Library Subscription: Guest
Begell Digital Portal Begell Digital Library eBooks Journals References & Proceedings Research Collections
International Journal for Multiscale Computational Engineering

Impact factor: 1.103

ISSN Print: 1543-1649
ISSN Online: 1940-4352

International Journal for Multiscale Computational Engineering

DOI: 10.1615/IntJMultCompEng.v9.i4.80
pages 459-480


Irene J. Beyerlein
Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico, 87545, USA
R. J. McCabe
Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
C. N. Tome
Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA


Deformation twinning is an important mechanism for metals with hexagonal close-packed (hcp) crystal structures such as titanium, magnesium, beryllium, and zirconium, as well as metals with other low-symmetry crystal structures. This article presents a multiscale constitutive model for the plastic deformation of hcp polycrystalline metals that is built upon the viscoplastic self-consistent (VPSC) polycrystal scheme. This framework includes a novel probabilistic model for predicting when, where, and which variants nucleate, a dislocation density model for crystallographic slip, and a micromechanical model for twin lamella thickening and twin reorientation. Length scales of an individual slip or twinning system and the polycrystalline aggregate are interactively connected. Here, this constitutive model is applied to high-purity magnesium (Mg) and zirconium (Zr) deformed under loading conditions where twinning is intense. Correlations are made between the formation of deformation twins, bulk stress-strain behavior and texture development, and individual grain properties such as size and crystallographic orientation.


  1. Agnew, S. R., Tomé, C. N., Brown, D. W., Holden, T. M., and Vogel, S. C., Study of slip mechanisms in a magnesium alloy by neutron diffraction and modeling. DOI: 10.1016/S1359-6462(02)00591-2

  2. Armstrong, R., Codd, I., Douthwaite, R. M., and Petch, N. J., The plastic deformation of polycrystalline aggregates. DOI: 10.1080/14786436208201857

  3. Barnett, M. R., A rationale for the strong dependence of mechanical twinning on grain size. DOI: 10.1016/j.scriptamat.2008.05.027

  4. Barnett, M. R., Keshavarz, Z., Beer, A. G., and Atwell, D., Influence of grain size on the compressive deformation of wrought Mg-3Al-1Zn. DOI: 10.1016/j.actamat.2004.07.015

  5. Beyerlein, I. J., Capolungo, L., Marshall, P. E., McCabe, R. J., and Tomé, C. N., Statistical analyses of deformation twinning in magnesium. DOI: 10.1080/14786431003630835

  6. Beyerlein, I. J. and Tomé, C. N., A dislocation-based constitutive law for pure Zr including temperature effects. DOI: 10.1016/j.ijplas.2007.07.017

  7. Beyerlein, I. J. and Tomé, C. N., A probabilistic twin nucleation model for HCP polycrystalline metals. DOI: 10.1098/rspa.2009.0661

  8. Bronkhorst, C. A., Hansen, B. L., Cerreta, E. K., and Bingert, J. F., Modeling the microstructural evolution of metallic polycrystalline materials under localization conditions. DOI: 10.1016/j.jmps.2007.03.019

  9. Brown, D. W., Beyerlein, I. J., Sisneros, T. A., Clausen, B., and Tomé, C. N., Role of deformation twinning and slip during compressive deformation of beryllium as a function of strain rate.

  10. Capolungo, L., Beyerlein, I. J., and Tomé, C. N., Slip-assisted twin growth in hexagonal close-packed metals. DOI: 10.1016/j.scriptamat.2008.08.044

  11. Capolungo, L., Beyerlein, I. J., Kaschner, G. C., and Tomé, C. N., On the interaction between slip dislocations and twins in HCP Zr. DOI: 10.1016/j.msea.2009.01.035

  12. Capolungo, L., Marshall, P. E., McCabe, R. J., Beyerlein, I. J., and Tomé, C. N., Nucleation and growth of twins in Zr: A statistical study. DOI: 10.1016/j.actamat.2009.08.030

  13. Christian, J. W. and Mahajan, S., Deformation twinning.

  14. Chun, J. S., Byrne, J. G., and Borneman, A., Inhibition of deformation twinning by precipitates in a magnesium-zinc alloy. DOI: 10.1080/14786436908228701

  15. Eshelby, J. D., The determination of the elastic field of an ellipsoidal inclusion and related problems. DOI: 10.1098/rspa.1957.0133

  16. Henrie, B. L. and Mason, T. A., A fully automated technique for twin identification through electron backscatter diffraction.

  17. Hull, D., Effect of grain size and temperature on slip, twinning, and fracture in 3% silicon iron (with 0.037% carbon).

  18. Kaschner, G. C., Tomé, C. N., Beyerlein, I. J., Vogel, S. C., Brown, D. W., and McCabe, R. J., Role of twinning in the hardening response of zirconium during temperature reloads. DOI: 10.1016/j.actamat.2006.02.036

  19. Kocks, U. F. and Mecking, H., Physics and phenomenology of strain hardening: The FCC case. DOI: 10.1016/s0079-6425(02)00003-8

  20. Lahaie, D., Embury, J. D., Chadwick, M. M., and Gray, G. T., A note on the deformation of fine-grained magnesium alloys.

  21. Lebensohn, R. A. and Tomé, C. N., A self-consistent anisotropic approach for the simulation of plastic deformation and texture development of polycrystals: Application to zirconium alloys.

  22. Lebensohn, R. A., Liu, Y., and Castaneda, P. P., On the accuracy of the self-consistent approximation for polycrystals: Comparison with full-field numerical simulations. DOI: 10.1016/j.actamat.2004.07.040

  23. Madec, R., Devincre, B., Kubin, L., Hoc, T., and Rodney, D., The role of collinear interaction in dislocation-induced hardening. DOI: 10.1126/science.1085477

  24. Marshall, P., Proust, G., Rogers, J. T., and McCabe, R. J., Automatic twin statistics from electron backscattered diffraction data. DOI: 10.1111/j.1365-2818.2009.03343.x

  25. McCabe, R. J., Proust, G. N. L., Cerreta, E. K., and Misra, A., Quantitative analysis of deformation twinning in zirconium. DOI: 10.1016/j.ijplas.2008.03.010

  26. Meyers, M. A., Vohringer, O., and Lubarda, V. A., The onset of twinning in metals: A constitutive description. DOI: 10.1016/S1359-6454(01)00300-7

  27. Molinari, A, Canova, G. R., and Ahzi, S., A self-consistent approach of the large deformation polycrystal viscoplasticity. DOI: 10.1016/0001-6160(87)90297-5

  28. Okazaki, K. and Conrad, H., Effects of interstitial content and grain size of the strength of titanium at low temperatures. DOI: 10.1016/0001-6160(73)90028-X

  29. Partridge, P. G., The crystallography and deformation modes of hexagonal close-packed metals. DOI: 10.1179/095066067790138184

  30. Price, P. B., Nucleation and growth on twins in dislocation-free zinc crystals. DOI: 10.1098/rspa.1961.0031

  31. Priestner, R. and Leslie, W. C., Nucleation of deformation twins at slip plane intersections in B.C.C. metals. DOI: 10.1080/14786436508223953

  32. Proust, G., Tomé, C. N., and Kaschner, G. C., Modeling texture, twinning and hardening evolution during deformation of hexagonal materials. DOI: 10.1016/j.actamat.2006.11.017

  33. Proust, G., Tomé, C. N., Jain, A., and Agnew, S. R., Modeling the effect of twinning and detwinning during strain-path changes of magnesium alloy AZ31. DOI: 10.1016/j.ijplas.2008.05.005

  34. Rapperport, E. J. and Hartley, C. S., Deformation modes of zirconium at 77-degrees-K, 575-degrees-K, and 1075-degrees-K.

  35. Reed-Hill, R. E., Role of Deformation Twinning in the Plastic Deformation of a Polycrystalline Anisotropic Metal.

  36. Song, S. G. and Gray, G. T., Structural interpretation of the nucleation and growth of deformation twins in Zr and Ti, 1. Application of the coincidence site lattice (CSL) theory to twinning problems in hcp structures. DOI: 10.1016/0956-7151(94)00433-1

  37. Tomé, C. N. and Lebensohn, R. A., Self consistent homogenization methods for texture and anisotropy.

  38. Wang, J., Beyerlein, I. J., and Tomé , C. N., An atomic and probabilistic perspective on twin nucleation in Mg. DOI: 10.1016/j.scriptamat.2010.01.047

  39. Yoo, M. H., Slip, twinning, and fracture in hexagonal closed packed materials. DOI: 10.1007/BF02648537