Statistical analysis of bend strength data according to different evaluation methods

The strength values obtained in four series of bend tests on two monolithic ceramic materials have been statistically evaluated. Statistical mapping procedures were used to check whether a Weibull distribution fits the strength data. Where this has been found to be the case, the value of the Weibull parameters determined according to different evaluation methods fall within each other's confidence interval. The values of the modulus m and of the characteristic strength σ₀ of the two-parameter distribution can differ significantly from the corresponding values in the three-parameter distribution.     

Surface treatment of wire electro-discharge machined engineering ceramics by abrasive blasting

The surface integrity of electro-discharge machined engineering ceramics and their surface modification by abrasive blasting have been investigated in this study. Flexural strength was used for evaluating the effect of the two machining processes on the surface of machined specimens. The distributions of strength data were further analyzed by the Weibull statistical method to give a quantitative measure of the surface integrity. The test results show that the mean flexural strength values of wire electro-discharge machined Syalon 501 ceramics are considerably low, only about 33-52% of the original value of the material, 825 MPa. The value of the Weibull modulus, m, is very low, in the range of 4.2-8.8. Wire electro-discharge machined ceramic surfaces are of poor surface integrity and low reliability, so it is necessary to treat them before practical application. After undergoing abrasive blasting, the mean flexural strength values were found to be 20-25% higher than those of wire-EDM pre-machined specimens. The calculated Weibull modulus, m, is in the range of 14-15.5, which is much higher than that of wire-EDM pre-machined specimens, 8.1. The test results show that with most of the abrasive blasting conditions, the ceramic specimens behave fairly consistently and their properties vary narrowly from the mean value. The Weibull modulus, in, based on these small populations, increased with decreasing compressed air pressure and grain size of the abrasives. Abrasive blasting is an effective machining procedure to modify ceramic surfaces subjected to wire-EDM.     

A Comparison of the Effects of Microwave Versus Conventional Drying on the Mechanical Properties Distribution of Dried Green Porcelains

The effect of fast microwave drying of electroporcelain insulator component was studied by determining the reliability parameter. The Weibull modulus was calculated using the three-point bend strength data of a large number of green samples which were dried using microwave energy. The results were compared with those obtained by conventional drying methods. It was observed that in most cases, microwave-dried components yielded higher Weibull modulus than their conventionally dried counterparts. A high modulus value of >15 was achieved on the microwave-dried samples. The analysis of the result was useful in understanding the fast drying process in ceramics.     

Strength Distribution in Commercial Silicon Carbide Materials

Four types of commercial silicon carbide samples from different sources were characterized in terms of baseline strength and strength distribution (reliability). Four-point flexural strength of each material was determined on 30 test bars, 5.1 by 0.64 by 0.32 cm, for a reliable estimate of the Weibull modulus values. The results show that the average strength of these sintered silicon carbide samples ranged from 380 to 482 MPa (55 to 69 ksi) at room temperature and 307 to 470 MPa (45 to 68 ksi) at 1370°C (2500°F). Considerable variations in strength were found among specimens of each material. Baseline Weibull modulus values ranged from 8 to 11 at room temperature and 7 to 11 at 1370°C (2500°F). The strength scatter clearly reflected flaw variability, which must be minimized to improve reliability in sintered silicon carbide materials.     

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.     

Is Weibull distribution the most appropriate statistical strength distribution for brittle materials?

Strength reliability, one of the critical factors restricting wider use of brittle materials in various structural applications, is commonly characterized by Weibull strength distribution function. In the present work, the detailed statistical analysis of the strength data is carried out using a larger class of probability models including Weibull, normal, log-normal, gamma and generalized exponential distributions. Our analysis is validated using the strength data, measured with a number of structural ceramic materials and a glass material. An important implication of the present study is that the gamma or log-normal distribution function, in contrast to Weibull distribution, may describe more appropriately, in certain cases, the experimentally measured strength data.     

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.     

Strength Analysis of Self-Supported Films Produced by Aqueous Electrophoretic Deposition

The goal of this work is to study the feasibility of the characterization of the fracture strength of porous alumina/zirconia thin layers by three-point bending and Weibull analysis. Films have been obtained by electrophoretic deposition on graphite and thermo-gelation of the deposit with carrageenan. On sintering, graphite is burned out and self-supported films are obtained. Strength values are well fitted to a simple two-parameter Weibull distribution. The fracture origins are subcritical growth cracks that originated at the surface irregularities associated with the processing method. A Weibull modulus around 3 is obtained.     

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。     

Bend strength variation of ceramics in serial fabrication

We have performed a statistical evaluation of more than 10 000 experimental strength values of test pieces from a serial production of alumina products where in each production series 12 samples were broken. The Weibull parameters were obtained by three different methods: linear regression, maximum-likelihood and moments’ method. The methods give different values of parameters even for this large number of data, but all the correlation coefficients are high and similar. Evaluating Weibull parameters for each testing group gives expected systematically different values of particular Weibull modulus as compared to the whole population of collected data. However, when the order of experimental data is mixed, the average Weibull modulus is lower than that corresponding to time ordered data. This difference can be served as an indication for variation of products’ quality from series to series.     

Accurate determination of fiber strength distributions

Tensile strengths of small‐diameter ceramic fibers are commonly obtained from measured fracture loads on individual fibers and the average cross‐sectional area of the entire fiber population. The goal of the present article is to provide a critical assessment of the consequences of using the average fiber area in the inferred strength distribution. The issues are addressed through established theorems in convolution and uncertainty propagation as well as Monte Carlo simulations. Systematic errors introduced by using the average area are well‐represented by simple analytical formulae. The formulae are couched in terms of the coefficient of variation in fiber area and the dispersion in fiber strengths, characterized by the Weibull modulus. In turn, the formulae are used to determine the true values of Weibull modulus and reference strength from their nominal values. Random uncertainties associated with a finite number of tests decay slowly with number, in accordance with an inverse root scaling. When systematic errors are conflated with random uncertainties, accurate determination of the true Weibull modulus becomes increasingly challenging, even for seemingly large numbers of strength measurements. The results are used to assess the fidelity of previously‐reported experimental results based on nominal strength data.     

Measurement of adhesive shear properties by short beam shear test based on higher order beam theory

This paper refers to the measurement of the shear properties of adhesive bonding by a new beam theory using the short beam shear (SBS) test configuration. A novel higher-order sandwich beam theory has been developed to analyze the adhesive bonded beam that consists of two adhered laminates and a single layer of adhesive in between. The closed form analytical solution for the SBS test model of the adhesively bonded beam is obtained in terms of deflection and stress distribution. The present theory has been used for calculating the adhesive shear modulus from the structural compliance. The initiation of stiffness degradation for the short beam shear test model was used as the critical load value for deriving the adhesive shear strength. A finite element model is built for validating the present model, and to evaluate its suitability for measuring adhesive shear properties. The present theory shows better accuracy for measuring the shear modulus than existing theories for both thin and thick adhesive layers. The measured strength values are more accurate than those obtained from the single lap joint shear test model. This theory can be used for adhesive materials with linear elastic deformation behavior.     

Single-phase photo-cross-linkable adhesive synthesized from methacrylic acid-grafted 1-decene/9-decene-1-ol cooligomer

The cooligomerization of 1-decene with 9-decene-1-ol was conducted by using a Ti amine bis-phenolate catalyst. Light-curable adhesive was prepared by the reaction of methacryloyl chloride with the hydroxyl groups of the synthesized cooligomer, which led to the introduction of photo-polymerizable CC double bonds into the cooligomer chains. Comonomer insertion into 1-decene oligomeic chains and also methacryloyl chloride reaction with cooligomer were confirmed by both FT-IR and NMR spectroscopy. Three-point bending analysis results of cured adhesive sample (cured with blue light) showed flexural modulus and flexural strength values of 1.41 GPa and 1.66 MPa, respectively. Maximum weight loss temperature of 444°C showed high thermal stability of cured adhesive sample. In order to explore adhesion abilities of the synthesized adhesive to different substrates including polymethylmethacrylate (PMMA), polycarbonate (PC), polystyrene (PS), nylon and aluminum (Al), tensile shear bond strength, and peeling tests were conducted. Synthesized adhesive demonstrated tensile shear strength values of 1.28, 1.95, 1.10, 2.15, and 2.42 N/mm² for PMMA, PC, PS, nylon, and Al substrates, respectively. Furthermore, obtained adhesive indicated greater tendency to polar substrates in comparison to nonpolar ones by the factor of 16–95%. Obtained results suggested a new photo-curable adhesive with privileged features, which has capability to be used in high temperature applications.     

Mechanical and structural characterization of electrospun PAN-derived carbon nanofibers

The mechanical and structural properties of individual electrospun PAN-derived carbon nanofibers are presented. EELS spectra of the carbonized nanofibers shows the C atoms to be partitioned into ∼80% sp² bonds and ∼20% sp³ bonds which agrees with the observed structural disorder in the fibers. TEM images show a skin-core structure for the fiber cross-section. The skin region contains layered planes oriented predominantly parallel to the surface, but there are some crystallites in the skin region misoriented with respect to the fiber long axis. Microcombustion analysis showed 89.5% carbon, 3.9% nitrogen, 3.08% oxygen and 0.33% hydrogen. Mechanical testing was performed on individual carbonized nanofibers a few microns in length and hundreds of nanometers in diameter. The bending modulus was measured by a mechanical resonance method and the average modulus was 63 GPa. The measured fracture strengths were analyzed using a Weibull statistical distribution. The Weibull fracture stress fit to this statistical distribution was 0.64 GPa with a failure probability of 63%.     

Bonding performance and fracture morphology of a hybrid multiscale epoxy adhesive on oil‐covered substrates

A hybrid multiscale epoxy adhesive reinforced with a combination of short carbon fibers and rubber nanoparticles was prepared for bonding oil‐covered aluminum substrates. The shear performance of the bonded joints was investigated as a function of the oil layer thickness. Scanning electron microscopy and energy‐dispersive X‐ray analysis studies were carried out to evaluate the oil‐diffusion behavior near the substrate–adhesive interface. The results show that the shear strength decreased, whereas the distribution range of the testing results increased as the oil layer thickness increased. When the oil layer was thinner than 10 μm, the oil‐accommodating adhesive could be used directly without degreasing, whereas over 96% of the bonding strength could be retained with almost no change in the failure probability. The analysis of Weibull distribution indicated that the shear strength and Weibull modulus were 18.89 MPa and 13.503, respectively. By analyzing the relationship between the shear strength results and the failure model of the fracture surface, we found a correlation. © 2015 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2016 , 133, 42898.     

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.     

Strength of adhesively bonded joints under mixed axial and shear loading

This study aims at optimising adhesive properties in an aluminium/structural epoxy assembly for different conditions of surface pre-treatment. We consider the mechanical behaviour and failure under proportional, multi-axial loading using an instrumented, Arcan-type test. Values of fracture strength were found to be dispersed (even for a given surface treatment). Typically dispersion was of the order of 15%. This statistical behaviour, also observed with a simple tensile test, seems to be related to the heterogeneous nature of the microstructure of the adhesive bond, which contains voids, as well as mineral particles for reinforcement. A statistical analysis is suggested for use in conjunction with a strength envelope in practical design, for cases when the stress distribution is significantly heterogeneous. It is believed that this approach may be developed in order to understand the well-known scatter of adhesion strength results, and thus contribute to better reliability assessment.     

Effect of Residual Surface Stress on the Strenght Distribution of Brittle Materials

The introduction of residual surface stresses into a material can change the strength distribution simply due to variability in the stress intensity factor of surface cracks. This variability arises from the distribution in surface (critical) crack lengths. A fracture mechanics approach was used to determine the influence of surface compression on the average strength and the standard deviation of the strength distribution. The strengths of the stress-free samples were assumed to fit a twoparameter Weibull distribution, and the increases in strength resulting from the surface compression were determined using fracture mechanics. It was determined from the analysis that the standard deviation/average strength ratio (coefficient of variation) initially increases, passes through a maximum, and ultimately reaches a plateau value below the initial value, as one increases the depth of surface compression. The maximum increase in the strength scatter occurs when the depth of the surface compression is approximately equal to the characteristic crack size. These changes were found to be dependent on the magnitude of the surface stress, as well as the characteristic strength, Weibull modulus, and fracture toughness of the stress-free material.     

Statistical distribution of adhesion strength developed at self-healed symmetric interfaces of glassy monodisperse polystyrene

The distribution of the lap-shear strength developed during the contact of the bulk samples of amorphous entangled monodisperse polystyrene (PS) at healing temperatures below the bulk glass transition temperature by 13–33 K has been analyzed by using a Weibull statistical model. The Weibull modulus and the scale parameter have been estimated for two symmetric PS–PS interfaces with different molecular weights of 105 and 106 g/mol and compared with those reported recently for the interfaces of amorphous polydisperse polymers.     

Corrugated board bonding defect visualization and characterization

Adhesive bonding of fluted medium to linerboard is a fundamental process in manufacturing of wood-fiber based corrugated combined board for packaging. The quality of bonds requires frequent testing since production speed and container box stacking capacity are affected. Several different testing techniques are investigated in this paper that complement the standard tests commonly used: bond tensile strength “pin adhesion” (Technical Association of the Pulp and Paper Industry (TAPPI) method T 821), visual qualitative inspection of adhesive distribution by iodine stained separated components (TAPPI method T 610), and examination of manually peeled separated boards. A specially prepared corrugated board sample set was made on a pilot corrugating machine producing a range of bonding defects associated with common inadvertent improper corrugating operating conditions. A thermoelastic stress analysis using infrared image processing applied to the produced samples demonstrates a patterned localization of strains that is associated with adhesive distribution and bond strength. Analysis of load-displacement data of the pin adhesion test indicates significant measurable changes in the elastic properties of the corrugated board structure corresponding to bond quality. The experimental results supported by Finite Element Analysis indicate that increased bond strength arises from an increased localized modulus attributable to a combination of adhesive penetration into the substrate and formation of covalent bonds. Infra-red imaging of back-lighted board samples provides a complementary convenient means to assess the glue distribution.