Vladimir A. Skripnyak1, Nataliya V. Skripnyak1,2(*), Vladimir V. Skripnyak1, and Evgeniya G. Skripnyak1
1National Research Tomsk State University, Tomsk, Russia
2Linköping University, Linköping, Sweden
(*)Email: [email protected]
ABSTRACT
The results of the development of a physical-mechanical model for predicting the mechanical and deformation properties of Zr−Nb in a wide range of strain rates are presented. The model was used to study the mechanical behavior of coarse-grained and ultrafine Zr-Nb alloys under quasi-static and dynamic loading conditions. It was shown that the creation of bimodal grain structures in Zr−Nb alloys causes an increase in the flow stress while maintaining the ductile fracture in a wide range of strain rates. It was shown the strain rate sensitivity of the yield stress of Zr–Nb alloys strongly depends on the concentration of Nb. The concentration of Nb in Zr−Nb alloys, temperature and pressure determine the phase state. Martensitic phase transitions α→ω and β→ω cause not only changes in the elastic properties and parameters of the Hugoniot adiabat of Zr−Nb alloys, but also their strain hardening and the spall strength. The results can be used in engineering analysis of designed technical systems for nuclear reactors.
Keywords: computer simulation, mechanical behavior, ductility, zirconium-niobium alloys, high strain rate
INTRODUCTION
Improvement in technology of fabrication of fuel claddings and some constructional elements of nuclear reactors is connected with computer simulation of mechanical properties and structural evolution of radiation-resistant alloys Zr–Nb. In this regard, there is an increasing need to develop computational models of the mechanical behavior of advanced Zr−Nb in loading conditions close to operating ones. The Zr–Nb has a unique complex of physical and mechanical properties and is considered as promising structural alloys for nuclear reactors of IV generation. Zirconium alloys with a concentration of Nb below 2.5 weight % and additionally doped with Mo, Fe, Cr for the stabilization of precipitations of beta-phase Zr were studied during last decade (Xiao, 2010). A new precipitation-strengthening theory was present by Fang and coworkers (Fang,2019). This theory describes a probability-dependent precipitation-strengthening mechanism, to more accurately predict the yield strength of alloys. Precipitation strengthening of Zr-Nb alloys requires detailed investigation. It is known that the mechanical behavior of Zr-Nb alloys during the α→β phase transformation changes significantly (Hazell, 2014, Kazakov,2015, Skripnyak,2014, Skripnyak,2017). In this regard, the mechanical behavior of α, and α+β Zr–Nb alloys was studied in a wide strain rates.
RESULTS AND CONCLUSIONS
Mechanical behavior of Zr−1%Nb and Zr−2,5 % Nb alloys (Grades E110, E625, E125) was studied in the strain rate range from 10-3 to 106 s-1 by the numerical simulation method. The
model took into account the multiphase state of Zr−Nb alloys, different resistance of α, β and ω phases to plastic flow. Simulation of plastic flow, evolution of damages and destruction of alloys at uniaxial tension and compression of samples in quasi-static conditions, loading of samples by plane shock waves was carried out. It was shown the strain rate sensitivity of the flow stress of alpha Zr−1%Nb in the range from 10-3 to 103 s-1 is less then at strain rates above 103 s-1. The creation of the three-wave configuration was predicted in Zr−1%Nb due to polymorphous α → ω transition at ~11 GPa. The Hugoniot elastic limit (σHEL) and spall strength of Zr−х%Nb alloys strongly depends on beta phase concentration. Calculations have shown that the increase in the dynamic yield strength σsd = 1.5σHEL(1 − (cb/cl)2 can be caused by an increase in the volume concentration of the beta phase in Zr−х%Nb alloys (cb, and cl are thebulk and the longitudinal sound velocity, respectively). The increase in the β phase concentration at elevated temperatures causes an increasing of the dynamic yield strength of Zr−1%Nb alloys. It was shown that ZrFe3 and βNb precipitations in Zr−2,5%Nb caused increasing of σsd and the spall strength.
ACKNOWLEDGMENTS
This work was supported by the Russian Science Foundation (RSF), grant № 18-71-00117. The authors are grateful for the support of this research.
REFERENCES
Fang Q, Li L, Li J, Wu H, Huang Z, Liu B, Liu Y, Liaw PK. A statistical theory of probability-dependent precipitation strengthening in metals and alloys. Journal of the Mechanics and Physics of Solids, 2019, 122, p. 177–189.
Hazell PJ, Appleby-Thomas GJ, Wielewski E., and Escobedo J. P. The shock and spall response of three industrially important hexagonal close-packed metals: magnesium, titanium and zirconium. Philosophical Transactions of The Royal Society A, 2014, 372: 20130204.
Kazakov DN, Kozelkov OE, Mayorova AS. Dynamic behavior of zirconium alloy E110 under sub microsecond shock-wave loading. EPJ Web of Conferences, 2015, 94, p.1–5.
Skripnyak N.V., Skripnyak E.G., Skripnyak V.A., Skripnyak V.V., Vaganova I.K. Failure mechanisms of light alloys with a bimodal grain size distribution 11th World Congress on Computational Mechanics, WCCM 2014, 5th European Conference on Computational Mechanics, ECCM 2014 and 6th European Conference on Computational Fluid Dynamics, ECFD, 2014, p. 3915-392.
Skripnyak VA and Skripnyak EG. Mechanical behaviour of nanostructured and ultrafine-grained metal alloy under intensive dynamic loading. In: Nanomechanics. Eds.by A. Vakhrushev, 2017.
Intech open. 68291.
Skripnyak VA, Skripnyak NV, Skripnyak EG, Skripnyak VV. Influence of grain size distribution on the mechanical behavior of light alloys in wide range of strain rates, AIP Conference Proceedings, 2017, 1793, art. No. 110001.
Xiao D, Li Y, Hu S. High Strain Rate Deformation Behavior of Zirconium at Elevated Temperatures. Journal of Materials Science & Technology, 2010, 26, p. 878-882.
INFLUENCE OF GRAIN SIZE DISTRIBUTION ON THE MECHANICAL BEHAVIOUR OF Ti–Nb ALLOYS
Vladimir A. Skripnyak1(*), Vladimir V. Skripnyak2, and Evgeniya G. Skripnyak1
1National Research Tomsk State University, Tomsk, Russia
(*)Email: [email protected]
ABSTRACT
This article presents the results of modelling of the mechanical behaviour of coarse grained (CG) and ultrafine-grained (UFG) Ti–Nb alloys in the range of strain rates from 10-3 to 103 s-1 at temperatures from 297 K to 1273 K. Modification of the micro-dynamical model was proposed for the description of Ti–Nb ultrafine grained and coarse grained α+β and β alloys.
It was shown that the HCP → BCC phase transformation in Ti–Nb alloys leads to a sharp changing in resistance to plastic flow and kinetics of growth of damage. The results can be used for engineering analysis of designed constructive elements of technical and biomedical applications.
Keywords: mechanical behaviour, ultra-fine grained, titanium alloys.
INTRODUCTION
Last years a number of α+β and β Ti-Nb-Zr alloys were developed and studied. These alloys have remarkable properties such as low density, high melting point, good oxidation resistance and high specific strengths, low elastic moduli, biocompatibility, etc. (Sharkeev,2018, Bobbili,2017, Bobbili, 2016, Nikonov,2015). Understanding of the mechanical behavior of Ti-Nb-Zr alloys in wide temperature range is extremely essential for the numerical modeling of various applications and manufacturing technologies. It has been shown that beta titanium alloys have low modulus of elasticity (Nikonov,2015). The effect of bimodal grain size distribution on plastic flow stress and deformation to fracture of GPU alloys in a wide range of strain rates has been shown (Skripnyak,2017). Deformation mechanisms and mechanical behavior of UFG metastable titanium alloys β at high strain rates are of great interest. In this regard, the mechanical behavior of Zr-1%Nb alloy was studied by numerical simulation method in the practically important temperature range from 297 K to 1243 K. Mechanical behavior of Ti-13Nb-13Zr alloy was simulated in strain rate range from 0.01 to 103 s-1 at room temperature.
RESULTS AND CONCLUSIONS
Fig. 1a shows the calculated stress versus strain curves of coarse grained Ti-13Nb-13 Zr alloy at the tensile strain rate of 10-2 s-1. Results of simulation agree with experimental data within temperature range from 298 K to 873 K. In this temperature range, the Ti-13Nb-13Zr alloy remains two-phase. The strong increasing of the ultimate tensile strength of Ti-45Nb alloy was predicted. It was shown that the dependence of the normalized yield strength of Ti-13Nb-13Zr from normalized temperature can be approximated by a bilinear relation. The change in slope is due to phase transition α → β.
a) b)
Fig. 1.a − Calculated stress versus strain of Ti-13Nb-13Zr alloy at the tensile strain rate of 10-2 s-1. Symbols are experimental data (Bobbili, 2017); b. True stress−true strain diagrams for Ti−45Nb alloy in the CG
(curves 1) and UFG (curves 2) states
The effects of strain hardening and thermal softening were considered in the computational model. Results of numerical simulation of quasi static loading of Ti-13Nb-13Zr alloys have a good correlation with experimental data. The calculated stress-strain curves were obtained for UFG alloys taking into account changes in coefficient of the Hall-Petch relation in comparison with the value for GC alloys.
ACKNOWLEDGMENTS
This work was supported by the Russian Science Foundation (RSF), grant № 18-71-00117. The authors are grateful for the support of this research.
REFERENCES
Bobbili R, and Madhu V. Constitutive modeling and fracture behaviour of a biomedical Ti–
13Nb-13Zr alloy // Materials Science and Engineering A. 2017, 700, p. 82-91.
Bobbili R, and Madhun V. Flow and fracture characteristics of near alpha titanium alloy. Journal of Alloys and Compounds 2016, 684, p.162-170.
Nikonov AY, Zharmukhambetova AM, Skripnyak NV, Ponomareva AV, Abrikosov IA, Barannikova SA, and Dmitriev AI. Calculation of mechanical properties of BCC Ti-Nb alloys.
AIP Conference Proceedings, 2015, 1683 (020165).
Sharkeev Y, Vavilov V, Skripnyak VA, Belyavskaya O, Legostaeva E, Kozulin A, Chulkov A, Sorokoletov A, Skripnyak VV, Eroshenko A, and Kuimov M. Analyzing the Deformation and Fracture of Bioinert Titanium, Zirconium and Niobium Alloys in Different Structural States by the Use of Infrared Thermography. Metals, 2018, 8, 703, 15p.
Skripnyak VA, Skripnyak NV, Skripnyak EG, Skripnyak VV. Influence of grain size distribution on the mechanical behavior of light alloys in wide range of strain rates, AIP Conference Proceedings, 2017, 1793, art. No. 110001