Bifurcation into shear bands on the Bishop and Hill polyhedron. Part 2, Case of the vertices

• Autorzy: Darrieulat M. , Chapelle D.
• Języki publikacji: EN

Abstrakty

EN

The present paper is the second of a series of three papers devoted to the micro-mechanical conditions which render possible the appearance of shear bands in crystalline materials. It focuses on the deformation at the vertices of the Bishop and Hill polyhedron, which are important because most of the shear bands originate at the grain boundaries where many slip systems are active. The conditions of bifurcation are analysed on the scale of the slip systems by crystallographic class of vertices. An application is given in the case of channel-die compression and it shows that the texture components are unequally liable to shear banding, the Copper one, for example, being more sensitive than Goss, as known experimentally. There is also a good agreement of the predictions with the geometry of the bands, especially the characteristic feature of the inclination at 35o with respect to the rolling axis. Considerations follow on the actual implementation, by micro-structural phenomena, of the localization whose mechanical possibility has been discussed in the article.

Słowa kluczowe

EN

shear bands; channel-die compression; bifurcation; vertex

PL

pasma ścinania; ściskanie nieswobodne; bifurkacja; wierzchołek wielościanu

• Wydawca: Instytut Podstawowych Problemów Techniki PAN
• Czasopismo: Archives of Mechanics
• Rocznik: 2004
• Tom: Vol. 56, nr 6
• Strony: 465--484
• Opis fizyczny: Bibliogr. 24 poz.

Twórcy

autor

Darrieulat M.

• SMS, R3M, UMR CNRS 5146, Ecole Nationale Supérieure des Mines de Saint-Etienne, 158 cours Fauriel, 42023 Saint-Etienne cedex 2, France

autor

Chapelle D.

• LMARC, Institut FEMTO ST, UMR CNRS 6174, 24 rue de l’Epitaphe, 25000 Besançon, France

Bibliografia

• 1. M. Darrieulat, A. Chenaoui, Bifurcation into shear bands of the Bishop and Hill polyhedron, Part I: General analysis, Arch. Mech., 56, 137–156, 2004.
• 2. S. Stören, J.R. Rice, Localized necking in thin sheets, J. Mech. Phys. Solids, 23, 421–441, 1975.
• 3. P. Dubois, Etude cristallographique de l’initiation et de la propagation de bandes de cisaillement dans les métaux purs, Ph. D. thesis, Université Paris Nord, France 1988.
• 4. U.F. Kocks, G.R. Canova, How many slip systems and which? [in:] Deformation of polycrystals: mechanisms and microstructures. Invited contribution to the Second Risø Symposium on Metallurgy and Material Science, Risø, Denmark 1981.
• 5. G.I. Taylor, Plastic strain in metals, J. Inst. Metals, 62, 307–324, 1938.
• 6. C.N. Reid, Deformation geometry for material scientists, Pergamon Press, 162–163, Oxford 1973.
• 7. P. Gilormini , B. Bacroix, J.J. Jonas, Theoretical analyses of <111> pencil glide in b.c.c. crystals, Acta Metall., 36, 2, 231–256, 1988.
• 8. M. Gaspérini, C. Rey, Effect of initial orientation and of predeformation on shearbanding in copper single crystals submitted to tensile tests, [in:] C. Teodosiou, J.L. Raphanel, F. Sidoroff, Large Plastic Deformations: Fundamental Aspects and Applications to Metal Forming, Balkema, Rotterdam, 229–237, 1993.
• 9. R. Fortunier, J. Linhart, Solid angles in N dimensional space: application of spherical volume theory to crystal yield surfaces, Int. J. Plast., 5, 477–499, 1989.
• 10. A. Korbel, P.L. Martin, Microscopic versus macroscopic aspect of shear band deformation, Acta Metall., 34, 10, 1905–1909, 1986.
• 11. S.V. Harren, H.E. Deve, R.J. Asaro, Shear band formation in plane strain compression, Acta Metall., 36, 9, 2435–2480, 1986.
• 12. A.R. Mokhtari-Dolui, Contribution à l’étude des bandes de cisaillement sur quelques alliages de l’aluminium, Ph. D. thesis, Université Paris-Sud, France, 1986.
• 13. K.F. Karhausen, J. Savoie, C.M. Allen, D. Piot, R. Luce, Material testing, constitutive modeling and implementation of material models into hot rolling models for alloy AA3103, Materials Science Forum, 396–402, 2002.
• 14. J.Y. Poussardin, M. Darrieulat, Hétérogénéités de déformation plastique dans les monocristaux d’Al 1%Mn soumis à compression plane bi-encastrée, Colloque Matériaux, Tours, France 2002.
• 15. M. Richert, A. Korbel, The position of shear bands in rolled f.c.c. metals. Z. Metallkunde, 446–451, 1988.
• 16. Y.W. Chang, R.J. Asaro, An experimental study of shear localization in aluminiumcopper single crystals, Acta Metall., 29, 241–257, 1981.
• 17. D.G. Attwood, P.M. Hazzledine, A fiducial grid for high resolution metallography, Metallography , 9, 483–500, 1976.
• 18. D. Chapelle, M. Darrieulat, The occurrence of shear banding in a millimetric scale (¯1¯23) [634] grain of a Al-4.5Mg alloy during plane strain compression, Mat. Sci. Eng. A, 347, 32–41, 2003.
• 19. A. Korbel, J.D. Embury, M. Hatherly, P.L. Martin, H.W. Erbsloth, Microstructural aspects of strain localization in Al-Mg alloys, Acta Metall., 34, 10, 1999–2009, 1986.
• 20. A. Korbel, F. Dobrzański, M. Richert, Strain hardening of aluminium at high strains, Acta Metall., 31, 293–298, 1983.
• 21. W. Oliferuk, A. Korbel, M. Grabski, Mode of deformation and the rate of energy storage during uniaxial tensile deformation of austenitic steel, Mat. Sci. Eng. A, 220, 123–128, 1996.
• 22. Z. Jasieński, A. Piątkowski, Nature des bandes de cisaillement macroscopiques dans les monocristaux de cuivre sollicités en compression plane, Arch. Metall., Warszawa, 38, 3, 279–301, 1993.
• 23. K. Morii, H. Mecking, Y. Nakayama, Development of shear bands in f.c.c. single crystals, Acta Metall., 33, 1, 379–388, 1985.
• 24. H. Paul, Z. Jasieński, A. Piątkowski, K. Pawlik, A. Litwora, The influence of the ‘Brass’ type shear bands on the global texture of copper and CuAl2% C-oriented single crystals compressed in channel-die, [in:] X Conference on Electron Microscopy of Solids, Warsaw-Serock, Poland, 307–312, September 20–23, 1999.