Relation between defect position in bending test and strength variance

Schultrich, B.; Fahrmann, Michael G.

doi:10.1007/bf00719622

Cited by 6 publications

(2 citation statements)

References 2 publications

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“…On the other hand, a material with a large scatter in flaw size, and hence a low Weibull modulus, has a greater dispersion of fracture locations. Examples have been shown previously [53][54][55]. An unusual concentration of primary fracture origins near an inner loading point in four-point bending may indicate a fixture misalignment.…”

Section: Break Locationsmentioning

confidence: 70%

Flexural Strength of Ceramic and Glass Rods

Quinn

Sparenberg

Koshy

et al. 2009

Journal of Testing and Evaluation

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Flexural testing is the most common method used to measure the uniaxial tensile strength of ceramics and glasses. Although standard test methods have been developed for rectangular specimens, cylindrical rod specimens may be preferred in many cases. This paper summarizes how rods have been tested in the past, identifies key experimental errors and remedies, and serves as the foundation for a new standard test method for ceramics and glasses.

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Section: Break Locationsmentioning

confidence: 70%

Flexural Strength of Ceramic and Glass Rods

Quinn

Sparenberg

Koshy

et al. 2009

Journal of Testing and Evaluation

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show abstract

“…Using the Weibull model, the probability of fracture of the beam at maximum stress, o-, is given by F(a) = 1 -exp --jv d (2) where V = lbh/2, ao is a scaling parameter and m is the Weibull modulus. y <~ h/2, 0 ~ z ~ b, and o.…”

mentioning

confidence: 99%

Estimation of the Weibull modulus from bending tests using both the fracture position and the failure stress

Trustrum

1987

J Mater Sci Lett

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In the three-point bending of a beam of width, b, height, h, and length, l, subject to a central load, P, the tensile stress, s, at distance, x, from the nearest end point and depth, y, from the central axis is 4axy s = (1) lh where 0 ~ x ~ 1/2, 0 <. y <~ h/2, 0 ~ z ~ b, and o. = 3Pl/2bh 2 is the maximum stress attained. For h/2 <~ y < 0, the stress is compressive, so failure is unlikely to occur. Using the Weibull model, the probability of fracture of the beam at maximum stress, o-, is given by F(a) = 1 -exp --jv d (2) where V = lbh/2, ao is a scaling parameter and m is the Weibull modulus. Oh and Finnie [1] and Schultrich and Fahrmann [2] have shown that the joint probability density of failure at maximum stress, a, and position (x, y, z) is f ( a , x , y , zl = [1 -F ( a ) ]~ (3) where 0 [1 ( s '~ m ]is the probability that failure occurs in d V as the maximum stress is increased from o-to a + do-and [1 -F(a)] is the probability that in the remaining volume no failure occurs before a to first order in dV. On substituting for s from Equation 1 and evaluating the integral in Equation 2

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

Matsuo

Kitakami

1986

Fracture Mechanics of Ceramics

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Relation between defect position in bending test and strength variance

Cited by 6 publications

References 2 publications

Flexural Strength of Ceramic and Glass Rods

Flexural Strength of Ceramic and Glass Rods

Estimation of the Weibull modulus from bending tests using both the fracture position and the failure stress

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

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