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A generalized weakest-link model for size effect on strength of quasi-brittle materials

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Abstract

The work contributes to the statistical approach to unitedly characterize the random variation and size effect of brittle fracture strength of materials. Current practices rely on the conventional Weibull statistics and more recently on the weakest-link statistical model conforming to the uniform spatial distribution of microcracks. Based on the understanding that the weakest-link postulate is built on the mutual independence of microcracks and is not necessarily bounded to the uniform spatial distribution of microcracks, this work develops a generic weakest-link statistical formulation pertaining to a power-law spatial distribution of mutually non-interactive microcracks to synchronize the random variation and size effect of brittle fracture strength. The formulation encompasses both Weibull statistics and the uniform spatial distribution law-based weakest-link model as its subordinate members. A resultant master curve behavior between a compound parameter and the nominal fracture strength is identified for size scaling of strength and is validated by the strength data of a wide spectrum of quasi-brittle materials including wood, concrete, coal, gamma titanium aluminum alloy, nuclear-grade graphite and aluminum foam on geometrically self-similar specimens under same loading conditions.

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Acknowledgement

The author’s interest in statistical modeling of fracture was initiated due to an earlier research stay in the Institute of Ferrous Metallurgy (IEHK) of RWTH Aachen University. The author gratefully acknowledges Prof. Winfried Dahl and Prof. Wolfgang Bleck for many valuable discussions and the Alexander von Humboldt Foundation for the financial support. Dr. Clovis Gonzatti of Department of Mineralogy and Petrography of the Federal University of Rio Grande do Sul (Brazil) kindly offered the author his tabulated experimental data of coal strength relating to his work published in Int J Min Sci Technol (as reference 27 of present work). The suggestions from anonymous reviewers on improving the readability and further evaluating the proposed model under heterogeneous multiaxial loading conditions are greatly appreciated.

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  1. Wei-Sheng Lei

    Present address: Applied Materials, Inc, 974 East Arques Avenue, Sunnyvale, CA, 94085, USA

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    Lei, WS. A generalized weakest-link model for size effect on strength of quasi-brittle materials. J Mater Sci 53, 1227–1245 (2018). https://doi.org/10.1007/s10853-017-1574-8

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