Random polycrystals of grains containing cracks: Model ofquasistatic elastic behavior for fractured systems

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A model study on fractured systems was performed using aconcept that treats isotropic cracked systems as ensembles of crackedgrains by analogy to isotropic polycrystalline elastic media. Theapproach has two advantages: (a) Averaging performed is ensembleaveraging, thus avoiding the criticism legitimately leveled at mosteffective medium theories of quasistatic elastic behavior for crackedmedia based on volume concentrations of inclusions. Since crack effectsare largely independent of the volume they occupy in the composite, sucha non-volume-based method offers an appealingly simple modelingalternative. (b) The second advantage is that both polycrystals andfractured media are stiffer than might otherwise be expected, due tonatural bridging effects of ... continued below

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Berryman, James G. & Grechka, Vladimir July 8, 2006.

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A model study on fractured systems was performed using aconcept that treats isotropic cracked systems as ensembles of crackedgrains by analogy to isotropic polycrystalline elastic media. Theapproach has two advantages: (a) Averaging performed is ensembleaveraging, thus avoiding the criticism legitimately leveled at mosteffective medium theories of quasistatic elastic behavior for crackedmedia based on volume concentrations of inclusions. Since crack effectsare largely independent of the volume they occupy in the composite, sucha non-volume-based method offers an appealingly simple modelingalternative. (b) The second advantage is that both polycrystals andfractured media are stiffer than might otherwise be expected, due tonatural bridging effects of the strong components. These same effectshave also often been interpreted as crack-crack screening inhigh-crack-density fractured media, but there is no inherent conflictbetween these two interpretations of this phenomenon. Results of thestudy are somewhat mixed. The spread in elastic constants observed in aset of numerical experiments is found to be very comparable to the spreadin values contained between the Reuss and Voigt bounds for thepolycrystal model. However, computed Hashin-Shtrikman bounds are much tootight to be in agreement with the numerical data, showing thatpolycrystals of cracked grains tend to violate some implicit assumptionsof the Hashin-Shtrikman bounding approach. However, the self-consistentestimates obtained for the random polycrystal model are nevertheless verygood estimators of the observed average behavior.

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  • Journal Name: Journal of Applied Physics; Journal Volume: 100; Journal Issue: 11; Related Information: Journal Publication Date: 12/01/2006

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  • Report No.: LBNL--61135
  • Grant Number: DE-AC02-05CH11231
  • DOI: 10.1063/1.2399891 | External Link
  • Office of Scientific & Technical Information Report Number: 920258
  • Archival Resource Key: ark:/67531/metadc897902

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  • July 8, 2006

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  • Sept. 27, 2016, 1:39 a.m.

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  • Oct. 31, 2016, 3:55 p.m.

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Berryman, James G. & Grechka, Vladimir. Random polycrystals of grains containing cracks: Model ofquasistatic elastic behavior for fractured systems, article, July 8, 2006; Berkeley, California. (digital.library.unt.edu/ark:/67531/metadc897902/: accessed December 11, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.