In this paper, a multiscale numerical method is presented with the aim to model the response of a Ti6Al4V sheet under explosive forming. The numerical modelling focuses on the accurate definition of the plastic deformation of the Ti6Al4V specimens based on the texture of the material. The viscoplastic self-consistent polycrystal model code (VPSC) is used as a link between macroscopic response and the underlying microstructure taking into account the viscoplastic deformation of the specimen. Comparison is made with experimental results. The Cazacu–Barlat (CB06) material model is used because of its capability to describe the yielding asymmetry between tension and compression and to take into account the anisotropic behaviour of the sheet. The study focuses on the evaluation of the material model parameters and on how these affect the structural response of the Ti6Al4V specimens under explosive loading.
This paper is part of a Themed Issue on Euromech 570: Interface-dominated materials.
GalánJ., VerleysenP. and DegrieckJ.: ‘Thermal effects during tensile deformation of Ti-6Al-4V at different strain rates’, Strain, 2013, 49, 354–365. doi: 10.1111/str.12042
2.
PeirsJ., VerleysenP., Van PaepegemW. and DegrieckJ.: ‘Determining the stress-strain behaviour at large strains from high strain rate tensile and shear experiments’, Int. J. Impact Eng., 2011, 38, 406–415. doi: 10.1016/j.ijimpeng.2011.01.004
3.
GillesG., HammamiW., LibertiauxV., CazacuO., YoonJ. H., KuwabaraT. and HebrakenA. M.: ‘Experimental characterization and elasto-plactis modeling of the quasistatc mechanical response of TA-6V at room temperature’, Int. J. Solids Struct., 2011, 48, 1277–1289. doi: 10.1016/j.ijsolstr.2011.01.011
4.
SinghA. K. and SchwarzerR. A.: ‘Texture and anisotropy of mechanical properties in titanium ans its alloys’, Z. Metall., 2000, 91, 702–716.
5.
ToméC. N. and LebensohnR. A.: ‘Manual for code VISCO-PLASTIC SELF-CONSISTENT (VPSC)’, Version 7b; 2007, Los Alamos National Laboratory.
6.
LebensohnR. A. and ToméC. N.: ‘A self-consistent anisotropic approach for the simulation of plastic deformation and texture development of poly crystals: Application to zirconium alloys’, Acta Metall. Mater., 1993, 41, 2611–2624. doi: 10.1016/0956-7151(93)90130-K
7.
CastelnauO., CanovaG., LebensohnR. and DuvalP.: ‘Modelling viscoplastic behavior of anisotropic polycrystalline ice with a self-Consistent approach’, Acta Mater., 1997, 45, 4823–4834. doi: 10.1016/S1359-6454(97)00098-0
8.
LebensohnR., WenkH.-R. and TomeC.: ‘Modelling deformation and recrystallization textures in calcite’, Acta Mater., 1998, 46, 2683–2693. doi: 10.1016/S1359-6454(97)00477-1
9.
LebensohnR. and ToméC.: ‘A self-consistent viscoplastic model: Prediction of rolling textures of anisotropic polycrystals’, Mater. Sci. Eng. A, 1994, 175, 71–82. doi: 10.1016/0921-5093(94)91047-2
10.
CogheF., TirryW., RabetL., SchryversD., and HoutteP. V.: ‘Importance of twinning in static and dynamic compression of a Ti-6Al-4V titanium alloy with an equiaxed microstructure’, Mater. Sci. Eng. A, 2012, 537, 1–10. doi: 10.1016/j.msea.2011.12.047
11.
LebensohnR. and CanovaG.: ‘A self-consistent approach for modelling texture development of two-phase polycrystals: Application to titanium alloys’, Acta Mater., 1997, 45, 3687–3694. doi: 10.1016/S1359-6454(97)00067-0
12.
ToméC., NeckerC. and LebensohnR.: ‘Mechanical anisotropy and grain interaction in recrystallized aluminum’, Metall. Trans. A, 2002, 33, 2635–2648. doi: 10.1007/s11661-002-0385-x
13.
KnezevicM., LebensohnR. A., CazacuO., Revil-BaudardB., ProustG., VogelS. C. and NixonM. E.: ‘Modeling bending of α-titanium with embedded polycrystal plasticity in implicit finite elements’, Mater. Sci. Eng. A, 2013, 564, 116–126. doi: 10.1016/j.msea.2012.11.037
14.
CazacuO., PlunkettB. and BarlatF.: ‘Orthotropic yield criterion for hexagonal closed packed metals’, Int. J. Plast., 2006, 22, 1171–1194. doi: 10.1016/j.ijplas.2005.06.001
15.
PlunkettB., CazacuO. and BarlatF.: ‘Orthotropic yield criteria for description of the anisotropy in tension and compression of sheet metals’, Int. J. Plast., 2008, 24, 847–866. doi: 10.1016/j.ijplas.2007.07.013
16.
CazacuO., IonescuI. R. and YoonJ. W.: ‘Orthotropic strain rate potential for the description of anisotropy in tension and compression of metals’, Int. J. Plast., 2010, 26, 887–904. doi: 10.1016/j.ijplas.2009.11.005
17.
PlunkettB., CazacuO., LebensohnR. A. and BarlatF.: ‘Elastic-viscoplastic anisotropic modeling of rtextured metals and validation using the Taylor cylinder impact test’, Int. J. Plast., 2007, 23, 1001–1021. doi: 10.1016/j.ijplas.2006.10.008
18.
KhanA. S., KazmiR. and FarrokhB.: ‘Multiaxial and non-propotional loading responses, anisotropy and modeling of Ti-6Al-4V titanium alloy ove wide ranges of strain rates and temperatures’, Int. J. Plast., 2007, 23, 931–950. doi: 10.1016/j.ijplas.2006.08.006
19.
KotkundeN., DeoleA. D., GuptaA. K. and SinghS. K.: ‘Experimental and numerical investigation of anisotropic yield criteria for warm deep drawing of Ti–6Al–4V alloy’, Mater. Des., 2014, 63, 336–344. doi: 10.1016/j.matdes.2014.06.017
20.
OdenbergerE. L., SchillM. and OldenburgM.: ‘Thermo-mechanical sheet metal forming of aero engine components in Ti-6Al-4V—PART 2: Constitutive modelling and validation’, Int. J. Mater. Form., 2013, 6, 403–416. doi: 10.1007/s12289-012-1094-7
21.
TuninettiV., GillesG., MilisO., PardoenT. and HabrakenA. M.: ‘Anisotropy and tension–compression asymmetry modeling of the room temperature plastic response of Ti–6Al–4V’, Int. J. Plast., 2015, 67, 53–68. doi: 10.1016/j.ijplas.2014.10.003
22.
TuninettiV. and HabrakenA. M.: ‘Impact of anisotropy and viscosity to model the mechanical behavior of Ti–6Al–4V alloy’, Mater. Sci. Eng. A, 2014, 605, 39–50. doi: 10.1016/j.msea.2014.03.009
23.
KhanA. S., YuS. and LiuH.: ‘Deformation induced anisotropic responses of Ti–6Al–4V alloy. Part II: A strain rate and temperature dependent anisotropic yield criterion’, Int. J. Plast., 2012, 38, 14–26. doi: 10.1016/j.ijplas.2012.03.013
24.
LouY., HuhH. and YoonJ. W.: ‘Consideration of strength differential effect in sheet metals with symmetric yield functions’, Int. J. Mech. Sci., 2013, 66, 214–223. doi: 10.1016/j.ijmecsci.2012.11.010
25.
ChenY., KibbleK., HallR. and HuangX.: ‘Numerical analysis of superplastic blow forming of Ti–6Al–4V alloys’, Mater. Des., 2001, 22, 679–685. doi: 10.1016/S0261-3069(01)00009-7
26.
KadB. K., SchoenfeldS. E. and BurkinsM. S.: ‘Through thickness dynamic impact response in textured Ti–6Al–4V plates’, Mater. Sci. Eng. A, 2002, 322, 241–251. doi: 10.1016/S0921-5093(01)01135-2
27.
LiF. Q., MoJ. H., LiJ. J., HuangL. and ZhouH. Y.: ‘Formability of Ti–6Al–4V titanium alloy sheet in magnetic pulse bulging’, Mater. Des., 2013, 52, 337–344. doi: 10.1016/j.matdes.2013.05.064
28.
GillesG., HabrakenA. M. and DuchêneL.: ‘Material parameter identification of Cazacu's model for Ti6Al4V using the simulated annealing algorithm’, Mater. Sci. Forum, 2010, 636–637, 1125–1130. doi: 10.4028/www.scientific.net/MSF.636-637.1125
29.
KakogiannisD., CogheF. and RabetL.: ‘Modelling the deformation of Ti64 sheets under explosive loading’, Design and analysis of protective structures: Proceedings of the 3rd International Conference on Protective Structures (ICPS3), (ed. M. G. Stewart and M. D. Netherton), Newcastle, Australia, February 2015.
30.
OusjiH., LouarM. A., BelkassemB., PylL. and VantommeJ.: ‘Parametric study of an explosive driven shock tube’, 23rd International Symposium on Military Aspects of Blast and Shock (MABS 23), Oxford, UK, September 2014.
31.
LouarM. A., BelkassemB., OusjiH., SpranghersK., KakogiannisD., PylL. and VantommeJ.: ‘Explosive driven shock tube loading of aluminium plates: Experimental study’, Int. J. Impact Eng., 2015, 86, 111–123. doi: 10.1016/j.ijimpeng.2015.07.013
