National Research Nuclear University MEPhI, Moscow, Russia:

M. G. Isaenkova, Doctor of Physical and Mathematical Sciences, Professor
Yu. A. Perlovich, Doctor of Physical and Mathematical Sciences, Professor
O. A. Krymskaya, Junior Researcher
D. I. Zhuk, Engineer, e-mail: dimazhuk@gmail.com

In this work, the process of deformation of zirconium, which is widely used in nuclear power plants, was investigated using crystal plasticity modeling. This approach allows analyzing of the reorientation of grains and studying the process of material structure changing: splitting of grains due to the development of twinning and the formation of high-angle boundaries. DAMASK code was used for the numerical solution of problems. It is based on a mathematical method for solving systems of partial differential equations using fast Fourier transformation. The program has been developed for processing simulation data and reorientation of crystallite twins in which stresses exceed a certain critical level corresponding to this material. For verification of the created method, the data of rolling zirconium single crystal plates was used. These plates were cut using the spark method from a cylindrical single crystal of pure Zr obtained by solid-phase recrystallization. The qualitative correspondence of the modeled pole figures to the experimental ones was found. The efficiency of the created model of plastic deformation in the case of simultaneous activation of slip and twinning systems is demonstrated. The dependences of the distribution of contributions to the deformation of various slip and twinning systems on the degree of deformation during rolling are constructed. According to the simulation data, the share of twinning in texture reorientation is 87%. Moreover, 66% is the share of twinning systems of the type. At further stages, the influence of twins on the texture is rather small, in total for all systems ~ 5%.

1. Isaenkova M. G., Perlovich Yu. A. Evolution of crystallographic texture and substructural heterogeneity in zirconium alloys under deformation and heat treatment. Moscow : NRNU MEPhI, 2014. 528 p.

2. Perlovich Yu. A., Fesenko V. A., Krymskaya O. A., Krapivka N. A. et al. Regularities of recrystallization of rolled single crystals and polycrystals of zirconium and alloy Zr – 1% Nb. The Physics of Metals and Metallography. 2014. Vol. 115, No. 8. pp. 756–764.
3. Tenckhoff E. Review of deformation mechanisms, texture, and mechanical anisotropy in zirconium and zirconium base alloys. Journal of ASTM International. 2005. Vol. 2, Iss. 4. pp. 1–26.
4. Isaenkova M., Perlovich Y., Fesenko V., Stolbov S., Klyukova K. et al. Features of Formation of Crystallographic Texture in Cells of Spacing Grid at their Stamping. KnE Materials Science. 2018. Vol. 4, No. 1. pp. 9–19.
5. Mareau C., Daymond M. R. Micromechanical modelling of twinning in polycrystalline materials: Application to magnesium. International Journal of Plasticity. 2016. Vol. 85. pp. 156–171.
6. Mahesh S. Prediction of deformation twinning statistics in zirconium using the Taylor, ALAMEL and binary tree models and a classical twinning criterion. International Journal of Plasticity. 2017. Vol. 98. pp. 83–105.
7. Shao Y., Tang T., Li D., Tang W., Peng Y. Crystal plasticity finite element modelling of the extrusion texture of a magnesium alloy. Modelling and Simulation in Materials Science and Engineering. 2015. Vol. 23, Iss. 5. 055011.
8. Isaenkova M., Perlovich Y., Zhuk D., Krymskaya O. Crystal plasticity simulation of Zirconium tube rolling using multi-grain representative volume element. AIP Conference Proceedings. AIP Publishing. 2017. Vol. 1896. p. 160023.
9. Roters F., Diehl M., Shanthraj P., Eisenhohr P., Reuber C. et al. DAMASK – The Düsseldorf Advanced Material Simulation Kit for modeling multi-physics crystal plasticity, thermal, and damage phenomena from the single crystal up to the component scale. Computational Materials Science. 2019. Vol. 158. pp. 420–478.
10. Eghtesad A., Zecevic M., Lebensohn R. A., Mc.Cabe R. J., Knezevic M. Spectral database constitutive representation within a spectral micromechanical solver for computationally efficient polycrystal plasticity modelling. Computational Mechanics. 2018. Vol. 61. pp. 89–104.
11. Kocks U. F., Tome C. N., Wenk H.-R. Texture and anisotropy: preferred orientations in polycrystals and their effect on materials properties. Cambridge University press, 2000.
12. Hobson D. O. Textures in deformed zirconium single crystals. Oak Ridge National Lab., Tennessee, 1968.
13. Kanit T., Forest S., Galliet I., Mounoury V., Jeulin D. Determination of the size of the representative volume element for random composites: statistical and numerical approach. International Journal of Solids and Structures. 2003. Vol. 40, Iss. 13-14. pp. 3647–3679.
14. Bachmann F., Hielscher R., Schaeben H. Texture analysis with MTEX–free and open source software toolbox. Solid State Phenomena. 2010. Vol. 160. pp. 63–68.
15. Alharthi H., Hazra S., Alghamdi A., Banabic D., Dashwood R. Determination of the yield loci of four sheet materials (AA6111-T4, AC600, DX54D+ Z, and H220BD+ Z) by using uniaxial tensile and hydraulic bulge tests. The International Journal of Advanced Manufacturing Technology. 2018. Vol. 98. pp. 1307–1319.