A Statistical Theory for the Fracture of Brittle Structures Subjected to Nonuniform Polyaxial Stresses

Batdorf, S. B.; Crose, James G.

doi:10.1115/1.3423310

Cited by 292 publications

(118 citation statements)

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“…Finally, elemental failure is assumed to occur independently, meaning without mechanical interaction between elements, and with equal probability. Material failure is thus characterized by unstable catastrophic flaw propagation throughout the bulk of the solid, independently of the strength of the other elements encountered on the crack path [Batdorf and Crose, 1974;Batdorf and Heinisch, 1978;Bazant et al, 1991;Chao and Shetty, 1990;Lamon, 1988;Matthews et al, 1976;Quinn and Morrell, 1991;Scholten, 1993].…”

Section: Background On Weibull Weakest Link Theorymentioning

confidence: 99%

Failure behavior of single sand grains: Theory versus experiment

et al. 2011

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[1] Grain-scale brittle fracture and grain rearrangement play an important role in controlling the compaction behavior of reservoir rocks during the early stages of burial. Therefore, the understanding of single-grain failure is important. We performed constant displacement rate crushing tests carried out on selected, well-rounded, single sand grains and on randomly sampled grains from different grain size (d) batches of pure quartz sand. Applying a Hertzian fracture mechanics model for grain crushing, the critical load at failure (F c ) data obtained for the selected grains were converted into an accurate estimate of the size of flaws associated with failure (c f ). Similarly, the distributed F c data obtained from the different batch samples were converted into distributions of grain failure stress. Weibull weakest link theory could not explain the observed grain failure behavior. On the contrary, the Hertzian grain failure criterion enabled the conversion of the distributed F c data, for the batch samples, into distributions of c f , assuming spherical grains, or of "effective" radius of curvature (r g ), characterizing contact surface asperities in the case of nonspherical grains. In contrast to the model of Zhang et al. (1990), our work shows that there is no clear physical basis for a grain size dependence of c f . However, since roundness data for dune sands exhibit a similar relation between r g and d, as seen in our grain size batches, it is inferred that the Hertzian fracture mechanics model assuming nonspherical grains with a distributed r g is the most physically reasonable model for grain failure.

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Section: Background On Weibull Weakest Link Theorymentioning

confidence: 99%

Failure behavior of single sand grains: Theory versus experiment

et al. 2011

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“…But these tests were made on fine-grained ceramics (with grain size 20e30 mm), for which the deterministic size effect is, at normal laboratory scale, nil and only the Weibull statistical size effect operates. These contrary results have been supported by Batdorf statistics (Batdorf and Crose 1974) according to which the biaxial tension gives a higher failure probability than the uniaxial tension.…”

Section: Comparison With the Size Effect On Uniaxial Strength In Beammentioning

confidence: 34%

Fracture and Size Effect on Strength of Plain Concrete Disks under Biaxial Flexure Analyzed by Microplane Model M7

Kirane¹,

Bažant

2014

J. Eng. Mech.

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Abstract:The biaxial tensile strength of concrete (and ceramics) can be easily tested by flexure of unreinforced circular disks. A recent experimental study demonstrated that, similar to plain concrete beams, the flexural strength of disks suffers from a significant size effect. However, the experiments did not suffice to determine the size effect type conclusively. The purpose of this study is to use three-dimensional stochastic finite-element analysis to determine the size effect type and shed more light on the fracture behavior. A finite-element code using the microplane constitutive Model M7 is verified and calibrated by fitting the previously measured load-deflections curves and fracture patterns of disks of thicknesses 30, 48, and 75 mm, similar in three dimensions, and on flexure tests on four-point loaded beams. It is found that the deformability of the supports and their lifting and sliding has a large effect on the simulations, especially on the fracture pattern, and the strength and Young's modulus of concrete must be treated as autocorrelated random fields. The calibrated model is then used to analyze the size effect over a much broader range of disk thicknesses ranging from 20 to 192 mm. The disks are shown to exhibit the typical energetic size effect of Type I, that is, the disks fail (under load control) as soon as the macrofracture initiates from the smooth bottom surface. The curve of nominal strength versus size has a positive curvature and its deterministic part terminates with a horizontal asymptote. The fact that material randomness had to be introduced to fit the fracture patterns confirms that the Type 1 size effect must terminate at very large sizes with a Weibull statistical asymptote, although the disks analyzed are not large enough to discern it.

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“…This implies that for multiaxial stress, the probability of survival is simply the product of the probabilities of survival associated with each nonzero principal stress's acting alone. Batdorf (1974B) argued that the PIA is not appropriate because all nonzero principal stresses contribute to the normal stress experienced by a flaw not aligned with any principal axis.…”

Section: Design Methodology (Dm)mentioning

confidence: 99%

An assessment of the state of the art in predicting the failure of ceramics: Final report

Boulet¹

1988

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A Statistical Theory for the Fracture of Brittle Structures Subjected to Nonuniform Polyaxial Stresses

Cited by 292 publications

References 0 publications

Failure behavior of single sand grains: Theory versus experiment

Failure behavior of single sand grains: Theory versus experiment

Fracture and Size Effect on Strength of Plain Concrete Disks under Biaxial Flexure Analyzed by Microplane Model M7

An assessment of the state of the art in predicting the failure of ceramics: Final report

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