Deriving the primary cumulative distribution function of fracture stress for brittle materials from 3- and 4-point bending tests

Przybilla, Constanze; Fernández‐Canteli, Alfonso; Castillo, Enrique

doi:10.1016/j.jeurceramsoc.2010.11.007

Cited by 38 publications

(18 citation statements)

References 7 publications

(3 reference statements)

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“…25 Alternatively, Schula et al 26 suggested the use of the log-normal distribution. Questions have been raised about the existence of a threshold for the glass strength, 22,27 presenting arguments in support of this conjecture. 28 Following this rationale, the use of a threeparameter 22,27 or left-truncated Weibull distributions 28 have been indicated as a possibility.…”

Section: The Assumed Statistical Distributionsmentioning

confidence: 99%

Statistical interference of material strength and surface prestress in heat‐treated glass

Pisano

Royer-Carfagni

2016

J Am Ceram Soc

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It is customary to assume that the characteristic design value for heat‐treated glass is represented by the sum of the characteristic values of the annealed glass strength and of the heat‐induced surface prestress, even though experiments have provided evidence that the resulting strength may be much higher. Here, we investigate the statistical interference between an assumed two‐parameter Weibull distribution for the annealed glass strength and a Gaussian distribution for the surface prestress. We show how the compound distribution confirms the experimental findings and, in particular, that the type of stress induced by the applied loads, ie, uniaxial vs biaxial, has an important role. This effect, which is more relevant for “weak” than for “strong” glasses, is the mechanical counterpart of the well‐known principle of diversification of investments in economy, and leads to a critical consideration of the design approach commonly suggested by structural standards.

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Section: The Assumed Statistical Distributionsmentioning

confidence: 99%

Statistical interference of material strength and surface prestress in heat‐treated glass

Pisano

Royer-Carfagni

2016

J Am Ceram Soc

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“…Over recent years, probabilistic failure models have been developed that take into account the statistical scatter of concrete strength in the estimation of the number of fatigue cycles [28,[60][61][62][63].…”

Section: Probabilistic Modelsmentioning

confidence: 99%

High-Performance Concrete and Fiber-Reinforced High- Performance Concrete under Fatigue Efforts

Vicente¹,

Mínguez²,

Martínez³

et al. 2016

High Performance Concrete Technology and Applications

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Fatigue is the process of mechanical degradation of a material, which leads to its collapse. Repeated load applications with a maximum value lower than the one that provokes the static failure of the material, causes internal damage in the material that, progressively, reduces its mechanical capacity until it finally collapses. The increasingly widespread use of high-strength concretes permits the construction of more lightweight structures. This implies that the variable loads (which are the causes of fatigue) represent an ever larger percentage of the total load. In consequence, fatigue is an increasingly important factor in concrete structures. In some cases, it even begins to be the dimensioning load of the structure. In addition, the presence of fibers within the concrete modifies the fatigue response of the concrete. In this chapter, the classic theory of fatigue is presented in detail and the most recent developments in the study of concrete fatigue are discussed.

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“…Therefore, if the optimum is achieved with a zero value of threshold stress, this set will be fitted to a two-parameter Weibull distribution. The Weibull cdf was originally proposed to characterize the probability of failure of a uni-axially and uniformly tensioned materials (Figure 7) [21,22]. It assumes that the random nature of the spatial distribution of defects implies that the strength will decrease with an increase of the stressed area because the probability of having a critical defect will also increase.…”

Section: Statistical Evaluationmentioning

confidence: 99%

On the mechanical strength of monocrystalline, multicrystalline and quasi‐monocrystalline silicon wafers: a four‐line bending test study

Barredo¹,

Parra

Guerrero

et al. 2013

Progress in Photovoltaics

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Quasi-monocrystalline silicon wafers have appeared as a critical innovation in the PV industry, joining the most favorable characteristics of the conventional substrates: the higher solar cell efficiencies of monocrystalline Czochralski-Si (Cz-Si) wafers and the lower cost and the full square-shape of the multicrystalline ones. However, the quasi-monocrystalline ingot growth can lead to a different defect structure than the typical Cz-Si process. Thus, the properties of the brand new quasimonocrystalline wafers, based on low and high crystal defect densities, have been for the first time studied from a mechanical point of view, comparing their strength with that of both Cz-Si monocrystalline and typical multicrystalline materials. The study has been carried out employing the four line bending test and simulating them by means of FE models. For the analysis, failure stresses were fitted to a three-parameter Weibull distribution. High mechanical strength was found in all the cases. However, the quasi-monocrystalline wafers characterized by large density of bulk defects, due to the noticeable density of extended defects, showed lower fracture tensions.

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Deriving the primary cumulative distribution function of fracture stress for brittle materials from 3- and 4-point bending tests

Cited by 38 publications

References 7 publications

Statistical interference of material strength and surface prestress in heat‐treated glass

Statistical interference of material strength and surface prestress in heat‐treated glass

High-Performance Concrete and Fiber-Reinforced High- Performance Concrete under Fatigue Efforts

On the mechanical strength of monocrystalline, multicrystalline and quasi‐monocrystalline silicon wafers: a four‐line bending test study

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