Phenomenological modeling of phase and structural deformations in shape memory alloys. one-dimensional case
DOI:
https://doi.org/10.7242/1999-6691/2018.11.1.4Keywords:
phenomenological model, shape memory alloys, phase deformation, structural deformationAbstract
The elements of construction made of shape memory alloys (SMA) during their exploitation are subjected to cooling and heating under varying stresses. This leads to simultaneous phase and structural transformations affecting each other and causing such accompanying phenomena as shape memory, cross-hardening, and martensitic inelasticity. Furthermore, stress variations provoke the shift of phase transformation temperatures and can predetermine forward and reverse phase transformations when the isothermal load increases or decreases (superelasticity phenomenon). This work presents a phenomenological model for describing, in the framework of the uniform approach, the listed phenomena because they have a significant effect on the stress-strain state of the structure. The model is based on the interconnection of forward transition and martensitic inelasticity diagrams which allows one to uniformly describe phase and structural deformations because both of them are related to the formation of the oriented martensite. We study a set of martensitic structural elements connected in series, each having a unique structural transformation factor (initial stress). The structural transformation factor is defined by the element emergence conditions at forward phase transformation and by the subsequent deformation behavior. This approach allows us to take into account, first, the mutual influence of the processes of phase and structural transformations, and second, the influence of the deformation history on further transition. The problem of joint deformation of the package of SMA rods is solved to illustrate the evolution of the stress-strain state of the system at simultaneous phase and structural transformations caused by the external thermomechanical effect.
Downloads
References
Беляев С.П., Волков А.Е., Ермолаев В.А., Каменцева З.П., Кузьмин С.Л., Лихачев В.А., Мозгунов В.Ф., Разов А.И., Хайров Р.Ю. Материалы с эффектом памяти формы: Справочное издание / Под ред. В.А. Лихачева. – Т. 2 – СПб.: Изд-во НИИХ СПбГУ, 1998. – 374 с.
Кузьмин С.Л., Лихачев В.А., Тошпулатов Ч.X. Эффект реверсивной памяти формы признакопеременном деформировании // Физ. Мет. Металловед. – 1986. – Т. 61, № 1-3. – С. 79-85.
Беляев С.П., Ермолаев В.А., Кузьмин С.Л., Лихачев В.А., Чунарева Е.Н. Эффект реверсивной обратимой памяти формы в сплавах на основе никелида титана // Физ. Мет. Металловед. – 1988. – Т.66, вып. 5. – С. 926-934.
Бречко Т. Эффект памяти формы и остаточные напряжения // Ж. тех. физ. – 1996. – Т.66, № 11. – С. 72-78.
Волков А.Е. Микроструктурное моделирование деформации сплавов при повторяющихся мартенситных превращениях // Изв. Акад. Наук, Сер. Физ. – 2002. – Т. 66, № 9. – С. 1290-1297.
Волков А.Е., Евард М.Е., Курзенева Л.Н., Лихачев В.А., Сахаров В.Ю., Ушаков В.В. Математическое моделирование мартенситной неупругости и эффектов памяти формы // Ж. тех. физ. – 1996. – Т. 66, № – С. 3-35.
Лихачев В.А., Малинин В.Г. Структурно-аналитическая теория прочности. – СПб.: Наука, 1993. – 470 с.
Мовчан А.А., Мовчан И.А. Одномерная микромеханическая модель нелинейного деформирования сплавов с памятью формы при прямом и обратном термоупругих превращениях // Механика композиционных материалов и конструкций. – 2007. – Т. 13, №. 3 – С. 297-322.
Huang M., Gao X., Brinson L.C. A multivariant micromechanical model for SMAs Part 2. Polycrystal model // Int. J. Plast. – 2000. – Vol. 16, 10. – P. 1371-1390. DOI
Manchiraju S., Anderson P. M. Coupling between martensitic phase transformations and plasticity: a microstructure-based finite element model // Int. J. Plast. – 2010. – Vol. 26, no. 10. – P. 1508-1526. DOI
Patoor E., Lagoudas D.C., Entchev P.B., Brinson L.X., Gao X. Shape memory alloys, Part I: General properties and modeling of single crystals // Mech. Mater. – 2006. – Vol. 38, no. 5. – P. 391-429. DOI
Thamburaja P., Pan H., Chau F.S. The evolution of microstructure during twinning: Constitutive equations, finite-element simulations and experimental verification // Int. J. Plast. – 2009. – Vol. 25, no. 11. – P. 2141-2168. DOI
Wang X.M., Xu B.X., Yue Z.F. Micromechanical modelling of the effect of plastic deformation on the mechanical behaviour in pseudoelastic shape memory alloys // Int. J. Plast. – 2008. – Vol. 24, no. 8. – P. 1307-1332. DOI
Yu C., Kang G., Kan Q. Crystal plasticity based constitutive model of NiTi shape memory alloy considering different mechanisms of inelastic deformation // J. Plast. – 2014. – Vol. 54. – P. 132-162. DOI
Arghavani J., Auricchio F., Naghdabadi R., Reali A. An improved, fully symmetric, finite-strain phenomenological constitutive model for shape memory alloys // Finite Elements in Analysis and Design. – 2011. – Vol. 47. – P. 166-174. DOI
Lagoudas D., Hartl D., Chemisky Y., Machado L., Popov P. Constitutive model for the numerical analysis of phase transformation in polycrystalline shape memory alloys // Int. J. Plast. – 2012. – Vol. 32-33. – P. 155-183. DOI
Mehrabi R., Andani T., Elahinia M., Kadkhodaei M. Anisotropic behavior of superelastic NiTi shape memory alloys; an experimental investigation and constitutive modeling // Mech. Mater. – 2014. – Vol. 77. – P. 110-124. DOI
Müller C., Bruhns O.T. A thermodynamic finite-strain model for pseudoelastic shape memory alloys // Int. J. Plast. – 2006. – Vol. 22, no. 9. – P. 1658-1682. DOI
Zaki W. An efficient implementation for a model of martensite reorientation in martensitic shape memory alloys under multiaxial nonproportional loading // J. Plast. – 2012. – Vol. 37. – P. 72-94. DOI
Мишустин И.В., Мовчан А.А. Аналог теории пластического течения для описания деформации мартенситной неупругости в сплавах с памятью формы // Изв. РАН. МТТ. – 2015, № 2. – С. 78-95. (English version DOI)
Auricchio F., Bonetti E., Scalet G., Ubertini F. Theoretical and numerical modeling of shape memory alloys accounting for multiple phase transformations and martensite reorientation // Int. J. Plast. – 2014. – Vol. 59. – P. 30-54. DOI
Chemisky Y., Duval, Patoor E., Ben Zineb T. Constitutive model for shape memory alloys including phase transformation, martensitic reorientation and twins accommodation // Mech. Mater. – 2011. – Vol. 43, no. 7. – P. 361-376. DOI
Panico M., Brinson L.C. A three-dimensional phenomenological model for martensite reorientation in shape memory alloys // Journal of the Mechanics and Physics of Solids. – 2007. – Vol. 55, no. – P. 2491-2511. DOI
Мишустин И.В., Мовчан А.А. Моделирование фазовых и структурных превращений в сплавах спамятью формы, происходящих под действием немонотонно меняющихся напряжений // Изв. РАН. МТТ. – 2014, №. 1. – С. 37-53. (English version DOI)
Мовчан А.А., Мовчан И.А., Сильченко Л.Г. Микромеханическая модель нелинейного деформирования сплавов с памятью формы при фазовых и структурных превращениях // Изв. РАН. МТТ. – 2010, № 3.– С. 118-130. (English version DOI)
Мовчан А.А., Сильченко А.Л., Казарина С.А. Экспериментальное исследование и теоретическое моделирование эффекта перекрестного упрочнения сплавов с памятью формы // Деформация и разрушение материалов. – 2017, № 3. – С. 20-27.
Wu X.D., Sun G.J., Wu J.S. The nonlinear relationship between transformation strain and applied stress for nitinol // Mater. Lett. – 2003. – Vol. 57. – P. 1334-1338. DOI
Тихомирова К.А. Разработка и численная реализация одномерной феноменологической модели фазовой деформации в сплавах с памятью формы // Вычисл. мех. сплош. сред. – 2016. – Т. 9, № 2. – С. 192-206. (English version DOI)
Вейман С.М. Деформация, механизм явления и другие характеристики сплавов с эффектом запоминания формы // Эффект памяти формы в сплавах / Под ред. В.А. Займовского. – М.:Металлургия, 1979. – С. 9- (English version DOI)
Elibol C., Wagner M.F.-X. Investigation of the stress-induced martensitic transformation in pseudoelastic NiTi under uniaxial tension, compression and compression–shear // Mater. Sci. Eng., A. – 2015. – Vol. 621. – P. 76-81. DOI
Yoo Y.-I., Kim Y.-J., Shin D.-K., Lee J.-J. Development of martensite transformation kinetics of NiTi shape memory alloys under compression // International Journal of Solids and Structures. – 2015. – Vol. 64. – P. 51-61. DOI
Мовчан А.А., Чжо Т.Я. Решение связной термоэлектромеханической задачи для стержня из сплава спамятью формы в рамках теории нелинейного деформирования этих материалов // Механика композиционных материалов и конструкций. – 2008. – Т. 14, № 3. – С. 443-460.
Rogovoy A.A., Stolbova O.S. Modeling the magnetic field control of phase transition in ferromagnetic shape memory alloys // Int. J. Plast. – 2016. – Vol. 85. – P. 130-155. DOI
Тихомирова К.А. Изотермическое деформирование сплава с памятью формы в разных температурных интервалах. Случай одноосного растяжения // Механика композиционных материалов и конструкций. – 2017. – Т. 23, № 2. – С. 263-282.
Mishustin I.V., Movchan A.A. The microstructural model of mechanical behavior of a shape-memory alloy // Nanomechanics science and technology: An International Journal. – 2016. – Vol. 7, no. 1. P. 77-91. DOI
Андронов И.Н., Богданов Н.П., Северова Н.А., Тарсин А.В. Метод количественного описания зависимости модуля Юнга никелида титана от температуры // Известия Коми научного центра УрО РАН. – 2013, № 3. – C. 87-90.
Матвеенко В.П., Сметанников О.Ю., Труфанов Н.А., Шардаков И.Н. Термомеханика полимерных материалов в условиях релаксационного перехода – М.: Физматлит, 2009. – 174 с.
Турусов Р.А. Механические явления в полимерах и композитах (в процессах формования) / Дисс. докт. физ.-мат. наук. – М., 1983.
Мовчан А.А., Казарина С.А. Материалы с памятью формы как объект механики деформируемого твердого тела: экспериментальные исследования, определяющие соотношения, решение краевых задач // Физ. Мезомех. – 2012. – Т. 15, № 1. – С. 105-116.
Auricchio F., Petrini L. A three-dimensional model describing stress-temperature induced solid phase transformations: thermomechanical coupling and hybrid composite applications // Int. J. Numer. Methods Engineering. – 2004. – Vol. 61, no. 5. – P. 716-737. DOI
###
Beliaev S.P., Volkov A.E., Ermolaev V.A., Kamentseva Z.P., Kuz’min S.L., Likhachev V.A., Mozgunov V.F., Razov A.I., Khairov R.Iu. Materialy s effektom pamiati formy [Materials with shape memory effect]. Spravochnoe izdanie. Pod redaktsiei Likhacheva V.A. Saint Petersburg, Izdatel’stvo NIIKh SPbGU, 1998, vol. 2. 374 p.
Kuz’min S.L., Lihachev V.A., Toshpulatov Ch.X. Jeffekt reversivnoj pamjati formy pri znakoperemennom deformirovanii [Effect of two-way shape memory under alternating-sign deformation]. Met. Metalloved. – Phys. Met. Metallogr., 1986, vol. 61, no. 1-3, pp. 79-85.
Beljaev S.P., Ermolaev V.A., Kuz’min S.L., Lihachev V.A., Chunareva E.N. Jeffekt reversivnoj obratimoj pamjati formy v splavah na osnove nikelida titana [Effect of two-way reversible shape memory in NiTi-based alloys]. Met. Metalloved. – Phys. Met. Metallogr., 1988, vol. 66, ed. 5, pp. 926-934.
Brechko T. Jeffekt pamjati formy i ostatochnye naprjazhenija [Shape memory effect and residual stresses]. Tekh. Fiz. – Tech. Phys., 1996, vol. 66, no. 11, pp. 72-78.
Volkov A.E. Mikrostrukturnoe modelirovanie deformacii splavov pri povtorjajushhihsja martensitnyh prevrashhenijah [Microstructural modeling of the alloy deformation under repeated martensitic transformations]. Akad. Nauk, Ser. Fiz. – Bull. Russ. Acad. Sci.: Phys., 2002, vol. 66, no. 9, pp. 1290-1297.
Volkov A.E., Evard M.E., Kurzeneva L.N., Lihachev V.A., Saharov V.Ju., Ushakov V.V. Matematicheskoe modelirovanie martensitnoj neuprugosti i jeffektov pamjati formy [Mathematical modeling of martensitic inelasticity and the shape memory effect]. Tekh. Fiz. – Tech. Phys., 1996, vol. 66, no. 11, pp. 3-35.
Lihachev V.A., Malinin V.G. Strukturno-analiticheskaja teorija prochnosti [Structural-analytical theory of strength]. Saint Petersburg, Nauka, 1993. 470 p.
Movchan A.A., Movchan I.A. Odnomernaja mikromehanicheskaja model’ nelinejnogo deformirovanija splavov s pamjat’ju formy pri prjamom i obratnom termouprugih prevrashhenijah [One-dimensional micromechanical model for nonlinear deformation of shape memory alloys under forward and inverse thermoelastic transformations]. Mekhanika kompozitsionnykh materialov i konstruktsii – Composite Mechanics and Design, 2007, vol. 13, no. 3, pp. 297-322.
Huang M., Gao X., Brinson L.C. A multivariant micromechanical model for SMAs Part 2. Polycrystal model. J. Plast., 2000, vol. 16, no. 10, pp. 1371-1390. DOI
Manchiraju S., Anderson P. M. Coupling between martensitic phase transformations and plasticity: a microstructure-based finite element model. J. Plast., 2010, vol. 26, no. 10, pp. 1508-1526. DOI
Patoor E., Lagoudas D.C., Entchev P.B., Brinson L.X., Gao X. Shape memory alloys, Part I: General properties and modeling of single crystals. Mater., 2006, vol. 38, no. 5, pp. 391-429. DOI
Thamburaja P., Pan H., Chau F.S. The evolution of microstructure during twinning: Constitutive equations, finite-element simulations and experimental verification. J. Plast., 2009, vol. 25, no. 11, pp. 2141-2168. DOI
Wang X.M., Xu B.X., Yue Z.F. Micromechanical modelling of the effect of plastic deformation on the mechanical behaviour in pseudoelastic shape memory alloys. J. Plast., 2008, vol. 24, no. 8, pp. 1307-1332. DOI
Yu C., Kang G., Kan Q. Crystal plasticity based constitutive model of NiTi shape memory alloy considering different mechanisms of inelastic deformation. J. Plast., 2014, vol. 54, pp. 132-162. DOI
Arghavani J., Auricchio F., Naghdabadi R., Reali A. An improved, fully symmetric, finite-strain phenomenological constitutive model for shape memory alloys. Finite Elements in Analysis and Design, 2011, vol. 47, pp. 166-174. DOI
Lagoudas D., Hartl D., Chemisky Y., Machado L., Popov P. Constitutive model for the numerical analysis of phase transformation in polycrystalline shape memory alloys. J. Plast., 2012, vol. 32-33, pp. 155-183. DOI
Mehrabi R., Andani T., Elahinia M., Kadkhodaei M. Anisotropic behavior of superelastic NiTi shape memory alloys; an experimental investigation and constitutive modeling. Mech. Mater., 2014, vol. 77, pp. 110-124. DOI
Müller C., Bruhns O.T. A thermodynamic finite-strain model for pseudoelastic shape memory alloys. J. Plast., 2006, vol. 22, no. 9, pp. 1658-1682. DOI
Zaki W. An efficient implementation for a model of martensite reorientation in martensitic shape memory alloys under multiaxial nonproportional loading. J. Plast., 2012, vol. 37, pp. 72-94. DOI
Mishustin I.V., Movchan A.A. Analog of the plastic flow theory for describing martensitic inelastic strains in shape memory alloys. Solids, 2015, vol. 50, no. 2, pp. 72-94. DOI
Auricchio F., Bonetti E., Scalet G., Ubertini F. Theoretical and numerical modeling of shape memory alloys accounting for multiple phase transformations and martensite reorientation. J. Plast., 2014, vol. 59, pp. 30-54. DOI
Chemisky Y., Duval, Patoor E., Ben Zineb T. Constitutive model for shape memory alloys including phase transformation, martensitic reorientation and twins accommodation. Mech. Mater., 2011, vol. 43, no. 7, pp. 361-376. DOI
Panico M., Brinson L.C. A three-dimensional phenomenological model for martensite reorientation in shape memory alloys. Journal of the Mechanics and Physics of Solids, 2007, vol. 55, no. 11, pp. 2491-2511. DOI
Mishustin I.V., Movchan A.A. Modeling of phase and structure transformations occurring in shape memory alloys under nonmonotonically varying stresses. Solids, 2014, vol. 49, no. 1, pp. 27-39. DOI
Movchan A.A., Movchan I.A., Sil’chenko L.G. Micromechanical model of nonlinear deformation of shape memory alloys under phase and structure transitions. Solids, 2010, vol. 45, no. 3, pp. 406-416. DOI
Movchan A.A., Sil’chenko A.L., Kazarina S.A. Eksperimental’noe issledovanie i teoreticheskoe modelirovanie effekta perekrestnogo uprochneniia splavov s pamiat’iu formy [Experimental investigation and theoretical simulation of cross-hardening phenomena in shape memory alloys]. Deformatsiia i razrushenie materialov – Russian metallurgy (Metally), 2017, no. 3, pp. 20-27.
Wu X.D., Sun G.J., Wu J.S. The nonlinear relationship between transformation strain and applied stress for nitinol. Lett., 2003, vol. 57, pp. 1334-1338. DOI
Tikhomirova K.A. Razrabotka i chislennaia realizatsiia odnomernoi fenomenologicheskoi modeli fazovoi deformatsii v splavakh s pamiat’iu formy [Development and numerical implementation of one-dimensional phenomenological model for phase deformation in shape memory alloys]. Mekh. Splosh. Sred – Computational Continuum Mechanics, 2016, vol. 9, no. 2, pp.192-206. DOI
Wayman C.M. Deformation, mechanisms and other characteristics of shape memory alloys. Shape Memory Effects in Alloys, ed. by J. Perkins. New York, Springer US, 1975. Pp. 1-27. DOI
Elibol C., Wagner M.F.-X. Investigation of the stress-induced martensitic transformation in pseudoelastic NiTi under uniaxial tension, compression and compression–shear. Sci. Eng., A, 2015, vol. 621, pp. 76-81. DOI
Yoo Y.I., Kim Y.-J., Shin D.-K., Lee J.-J. Development of martensite transformation kinetics of NiTi shape memory alloys under compression. International Journal of Solids and Structures, 2015, vol. 64, pp. 51-61. DOI
Movchan A.A., Kyaw Thu Ya. Reshenie svjaznoj termojelektromehanicheskoj zadachi dlja sterzhnja iz splava s pamjat’ju formy v ramkah teorii nelinejnogo deformirovanija jetih materialov [Solution of the coupled thermoelectromechanics problem for the beam from shape memory alloys in the framework of the non-linear theory of deformation of these materials]. Mekhanika kompozitsionnykh materialov i konstruktsii – Composite Mechanics and Design, 2008, vol. 14, no. 3, pp. 443-460.
Rogovoy A.A., Stolbova O.S. Modeling the magnetic field control of phase transition in ferromagnetic shape memory alloys. J. Plast., 2016, vol. 85, pp. 130-155. DOI
Tikhomirova K.A. Izotermicheskoe deformirovanie splava s pamiat’iu formy v raznykh temperaturnykh intervalakh. Sluchai odnoosnogo rastiazheniia [Isothermal deformation of shape memory alloy in different temperature ranges. Uniaxial case]. Mekhanika kompozitsionnykh materialov i konstruktsii – Composite Mechanics and Design, 2017, vol. 23, no. 2, pp. 263-282.
Mishustin I.V., Movchan A.A. The microstructural model of mechanical behavior of a shape-memory alloy. Nanomechanics science and technology. An International Journal, 2016, vol. 7, no. 1, pp. 77-91. DOI
Andronov I.N., Bogdanov N.P., Severova N.A., Tarsin A.V. Metod kolichestvennogo opisanija zavisimosti modulja Junga nikelida titana ot temperatury [Method of quantitative describing of temperature dependence of NiTi Young’s modulus]. Izvestija Komi nauchnogo centra UrO RAN – Proceedings of Komi scientific center of UB RAS, 2013, no. 3, pp. 87-90.
Matveenko V.P., Smetannikov O.Ju., Trufanov N.A., Shardakov I.N. Termomehanika polimernyh materialov v uslovijah relaksacionnogo perehoda [Thermomechanics of polymeric materials under relaxation transition]. Moscow, Fizmatlit, 2009, 174 p.
Turusov R.A. Mehanicheskie javlenija v polimerah i kompozitah (v processah formovanija) [Mechanical phenomena in polymers and composites (in molding processes)]. Ph.D Dissertation, Moscow, 1983.
Movchan A.A., Kazarina S.A. Shape memory materials as an object of solid state mechanics: experimental study, constitutive relations, solution of boundary value problems. Physical mesomechanics, 2012, vol. 15, no. 3-4, pp. 214-223.
Auricchio F., Petrini L. A three-dimensional model describing stress-temperature induced solid phase transformations: thermomechanical coupling and hybrid composite applications. J. Numer. Methods Engineering, 2004, vol. 61, no. 5, pp. 716-737. DOI
Downloads
Published
Issue
Section
License
Copyright (c) 2018 Computational Continuum Mechanics
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
