1 Quasibrittle Size Effect: Problems and Progress
Abstract: Qualitatively proposed by Mariotte and mathematically formulated by Weibull, the statistical theory of size effect reigned supreme until the 1980s. However, beginning in 1976, a different, nonstatistical theory of size effect gradually emerged and was shown to be important for brittle hete...
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ftciteseerx:oai:CiteSeerX.psu:10.1.1.694.4600 2023-05-15T18:18:47+02:00 1 Quasibrittle Size Effect: Problems and Progress Zdeněk P. Bažant Jia-liang Le Qiang Yu The Pennsylvania State University CiteSeerX Archives application/pdf http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.694.4600 http://www.civil.northwestern.edu/people/bazant/PDFs/Papers/C72.pdf en eng http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.694.4600 http://www.civil.northwestern.edu/people/bazant/PDFs/Papers/C72.pdf Metadata may be used without restrictions as long as the oai identifier remains attached to it. http://www.civil.northwestern.edu/people/bazant/PDFs/Papers/C72.pdf text ftciteseerx 2016-01-08T18:34:03Z Abstract: Qualitatively proposed by Mariotte and mathematically formulated by Weibull, the statistical theory of size effect reigned supreme until the 1980s. However, beginning in 1976, a different, nonstatistical theory of size effect gradually emerged and was shown to be important for brittle heterogeneous materials, concisely termed “quasibrittle”, which include concrete, fiber composites, sea ice, rocks, stiff cohesive soils, snow slabs, foams, wood, paper, bone and many materials on micrometer scale. In these materials, the maximum load is attained only after the stable formation of either (1) a large fracture process zone (FPZ), with distributed cracking, or (2) a large crack. The lecture first reviews the sources of these type I and II size effects, consisting of the energy release associated with stress redistribution prior to maximum load, and combined in Type I size effect with the statistical weakest link model for a finite chain. Numerical simulation, requiring nonlocal and stochastic approaches, is discussed. The asymptotic matching approach (anchored through dimensional analysis) to the development of analytical laws for Type I and Type II quasibrittle size effects, is then outlined. It is explained that while in Type 2 material randomness affects only the variance and the tail of the cumulative distribution of RVE strength is unimportant, in Type I it also strongly (though not totally) affects the mean, and the far-left tail plays a major role. This role can be theoretically predicted by nano-fracture mechanics of cracks in the atomic lattice based on crack length dependence of the activation energy barriers for the metastable states of the free energy potential of the atomic lattice. Extensions to reentrant corners, time dependence, and cyclic loading are pointed out. Various structural applications, experimental evidence, and reinterpretation of some structural disasters are discussed. Finally, some important open problems are highlighted. Text Sea ice Unknown |
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Abstract: Qualitatively proposed by Mariotte and mathematically formulated by Weibull, the statistical theory of size effect reigned supreme until the 1980s. However, beginning in 1976, a different, nonstatistical theory of size effect gradually emerged and was shown to be important for brittle heterogeneous materials, concisely termed “quasibrittle”, which include concrete, fiber composites, sea ice, rocks, stiff cohesive soils, snow slabs, foams, wood, paper, bone and many materials on micrometer scale. In these materials, the maximum load is attained only after the stable formation of either (1) a large fracture process zone (FPZ), with distributed cracking, or (2) a large crack. The lecture first reviews the sources of these type I and II size effects, consisting of the energy release associated with stress redistribution prior to maximum load, and combined in Type I size effect with the statistical weakest link model for a finite chain. Numerical simulation, requiring nonlocal and stochastic approaches, is discussed. The asymptotic matching approach (anchored through dimensional analysis) to the development of analytical laws for Type I and Type II quasibrittle size effects, is then outlined. It is explained that while in Type 2 material randomness affects only the variance and the tail of the cumulative distribution of RVE strength is unimportant, in Type I it also strongly (though not totally) affects the mean, and the far-left tail plays a major role. This role can be theoretically predicted by nano-fracture mechanics of cracks in the atomic lattice based on crack length dependence of the activation energy barriers for the metastable states of the free energy potential of the atomic lattice. Extensions to reentrant corners, time dependence, and cyclic loading are pointed out. Various structural applications, experimental evidence, and reinterpretation of some structural disasters are discussed. Finally, some important open problems are highlighted. |
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The Pennsylvania State University CiteSeerX Archives |
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Zdeněk P. Bažant Jia-liang Le Qiang Yu |
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Zdeněk P. Bažant Jia-liang Le Qiang Yu 1 Quasibrittle Size Effect: Problems and Progress |
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Zdeněk P. Bažant Jia-liang Le Qiang Yu |
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Zdeněk P. Bažant |
title |
1 Quasibrittle Size Effect: Problems and Progress |
title_short |
1 Quasibrittle Size Effect: Problems and Progress |
title_full |
1 Quasibrittle Size Effect: Problems and Progress |
title_fullStr |
1 Quasibrittle Size Effect: Problems and Progress |
title_full_unstemmed |
1 Quasibrittle Size Effect: Problems and Progress |
title_sort |
1 quasibrittle size effect: problems and progress |
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http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.694.4600 http://www.civil.northwestern.edu/people/bazant/PDFs/Papers/C72.pdf |
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http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.694.4600 http://www.civil.northwestern.edu/people/bazant/PDFs/Papers/C72.pdf |
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