Statistical Theory for Predicting the Failure of Brittle Materials

She, Sixuan; Landes, J. D.; Boulet, J. A. M.; Stoneking, J.E.

doi:10.1115/1.2897177

Cited by 14 publications

(12 citation statements)

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“…Under tensile strain, the probability that microcracks coalesce to a crack of length > ℓ cr is higher for a longer conductor. This length dependence of the rupture strain is similar to the often-observed size dependence of the statistical strength of brittle materials [16,17]. …”

supporting

confidence: 77%

Size-dependent rupture strain of elastically stretchable metal conductors

Graudejus

Jia

et al. 2012

Scripta Materialia

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Experiments show that the rupture strain of gold conductors on elastomers decreases as the conductors are made long and narrow. Rupture is caused by the irreversible coalescence of microcracks into one long crack. A mechanics model identifies a critical crack length ℓcr, above which the long crack propagates across the entire conductor width. ℓcr depends on the fracture toughness of the gold film and the width of the conductor. The model provides guidance for the design of highly stretchable conductors.

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supporting

confidence: 77%

Size-dependent rupture strain of elastically stretchable metal conductors

Graudejus

Jia

et al. 2012

Scripta Materialia

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“…A general statistical model for fracture of brittle materials was developed and presented in [1]. This model was based on a fracture criteria for a microcrack under any given stress state.…”

Section: General Model For Brittle Materialsmentioning

confidence: 99%

“…Applying critical strain energy release rate G as a fracture criterion for microcracks, the general formula for the failure probability of brittle materials given in [1] is…”

Section: Applying the Statistical Model To Graphitementioning

confidence: 99%

“…Thus, a general statistical theory for predicting the failure of brittle materials could be applied to analyze the failure of graphite. In previous work, a general statistical theory for predicting the failure of brittle materials was developed [1]. The theory assumes that there is a distribution of penny-shaped microcracks in materials and that propagation of one microcrack will cause the global failure of the brittle material.…”

Section: Introductionmentioning

confidence: 99%

“…Therefore, the general model of [1] is a good candidate model to apply to graphite failure. Although other models for the failure of graphite, such as the Rose and Tucker [2,3] model, have been suggested, the model described in this report is more general because it can be used in a complex three-dimensional stress state for which the Rose/Tucker model is difficult to apply.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Statistical analysis of fracture in graphite

She

Landes

1993

Int J Fract

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A statistical model is proposed to study the fracture of graphite. This model, based on a more general one proposed by She et al., uses a local fracture criterion for a microcrack, a distribution function for microcracks and the weakest link principle to predict failure probability as a function of applied loading and distribution of microcracks. The model considers the effect of the three-dimensional stress state and therefore gives a general representation of both the effects of complex loading and microcrack distribution. The inputs to the model can be determined by either studying the microstructural features of the graphite or by choosing inputs to make the model prediction fit a set of experimental results. The latter method is used to apply the model to failure results of Rose and Tucker. One set of results is used to calibrate the model which is then applied to predict the failure behavior of a second set of experimental results. Finally, the effect of the various input variables on failure probability is studied first by considering a graphical representative of failure probability as a function of input variables and second by writing the equations in terms of nondimensional variables.

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Probabilistic reliability of thermoplastic piping networks and maintenance strategy choice using Weibull distribution

Farajian

Rhanim

Mohammed

et al. 2020

Mat Design & Process Comms

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In this paper, deterministic and probabilistic approaches of failure modeling of high‐density polyethylene (HDPE) pipes have been introduced. They are based on determining the experimental parameters of HDPE through burst and tensile tests. In fact, reliability criteria have been determined through 11 damages models, and the critical life fraction have been reached for both of the approaches. Besides, the mean time between failures (MTBF), the probability density, and the failure rate have been defined for each loading level by using the Weibull parameters. The comparison of the failure rate bathtub curves to those obtained through the damage‐reliability curves present a fast tool to choose accurately the maintenance decision to undertake the sudden failures' occurrence and oblige the preventive measures instead of the corrective ones. The reliability prediction through a simplified equation of MTBF have been developed. The introduced approaches can be applied to all the thermoplastic pipes.

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Statistical Theory for Predicting the Failure of Brittle Materials

Cited by 14 publications

References 0 publications

Size-dependent rupture strain of elastically stretchable metal conductors

Size-dependent rupture strain of elastically stretchable metal conductors

Statistical analysis of fracture in graphite

Probabilistic reliability of thermoplastic piping networks and maintenance strategy choice using Weibull distribution

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