Analytical and numerical investigation of non-uniform straining and subgrain initiation in bicrystals in channel die compression

Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences

Volumn 355, Issue 1730, 1997, Pages 1905-1943

  Wu, S C ^a,b   Havner, K S ^a  

^a North Carolina State University   (United States)

^b Science Based Industrial Park   (Taiwan)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 3042869075     PISSN: 1364503X     EISSN: None     Source Type: Journal    
DOI: 10.1098/rsta.1997.0095     Document Type: Article

References (29)

1. Bay, B., Hansen, N., Hughes, D. A. & Kuhlmann-Wilsdorf, D. 1992 Evolution of f.c.c. deformation structures in polyslip. Acta. Metall. Mater. 40, 205-219.
2. Bay, B., Hansen, N. & Kuhlmann-Wilsdorf, D. 1989 Deformation structures in lightly rolled pure aluminium. Mater. Sci. Engng A 113, 385-397.
3. Chester, C. R. 1972 Techniques in partial differential equations. New York: McGraw-Hill.
4. Chidambarrao, D. & Havner, K. S. 1988a Finite deformation analysis of f.c.c. crystals in (110)(11̄2̄)(1̄11̄) channel die compression. Int. J. Plasticity 4, 1-27.
5. Chidambarrao, D. & Havner, K. S. 1988b On finite deformation of f.c.c. crystals in (110) channel die compression. J. Mech. Phys. Solids 36, 285-315.
6. Chin, G. Y., Nesbitt, E. A. & Williams, A. J. 1960 Anisotropy of strength in single crystals under plane strain compression. Acta Metall. 14, 467-476.
7. Driver, J. H. & Skalli, A. 1982 L'essai de compression plane de monocristaux encastres: methode d'étude du comportement d'un cristal soumis à une deformation plastique imposée. Rev. Phys. Appl. 17, 447-451.
8. Fuh, S. 1989 Applications of a postulate of minimum plastic spin in crystal mechanics. Ph.D. thesis, North Carolina State University.
9. Fuh, S. & Havner, K. S. 1986 On uniqueness of multiple-slip solutions in constrained and unconstrained f.c.c. crystal deformation problems. Int. J. Plasticity 2, 329-345.
10. Fuh, S. & Havner, K. S. 1989 A theory of minimum plastic spin in crystal methanics. Proc. R. Soc. Lond. A 422, 193-239.
11. Havner, K. S. 1971 A discrete model for the prediction of subsequent yield surfaces in polycrystalline plasticity. Int. J. Solids Struct. 7, 719-730.
12. Havner, K. S. 1984 First- and second-order analysis of axially loaded crystals in n-fold symmetry. Phil. Trans. R. Soc. Lond. A 311, 469-493.
13. Havner, K. S. 1992 Finite plastic deformation of crystalline solids. Cambridge University Press.
14. Havner, K. S. & Chidambarrao, D. 1987 Analysis of a family of unstable lattice orientations in (110) channel die compression. Acta Mech. 69, 243-269.
15. Havner, K. S. & Sue, P. L. 1985 Theoretical analysis of the channel die compression test. II. First- and second-order analysis of orientation [110][001̄][1̄10] in f.c.c. crystals. J. Mech. Phys. Solids 33, 285-313.
16. Havner, K. S. & Wu, S.-C. 1995 An analytical investigation of inhomogeneous straining, subgrain formation, and the initiation of microshear bands in bicrystals. In Proc. IUTAM Symp. on Anisotropy, Inhomogeneity and Nonlinearity in Solid Mechanics (ed. D. F. Parker & A. H. England), pp. 211-216. Dordrecht: Kluwer.
17. Havner, K. S., Wu, S.-C. & Fuh, S. 1994 On symmetric bicrystals at the yield point in (110) channel die compression. J. Mech. Phys. Solids 42, 361-379.
18. Hu, X., Wei, C., Margolin, H. & Nourbakhsh, S. 1993 The stresses in a face-centered cubic single crystal under uniaxial tension. Metall. Trans. A 24, 875-881.
19. Hughes, D. A. 1993 Microstructural evolution in a non-cell forming metal: Al-Mg. Acta Metall. Mater. 41, 1421-1430.
20. Hughes, D. A. & Nix, W. D. 1989 Strain hardening and substructural evolution in Ni-Co solid solutions at large strains. Mater. Sci. Engng A 122, 153-172.
21. Kocks, U. F. & Chandra, H. 1982 Slip geometry in partially constrained deformation. Acta Metall 30, 695-709.
22. Nye, J. F. 1957 Physical properties of crystals. Oxford University Press.
23. Skalli, A. 1984 Etude théorique et experimentale de la deformation plastique en compression plane de cristaux d'aluminium. Thèse d'Etat, Ecoles des Mines de St. Etienne.
24. Skalli, A., Driver, J. H. & Wintenberger, M. 1983 Etude théorique et experimental de la deformation plastique de monocristaux d'aluminium. Deuxieme partie: compression plane partiellement imposée. Mem. Et. Sci. Revue Metall. 80, 293-302.
25. Sue, P. L. & Havner, K. S. 1984 Theoretical analysis of the channel die compression test. I. General considerations and finite deformation of f.c.c. crystals in stable lattice orientations. J. Mech. Phys. Solids 32, 417-442.
26. Wonsiewicz, B. C. & Chin, G. Y. 1970 Plane strain compression of copper, Cu 6Wt Pet Al, and Ag 4Wt Pet Sn crystals. Metal. Trans. 1, 2715-2722.
27. Wonsiewicz, B. C., Chin, G. Y. & Hart, R. R. 1971 Lateral constraints in plane strain compression of single crystals. Metall. Trans. 2, 2093-2096.
28. Wu, S. C. 1995 Analysis of symmetric bicrystals in (110) channel die compression. Ph.D. thesis, North Carolina State University.
29. Wu, S. C. & Havner, K. S. 1995 Exact stress states and velocity fields in bicrystals at the yield point in channel die compression. Z. Angew. Math. Phys. 46, S446-S465.