The random polycrystalline microstructure of microbeams necessitates a reexamination of the crack driving force G stemming from the Griffith fracture criterion. It is found that, in the case of dead-load conditions, G computed by straightforward averaging of the spatially random elastic modulus E is lower than that obtained by correct ensemble averaging of the stored elastic energy. This result holds for both Euler-Bernoulli and Timoshenko models of micro-beams. However, under fixed-grip conditions G is to be computed by a direct ensemble averaging of E. It turns out that these two cases provide bounds on G under mixed loading. Furthermore, crack stability is shown to involve a stochastic competition between potential and surface energies, whose weak randomness leads to a relatively stronger randomness of the critical crack length.
Fracture of Brittle Microbeams
Contributed by the Applied Mechanics Division of THE AMERICAN SOCIETY OF MECHANICAL ENGINEERS for publication in the ASME JOURNAL OF APPLIED MECHANICS. Manuscript received by the ASME Applied Mechanics Division, Dec. 16, 2002; final revision, Aug. 1, 2003. Associate Editor: M.-J. Pindera.
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Ostoja-Starzewski , M. (June 22, 2004). "Fracture of Brittle Microbeams ." ASME. J. Appl. Mech. May 2004; 71(3): 424–427. https://doi.org/10.1115/1.1651091
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