Constitutive description of severely deformed metals based on dimensional analysis

References

• Huang M., Rivera-Díaz-del-Castillo P. E. J., Bouaziz O. and van der Zwaag S.: ‘Modelling strength and ductility of ultrafine grained BCC and FCC alloys using irreversible thermodynamics’, Mater. Sci. Technol., 2009, 25, 833–839.
   Web of Science ®Google Scholar
• Milner J. L., Bunget C., Abu-Farha F., Kurfess T. and Hammond V. H.: ‘Modeling tensile strength of materials processed by accumulative roll bonding’, J. Manuf. Process., 2013, 15, 219–226.
   Web of Science ®Google Scholar
• Estrin Y. and Vinogradov A.: ‘Extreme grain refinement by severe plastic deformation: A wealth of challenging science’, Acta Mater., 2013, 61, 782–817.
   Web of Science ®Google Scholar
• Rollett A. D. and Kocks U. F.: ‘A review of the stages of work hardening’, Solid State Phenom., 1993, 35–36, 1–18.
   Google Scholar
• Hockauf M. and Meyer L. W.: ‘Work-hardening stages of AA1070 and AA6060 after severe plastic deformation’, J. Mater. Sci., 2010, 45, 4778–4789.
   Web of Science ®Google Scholar
• Zhu B., Asaro R. J., Krysl P. and Bailey R.: ‘Transition of deformation mechanisms and its connection to grain size distribution in nanocrystalline metals’, Acta Mater., 2005, 53, 4825–4838.
   Web of Science ®Google Scholar
• Li S., Bourke M. A. M., Beyerlein I. J., Alexander D. J. and Clausen B.: ‘Finite element analysis of the plastic deformation zone and working load in equal channel angular extrusion’, Mater. Sci. Eng. A, 2004, A382, 217–236.
   Web of Science ®Google Scholar
• Kim H. S. and Estrin Y.: ‘Microstructural modelling of equal channel angular pressing for producing ultrafine grained materials’, Mater. Sci. Eng. A, 2005, 410–411, 285–289.
   Web of Science ®Google Scholar
• Estrin Y., Toth L. S., Molinari A. and Brechet Y.: ‘A dislocation-based model for all hardening stages in large strain deformation’, Acta Mater., 1998, 46, 5509–5522.
   Web of Science ®Google Scholar
• Baik S. C., Estrin Y., Kim H. S. and Hellmig R. J.: ‘Dislocation density-based modeling of deformation behavior of aluminum under equal channel angular pressing’, Mater. Sci. Eng. A, 2003, A351, 86–97.
   Web of Science ®Google Scholar
• Baik S. C., Hellmig R. J., Estrin Y. and Kim H. S.: ‘Modeling of deformation behavior of copper under equal channel angular pressing’, Z. Metallkd., 2003, 94, 754–760.
   Google Scholar
• Toth L. S., Molinari A. and Estrin Y.: ‘Strain hardening at large strains as predicted by dislocation based polycrystal plasticity model’, J. Eng. Mater. Technol., 2002, 124, 71–77.
   Web of Science ®Google Scholar
• Rezaee-Bazzaz A., Ahmadian S. and Reihani H.: ‘Modeling of microstructure and mechanical behavior of ultra fine grained aluminum produced by accumulative roll-bonding’, Mater. Des., 2011, 32, 4580–4585.
   Web of Science ®Google Scholar
• Mckenzie P. W. J., Lapovok R. and Estrin Y.: ‘The influence of back pressure on ECAP processed AA 6016: Modeling and experiment’, Acta Mater., 2007, 55, 2985–2993.
   Web of Science ®Google Scholar
• Kazeminezhad M. and Hosseini E.: ‘Modeling of induced empirical constitutive relations on materials with FCC, BCC, and HCP crystalline structures: severe plastic deformation’, Int. J. Adv. Manuf. Technol., 2010, 47, 1033–1039.
   Web of Science ®Google Scholar
• Chinh N. Q., Horvath G., Horita Z. and Langdon T. G.: ‘A new constitutive relationship for the homogeneous deformation of metals over a wide range of strain’, Acta Mater., 2004, 52, 3555–3563.
   Web of Science ®Google Scholar
• Wei W., Wei K. X. and Fan G. J.: ‘A new constitutive equation for strain hardening and softening of fcc metals during severe plastic deformation’, Acta Mater., 2008, 56, 4771–4779.
   Web of Science ®Google Scholar
• Parsa M. H. and Ohadi D.: ‘A constitutive equation for hot deformation range of 304 stainless steel considering grain sizes’, Mater. Des., 2013, 52, 412–421.
   Web of Science ®Google Scholar
• Buckingham E.: ‘On physically similar systems: illustrations of the use of dimensional equations’, Phys. Rev., 1914, 4, 345–376.
   Web of Science ®Google Scholar
• Chakrabarti S. K.: ‘On constitutive equations and dimensional analysis’, J. Franklin Inst., 1973, 296, 339–346.
   Web of Science ®Google Scholar
• Malvern L. E.: ‘Introduction to the mechanics of a continuous medium’; 1969, New Jersey, Prentice-Hall Inc.
   Google Scholar
• Szirtes T.: ‘Applied dimensional analysis and modeling’, 2nd edn; 2007, Amsterdam, Elsevier.
   Google Scholar
• Cao Y. P. and Lu J.: ‘A new method to extract the plastic properties of metal materials from an instrumented spherical indentation loading curve’, Acta Mater., 2004, 52, 4023–4032.
   Web of Science ®Google Scholar
• Phaniraj M. P. and Lahiri A. K.: ‘Constitutive equation for elevated temperature flow behavior of plain carbon steels using dimensional analysis’, Mater. Des., 2008, 29, 734–738.
   Web of Science ®Google Scholar
• Gubicza J., Chinh N. Q., Csanadi T., Langdon T. G. and Ungar T.: ‘Microstructure and strength of severely deformed fcc metals’, Mater. Sci. Eng. A, 2007, A462, 86–90.
   Web of Science ®Google Scholar
• Eizadjou M., Manesh H. D. and Janghorban K.: ‘Microstructure and mechanical properties of ultra-fine grains (UFGs) aluminum strips produced by ARB process’, J. Alloys Compd, 2009, 474, 406–415.
   Web of Science ®Google Scholar
• Mishra A., Kad B. K., Gregori F. and Meyers M. A.: ‘Microstructural evolution in copper subjected to severe plastic deformation: Experiments and analysis’, Acta Mater., 2007, 55, 13–28.
   Web of Science ®Google Scholar
• Khodabakhshi F. and Kazeminezhad M.: ‘The effect of constrained groove pressing on grain size, dislocation density and electrical resistivity of low carbon steel’, Mater. Des., 2011, 32, 3280–3286.
   Web of Science ®Google Scholar
• Dieter G. E.: ‘Mechanical metallurgy’, 3rd edn; 1988, New York, McGraw-Hill.
   Google Scholar
• Murr L. E.: ‘Interfacial phenomena in metals and alloys’; 1975, London, Addison-Wesley.
   Google Scholar
• Charnock W. and Nutting J.: ‘The Effect of Carbon and Nickel upon the Stacking-Fault Energy of Iron’, Metal Sci., 1967, 1, 123–127.
   Google Scholar
• Hansen N. and Ralph B.: ‘The strain and grain size dependence of the flow stress of copper’, Acta Metall., 1982, 30, 411–417.
   Google Scholar
• Qu S., An X. H., Yang H. J., Huang C. X., Yang G., Zang Q. S., Wang Z. G., Wu S. D. and Zhang Z. F.: ‘Microstructural evolution and mechanical properties of Cu–Al alloys subjected to equal channel angular pressing’, Acta Mater., 2009, 57, 1586–1601.
   Web of Science ®Google Scholar
• Humphreys F. J. and Hatherly M.: ‘Recrystallization and related annealing phenomena’, 2nd edn; 2004, Oxford, Elsevier.
   Google Scholar
• Roters F., Raabe D. and Gottstein G.: ‘Work hardening in heterogeneous alloys–a microstructural approach based on three internal state variables’, Acta Mater., 2000, 48, 4181–4189.
   Web of Science ®Google Scholar
• Dalla Torre F., Lapovok R., Sandlin J., Thomson P. F., Davies C. H. J. and Pereloma E. V.: ‘Microstructures and properties of copper processed by equal channel angular extrusion for 1–16 passes’, Acta Mater., 2004, 52, 4819–4832.
   Web of Science ®Google Scholar
• Mazilkin A. A., Straumal B. B., Rabkin E., Baretzky B., Enders S., Protasova S. G., Kogtenkova O. A. and Valiev R. Z.: ‘Softening of nanostructured Al–Zn and Al–Mg alloys after severe plastic deformation’, Acta Mater., 2006, 54, 3933–3939.
   Web of Science ®Google Scholar
• Li Y. J., Valiev R. and Blum W.: ‘Deformation kinetics of ultrafine-grained Cu and Ti’, Mater. Sci. Eng. A, 2005, A410–A411, 451–456.
   Web of Science ®Google Scholar
• Shih M. H., Yu C. Y., Kao P. W. and Chang C. P.: ‘Microstructure and flow stress of copper deformed to large plastic strains’, Scr. Mater., 2001, 45, 793–799.
   Web of Science ®Google Scholar
• Wei Q., Kecskes L., Jiao T., Hartwig K. T., Ramesh K. T. and Ma E.: ‘Adiabatic shear banding in ultrafine-grained Fe processed by severe plastic deformation’, Acta Mater., 2004, 52, 1859–1869.
   Web of Science ®Google Scholar
• Mirzadeh H. and Zomorodian A.: ‘Ball milling criteria for producing nano intermetallic compounds’, Mater. Sci. Technol., 2010, 26, 281–284.
   Web of Science ®Google Scholar
• von Eye A. and Mun E.-Y.: ‘Log-linear modeling: concepts, interpretation, and application’; 2013, New York, Wiley.
   Google Scholar