Anisotropic response of high-purity \(\alpha \)-titanium: experimental characterization and constitutive modeling. (English) Zbl 1426.74052
Summary: This paper presents a comprehensive experimental and theoretical investigation of the deformation behavior of high-purity, polycrystalline \(\alpha \)-titanium under quasi-static conditions at room temperature. The initial material in this study was a cross-rolled plate with a strong basal texture. To quantify the plastic anisotropy and the tension – compression asymmetry of this material, monotonic tensile and compressive tests were conducted, on samples cut along different directions of the plate. A new anisotropic elastic/plastic model was developed to describe the quasi-static macroscopic response of the aggregate. Key in its formulation is the use of an anisotropic yield criterion that captures strength-differential effects and an anisotropic hardening rule that accounts for texture evolution associated to twinning. A very good agreement between FE simulations using the model developed and uniaxial data was obtained.
MSC:
| 74C05 | Small-strain, rate-independent theories of plasticity (including rigid-plastic and elasto-plastic materials) |
| 74E10 | Anisotropy in solid mechanics |
| 74-05 | Experimental work for problems pertaining to mechanics of deformable solids |
| 74S05 | Finite element methods applied to problems in solid mechanics |
Keywords:
twinning; \(\alpha \)-titanium; tension; compression asymmetry; orthotropic elasto-plastic model; finite elementReferences:
| [1] | Barlat, F.; Cazacu, O.; Zyczkowski, M.; Banabic, D.; Yoon, J.: Yield surface plasticity and anisotropy in sheet metals, Continuum scale simulation of engineering materials, fundamentals – microstructures – process applications, 145-178 (2004) |
| [2] | Barlat, F.; Yoon, J.; Cazacu, O.: On linear transformation-based anisotropic yield functions, International journal of plasticity 23, 876-896 (2007) · Zbl 1359.74014 |
| [3] | Cazacu, O.; Barlat, F.: Generalization of Drucker’s yield criterion to orthotropy, Mathematics and mechanics of solids 6, 613-630 (2001) · Zbl 1128.74303 · doi:10.1177/108128650100600603 |
| [4] | Cazacu, O.; Barlat, F.: A criterion for description of anisotropy and yield differential effects in pressure-insensitive metals, International journal of plasticity 20, 2027-2045 (2004) · Zbl 1107.74006 · doi:10.1016/j.ijplas.2003.11.021 |
| [5] | Cazacu, O.; Barlat, F.: Modeling plastic anisotropy and strength differential effects in metallic materials, Multiscale modeling of heterogeneous materials: from microstructure to macro-scale properties, 71-87 (2008) |
| [6] | Cazacu, O.; Plunkett, B.; Barlat, F.: Orthotropic yield criterion for hexagonal closed packed metals, International journal of plasticity 22, 1171-1194 (2006) · Zbl 1090.74015 · doi:10.1016/j.ijplas.2005.06.001 |
| [7] | Chun, Y. B.; Yu, S. L.; Semiatin, S. L.; Hwang, S. K.: Effect of deformation twinning on microstructure and texture evolution during cold rolling of cp-titanium, Materials science and engineering A 398, 209-219 (2005) |
| [8] | Follansbee, P. S.; Gray, G.; Wu, P. D.: An analysis of the low temperature, low and high strain-rate deformation of ti – 6Al – 4V, Metallurgical transactions A 20, 863-874 (1989) |
| [9] | Graff, S.; Brocks, W.; Steglich, D.: Yielding of magnesium: from single crystal to polycrystalline aggregates, International journal of plasticity 23, 1957-1978 (2007) · Zbl 1129.74011 · doi:10.1016/j.ijplas.2007.07.009 |
| [10] | Hill, R.: A theory of the yielding and plastic flow of anisotropic metals, Proceedings of the royal society of London A 193, 281-297 (1948) · Zbl 0032.08805 · doi:10.1098/rspa.1948.0045 |
| [11] | Hosford, W.: Mechanical behavior of materials, (2005) · Zbl 1188.74001 |
| [12] | Hosford, W. F.; Allen, T.: Deformation characteristics of textured magnesium, Transactions of the TMS-AIME 242, 654-661 (1968) |
| [13] | Hosford, W. F.; Allen, T.: Twinning and directional slip as a cause for a strength differential effect, Metallurgical transactions 4, 1424-1425 (1973) |
| [14] | Johnson, G.R., Beissel, S.R., Stryk, R.A., Gerlach, C.A., Holmquist, T.J., October 2003. User instructions for the 2003 version of the EPIC code. Tech. Rep., Network Computing Services Inc., Minneapolis, MN. |
| [15] | Kaschner, G.C., Lovato, M.L., Stout, M.G., Proust, G., Liu, C., Beyerlein, I.J., Usov, I., Wang, Y., Tome, C.N., in press. Mini-tensile experiments of clock-rolled zirconium plate. Experimental Mechanics, doi:10.1007/s11340-008-9213-6. |
| [16] | Khan, A.; Suh, Y.; Kazmi, R.: Quasi-static and dynamic loading responses and constitutive modeling of titanium alloys, International journal of plasticity 20, 2233-2248 (2004) · Zbl 1135.74300 · doi:10.1016/j.ijplas.2003.06.005 |
| [17] | Khan, A.; Kazmi, R.; Farroch, B.: Multiaxial and non-proportional loading responses, anisotropy and modeling of ti – 6Al – 4V titanium alloy over wide ranges of strain rates and temperatures, International journal of plasticity 23, 931-950 (2007) · Zbl 1148.74304 · doi:10.1016/j.ijplas.2006.08.006 |
| [18] | Kuwabara, T., Katami, C., Kikuchi, M., Shindo, T., Ohwue, T., 18 – 20 June 2001. Cup drawing of pure titanium sheet – finite element analysis and experimental validation. In: Proceedings of the Seventh International Conference on Numerical Methods in Industrial Forming Processes, Toyohashi, Japan. pp. 781 – 787. |
| [19] | Lee, D.; Backofen, W. A.: Yielding and plastic deformation in textured shett of titanium and its alloys, Transactions of the TMS-AIME 236, 1703-1966 (1966) |
| [20] | Lee, W. S.; Lin, M.: The effects of strain rate and temperature on the compressive deformation behavior of ti – 6Al – 4V alloy, Journal of materials processing technology 71, 235-246 (1997) |
| [21] | Lee, M. -G.; Wagoner, R.; Lee, J.; Chung, K.; Kim, H.: Constitutive modeling for anisotropic/asymmetric hardening behavior of magnesium alloy sheets, International journal of plasticity 24, 545-582 (2008) · Zbl 1214.74004 · doi:10.1016/j.ijplas.2007.05.004 |
| [22] | Li, Q.; Xu, Y.; Bassim, M. N.: Dynamic mechanical behavior of pure titanium, Journal of materials processing technology 155, 1889-1892 (1997) |
| [23] | Li, S.; Hoferlin, E.; Bael, A. V.; Houtte, P. V.; Teodosiu, C.: Finite-element modeling of plastic anisotropy induced by texture and strain-path changes, International journal of plasticity 19, 647-674 (2003) · Zbl 1134.74408 · doi:10.1016/S0749-6419(01)00079-1 |
| [24] | Lou, X.; Li, M.; Boger, R.; Agnew, S.; Wagoner, R.: Hardening evolution of AZ31B mg sheet, International journal of plasticity 23, 44-86 (1997) · Zbl 1331.74007 |
| [25] | Nemat-Nasser, S.; Guo, W. -G.; Nesterenko, V.; Indrakanti, S.; Gu, Y. -B.: Dynamic response of conventional and hot isostatically pressed ti – 6Al – 4V alloys: experiments and modeling, Mechanics of materials 33, 425-439 (2001) |
| [26] | Picu, R.; Majorell, A.: Mechanical behavior of ti – 6Al – 4V at high and moderate temperatures. Part II: Constitutive modeling, Materials science and engineering A 326, 306-316 (2002) |
| [27] | Plunkett, B.; Cazacu, O.: Viscoplastic modeling of anisotropic textured metals, Multiscale modeling of heterogeneous materials: from microstructure to macro-scale properties, 111-126 (2008) |
| [28] | Plunkett, B.; Lebensohn, R. A.; Cazacu, O.; Barlat, F.: Evolving yield function of hexagonal materials taking into account texture development and anisotropic hardening, Acta materialia 54, 4159-4169 (2006) |
| [29] | Proust, G.; Tome, C. N.; Kaschner, G. C.: Modeling texture, twinning, and hardening evolution during deformation of hexagonal materials, Acta materialia 55, 2137-2148 (2007) |
| [30] | Salem, A. A.; Kalidindi, S. R.; Doherty, R. D.: Strain hardening of titanium: role of deformation twinning, Acta materialia 51, 4225-4237 (2003) |
| [31] | Simo, J.; Hughes, T.: Computational inelasticity, (1998) · Zbl 0934.74003 |
| [32] | Staroselsky, A.; Anand, L.: A constitutive model for hcp metals deforming by slip and twinning: application to magnesium alloy AZ31, International journal of plasticity 19, 1843-1864 (2003) · Zbl 1098.74546 · doi:10.1016/S0749-6419(03)00039-1 |
| [33] | Tome, C. N.; Lebensohn, R. A.: Self-consistent homogenization methods for texture and anisotropy, Continuum scale simulation of engineering materials, fundamentals – microstructures - process applications, 473-497 (2004) |
| [34] | Tome, C. N.; Maudlin, P. J.; Lebensohn, R. A.; Kaschner, G. C.: Mechanical response of zirconium: I. Derivation of a polycrystal constitutive law and finite element analysis, Acta materialia 49, 3085-3096 (2001) |
| [35] | Vitek, V.; Mrovec, M.; Bassani, J. L.: Influence of non-glide stresses on plastic flow: from atomistic to continuum modeling, Materials science and engineering A 365, 31-37 (2004) |
| [36] | Wu, X.; Kalidindi, S. R.; Necker, C.; Salem, A.: Prediction of crystallographic texture evolution and anisotropic stress – strain curves during large plastic strains in high purity \(\alpha \)-titanium using a Taylor-type crystal plasticity model, Acta materialia 55, 423-432 (2007) |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
