Fracture statistics of ceramics – Weibull statistics and deviations from Weibull statistics

Dänzer, Robert; Supancic, Peter; Pascual, Javier; Lube, Tanja

doi:10.1016/j.engfracmech.2006.05.028

Cited by 254 publications

(161 citation statements)

References 19 publications

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“…should fail at higher average loads. This is due to the likelihood of finding a critical destructive flaw in larger specimens being greater then that in smaller ones [16]. The empirical data shows no apparent size effect for the strength of the tested PCD grades, a result that has been noted previously by Lu et al.…”

Section: Best-fit Proceduressupporting

confidence: 72%

The influence of microstructure on the fracture statistics of polycrystalline diamond and polycrystalline cubic boron nitride

McNamara

Carolan

Alveen

et al. 2014

Ceramics International

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Flexural Strength data of a number of grades of polycrystalline diamond (PCD), and polycrystalline cubic boron nitride (PCBN) were analysed using Weibull, normal and lognormal distributions. The role of microstructure in the failure mechanism of such material was analysed in terms of the chosen strength distributions. The best-fit distributions were determined using the maximum log-likelihood criteria and a comparison between the best and worst fit was conducted using the Akaike Information Criteria (AIC). Both large and small specimens were tested to investigate possible volume scaling effects for these materials. The different microstructures between the two materials was shown to have an effect on the statistical strength distributions. It was found that for PCD, in general, a lognormal distribution provided a better fit than the other distributions and no specimen size effect was observed. For PCBN a significant specimen size effect was observed and * Corresponding Author

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Section: Best-fit Proceduressupporting

confidence: 72%

The influence of microstructure on the fracture statistics of polycrystalline diamond and polycrystalline cubic boron nitride

McNamara

Carolan

Alveen

et al. 2014

Ceramics International

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“…There are also some cases, however, where the Weibull distribution fails to fit strength data of ceramics [12][13][14][15][16]. Danzer [12] reported that the M a n u s c r i p t 3 Weibull theory is inconsistent in estimating the strength of small specimens because their effective volumes become less than the fracture origin.…”

Section: Introductionmentioning

confidence: 99%

“…It is a distribution that can take on the characteristics of other types of distributions, based on the shape parameter. The simplest form of a Weibull function can be written as [13,14] …”

Section: Distribution Functionsmentioning

confidence: 99%

“…Danzer [12] reported that the M a n u s c r i p t 3 Weibull theory is inconsistent in estimating the strength of small specimens because their effective volumes become less than the fracture origin. Several potential reasons that cause deviation from the Weibull statistics were introduced, such as the multi-modal flaw size distribution, R-curve behavior, and subcritical crack growth [13]. In terms of a minimum information criterion, strength data of Si 3 N 4 , SiC and ZnO ceramics were fitted by normal and Weibull distributions [14].…”

Section: Introductionmentioning

confidence: 99%

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Fracture statistics of dental ceramics: Discrimination of strength distributions

Nohut

2012

Ceramics International

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The Weibull distribution is the most widely used function in the reliability analysis and structural design of dental ceramics; however, it is still unclear whether Weibull distribution is always the most suitable one. With wide applications of dental ceramics, a special attention has been paid in discriminating their strength distributions. In this paper, three versatile functions, involving normal, log-normal and Weibull distributions, are applied to the analysis of ten strength data sets of dental ceramics with different compositions and the results are compared in terms of the Akaike information criterion and the Anderson-Darling test. It reveals that various microstructures and compositions in the investigated dental ceramics cause their strength distributions deviated from the Weibull distribution. The influence of microstructure induced fracture properties (multiple-modal flaw size distribution, R-curve behavior and subcritical crack growth) on strength distributions is discussed.

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“…Weibull statistics [1] has been widely employed to model the variability in the fracture strength of brittle ceramics [2][3][4][5][6][7][8]. In general, a two-parameter form of the Weibull function is adopted to give the cumulative failure probability, P, of a component or specimen at a given applied stress, , as [2]:…”

Section: Introductionmentioning

confidence: 99%

Determination of the Weibull parameters from the mean value and the coefficient of variation of the measured strength for brittle ceramics

Deng

Jiang

2017

J Adv Ceram

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Accurate estimation of Weibull parameters is an important issue for the characterization of the strength variability of brittle ceramics with Weibull statistics. In this paper, a simple method was established for the determination of the Weibull parameters, Weibull modulus m and scale parameter 0  , based on Monte Carlo simulation. It was shown that an unbiased estimation for Weibull modulus can be yielded directly from the coefficient of variation of the considered strength sample. Furthermore, using the yielded Weibull estimator and the mean value of the strength in the considered sample, the scale parameter 0  can also be estimated accurately.

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Fracture statistics of ceramics – Weibull statistics and deviations from Weibull statistics

Cited by 254 publications

References 19 publications

The influence of microstructure on the fracture statistics of polycrystalline diamond and polycrystalline cubic boron nitride

The influence of microstructure on the fracture statistics of polycrystalline diamond and polycrystalline cubic boron nitride

Fracture statistics of dental ceramics: Discrimination of strength distributions

Determination of the Weibull parameters from the mean value and the coefficient of variation of the measured strength for brittle ceramics

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