An explicit formulation for multiscale modeling of bcc metals. (English) Zbl 1421.74024

Summary: Many materials for specialized applications exhibit a body-centered cubic structure; e.g., tantalum, vanadium, barium and chromium. In addition, the successful modeling of body-centered cubic (bcc) metals is a necessary step toward modeling of common structural materials such as iron. Implicit formulations for this class of materials exist
(e.g., [L. Stainier et al., J. Mech. Phys. Solids 50, No. 7, 1511–1545 (2002; Zbl 1071.74553); the first author et al., “A pressure-dependent multiscale model for bcc metals”, Preprint], but are impractical to resolve large-scale dynamic deformation processes. In this article, we describe a procedure analogous to [the first author et al., Int. J. Plast. 22, No. 10, 1988–2011 (2006; Zbl 1136.74310)]. wherein we construct an explicit formulation for the multiscale physics models. This update is based on the model of the first author et al. [Preprint, loc. cit.] using a power law representation for the plastic slip rates. The existing implicit form of the model provides qualitative matching with experiments at quasi-static strain rates. The model is recast in an explicit form and applied first to a high quasi-static strain rate to verify that the two forms of the model return similar predictions for similar input parameters. The explicit model is also applied to several high strain rates, showing that it captures characteristic features observed in experimental tests of high-rate deformations, such as the drop in stress immediately after yield that is present in split Hopkinson pressure bar (SHPB) experiments. This test provides qualitative evidence that the model is suitable for high-strain-rate applications. The utility of the model is further demonstrated by a one-dimensional simulation of a SHPB test. Finally, a test case modeling pressure impact of a Tantalum plate using 600,000 elements is shown. The simulations show that the explicit model is capable of recovering the salient features of the experiments while integrating the constitutive update in a robust manner.


74E15 Crystalline structure
74S30 Other numerical methods in solid mechanics (MSC2010)
Full Text: DOI


[1] Baskes, R.: The status role of modeling and simulation in materials science and engineering, Current opinion in solid state and materials science 4, No. 3, 273-277 (1999)
[2] Bulatov, V.; Kubin, L.: Dislocation modelling at atomistic and mesoscpic scales, Current opinion in solid state and materials science 3, No. 6, 558-561 (1998)
[3] Campbell, G.; Foiles, S.; Huang, H.; Hughes, D.; King, W.; Lassila, D.; De La Rubia, T.; Shu, J.; Smyshlyaev, V.: Multi-scale modeling of polycrystal plasticity: a workshop report, Materials science and engineering A 251, No. 1 – 2, 1-22 (1998)
[4] Cohen, R.; Gulseren, O.: Thermal equation of state of tantalum, Physical review B 63, No. 22, 224101-224111 (2000)
[5] Cuitiño, A.; Ortiz, M.: Computational modeling of single crystals, Modelling and simulation in materials science and engineering 1, 255-263 (1993)
[6] Cuitiño, A.; Stainier, L.; Wang, G.; Strachan, A.; Cagin, T.; Goddard, W.; Ortiz, M.: A multiscale approach for modeling crystalline solids, Journal of computer aided material design (2001)
[7] Furnish, M., Reinhart, W., Trott, W., Chhabildas, L., Vogler, T., 2006. Variability in dynamic properties of tantalum: Spall, hugoniot elastic limit and attenuation. In: AIP Conference Proceedings. vol. 845. pp. 615 – 618.
[8] Govindarajan, R.; Aravas, N.: Pressure-dependent plasticity models – loading – unloading criteria and the consistent linearizarion of an integration algorithm, Communications in numerical methods in engineering 11, No. 4, 339-345 (1995) · Zbl 0826.73019
[9] Graff, K. F.: Wave motion in elastic solids, (1975) · Zbl 0314.73022
[10] Gulseren, O.; Cohen, R.: High-pressure thermoelasticity of body-centered cubic tantalum, Physical review B – condensed matter 65, 064103 (2002)
[11] Kapoor, R.; Nemat-Nasser, S.: High rate deformation of single crystal tantalum: temperature dependence and latent hardening, Scripta materialia 40, No. 2, 159-164 (1999)
[12] Knezevic, M.; Kalidindi, S.; Fullwood, D.: Computationally efficient database and spectral interpolation for fully plastic Taylor-type crystal plasticity calculations of face-centered cubic polycrystals, International journal of plasticity 24, No. 7, 1264-1276 (2008) · Zbl 1154.74049
[13] Kolsky, H.: An investigation of the mechanical properties of materials at very high rates of loading, Proceedings of the physical society 62, 676-700 (1949)
[14] Kuchnicki, S.; Cuitiño, A.; Radovitzky, R.: Efficient and robust constitutive integrators for single-crystal plasticity modeling, International journal of plasticity 22, No. 10, 1988-2011 (2006) · Zbl 1136.74310
[15] Kuchnicki, S., Radovitzky, R., Cuitiño, A., Strachan, A., Ortiz, M., in preparation. A pressure-dependent multiscale model for bcc metals.
[16] Li, X.: Large-strain constitutive modeling and computation for isotropic creep elastoplastic damage solids, International journal for numerical methods in engineering 38, No. 5, 841-860 (1995) · Zbl 0824.73053
[17] Li, H.; Yang, H.; Sun, Z.: A robust integration algorithm for implementing rate dependent crystal plasticity into explicit finite element method, International journal of plasticity 24, No. 2 (2008)
[18] Ling, X.; Horstemeyer, M.; Potirniche, G.: On the numerical implementation of 3d rate dependent single crystal plasticity formulations, International journal for numerical methods in engineering 63, No. 4, 548-568 (2005) · Zbl 1140.74415
[19] Lubarda, V.; Krajcinovic, D.: Constitutive structure of the rate theory of damage in brittle elastic solids, Applied mathematics and computation 67, No. 1-3, 81-101 (1995) · Zbl 0852.73049
[20] Mcginty, R.; Mcdowell, D.: A semi-implicit integration scheme for rate independent finite crystal plasticity, International journal of plasticity 22, No. 6, 996-1025 (2006) · Zbl 1176.74036
[21] Meyers, M. A.: Dynamic behavior of materials, (1994) · Zbl 0893.73002
[22] Moriarty, J.; Xu, W.; Soderlind, P.; Belak, J.; Yanf, L.; Zhu, J.: Atomistic simulations for multiscale modeling in bcc metals, Journal of engineering materials and technology – transactions of the ASME 121, No. 2, 120-125 (1999)
[23] Nemat-Nasser, S.; Isaacs, J.; Starrett, J.: Hopkinson techniques for dynamic recovery experiments, Proceedings of the royal society of London A 435, No. 1894, 371-391 (1991)
[24] Nemat-Nasser, S.; Li, Y. -F.; Isaacs, J. B.: Experimental/computational evaluation of flow stress at high strain rates applicable to adiabatic shear banding, Mechanics of materials 17, No. 2 – 3, 111-134 (1994)
[25] Phillips, R.: Multiscale modeling in the mechanics of materials, Current opinion in solid state and materials science 3, No. 6, 526-532 (1998)
[26] Phillips, R.; Rodney, D.; Shenoy, V.; Tadmor, E.; Ortiz, M.: Heirarchical models of plasticity: dislocation nucleation and interaction, Modelling and simulation in materials science and engineering 7, No. 5, 769-780 (1999)
[27] Reid, C.: Deformation geometry for materials scientists, (1973) · Zbl 0308.73007
[28] Seeger, A.: Philosophical magazine, Philosophical magazine 1, 651 (1956)
[29] Stainier, L.; Cuitiño, A.; Ortiz, M.: A micromechanical model of hardening, rate sensitivity, and thermal softening in bcc crystals, Journal of the mechanics and physics of solids 50, No. 7, 1511-1545 (2002) · Zbl 1071.74553
[30] Strachan, A., Cagin, T., Gülseren, O., Mukherjee, S., Cohen, R., III, W.G., 2004. First principles force field for metallic tantalum. Modelling and Simulation in Materials Science and Engineering 12 (S445), 1 – 15.
[31] Svoboda, A.; Lindgren, L.; Oddy, A.: The effective stress function algorithm for pressure-dependent plasticity applied to hot isostatic pressing, International journal for numerical methods in engineering 43, No. 4, 587-606 (1998) · Zbl 0945.74080
[32] Vitek, V.; Mrovec, A.; Groger, R.; Bassani, J.; Racherla, V.; Lin, Y.: Effects of non-glide stresses on the plastic flow of single and polycrystals of molybdenum, Materials science and engineering A – structural material properties, microstructure and processing 387, 138-142 (2004)
[33] Wang, G., Strachan, A., Cagin, T., III, W.G., 2004. Calculating the peierls energy and peierls stress from atomic simulations of screw dislocation dynamics: application to bcc tantalum. Modelling and Simulation in Materials Science and Engineering 12 (S371), 1 – 19.
[34] Zhao, H.: Material behaviour characterisation using SHPB techniques, tests and simulations, Computers & structures 81, 1301-1310 (2003)
[35] Zhao, Z.; Kuchnicki, S.; Cuitiño, A.; Radovitzky, R.: Influence of in-grain resolution on the accuracy of f.c.c. Deformation texture simulation., Acta materialia 55, No. 7, 2361-2373 (2007)
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