Engineering Transactions, 67, 2, pp. 227–242, 2019

Multi-Scale Numerical Analysis of the Effect of Microstructural Features on the Mechanical Behavior of Polycrystalline Ti-6Al-4V Alloy

Université de Toulouse

Vincent VELAY
ICA, Université de Toulouse, CNRS, IMT Mines Albi, INSA, UPS, ISAE-SUPAERO, Compus Jarlard, Albi 81000

Mohammed CHEIKH
Université de Toulouse

Vanessa VIDAL
Université de Toulouse

Christine BOHER
Université de Toulouse

Université de Toulouse

The present work aims to model the influence of microstructural features of Ti-6Al-4V titanium alloy on its mechanical behavior. A multi-scale approach based on crystal plasticity is considered. The elasto-viscoplastic constitutive equations of Meric-Cailletaud are modified to take into consideration the effect of the grain size by introducing the Hall-Petch relationship at the local scale. This modified model is coupled with finite element calculations under small strain assumption to simulate the monotonic mechanical behavior of Ti-6A-4V at local and global scales. It is shown that the mechanical behavior of Ti-6Al-4V is drastically dependent upon the material features. Strong crystallographic texture can result in the formation
of hardened and less hardened areas. Moreover, by increasing the grain size scattering, the heterogeneously deformed areas are multiplied. By decreasing the average grain size, the yield strength increases. It is observed that the effects of grain size, grain size scattering and crystallographic texture are coupled.
Keywords: Ti-6Al-4V alloy; crystal plasticity; grain size; crystallographic texture; scattering of grain size; multi-scale modeling
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Berbenni S., Favier V., Berveiller M., Impact of the grain size distribution on the yield stress of heterogeneous materials, International Journal of Plasticity, 23(1): 114–142, 2007.

Berbenni S., Favier V., Berveiller M., Micro-macro modelling of the effects of the grain size distribution on the plastic flow stress of heterogeneous materials, Computational Materials Science, 39(1): 96–105, 2007.

Besson J., Foerch R., Large scale object-oriented finite element code design, Computer Methods in Applied Mechanics and Engineering, 142(1–2): 165–187, 1997.

Besson J., Leriche R., Foerch R., Cailletaud G., Object-oriented programming applied to the finite element method. Part II. Application to material behaviors, Revue Européenne des Éléments Finis, 7(5): 567–588, 1998,

Bridier F., McDowell D., Villechaise P., Mendez J., Crystal plasticity modeling of slip activity in Ti-6Al-4V under high cycle fatigue loading, International Journal of Plasticity, 25(6): 1066–1082, 2009.

Dick T., Cailletaud G., Fretting modelling with a crystal plasticity model of Ti6Al4V, Computational Materials Science, 38(1): 113–125, 2006.

Frederick C.O., Armstrong P.J., A mathematical representation of the multiaxial Bauschinger effect, Materials at High Temperature, 24(1): 1–26, 2007.

Fromm B.S, Adams B.L., Ahmadi S., Knezevic M., Grain size and orientation distributions: Application to yielding of _-titanium, Acta Materialia, 57(8): 2339–2348, 2009.

Gerard C., Field measurements and evaluation of crystal plasticity models [in French: Mesures de champs et identiffication de modéles de plasticité cristalline], PhD thesis, École Polytechnique, 91128 Palaiseau Cedex, France, 2008.

Germain L., Gey N., Humbert M., Bocher P., Jahazi M., Analysis of sharp microtexture heterogeneities in a bimodal IMI 834 billet, Acta Materialia, 53(13): 3535–3543, 2005.

Gilles G.,Hammami W., Libertiaux V., Cazacu O., Yoon J.H., Kuwabara T., Habraken A.M., Duchêne L., Experimental characterization and elasto-plastic modeling of the quasi-static mechanical response of TA-6 V at room temperature, International Journal of Solids and Structures, 48(9): 1277–1289, 2011.

Glavicic M.G., Bartha B.B., Jha S.K., Szczepanski C.J., The origins of microtexture in duplex Ti alloys, Materials Science and Engineering: A, 513–514: 325–328, 2009.

Hall E.O., The deformation and ageing of mild steel: III Discussion of results, Proceedings of the Physical Society, Section B, 64(9): 747–753, 1951.

Huber M.T., Speciffic work of strain as a measure of material effort, Archive of Mechanics, 56(3): 173–190, 2004 (originally Czasopismo Techniczne, XXII, 1904, Lwów, Proceedings of Lwów Polytechnic Society; translated into English in 2004 by A. Strek under scientific supervision of R.B. Pecherski).

Lunt D., da Fonseca Q.D., Rugg D., Preuss M., Microscopic strain localisation in Ti-6Al-4V during uniaxial tensile loading, Materials Science and Engineering: A, 680: 444–453, 2017.

Mayeur J.R., McDowell D.L., A three-dimensional crystal plasticity model for duplex Ti-6Al-4V, International Journal of Plasticity, 23(9): 1457–1485, 2007.

Méric L., Poubanne P., Cailletaud G., Single crystal modeling for structural calculations: Part 1 – Model presentation, Engineering Materials and Technology, 113(1): 162–170, 1991.

Petch N.J., The cleavage strength of polycrystals, Journal of the Iron and Steel Institute, 174: 25–28, 1953.

Philippe M.J., Bouzy E., Fundenberger J.-J., Textures and anisotropy of titanium alloys, Materials Science Forum, 273–275: 511–522, 1998.

Philippe M.J., Esling C., Hocheid B., Role of twinning in texture development and in plastic deformation of hexagonal materials, Textures, Stress, and Microstructures, 7(4): 265–301, 1988.

Philippe M.J., Serghat M., Van Houtte P., Esling C., Modelling of texture evolution for materials of hexagonal symmetry. II. Application to zirconium and titanium _or near _-alloys, Acta Metallurgica et Materialia, 43(4): 1619–1630, 1995.

Quey R., Dawson P.R., Barbe F., Large-scale 3D random polycrystals for the finite element method: Generation, meshing and remeshing, Computer Methods in Applied Mechanics and Engineering, 200(17–20): 1729–1745, 2011.

Ramtani S., Bui H.Q., Dirras G., A revisited generalized self-consistent polycrystal model following an incremental small strain formulation and including grain-size distribution effect, International Journal of Engineering Science, 47(4): 537–553, 2009.

Rugg D., Dixon M., Dunne F.P.E., Effective structural unit size in titanium alloys, The Journal of Strain Analysis for Engineering Design, 42(4): 269–279, 2007.

Schmid E., Boas W., Crystal plasticity [in German: Kristallplastizität], Verlag Julius Springer, Berlin, 1935.

Tabourot L., Fivel M., Rauch E., Generalised constitutive laws fo27. Tirry W., Coghe F., Bouvier S., Gasperini M., Rabet L., Schryvers D., A multiscale characterization of deformation twins in Ti6Al4V sheet material deformed by simple shear, Materials Science and Engineering: A, 527(16–17): 4136–4145, 2010.

Weng G.J., A micromechanical theory of grain-size dependance in metal plasticity, Journal of the Mechanics and Physics of Solids, 31(3): 193–203, 1983,

Williams J.C., Baggerly R.G., Paton N.E., Deformation behavior of HCP Ti-Al. alloy single crystals, Metallurgical and Materials Transactions A, 33(3): 837–850, 2002.

DOI: 10.24423/EngTrans.1014.20190615