On the Statistical Theory of Fracture Location Combined with Competing Risk Theory

Matsuo, Yohtaro; Kitakami, Koichi

doi:10.1007/978-1-4615-7023-3_17

Cited by 13 publications

(5 citation statements)

References 10 publications

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“…This is supported by the results from many experiments, for example, the experiments on Si 3 N 4 ceramics performed by Matsuo and Kitakami (1986). Here, V e · (β 1 + 1) 2 represents half the volume of a rectangular specimen, and A e · (β 2 + 1) represents the controllable surface area of a specimen.…”

Section: Weibull Model For Fracture Strength and Locationmentioning

confidence: 55%

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Optimum Specimen Sizes and Sample Allocation for Estimating Weibull Shape Parameters for Two Competing Failure Modes

Suzuki

Nakamoto²,

Matsuo³

2010

Technometrics

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In a bending load test for brittle materials such as ceramics for spacecraft and aircraft, the stress varies over the region under tension. Therefore, a Weibull model with nonuniform stress over the test specimen is generally used. Moreover, economic factors constrain the sample size. To reduce the number of test specimens, the optimum sizes of the specimens and the optimum allocation of a given total number of samples to each size are proposed for achieving the most precise estimation of the Weibull shape parameter. To do this, we examined data on both fracture strength and location based on two competing failure modesinternal and surface cracks. We found that the recommended number of specimen sizes is two and that the larger the ratio of the volumes of the two sizes, the more precise the estimation. Moreover, having an equal number of specimens for each size results in precision close to that of the optimal allocation. Using two different specimen sizes with an equal number of specimens for each reduces both the number and total volume of specimens drastically under ASTM C-1161-94 (standard test for flexural strength of advanced ceramics) compared to a conventional "single specimen size test" without any reduction in the precision of the estimators.

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Section: Weibull Model For Fracture Strength and Locationmentioning

confidence: 55%

“…Matsuo and Kitakami (1985) used this theory to estimate the Weibull shape parameter on the basis of the fracture origin location. Matsuo and Kitakami (1985) used this theory to estimate the Weibull shape parameter on the basis of the fracture origin location.…”

Section: Introductionmentioning

confidence: 99%

Optimum Specimen Sizes and Sample Allocation for Estimating Weibull Shape Parameters for Two Competing Failure Modes

Suzuki

Nakamoto²,

Matsuo³

2010

Technometrics

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“…In the previous paper [1,2], the authors derived a general probability density function for brittle fracture with three random variables, namely, fracture strength m , / ) , , (…”

Section: Joint Probability Density Function For Fracture Involving Th...mentioning

confidence: 99%

“…Using this equation, one can derive any probability density function as a marginal, for instance, probability density function of fracture strength, fracture location, flaw-size and flaw-orientation [1,2] taking jointly with fracture mechanics.…”

Section: Joint Probability Density Function For Fracture Involving Th...mentioning

confidence: 99%

The Role of Strength, Fracture Cause, and Fracture Location Data on the Reliability Analysis of Ceramics

Matsuo

Shiota

Yasuda

et al. 2007

KEM

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Strength reliability of ceramics depends on accuracy of parameters involved in the probability distribution function for fracture. The parameters are usually estimated by use of strength data. However, one may have additional information in the experiment, such as fracture cause data, fracture location data, flaw-size data and flaw-orientation data. In this paper, we will incorporate these additional information in the parameter estimation to improve the accuracy of the reliability. A new theory on the asymptotic variances is presented.

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“…As advanced Weibull strength theory, several researchers have studied brittle fracture on the basis of the Weakest link theory assuming that there are different types of fracture origins, such as cracks, pores and grain boundaries, and they have derived an useful equation of so-called "the additive risk of rupture", a type of the competing risk model [26][27][28]. The advantage of this theory is possible to treat factwe origins, whereas the Weibull strength theory can only treat macroscopic statistical strength.…”

Section: Statistical Theory Of Brittle Fracture With Competing Risk Mmentioning

confidence: 99%

Proposal of the Prediction Method Using a Competing Risk Model on the Bending Strength of 2D-C/C Composites

Ishihara¹,

Hanawa²,

Sogabe³

et al. 2004

Journal of the Society of Materials Science, Japan

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Bending strength of a 2D-C/C composite was studied by experimental and theoretical approaches, and the prediction method on the basis of stress-related fracture mode was proposed. In the experiment, three-point bending test and observation of fracture surface were carried out to clarify the stress-related fracture modes. From the fracture surface observation, three kinds of fracture modes were identified: the compressive, tensile and the shear fracture modes. In the theoretical approach, the Weibull strength theory and the proposed method were applied to estimate the bending strength prediction. As a result of this study, it was found that the proposed method is applicable to the bending strength prediction of the 2-C/C composite, whereas the Weibull strength theory is not applicable.

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On the Statistical Theory of Fracture Location Combined with Competing Risk Theory

Cited by 13 publications

References 10 publications

Optimum Specimen Sizes and Sample Allocation for Estimating Weibull Shape Parameters for Two Competing Failure Modes

Optimum Specimen Sizes and Sample Allocation for Estimating Weibull Shape Parameters for Two Competing Failure Modes

The Role of Strength, Fracture Cause, and Fracture Location Data on the Reliability Analysis of Ceramics

Proposal of the Prediction Method Using a Competing Risk Model on the Bending Strength of 2D-C/C Composites

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