An approach composed of the thermodynamics-based dislocation model and the Taylor theory is used to investigate the evolution of microstructure and flow stress during high-pressure torsion (HPT). The incremental temperature rise is considered through the modelling of HPT. The temperature can affect the annihilation of dislocations and thus the dislocation density. The model predicts the dislocation density, sub-grain size and flow stress during HPT. The modelling results are compared with the experimental data and the modelling results without considering the incremental temperature rise. A remarkable agreement is observed between the modelling results with considering the temperature rise effect and the experimental data.
ValievR. Z.: ‘Ultrafine-grained materials produced by severe plastic deformation: an introduction’, Ann. Chim. – Sci. Mat., 1996, 21, 369–378.
2.
SegalV. M., ReznikovV. I., DrobyshevskiiA. E. and KopylovV. I.: ‘Plastic working of metals by simple shear’, Russ. Metall. (Metally), 1981, 1, 99–105.
3.
SegalV. M.: ‘Materials processing by simple shear’, Mater. Sci. Eng. A, 1995, A197, 157–164. doi: 10.1016/0921-5093(95)09705-8
4.
SmirnovaN. A., LevitV. I., PilyuginV. I., KuznetsovR. I., DavydovaL. S. and SazonovaV. A.: ‘Evolution of the fcc single-crystal structure during severe plastic-deformations’, Fiz. Metal. Metalloved., 1986, 61, 1170–1177.
5.
SaitoY., TsujiN., UtsunomiyaH., SakaiT. and HongR. G.: ‘Ultra-fine grained bulk aluminum produced by accumulative roll-bonding (ARB) process’, Scripta Mater., 1998, 39, 1221–1227. doi: 10.1016/S1359-6462(98)00302-9
6.
ShinD. H., ParkJ. J., KimY. S. and ParkK. T.: ‘Constrained groove pressing and its application to grain refinement of aluminum’, Mater. Sci. Eng. A, 2002, A328, 98–103. doi: 10.1016/S0921-5093(01)01665-3
7.
FujitaT., HoritaZ. and LangdonT. G.: ‘Characteristics of diffusion in Al-Mg alloys with ultrafine grain sizes’, Philos. Mag. A, 2002, A82, 2249–2262. doi: 10.1080/01418610208235736
8.
HuangJ., ZhuY. T., AlexanderD. J., LiaoX., LoweT. C. and AsaroR. J.: ‘Development of repetitive corrugation and straightening’, Mater. Sci. Eng. A, 2004, A371, 35–39. doi: 10.1016/S0921-5093(03)00114-X
9.
BridgmanP. W.: ‘Effects of high shearing stress combined with high hydrostatic pressure’, Phys. Rev., 1935, 48, 825–847. doi: 10.1103/PhysRev.48.825
10.
BridgmanP. W.: ‘On torsion combined with compression’, J. Appl. Phys., 1943, 14, 273–283. doi: 10.1063/1.1714987
11.
ValievR. Z., KrasilnikovN. A., TsenevN. K.: ‘Plastic deformation of alloys with submicron-grained structure’, Mater. Sci. Eng. A, 1991, A137, 35–40. doi: 10.1016/0921-5093(91)90316-F
12.
ZhilyaevA. P., NurislamovaG. V., KimB. K., BaróaM. D., SzpunarJ. A. and LangdonT. G.: ‘Experimental parameters influencing grain refinement and microstructural evolution during high-pressure torsion’, Acta Mater., 2003, 51, 753–765. doi: 10.1016/S1359-6454(02)00466-4
13.
ReshadiF., FarajiG., AghdamifarS., YavariP. and MashhadiM. M.: ‘Deformation speed and temperature effects on magnesium AZ91 during tubular channel angular pressing’, Mater. Sci. Technol., 2015, doi:10.1179/1743284715Y.0000000039
14.
PimentelG., Toda-CaraballoI. and CapdevilaC.: ‘Experimental and computational analysis of abnormal grain growth’, Mater. Sci. Technol., 2015, 31, 1618–1626. doi: 10.1179/1743284715Y.0000000079
15.
PereiraP. H. R., FigueiredoR. B., HuangY., CetlinP. R. and LangdonT. G.: ‘Modeling the temperature rise in high-pressure torsion’, Mater. Sci. Eng. A, 2014, A593, 185–188. doi: 10.1016/j.msea.2013.11.015
16.
YamaguchiD., HoritaZ., NemotoM., LangdonT. G.: ‘Significance of adiabatic heating in equal-channel angular pressing’, Scripta Mater., 1999, 41, 791–796. doi: 10.1016/S1359-6462(99)00233-X
17.
HuangM., Rivera-Díaz-del-CastilloP. E. J., BouazizO. and van der ZwaagS.: ‘Irreversible thermodynamics modeling of plastic deformation of metals’, Mater. Sci. Technol., 2008, 24, 495–500. doi: 10.1179/174328408X294125
18.
VinogradovA., YasnikovI. S. and EstrinY.: ‘Irreversible thermodynamics approach to plasticity: dislocation density based constitutive modelling’, Mater. Sci. Technol., 2015, 31, 1664–1672. doi: 10.1179/1743284715Y.0000000069
19.
LeeD. J., YoonE. Y., AhnD. H., ParkB. H., ParkH. W., ParkL. J., EstrinY. and KimH. S.: ‘Dislocation density-based finite element analysis of large strain deformation behavior of copper under high-pressure torsion’, Acta Mater., 2014, 76, 281–293. doi: 10.1016/j.actamat.2014.05.027
20.
ZhilyaevA. P. and LangdonT. G.: ‘Using high-pressure torsion for metal processing: Fundamentals and applications’, Prog. Mater. Sci., 2008, 53, 893–979. doi: 10.1016/j.pmatsci.2008.03.002
21.
HumphreysF. J. and HatherlyM.: ‘Recrystallization and related annealing phenomena’, 2nd edn; 2004, New York, Pergamon.
22.
TaylorG. I.: ‘Plastic strain in metals’, J. Inst. Metal., 1938, 62, 307–324.
23.
TaylorG. I.: ‘The mechanism of plastic deformation of crystals. Part I – theoretical’, Proc. R. Soc. Lond. A, 1934, 145, 362–387. doi: 10.1098/rspa.1934.0106
24.
QinJ., HuangY., HwangK. C., SongJ. and PharrG. M.: ‘The effect of indenter angle on the microindentation hardness’, Acta Mater., 2007, 55, 6127–6132. doi: 10.1016/j.actamat.2007.07.016
25.
KocksU. F.: ‘The relation between polycrystal deformation and single crystal deformation’, Metall. Mater. Trans., 1970, 1, (5), 1121–1143.
26.
BishopJ. F. W. and HillR.: ‘CXXVIII. A theoretical derivation of the plastic properties of a polycrystalline face-centred metal’, Philos. Mag., 1951, 42, 1298–1307. doi: 10.1080/14786444108561385
27.
BishopJ. F. W. and HillR.: ‘XLVI. A theory of the plastic distortion of a polycrystalline aggregate under combined stresses.’, Philos. Mag., 1951, 42, 414–427. doi: 10.1080/14786445108561065
28.
HosseiniE. and KazeminezhadM.: ‘Integration of physically based models into FE analysis: Homogeneity of copper sheets under large plastic deformations’, Comput. Mater. Sci., 2010, 48, 166–173. doi: 10.1016/j.commatsci.2009.12.023
29.
HosseiniE. and KazeminezhadM.: ‘A new microstructural model based on dislocation generation and consumption mechanisms through severe plastic deformation’, Comput. Mater. Sci., 2011, 50, 1123–1135. doi: 10.1016/j.commatsci.2010.11.012
30.
HosseiniE. and KazeminezhadM.: ‘The effect of ECAP die shape on nano-structure of materials’, Comput. Mater. Sci., 2009, 44, 962–967. doi: 10.1016/j.commatsci.2008.07.002
31.
NesE.: ‘Modelling of work hardening and stress saturation in fcc metals’, Prog. Mater. Sci., 1997, 41, 129–193. doi: 10.1016/S0079-6425(97)00032-7
32.
AshbyM. F.: ‘A first report on deformation-mechanism maps’, Acta Metall., 1972, 20, 887–897. doi: 10.1016/0001-6160(72)90082-X
33.
HigginsR. A.: ‘Materials for engineers and technicians’, 5th edn; 2010, London, Routledge.
34.
MolodovD. A. (ed.): ‘Microstructural design of advanced engineering materials’, 1st edn; 2013, Weinheim, Wiley.
35.
NixW. D., GibelingJ. C. and HughesD. A.: ‘Time-dependent deformation of metals’, Metall. Trans. A, 1985, 16, 2215–2226. doi: 10.1007/BF02670420
36.
CottrellG. A.: ‘Void migration, coalescence and swelling in fusion materials’, Fusion Eng. Des., 2003, 66–68, 253–257. doi: 10.1016/S0920-3796(03)00299-0
37.
ZaiserM. and SandfeldS.: ‘Scaling properties of dislocation simulations in the similitude regime’, Model. Simul. Mater. Sci. Eng., 2014, 22, 065012. doi:10.1088/0965-0393/22/6/065012
38.
HolbrowC. H., LloydJ. N., AmatoJ. C., GalvezE. and ParksM. E.: ‘Modern introductory physics’, 2nd edn; 2010, New York, Springer.
BaikS. C., EstrinY., KimH. S. and HellmigR. J.: ‘Dislocation density-based modeling of deformation behavior of aluminium under equal channel angular pressing’, Mater. Sci. Eng. A, 2003, A351, 86–97. doi: 10.1016/S0921-5093(02)00847-X
41.
GubiczaJ., NamN. H., BaloghL., HellmigR. J., StolyarovV. V., EstrinY. and UngarT.: ‘Microstructure of severely deformed metals determined by X-ray peak profile analysis’, J. Alloys Compd., 2004, 378, 248–252. doi: 10.1016/j.jallcom.2003.11.162
42.
GubiczaJ., BaloghL., HellmigR. J., EstrinY., UngárT.: ‘Dislocation structure and crystallite size in severely deformed copper by X-ray peak profile analysis’, Mater. Sci. Eng. A, 2005, 400–401, 334–338. doi: 10.1016/j.msea.2005.03.042
43.
PandeyS. C., JosephM. A., PradeepM. S., RaghavendraK., RanganathV. R., VenkateswarluK. and LangdonT. G.: ‘A theoretical and experimental evaluation of repetitive corrugation and straightening: Application to Al–Cu and Al–Cu–Sc alloys’, Mater. Sci. Eng. A, 2012, A534, 282–287. doi: 10.1016/j.msea.2011.11.070
44.
HosseiniE. and KazeminezhadM.: ‘Coupling kinetic dislocation model and Monte Carlo algorithm for recrystallized microstructure modeling of severely deformed copper’, J. Mater. Sci., 2008, 43, 6081–6086. doi: 10.1007/s10853-008-2953-y
45.
DingH. and ShinY. C.: ‘Dislocation density-based grain refinement modeling of orthogonal cutting of commercially pure titanium’, ASME Int. Manuf. Sci. Eng. Conf., 2011, 2, 89–98.
46.
BaikS. C., HellmigR. J., EstrinY. and KimH. S.: ‘Modeling of deformation behavior of copper under equal channel angular pressing’, Z. Metallkd., 2003, 94, 754–760. doi: 10.3139/146.030754
47.
HanC. S., LimC., KimC. and KimS.: ‘The microstructural evolution during the equal channel angular pressing process and its relationship with the tensile behavior of oxygen-free copper’, Metall. Mater. Trans. A, 2005, 36, 467–470. doi: 10.1007/s11661-005-0318-6
48.
DobatkinS. V., SzpunarJ. A., ZhilyaevA. P., ChoJ. Y. and KuznetsovA. A.: ‘Effect of the route and strain of equal-channel angular pressing on structure and properties of oxygen-free copper’, Mater. Sci. Eng. A, 2007, A462, 132–138. doi: 10.1016/j.msea.2006.04.156
49.
KomuraS., HoritaZ., NemotoM. and LangdonT. G.: ‘Influence of stacking fault energy on microstructural development in equal-channel angular pressing’, J. Mater. Res., 1999, 14, 4044–4050. doi: 10.1557/JMR.1999.0546
