Abstract
We show how the theory of crystals with microstructure developed by Ortiz et al. can be applied to predict salient aspects of the body of experimental data compiled by Hughes et al. regarding lamellar dislocation structures in crystals deformed to large strains. The theory correctly predicts the statistics of misorientation angles and lamellar boundary spacings; and the scaling of the average misorientation and spacing with increasing macroscopic strain.
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References
Aubry, S. and Ortiz, M. (2002). The mechanics of deformation-induced subgrain dislocation structures in metallic crystals at large strains. submitted to Proceedings of the royal society of london.
Godfrey, A. and Hughes, D.A. (2000). Scaling of the spacing of deformation induced dislocation boundaries. Acta Materialia, 48(8), 1897–1905.
Hansen, N. and Hughes, D.A. (1995). Analysis of large dislocation populations in deformed metals. Physica Status Solidi A-Applied Research, 149(1), 155–172.
Hughes, D.A. and Hansen, N. (1997). High angle boundaries formed by grain subdivision mechanisms. Acta Materialia, 45(9), 3871–3886.
Hughes, D.A., Lui, A., Chrzan, D.C. and Hansen, N. (1997). Scaling of microstructural parameters: Misorientations of deformation induced boundaries. Acta Materialia, 45(1), 105–112.
Hughes, D.A. and Nix, W.D. (1989). Strain hardening and substructural evolution in ni-co solid solutions at large strains. Materials Science and Engineering, A122(2), 153–172.
Hughes, D.A. (2001). Deformation microstructures and selected examples of their recrystallization. Surface and Interface Analysis, 31(7), 560–570.
Hughes, D.A., Chrzan, D.C., Liu, Q. and Hansen, N. (1998). Scaling of misorientation angle distributions. Physical Review Letters, 81(21), 4664–4667.
Hughes, D.A. and Hansen, N. (1993). Microstructural evolution in nickel during rolling from intermediate to large strains. Metallurgical Transactions A-Physical Metallurgy and Materials Science, 24(9), 2021–2037.
Hughes, D.A. and Hansen, N. (1995). High-angle boundaries and orientation distributions at large strains. Scripta Metallurgica et Materialia, 33(2), 315–321.
Hughes, D.A. and Hansen, N. (1997). High angle boundaries formed by grain subdivision mechanisms. Acta Materialia, 45(9), 3871–3886.
Hughes, D.A. and Hansen, N. (2000). Microstructure and strength of nickel at large strains. Acta Materialia, 48(11), 2985–3004.
Hughes, D.A. and Hansen, N. (2001). Graded nanostructures produced by sliding and exhibiting universal behavior. Physical Review Letters, 8713(13), 5503—.
Hughes, D.A., Liu, Q., Chrzan, D.C. and Hansen, N. (1997). Scaling of microstructural parameters: Misorientations of deformation induced boundaries. Acta Materialia, 45(1), 105–112.
Kohn, R. V (1991). The relaxation of a double-well energy. Continuum Mechanics and Thermodynamics, 3, 193–236.
Kohn, R.V. and Strang, G. (1986). Optimal design and relaxation of variational problems i, ii, iii. Communication on Pure and Applied Mathematics, 39, 193–236, 139–182, 353–377.
Lee, E.H. (1969). Elastic-plastic deformation at finite strains. Journal ofApplied Mechanics, 36(1).
Okabe, A., Boots, B. and Sugihara, K. (1992). Spatial Tessellations: Concepts and Applications of Voronoi Diagrams. John Wiley and Sons. (Chapter 4).
Ortiz, M. and Repetto, E.A. (1999). Nonconvex energy minimization and dislocation structures in ductile single crystals. Journal of the Mechanics and Physics of Solids, 47(2), 397–462.
Ortiz, M., Repetto, E.A. and Stainier, L. (2000). A theory of subgrain dislocation structures. Journal of the Mechanics and Physics of Solids, 48(10), 2077–2114.
Rice, J.R. (1975). Continuum mechanics and thermodynamics of plasticity in relation to microscale deformation mechanisms. In Argon A. (Ed.), editor, Constitutive Equations in Plasticity, 23–79. MIT press, Cambridge (Mass).
Zimmer, W.H., Hecker, S.S., Rohr, D.L. and Murr, L.E. (1983). Large strain plastic deformation of commercially pure nickel. Metal Science, 17(4), 198–206.
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Aubry, S., Ortiz, M. (2003). Variational Methods in Non-Convex Plasticity. In: Miehe, C. (eds) IUTAM Symposium on Computational Mechanics of Solid Materials at Large Strains. Solid Mechanics and Its Applications, vol 108. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-0297-3_5
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DOI: https://doi.org/10.1007/978-94-017-0297-3_5
Publisher Name: Springer, Dordrecht
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