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BRIEF NOTES

Fracture of Brittle Microbeams

[+] Author and Article Information
M. Ostoja-Starzewski

Department of Mechanical Engineering, McGill University, 817 Sherbrooke Street West, Montreal, PQ H3A 2K6, Canadae-mail: martin.ostoja@mcgill.ca Fellow ASME

J. Appl. Mech 71(3), 424-427 (Jun 22, 2004) (4 pages) doi:10.1115/1.1651091 History: Received December 16, 2002; Revised August 01, 2003; Online June 22, 2004
Copyright © 2004 by ASME
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References

Griffith,  A. A., 1921, “The Phenomena of Rupture and Flow in Solids,” Philos. Trans. R. Soc. London, Ser. A, 221, pp. 163–198.
Gdoutos, E. E., 1993, Fracture Mechanics: An Introduction, Kluwer, Dordrecht, The Netherlands.
Chudnovsky,  A., and Kunin,  B., 1987, “A Probabilistic Model of Brittle Crack Formation,” J. Appl. Phys., 62(10), pp. 4124–4129.
Kunin,  B., 1994, “A Stochastic Model for Slow Crack Growth in Brittle Materials,” Appl. Mech. Rev., 47, pp. 175–183.
Altus,  E., 2001, “Statistical Modeling of Heterogeneous Micro-Beams,” Int. J. Solids Struct., 38(34–35), pp. 5915–5934.
Beran,  M. J., 1998, “The Use of Classical Beam Theory for Micro-Beams Composed of Crystals,” Int. J. Solids Struct., 35(19), pp. 2407–2412.
Ostoja-Starzewski, M., 2001, “Mechanics of Random Materials: Stochastics, Scale Effects, and Computation,” Mechanics of Random and Multiscale Microstructures, D. Jeulin and M. Ostoja-Starzewski, eds., CISM Courses and Lectures 430 , Springer, Wien, pp. 93–161.
Rudin, W., 1974, Real and Complex Analysis, McGraw-Hill, New York.
Ostoja-Starzewski,  M., 2002, “Microstructural Randomness Versus Representative Volume Element in Thermomechanics,” ASME J. Appl. Mech., 69, pp. 25–35.

Figures

Grahic Jump Location
Fracture of a microbeam of thickness L off a substrate. A statistical volume element (SVE) imposed by the random microheterogeneous structure characterized by scale d is shown.
Grahic Jump Location
Potential energy Π(〈1/E〉) (thick line) and its scatter shown by a parabolic wedge (thin lines), summed with the surface energy 〈Γ〉=2a〈γ〉 (thick line) and its scatter shown by a straight wedge (thin lines), results in Π(〈1/E〉)+〈Γ〉 (thick line) and having scatter shown by a wider parabolic wedge (thin lines). Dashed region indicates the range of a critical crack length ac(E(ω)), a random variable.

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