A general strength distribution function for brittle materials

Dänzer, Robert

doi:10.1016/0955-2219(92)90021-5

Cited by 209 publications

(99 citation statements)

References 19 publications

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“…where P(σ, V) is the cumulative failure probability of a ceramic component due to flaws, V is the volume of the component, V 0 is the unit volume, σ is the uniaxial applied stress, m is the M a n u s c r i p t 6 Weibull modulus which describes the scatter of strength, and σ 0 is the characteristic stress at which the failure probability is 63.2% for a specimen with V = V 0 . For a set of nominally identical samples (i.e., V = V 0 ), the cumulative failure probability is…”

Section: Distribution Functionsmentioning

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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Section: Distribution Functionsmentioning

confidence: 99%

“…Thus, in the design of dental ceramics, a probabilistic method is recommended [4][5][6]. Here, strength also depends on the stressed area or volume of the material because a larger area or volume increases the probability of existence of a critical flaw [7,8].…”

Section: Introductionmentioning

confidence: 99%

Fracture statistics of dental ceramics: Discrimination of strength distributions

Nohut

2012

Ceramics International

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“…4 stress equal to or lower than a given value, according to Weibull statistics [21,22]. The probability of failure increases with the magnitude of the load (i.e.…”

Section: Accepted Manuscriptmentioning

confidence: 99%

Influence of temperature on the biaxial strength of cemented carbides with different microstructures

Chicardi

Bermejo

Gotor

et al. 2018

International Journal of Refractory Metals and Hard Materials

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Abstract. The effect of the temperature on the mechanical strength of WC-Co cemented carbides with different microstructures (grain size and binder content) was evaluated. Biaxial flexural tests were performed on three cemented carbide grades at 600°C using the ball-on-three-balls (B3B) method. Results were interpreted by Weibull statistics and compared to biaxial strength results at room temperature. A detailed fractographic analysis, supported by Linear Elastic Fracture Mechanics, was performed to differentiate the nature and size of critical defects and the mechanism responsible for the fracture. A significant decrease in the mechanical strength (around 30%) was observed at 600ºC for all grades of cemented carbides. This fact was ascribed to the change in the critical flaw population from sub-surface (at room temperature) to surface defects, associated with the selective oxidation of Co. Additionally, an estimation of the fracture toughness at 600°C was attempted for the three cemented carbides, based upon the B3B strength results, the corresponding number of the tested specimens fragments and the macroscopic area of the B3B fracture surfaces. The fracture toughness was not ACCEPTED MANUSCRIPT A C C E P T E D M A N U S C R I P T2 affected by the temperature, at least up to 600ºC. In addition, the good agreement with the Single Edge Notch Beam toughness data suggests the possibility of employing this approach for fracture toughness evaluation of brittle materials under different testing conditions.

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“…Various derivations of the strength distribution function for a brittle solid are offered by e.g. Freudenthal (1968), Matthews et al (1976), Batdorf and Heinisch (1978), Evans and Jones (1978) and Danzer (1992). In general, the derivation is based on a subdivision of the stressed solid into regions.…”

Section: Introductionmentioning

confidence: 99%

A numerical method for analysis of fracture statistics of glass and simulations of a double ring bending test

Kinsella

Persson

2018

Glass Struct Eng

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The results from a new numerical method for simulating the strength and fracture locations of small glass specimens subjected to double ring bending are compared with experimental data. The method implements the weakest-link principle while assuming the existence of Griffith flaws. A Weibull distribution for the strength is simulated based on a single population of Pareto distributed crack sizes. The effect of using different fracture criteria is investigated. An alternative distribution is simulated based on two populations of flaws. This distribution models the apparent bimodality in the empirical data set. The numerical method is dependent on a representation of the surface flaws condition in glass. As new techniques become available for examining the surface characteristics, this numerical method is promising as a means for modelling the strength better than current methods do.

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A general strength distribution function for brittle materials

Cited by 209 publications

References 19 publications

Fracture statistics of dental ceramics: Discrimination of strength distributions

Fracture statistics of dental ceramics: Discrimination of strength distributions

Influence of temperature on the biaxial strength of cemented carbides with different microstructures

A numerical method for analysis of fracture statistics of glass and simulations of a double ring bending test

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