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Cosserat Modeling of Size Effects in Crystalline Solids

Published online by Cambridge University Press:  21 March 2011

Samuel Forest*
Affiliation:
Center des Matériaux / UMR 7633 Ecole des Mines de Paris / CNRS BP 87, 91003 Evry France. 91003, Evry France
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Abstract

The mechanics of generalized continua provides an efficient way of introducing intrinsic length scales into continuum models of materials. A Cosserat framework is presented here to descrine the mechanical behavior of crystalline solids. The first application deals with the problem of the stress field at a crak tip in Cosserat single crystals. It is shown that the strain localization patterns developping at the crack tip differ from the classical picture : the Cosserat continuum acts as a bifurcation mode selector, whereby kink bands arising in the classical framework disappear in generalized single crystal plasticity. The problem of a Cosserat elastic inclusion embedded in an infinite matrix is then considered to show that the stress state inside the inclusion depends on its absolute size lc. Two saturation regimes are observed : when the size R of the inclusion is much larger than a characteristic size of the medium, the classical Eshelby solution is recovered. When R is much small than the inclusion, a much higher stress is reached (for an inclusion stiffer than the matrix) that does not depend on the size any more. There is a transition regime for which the stress state is not homogeneous inside the inclusion. Similar regimes are obtained in the study of grain size effects in polycrystalline aggregates of Cosserat grains.

Type
Research Article
Copyright
Copyright © Materials Research Society 2001

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References

Refernces

1. Kröner, E., Kontinuumtheorie der Versetzungen und Eingenspannungen, Ergebnisse Der angewandten Mathematik, Vol. 5, Springer-Verlag, (1958).Google Scholar
2. Cuitino, A. M. and Oritiz, M., Modelling Simul. in Mater. Sci. Eng., 1, 225 (1993).Google Scholar
3. Dai, H. and Parks, D. M., Geometrically-necessary dislocation density and Scale-dependent crystal plasticity. In Proceeding of Plasticity '97, ed. Khan, A.S., pp. 1718. Neat press, Fulton, Marylandi, (1997).Google Scholar
4. Kröner, E., Mechanics of generalized continua, Proc. of the IUTAM-Symposium on the generalized Cosserat continuum and the continuum theory of dislocations with applications, Freudenstadt, Stuttgart, Springer-Verlag, (1997).Google Scholar
5. Eringen, A.C., Polar and non local field theories, in continuum Physicas, edited by Eringen, A.C, Volume IV, Academic Press, (1976).Google Scholar
6. Flect, N.A. and Hutchinson, J.W., Strains gradient plasticity. Advances in Applied Mechanics 33, 295 (1997).Google Scholar
7. Shu, J.Y. and Fleck, N.A., J. Mech. Phys. Solids, 47 297 (1999).Google Scholar
8. Forest, S., Gailletaud, G. and sievert, R., Arch. Mech., 49, 705 (1997).Google Scholar
9. Rice, J.R., Mechanics of Materials, 6, 317 (1987).Google Scholar
10. Forest, S., Acta Mater., 46, 3265 (1998). 1, 225 (1993).10.1016/S1359-6454(98)00012-3Google Scholar
11. Forest, S., Barbe, F. and Gailletaud, G., Int J. Solids Structures, 37, 7105(2000).Google Scholar
12. Forest, S., Boubidi, P., Sievert, R., Strain Localization Patterns at a Crack Tip in Generalized Single Crystal Plasticity, to appear in Scripta Materialia, (2000).Google Scholar
13. Giessen, E. van der, Cleveringa, H.H.M. and Needleman, A., Discrete Dislocation Plasticity and Crack Tip Fields in Single Crystals, Submitted (2000).Google Scholar
14. Forest, S., Dendievel, S. R., Canova, G.R., Estimating the overall properties of heterogeneous Cosserat materials, Modelling Simul. Mater. Sci. Eng., 7, 829 (1999).Google Scholar
15. Barbe, F., Cailletaud, G., Forest, S., Decker, L. and Jeulin, D., Intergrnular and intragranular behavior of polycrystalline aggregates, Parts I and II, to appear in Int. J. Plasticity (2001).10.1016/S0749-6419(00)00061-9Google Scholar
16. Parisot, R., Forest, S., Gourgues, A.–F., Pineau, A., A., , Computational Materials Science, 19, 189 (2001).Google Scholar
17. Ashby, M.F., The deformation of plastically non-homogeneous alloys, in Strengthening Methods in Crystals, edited by Kelly, A. and Nicholson, R.B., Applied Science Publishers, London, 137 (1971).Google Scholar
18. Forest, S., Sab, K., Ninth International Symposium on Continuum Models and Discrete Systems, CMDS9, ed. by Inan, E. and Markov, Z., World Scientific Publishing Company, 445 (1998).Google Scholar