The two-level elastic-viscoplastic model: analysis of the influence of crystallite orientation distribution in the reference configuration and the complexity of loading on the behavior of polycrystalline materials
DOI:
https://doi.org/10.7242/1999-6691/2021.14.4.33Keywords:
two-level physical elastic-viscoplastic model, equivalent isotropic material, residual mesoscopic stresses, crystallographic textureAbstract
Components and structural elements used in modern technology are often exposed to significant loads in wide ranges of high and low temperature and deformation rates, high stresses and loading rates.. All these factors, as well as complex loading schemes that must be considered when designing structures of different sizes - from miniature to large-scale -, put forward increased requirements for the properties of materials. A significant part of the structures used in various industries are made of polycrystalline metals and alloys. The physical and mechanical properties of polycrystalline aggregates in finished products depend on their phase and component composition, meso- and microstructure, including the orientation of crystallites (grains, subgrains), symmetry properties of subgrains, and on the initial (residual) stresses that occur during their manufacturing. Experimenting with full-scale structures requires considerable material and time expenditures, therefore mathematical modeling approaches are applied, especially for designing structures and their manufacturing processes. Mathematical modelling provides an opportunity to describe processes in any materials with this or that degree of accuracy. Constitutive relations (or constitutive models) are the most important element of the mathematical models developed for solving these problems. Currently, the most promising among these models are multilevel models based on the introduction of internal variables and crystal plasticity. When analyzing the elastic-plastic deformation of various products, the isotropic constitutive relations are often used to simplify the analysis of the elastic component of deformations. The present work is devoted to the study of errors arising when the anisotropic elastic properties of crystallites are replaced by the corresponding isotropic properties of the materials with BCC, FCC and HCP lattices for different laws of orientation distribution of crystallites in a polycrystalline aggregate in the reference configuration. Using the two-level model based on the elastic-viscoplastic crystal plasticity, a series of numerical experiments on simple shear loading, sequences of two simple loads and cyclic deformation were performed to analyze the evolution of the stress-strain state and to estimate the residual stresses in crystallites.
Downloads
References
Kachanov L.M. Osnovy teorii plastichnosti [Bases of the theory of plasticity]. Moscow, Nauka, 1969. 420 p.
Malinin N.N. Prikladnaya teoriya plastichnosti i polzuchesti [Applied theory of plasticity and creep]. Moscow, Mashinostroyeniye, 1975. 400 p.
Unksov E.P., Ovchinnikov A.G. (eds.) Teoriya plasticheskikh deformatsiy metallov [Theory of plastic deformations of metals] Moscow, Mashinostroyeniye, 1983. 598 p.
Vasin R.A. Opredelyayushchiye sootnosheniya teorii plastichnosti [Defining relations of the theory of plasticity]. Itogi nauki i tekhniki. Ser. Mekhanika tverdykh deformiruyemykh tel, 1990, vol. 21, pp. 3-75.
Il’yushin A.A. Plastichnost’. Ch. 1. Uprugo-plasticheskiye deformatsii [Plasticity. Part 1. Elastic-plastic deformations]. Moscow, Logos, 2004. 388 p.
Il’yushin A.A. Trudy (1946–1966). T. 2. Plastichnost’ [Proceedings (1946–1966). Vol. 2. Plasticity]. Moscow, Fizmatlit, 2004. 480 p.
Horstemeyer M.F. Multiscale modeling: A review. Practical aspects of computational chemistry, ed. J. Leszczynski, M.K. Shukla. Springer, 2009. Р 87-135. https://doi.org/10.1007/978-90-481-2687-3_4
McDowell D.L. A perspective on trends in multiscale plasticity. J. Plast., 2010, vol. 26, pp. 1280-1309. https://doi.org/10.1016/j.ijplas.2010.02.008
Roters F. Advanced material models for the crystal plasticity finite element method: Development of a general CPFEM framework. Aachen, RWTH Aachen, 2011. 226 р.
Trusov P.V., Shveykin A.I., Nechaeva E.S., Volegov P.S. Multilevel models of inelastic deformation of materials and their application for description of internal structure evolution. mesomech., 2012, vol. 15, pp. 155-175. https://doi.org/10.1134/S1029959912020038
Trusov P.V., Shveykin A.I. Mnogourovnevyye modeli mono- i polikristallicheskikh materialov: teoriya, algoritmy, primery primeneniya [Multilevel models of mono- and polycrystalline materials: theory, algorithms, application examples]. Novosibirsk, Silberian Branch of RAS, 2019. 605 p
Taylor G.I. Plastic strain in metals. Inst. Metals, 1938, vol. 62, pp. 307-324.
Lin T.H. Analysis of elastic and plastic strains of a face-centered cubic crystal. Mech. Phys. Solid., 1957, vol. 5, pp. 143‑149. https://doi.org/10.1016/0022-5096(57)90058-3
Sokolov A.S., Trusov P.V. Two-level elastic-viscoplastic model: application to the analysis of the crystal anisotropy influence. mekh. splosh. sred – Computational continuum mechanics, 2020, vol. 13, no. 2, pp. 219-230. https://doi.org/10.7242/1999-6691/2020.13.2.17
Pozdeyev A.A., Trusov P.V., Nyashin Yu.I. Bol’shiye uprugoplasticheskiye deformatsii: teoriya, algoritmy, prilozheniya [Lagre elastic-plastic deformations: theory, algorithms, applications]. Moscow, Nauka, 1986. 232 p.
Trusov P.V., Shveykin A.I., Yanz A.Yu. Motion decomposition, frame-indifferent derivatives, and constitutive relations at large displacement gradients from the viewpoint of multilevel modeling. Mesomech., 2017, vol. 20, pp. 357-376. https://doi.org/10.1134/S1029959917040014
Trusov P.V., Shveykin A.I. On motion decomposition and constitutive relations in geometrically nonlinear elastoviscoplasticity of crystallites. Mesomech., 2016, vol. 19, pp. 377-391. https://doi.org/10.1134/S1029959917040026
Lurie A.I. Nonlinear theory of elasticity. Elsevier, 1990. 617 p.
Kroner E. Allgemeine Kontinuumstheorie der Versetzungen und Eigenspannungen [Continuum theory of dislocations and residual stresses]. Rational Mech. Anal., 1959, vol. 4, pp. 273-334. https://doi.org/10.1007/BF00281393
Lee E.H. Elastic-plastic deformation at finite strain. Appl. Mech., 1969, vol. 36, pp. 1-6. https://doi.org/10.1115/1.3564580
Zhang Z., Cuddihy M.A., Dunne F.P.E. On rate-dependent polycrystal deformation: the temperature sensitivity of cold dwell fatigue. R. Soc. A, 2015, vol. 471, 20150214. https://doi.org/10.1098/rspa.2015.0214
Feng B., Bronkhorst C.A., Addessio F.L., Morrow B.M., Cerreta E.K., Lookman T., Lebensohn R.A., Low T. Coupled elasticity, plastic slip, and twinning in single crystal titanium loaded by split-Hopkinson pressure bar. Mech. Phys. Solid., 2018, vol. 119, pp. 274-297. https://doi.org/10.1016/j.jmps.2018.06.018
Zhang Z., Jun T.-S., Britton T.B., Dunne F.P.E. Determination of Ti-6242 α and β slip properties using micro-pillar test and computational crystal plasticity. Mech. Phys. Solid., 2016, vol. 95, pp. 393-410. https://doi.org/10.1016/j.jmps.2016.06.007
Zhang Z., Jun T.-S., Britton T.B., Dunne F.P.E. Intrinsic anisotropy of strain rate sensitivity in single crystal alpha titanium. Acta Mater., 2016, vol. 118, pp. 317-330. https://doi.org/10.1016/j.actamat.2016.07.044
Matsyuk K.V., Trusov P.V. Model for descrition viscoelastoplastic deformation of hcp crystals: asymmetric stress measures, hardening laws. Vestnik PNIPU. Mekhanika – PNRPU Mechanics Bulletin, 2013, no. 4, pp. 75-105. https://doi.org/10.15593/perm.mech/2013.4.75-105
Wu X., Kalidindi S.R., Necker C., Salemet A.A. Modeling anisotropic stress-strain response and crystallographic texture evolution on α-titanium during large plastic deformation using Taylor-type models: Influence of initial texture and purity. Mater. Trans. A, 2008, vol. 39, pp. 3046-3054. https://doi.org/10.1007/S11661-008-9651-X
Kondratev N.S., Trusov P.V. A mathematical model for deformation of BCC single crystals taking into consideration the twinning mechanism. mekh. splosh. sred – Computational continuum mechanics, 2011, vol. 4, no. 4, pp. 20-33. https://doi.org/10.7242/1999-6691/2011.4.4.36
Shermergor T.D. Teoriya uprugosti mikroneodnorodnykh tel [The theory of elasticity of micro-inhomogeneous bodies]. Moscow, Nauka, 1977. 399 p.
Hirth J., Lothe J. Theory of Dislocations. McGraw-Hill, 1968. 780 p.
Newnham R.E. Properties of materials. Anisotropy, symmetry, structure. Oxford University Press, 2005. 390 p.
Man C.-S., Huang M. A simple explicit formula for the Voigt-Reuss-Hill average of elastic polycrystals with arbitrary crystal and texture symmetries. Elast., 2011, vol. 105, pp. 29-48. https://doi.org/10.1007/s10659-011-9312-y
Krivosheina M.N., Tuch E.V., Khon Yu.A. Applying the Mises-Hill criterion to modeling the dynamic loading of highly anisotropic materials. Russ. Acad. Sci. Phys., 2012, vol. 76, pp. 80-84. https://doi.org/10.3103/S1062873812010169
Krivosheina M.N., Kobenko S.V., Tuch E.V. Averaging of properties of anisotropic structural materials in numerical simulation of their fracture. Mesomech., 2010, vol. 13, no. 2, pp. 55-60.
Raab G.I., Aleshin G.N., Fakhredinova E.I., Raab A.G., Asfandiyarov R.N., Aksenov D.A., Kodirov I.S. Prospects of development of new pilot-commercial SPD methods. MTD, 2019, vol. 1, no. 1, pp. 48-57.
Raab G.I., Kodirov I.S., Aleshin G.N., Raab A.G., Tsenev N.K. Influence of special features of the gradient structure formation during severe plastic deformation of alloys with different types of a crystalline lattice. Vestnik MGTU im. G.I. Nosova – Vestnik of Nosov Magnitogorsk State Technical University, 2019, vol. 17, no. 1, pp. 64-75. https://doi.org/10.18503/1995-2732-2019-17-1-64-75
Hama T., Kobuki A., Takuda H. Crystal-plasticity finite-element analysis of anisotropic deformation behavior in a commercially pure titanium Grade 1 sheet. J. Plast., 2017, vol. 91, pp. 77-108. https://doi.org/10.1016/j.ijplas.2016.12.005
Ji Y.T., Suo H.L., Ma L., Wang Z., Yu D., Shaheen K., Cui J., Liu J., Gao M.M. Formation of recrystallization cube texture in highly rolled Ni–9.3 at % W. Metals Metallogr., 2020, vol. 121, pp. 248-253. https://doi.org/10.1134/S0031918X20020180
Birger I.A. Ostatochnyye napryazheniya [Residual stresses]. Moscow, Mashgiz, 232 p.
Pozdeyev A.A., Nyashin Yu.I., Trusov P.V. Ostatochnyye napryazheniya: teoriya i prilozheniya Residual stresses: theory and applications]. Moscow, Nauka, 1974. 112 p.
Birger I.A., Shor B.F., Iosilevich G.V. Raschet na prochnost’ detaley mashin [Calculation of the strength of machine parts]. Moscow, Mashinostroyeniye, 1979. 702 p.
Abramov V.V. Ostatochnyye napryazheniya i deformatsii v metallakh [Residual stresses and deformations in metals]. Moscow, State Scientific and Technical Publishing House of Machine-building literature, 1963. 356 p.
Fridman Ya.B. Mekhanicheskiye svoystva metallov. Ch. 1. Deformatsiya i razrusheniye [Mechanical properties of metals. Part 1. Deformation and Destruction]. Moscow, Mashinostroyeniye, 1974. 472 p.
Kachanov L.M. Osnovy mekhaniki razrusheniya [Fundamentals of fracture mechanics]. Moscow, Nauka, 1974. 312p.
Collins J.A. Failure of materials in mechanical design: Analisys, prediction, prevention. John Wiley & Sons, 1981. 629 p.
Rabotnov Yu.N. Vvedeniye v mekhaniku razrusheniya [Introduction to fracture mechanics]. Moscow, Nauka, 1987. 80 p.
Besson J. Continuum models of ductile fracture: A Review. J. Damage Mechanics, 2010, vol. 19, pp. 3-52. https://doi.org/10.1177/1056789509103482
Downloads
Published
Issue
Section
License
Copyright (c) 2021 Computational Continuum Mechanics
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.