polishing, the whisker strength has a much stronger size dependence on diameter than predicted by the single-modal Weibull function, which indicates that factors other than those characterized by the Weibull function also play a role in the strength of sapphire whiskers. In this paper, the factors affecting the strengths of ceramic fibers and whiskers are analyzed in terms of Weibull statistics, fracture mechanics, and flaw size density variation with varying fiber diameters. A three-parameter modified Weibull distribution, which combines the above strength-affecting factors, is proposed to characterize both the diameter and the length dependence for ceramic fibers and whiskers with or without surface flaws. Characterization of the strength data of sapphire whiskers and Nicalon SiC fibers with varying diameters shows the validity of the modified Weibull distribution function.     

Evaluation of the Fracture Strength for Silicon Carbide Layers in the Tri-Isotropic-Coated Fuel Particle

A program to develop new methods to measure the fracture strength of the chemical vapor deposition SiC coatings in nuclear fuel particles has been carried out. Internal pressurization and crush test techniques were developed and applied to prototype-sized tubular and hemispherical shell specimens. The fracture strength measured from each test method applying the Weibull two-parameter distribution, and Weibull parameters were measured. It was shown that data generated with each test technique were independent of the test technique applied. This implies that the developed test methods are reliable and provide reasonable strength data. For the same material, fracture strength varied with the specimen geometry and loading configuration. These size and loading configuration effects on the fracture strength are explained with the concept of effective surface.     

Estimation of Weibull parameters for the flexural strength of PMMA‐based bone cements

The wide scatter of data observed in the strength of bone cements based on poly(methyl methacrylate) (PMMA) can be described properly by the two‐parameter Weibull function. However, the statistical character of the distribution leads to an uncertainty in the parameters evaluated from a limited number of experiments. This study is concerned with the analysis of the methods of estimation as well as sample size on the estimates of the Weibull parameters. The maximum likelihood method, moments method, and linear regression method were studied. Monte Carlo simulations were carried out in order to assess the influence of the number of specimens tested on the Weibull parameters calculated by the different methods. The number of specimens tested displayed a large influence upon the calculated Weibull modulus. By applying weighing factors to the linear regression method, the standard deviation of Weibull parameters decreased significantly. As a compromise between minimizing both the dispersion of the evaluation method and the experimental effort, the use is suggested of the linear regression method with a minimum number of 20 specimens in a nonweighted analysis and 10 in a weighted analysis.     

Extraction of Weibull Parameters of Fiber Strength from Means and Standard Deviations of Failure Loads and Fiber Diameters

The errors in using an average fiber diameter to calculate the mean strength (ς_m), Weibull reference strength (ς₀), and Weibull modulus ( m ) from failure loads of fibers were examined experimentally. Although the use of an average diameter gave very good estimates of ς_m, the error in the Weibull parameters (ς₀ and m ) was significant, which supported the recent simulation results. Computational approaches to reduce these errors have been considered, and a numerical procedure to extract the Weibull parameters from the means and standard deviations of the load and fiber diameter has been proven feasible, provided the sample population is large. Parametric studies have shown that sample populations of ∼175 are required to obtain results within an error of 10%. The recommended sample populations for commercial fibers are 75–200, depending on the scatter in the fiber diameter and the acceptable error.     

Ceramics Reliability: Statistical Analysis of Multiaxial Failure Using the Weibull Approach and the Multiaxial Elemental Strength Model

Methodology for designing reliable ceramic components requires a precise evaluation and correlation of strengths in different stress states. The present paper compares the merits of the Weibull approach and the multiaxial elemental strength model on an experimental case involving mixed-mode failure in the presence of bimodal flaw populations (surface and volume flaws). The experimental data were obtained using flexure specimens of Si₃N₄ tested at various spans, with the purpose of enhancing shearing effects. The analysis of data was refined by developing an advanced postprocessor program to finite-element codes for failure probability determination based upon the Barnett-Freudenthal approximation of the Weibull approach and the multiaxial elemental strength model. In a second step, the strengths of the specimens exhibiting failures from the two concurrent populations of flaws (intermediate span) were predicted using both approaches from data obtained with different span lengths (long and short spans). Comparison with experimental data showed that the multiaxial elemental strength model is an improvement over the Weibull approach. It also allowed the short-span bending test to be assessed. Finally, important implications for structural design with ceramics are discussed.     

Statistics on the fracture strength of bamboo fibers

Tensile strength is a key mechanical property of fibers used as sustainable reinforcements for advanced fiber‐reinforced composites. This study aims to conduct experimental investigation on the fracture strength of bamboo fibers of different dimensions subjected to longitudinal tensile loading. The statistical distributions of the fracture strength in bamboo fibers are correlated with the effects of fiber length and diameter variation. These are described according to Weibull statistics, which exhibit the random nature of fiber strength. The Weibull function parameters used for strength prediction are obtained from the test specimens. A comparison of predicted results and experimental data is presented to assess the accuracy of using weak‐link scaling. Furthermore, the findings of this study also indicate that fiber strength statistics dominate size dependence of tensile strength. POLYM. COMPOS., 221–228, 2016. © 2014 Society of Plastics Engineers     

冷热循环下纤维混凝土与高强钢筋间粘结强度损伤模型

通过对普通混凝土(PC)、钢纤维混凝土(SFRC)、聚丙烯纤维混凝土(PFRC)与HRB500E钢筋进行冷热循环作用后的中心拉拔试验,研究不同类型混凝土的劣化机理,分析冷热循环对PC、SFRC、PFRC的质量损失、相对动弹性模量以及粘结强度的影响.试验结果表明:冷热循环后,混凝土的质量损失和动弹性模量损失增加,钢筋与混...     

Comparison of evaluation procedures for the subcritical crack growth parameter n

The uncertainty in the determination of the exponent n in the equation of the subcritical crack velocity from four-point-bending experiments is investigated with respect to different evaluation methods. If the bending strength values are Weibull distributed, and the crack-extension parameter n is calculated by linear regression of the bending strength values of a number of experiments at different loading rates, an analytical solution can be given for the mean value and the standard deviation. It turns out that both the mean value and the standard deviation depend on the Weibull modulus m and the true value n₀. The analytical solution illustrates the essential features of this dependence on m and n₀. For other evaluation methods, e.g. the one proposed as the CEN standard, this dependence is investigated by a Monte-Carlo simulation for different crack-extension parameters n₀ and different Weibull moduli m. The standard deviation, which is calculated, is the theoretical lowest limit for certain evaluation procedures. By this, the estimation of the margin of error is put on a firm ground. Since the standard deviation increases with n₀, there is only a limited range in which n can be determined by four point-bending tests. A new evaluation method, which gives a better approximation than the method proposed as the CEN standard, is presented. The computational effort of this evaluation method is only slightly larger. It furthermore allows the number of experiments to be analytically calculated, which is necessary to obtain a certain accuracy.     

Effect of specimen shape on the behavior of brittle materials using probabilistic and deterministic methods

The main objective of this paper is to verify the activated defect localization under various loading rates for Modified Brazilian Disk (MBD) compared with spherical glass specimen frequently used in the literature. The geometry of specimen can considerably influence the mechanical response of material specially, the brittle materials which are very sensitive to the defects activations and finally corresponding Weibull statistic problematic for these materials. The high and low loading rates have been investigated using universal Instron machine compression and Compressive Hopkinson Pressures Bars (CHPB) on MBD lead glass specimen and then the experimental results have been compared via the Weibull's distribution for scatter strength variation. Finally, we observed the contact problem leading to the activated defects in this area on spherical glass specimen under static and dynamic loading not MBD specimen under both loading rates. Consequently, the probabilistic approach should be taken into account including the specimen geometry and also ‘Type’ of loading application due to the activated defect position arising from the sever contact problem for the brittle materials.     

Effect of pH variation on the subcritical crack growth parameters of glassy matrix ceramics

The goals of our study were to calculate the subcritical crack growth (SCG) parameters of two veneering ceramics stored in water or Streptococcus mutans (S. mutans) biofilm and remineralizing medium, with indentation flaws. Feldspar (VM7) and leucite-reinforced (VM13) glass ceramic disks (Vita Zahnfabrik, Bad Säckingen, Germany) were made according to ISO 6872. Some specimens were indented with a Vickers diamond and the crack dimensions were measured. The specimens were fractured for a calculation of inert strength or further stored in water or submitted to pH variation, under preloading tension. Finally, the SCG parameters were calculated after the specimens were fractured under four stressing rates (MPa/s). Weibull analysis was conducted on non-indented specimens. XPS was performed as qualitative analysis. The subcritical crack of leucite ceramic did not vary with the media storage, but the glass-ceramic experienced a retarded growth after pH variation. The materials presented low Weibull modulus. Qualitative elemental analyses showed chemical modification on both ceramics. Therefore, the crack growth of leucite-reinforced ceramic was less affected by the environment pH than glass-ceramic.     

Large-scale Weibull analysis of H-451 nuclear-grade graphite rupture strength

A Weibull analysis was performed of the strength distribution and size effects for 2000 specimens of H-451 nuclear-grade graphite. The data, generated elsewhere, measured the tensile and four-point-flexure room-temperature rupture strength of specimens cut from a single extruded graphite log. Strength variation versus specimen location, size, and orientation relative to the parent body were compared. In our study, data were progressively and extensively pooled into larger data sets to discriminate overall trends from local variations and investigate the strength distribution. Issues regarding size effect, Weibull parameter consistency, and nonlinear stress–strain response were investigated using the Ceramics Analysis and Reliability Evaluation of Structures Life Prediction Program (CARES/Life) and WeibPar codes. Overall, the Weibull distribution described the behavior of the pooled data very well. The Weibull modulus was shown to be clearly consistent between different tensile specimen sizes and orientations. However, the issue regarding the smaller-than-expected size effect remained. This exercise illustrated that a conservative approach using a two-parameter Weibull distribution is best for designing graphite components with low probability of failure for the in-core structures in the proposed Generation IV high-temperature gas-cooled nuclear reactors. This exercise also demonstrated the continuing need to better understand the mechanisms driving stochastic strength response.     

Controlling and Testing the Fracture Strength of Silicon on the Mesoscale

Strength characterizations and supporting analysis of mesoscale biaxial flexure and radiused hub flexure single-crystal silicon specimens are presented. The Weibull reference strengths of planar biaxial flexure specimens were found to lie in the range 1.2 to 4.6 GPa. The local strength at stress concentrations was obtained by testing radiused hub flexure specimens. For the case of deep reactive ion-etched specimens the strength at fillet radii was found to be significantly lower than that measured on planar specimens. This result prompted the introduction of an additional isotropic etch after the deep reactive ion etch step to recover the strength in such regions. The mechanical test results reported herein have important implications for the development of highly stressed microfabricated structures. The sensitivity of the mechanical strength to etching technique must be accounted for in the structural design cycle, particularly with regard to the selection of fabrication processes. The scatter of data measured in the mechanical tests clearly illustrated the need to use a probabilistic design approach. Weibull statistics may be the appropriate means to describe the data, although a simple two-parameter Weibull model only provides a moderately good fit to the experimental data reported in this study.     

不同拉伸条件下基于Weibull模型的粘胶基碳纤维强度分布研究

从粘胶基碳纤维的拉伸实验得到其 S-S曲线和强度、模量、断裂伸长等力学性能数据 ,表明该材料是典型的脆性断裂 ,且断裂分散性较大。采用 VB编程软件设计了 Weibull程序 ,该模型能计算出碳纤维的平均强度、Weibull模数、尺度参数 ,并能模拟碳纤维强度的累积概率分布和概率密度曲线。不同氧化拉伸条件下强度的实验数据基本上落在程序模拟出的累积概率分布直线上 ,证明了该数学模型适用于分析碳纤维强度分布。在氧化完全松弛的条件下 ,粘胶基碳纤维的平均强度较高 ,但 Weibull模型分析的结果表明氧化拉伸比为 -5 %时 ,Weibull模数最大 ,不匀率最小 ,而氧化拉伸对粘胶基碳纤维模量没有显著影响。     

Subcritical crack growth models for static fatigue of Hi-NicalonTM-S SiC fiber in air and steam

Three subcritical crack growth (SCG) laws were used to model strain-rates and failure times for static fatigue of Hi-Nicalon^TM-S SiC fiber tows in air and Si(OH)₄(g)-saturated steam. Models were fit to tow failure times ( t_f ) and steady-state strain rates ( ἑ ) for brittle creep measured at 700 to 1100°C under initial applied stresses ( σ_A ) of 260 to 1260 MPa. A power law, a reaction-rate law, and a bond-energy law were used to describe SCG that caused sequential filament failure, and ultimately tow failure. Two versions of each model were developed. One allowed access of chemisorbed species to flaws throughout the fiber (mode 1) and another only allowed access to flaws at the SiC-SiO₂ interface (mode 2). The stress increase on intact filaments as others fractured and as filaments oxidized, and the increase in stress intensity geometric factors ( Y ) as crack size increased were incorporated in the models. The fits to data were compared for the different models by using both simple regression analysis and orthogonal distance regression (ODR) analysis. Faster convergence and more consistent results were achieved using ODR analysis. Regression analyses found parameters for all models with similar error in data fits, so validity of a model could not be distinguished by regression analysis alone. For all models, the stress dependence of SCG rates was much stronger in steam than in air, and for most models activation energies were between 300 and 420 kJ/mol, regardless of environment. For the steam environment, the bond-length parameter ( δ ) for the bond-energy model was very close to the lattice parameter of β-SiC (.436 nm), but in air it was significantly lower at 0.25-0.26 nm, but still larger than the Si-C bond length of 0.189 nm. Other factors suggest that either a bond-energy based law or a modified version of a reaction-rate law are the best choices for a SCG law. Filament strength distributions initially described by Weibull distributions could not be described by such distributions after application of the models. SCG mechanisms are discussed.     

Interfacial shear strength of flax fibers in thermoset resins evaluated via tensile tests of UD composites

A method of interfacial shear strength evaluation, based on the length distribution of fibers pulled out from the tensile fracture surface of an oriented flax-reinforced composite, is applied to composites with vinyl ester and acrylated epoxidized soy oil resin matrices. Two approaches for characterizing the strength of fibers with modified Weibull distribution, fiber fragmentation tests and fiber tension tests, are compared in the analysis of pull-out data. Interfacial shear strength is found to increase by a few percent when loading rate is increased from 1.33% to 8%/min.