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Multiscale modeling of crystal plastic deformation of polycrystalline titanium at high temperatures. (English) Zbl 1440.74090
Summary: This paper presents a multiscale modeling framework based on microscale crystal plasticity theory and macroscale element-free methodology for computational simulation of polycrystalline metals. The element-free method employs an improved moving least squares (IMLS) shape function in the Ritz procedure for computational simulation. In the multiscale modeling scheme, the macroscale strain increments of polycrystalline metals are solved by the element-free method and transferred into the mesoscale grains through a scale transition law, and further transferred into the microscale slip systems through the Schmid’s law. The shear strain increments of all grains are then summed up and averaged to calculate the macroscale plastic strain increment. Functions of the temperature-related hardening parameters of the slip systems are determined by calibrating with experimental data. Then, tensile tests are performed on polycrystalline sheets to study their deformation behavior at elevated temperatures. The plasticity of polycrystalline sheets is found to be significantly affected by the grain size. The concentration of shear stress and additional hardening are occurred at the grain boundaries of soft and hard grains. Moreover, it is revealed that the yield strength of the polycrystalline sheets is greatly reduced as the hardening parameters and thermal softening factor decrease at elevated temperatures.
MSC:
74C15 Large-strain, rate-independent theories of plasticity (including nonlinear plasticity)
74S99 Numerical and other methods in solid mechanics
74F05 Thermal effects in solid mechanics
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[1] Veiga, C.; Davim, J. P.; Loureiro, A. J.R., Properties and applications of titanium alloys: a brief review, Rev. Adv. Mater. Sci., 32, 133-148 (2012)
[2] Boyer, R. R.; Briggs, R. D., The use of \(\beta\) titanium alloys in the aerospace industry, J. Mater. Eng. Perform., 14, 681-685 (2005)
[3] Rugg, D.; Dixon, M.; Burrows, J., High-temperature application of titanium alloys in gas turbines. Material life cycle opportunities and threats: an industrial perspective, Mater. High Temp., 33, 536-541 (2016)
[4] Sen, I.; Ramamurty, U., High-temperature (1023 k to 1273 k [750 c to 1000 c]) plastic deformation behavior of b-modified ti-6al-4v alloys: temperature and strain rate effects, Metal. Mater. Trans. A, 41, 2959-2969 (2010)
[5] Wu, F. Y.; Xu, W. C.; Jin, X. Z.; Zhong, X. M.; Wan, X. J.; Shan, D. B.; Guo, B., Study on hot deformation behavior and microstructure evolution of ti55 high-temperature titanium alloy, Metals, 7, 319 (2017)
[6] Liu, Z. G.; Li, P. J.; Xiong, L. T.; Liu, T. Y.; He, L. J., High-temperature tensile deformation behavior and microstructure evolution of ti55 titanium alloy, Mater. Sci. Eng. A, 680, 259-269 (2017)
[7] Fan, X. G.; Zhang, Y.; Gao, P. F.; Lei, Z. N.; Zhan, M., Deformation behavior and microstructure evolution during hot working of a coarse-grained Ti-5Al-5Mo-5V-3Cr-1Zr titanium alloy in beta phase field, Mater. Sci. Eng. A (2017)
[8] Ghanbari, E.; Zarei-Hanzaki, A.; Farghadany, E.; Abedi, H. R.; Khoddam, S., High-temperature deformation characteristics of a \(\beta \)-type ti-29nb-13ta-4.6zr alloy, J. Mater. Eng. Perform., 25, 1554-1561 (2016)
[9] Wang, Y. X.; Zhang, K. F.; Li, B. Y., Microstructure and high temperature tensile properties of ti22al25nb alloy prepared by reactive sintering with element powders, Mater. Sci. Eng. A, 608, 229-233 (2014)
[10] Matsumoto, H.; Kitamura, M.; Li, Y.; Koizumi, Y.; Chiba, A., Hot forging characteristic of Ti-5Al-5V-5Mo-3Cr alloy with single metastable \(\beta\) microstructure, Mater. Sci. Eng. A, 611, 337-344 (2014)
[11] Zhao, Z. L.; Li, H.; Fu, M. W.; Guo, H. Z.; Yao, Z. K., Effect of the initial microstructure on the deformation behavior of ti60 titanium alloy at high temperature processing, J. Alloys Compd., 617, 525-533 (2014)
[12] Wang, Z. J.; Qiang, H. F.; Wang, X. R.; Wang, G., Constitutive model for a new kind of metastable \(\beta\) titanium alloy during hot deformation, T. Nonferr. Metal. Soc., 22, 634-641 (2012)
[13] Lia, L. X.; Loub, Y.; Yanga, L. B.; Penga, D. S.; Rao, K. P., Flow stress behavior and deformation characteristics of Ti-3Al-5V-5Mo compressed at elevated temperatures, Mater. Des., 23, 451-457 (2002)
[14] Velay, V.; Matsumoto, H.; Vidal, V.; Chiba, A., Behavior modeling and microstructural evolutions of Ti-6Al-4V alloy under hot forming conditions, Int. J. Mech. Sci., 108-109, 1-13 (2016)
[15] Gao, F.; Li, W.; Meng, B.; Wan, M.; Zhang, X.; Han, X., Rheological law and constitutive model for superplastic deformation of ti-6al-4v, J. Alloys Compd., 701, 177-185 (2017)
[16] Kotkunde, N.; Krishnamurthy, H. N.; Puranik, P.; Gupta, A. K.; Singh, S. K., Microstructure study and constitutive modeling of Ti-6Al-4V alloy at elevated temperatures, Mater. Des., 54, 96-103 (2014)
[17] van den Boogaard, A. H.; Bolt, P.; Werkhoven, R., Modeling of Al-Mg sheet forming at elevated temperatures, Int. J. Form. Proc., 4, 361-375 (2001)
[18] Bobbili, R.; Madhu, V., Effect of strain rate and stress triaxiality on tensile behavior of titanium alloy Ti-10-2-3 at elevated temperatures, Mater. Sci. Eng. A, 667, 33-41 (2016)
[19] Ren, J.; Liew, K. M.; Meguid, S. A., Modelling and simulation of the superelastic behaviour of shape memory alloys using the element-free galerkin method, Int. J. Mech. Sci., 44, 2393-2413 (2002)
[20] Park, Y. H., Rigid-plastic analysis for metal forming processes using a reproducing kernel particle method, J. Mater. Process. Tech., 183, 256-263 (2007)
[21] Li, D. M.; Liew, K. M.; Cheng, Y. M., Analyzing elastoplastic large deformation problems with the complex variable element-free galerkin method, Comput. Mech., 53, 1149-1162 (2014)
[22] Zhang, G.; Li, Y.; Wang, H.; Zong, Z., A linear complementarity formulation of meshfree method for elastoplastic analysis of gradient-dependent plasticity, Eng. Anal. Bound. Elem., 73, 1-13 (2016)
[23] Barut, A.; Guven, I.; Madenci, E., A meshless grain element for micromechanical analysis with crystal plasticity, Internat. J. Numer. Methods Engrg., 67, 17-65 (2006)
[24] Zhang, H.; Dong, X.; Wang, Q.; Zeng, Z., An effective semi-implicit integration scheme for rate dependent crystal plasticity using explicit finite element codes, Comput. Mater. Sci., 54, 208-218 (2012)
[25] Roters, F.; Eisenlohr, P.; Hantcherli, L.; Tjahjanto, D. D.; Bieler, T. R.; Raabe, D., Overview of constitutive laws, kinematics, homogenization and multiscale methods in crystal plasticity finite-element modeling: theory, experiments, applications, Acta Mater., 58, 1152-1211 (2010)
[26] Doquet, V.; Barkia, B., Combined AFM, SEM and crystal plasticity analysis of grain boundary sliding in titanium at room temperature, Mech. Mater., 103, 18-27 (2016)
[27] Shahba, A.; Ghosh, S., Crystal plasticity Fe modeling of Ti alloys for a range of strain-rates. Part I: a unified constitutive model and flow rule, Int. J. Plast., 87, 48-68 (2016)
[28] Zhang, Z.; Jun, T.; Britton, T. B.; Dunne, F. P.E., Determination of ti-\(6242 \alpha\) and \(\beta\) slip properties using micro-pillar test and computational crystal plasticity, J. Mech. Phys. Solids, 95, 393-410 (2016)
[29] Park, Y. H., Rigid-plastic analysis for metal forming processes using a reproducing kernel particle method, J. Mater Process. Technol., 183, 2, 256-263 (2007)
[30] Yeon, J.; Youn, S., Variational multiscale analysis of elastoplastic deformation using meshfree approximation, Int. J. Solids Struct., 45, 17, 4709-4724 (2008)
[31] Zhang, G., A linear complementarity formulation of meshfree method for elastoplastic analysis of gradient-dependent plasticity, Eng. Anal. Bound. Elem., 73, 1-13 (2016)
[32] Hazama, O.; Okuda, H.; Wakatsuchi, K., A digital systematization of meshfree method and its applications to elasto-plastic infinitesimal deformation analysis, Adv. Eng. Softw., 32, 8, 647-664 (2001)
[33] Li, A.; Pang, J.; Zhao, J.; Zang, J.; Wang, F., FEM-simulation of machining induced surface plastic deformation and microstructural texture evolution of ti-6al-4v alloy, Int. J. Mech. Sci., 123, 214-223 (2017)
[34] Peirce, D.; Asaro, R. J.; Needleman, A., An analysis of nonuniform and localized deformation in ductile single crystals, Acta Metal., 30, 1087-1119 (1982)
[35] Zhang, L. W.; Liew, K. M., An improved moving least-squares Ritz method for two-dimensional elasticity problems, Appl. Math. Comput., 246, 268-282 (2014)
[36] Zhang, L. W.; Huang, D. M.; Liew, K. M., An element-free IMLS-Ritz method for numerical solution of three-dimensional wave equations, Comput. Methods Appl. Mech. Engrg., 297, 116-139 (2015)
[37] Ledbetter, H.; Ogi, H.; Kai, S.; Kim, S.; Hirao, M., Elastic constants of body-centered-cubic titanium monocrystals, J. Appl. Phys., 95, 4642-4644 (2004)
[38] Ogi, H.; Kai, S.; Ledbetter, H.; Tarumi, R.; Hirao, M.; Takashima, K., Titanium’s high-temperature elastic constants through the HCP-BCC phase transformation, Acta Mater., 52, 2075-2080 (2004)
[39] Liu, Z.; Li, P.; Xiong, L.; Liu, T.; He, L., High-temperature tensile deformation behavior and microstructure evolution of ti55 titanium alloy, Mater. Sci. Eng. A, 680, 259-269 (2017)
[40] Lim, H.; Carroll, J. D.; Battaile, C. C.; Buchheit, T. E.; Boyce, B. L.; Weinberger, C. R., Grain-scale experimental validation of crystal plasticity finite element simulations of tantalum oligocrystals, Int. J. Plast., 60, 1-18 (2014)
[41] Anahid, M.; Samal, M. K.; Ghosh, S., Dwell fatigue crack nucleation model based on crystal plasticity finite element simulations of polycrystalline titanium alloys, J. Mech. Phys. Solids, 59, 2157-2176 (2011)
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