J Shanghai Jiaotong Univ Sci

Journal of Shanghai Jiaotong University(Science) >

2021 , Vol. 26 >Issue 6: 774 - 785

DOI: https://doi.org/10.1007/s12204-021-2327-z

Material, Structure, Mechanics

Nonlinear Finite Element Method Considering Martensite Plasticity for Shape Memory Alloy Structure

Expand
  • (Department of Engineering Mechanics, College of Pipeline and Civil Engineering,China University of Petroleum, Qingdao 266580, Shandong, China)

Received date: 2019-07-20

  Online published: 2021-12-01

Fold

Abstract

This work presents a nonlinear finite element method to simulate the macroscopic mechanical responsesand the effects of martensite plasticity in a shape memory alloy (SMA) structure. A linear relationshipformulation is adopted to express the influence of martensite plasticity on the inverse martensitic phase transitionof SMA material. Incorporating with a trigonometric-type phase transition evolution law and an exponential-typeplastic flow evolution law, an incremental mechanical model with two internal variables is supposed based onthe macroscopic experimental phenomena. A nonlinear finite element equation is formulated and solved by theprinciple of virtual displacement and Newton-Raphson method respectively. By employing the proposed nonlinearfinite element method, the uniform tensile bar and three-point bending beam are simulated and analyzed. Resultsillustrate that the presented nonlinear finite element method is suitable to act as an effective computational toolfor the wide applications based on the SMA material considering the effects of martensite plasticity because allmaterial constants related to the method can be obtained from macroscopic experiments.

Key words： shape memory alloy (SMA) structure, martensite plasticity, incremental mechanical model, nonlinearfinite element method

Cite this article

ZHOU Bo∗ (周博), KANG Zetian (康泽天), WANG Zhiyong (王志勇), XUE Shifeng (薛世峰) . Nonlinear Finite Element Method Considering Martensite Plasticity for Shape Memory Alloy Structure[J]. Journal of Shanghai Jiaotong University(Science), 2021 , 26(6) : 774 -785 . DOI: 10.1007/s12204-021-2327-z

References

[1] ZHOU B, YOON S H, LENG J S. A three-dimensionalconstitutive model for shape memory alloy [J]. SmartMaterials and Structures, 2009, 18(9): 095016. [2] RULAND A, TAYLOR J M, ZILLINGER C. Convexintegration arising in the modelling of shape-memoryalloys: Some remarks on rigidity, flexibility and somenumerical implementations [J]. Journal of NonlinearScience, 2019, 29: 2137-2184. [3] DELLA PORTA F. Analysis of a moving mask hypothesisfor martensitic transformations [J]. Journalof Nonlinear Science, 2019, 29: 2341-2384. [4] TANAKA K. Thermomechanical sketch of shape memoryeffect: One-dimensional tensile behavior [J]. ResMechanica: International Journal of Structural Mechanicsand Materials Science, 1986, 18(3): 251-263. [5] LIANG C, ROGERS C A. One-dimensional thermomechanicalconstitutive relations for shape memorymaterials [J]. Journal of Intelligent Material Systemsand Structures, 1990, 1(2): 207-234. [6] BOYD J G, LAGOUDAS D C. Thermomechanical responseof shape memory composites [J]. Journal of IntelligentMaterial Systems and Structures, 1994, 5(3):333-346. [7] BRINSON L C. One-dimensional constitutive behaviorof shape memory alloys: Thermomechanical derivationwith non-constant material functions and redefinedmartensite internal variable [J]. Journal of IntelligentMaterial Systems and Structures, 1993, 4(2):229-242. [8] LIM T J, MCDOWELL D L. Mechanical behavior ofan Ni-Ti shape memory alloy under axial-torsional proportionaland nonproportional loading [J]. Journal ofEngineering Materials and Technology, 1999, 121(1):9-18. [9] PENG X, YANG Y, HUANG S. A comprehensive descriptionfor shape memory alloys with a two-phaseconstitutive model [J]. International Journal of Solidsand Structures, 2001, 38(38/39): 6925-6940. [10] ZHOU B, YOON S H. A new phase transformationconstitutive model of shape memory alloys [J]. SmartMaterials and Structures, 2006, 15(6): 1967-1973. [11] MIRZAEIFAR R, DESROCHES R, YAVARI A. Acombined analytical, numerical, and experimentalstudy of shape-memory-alloy helical springs [J]. InternationalJournal of Solids and Structures, 2011,48(3/4): 611-624. [12] MERZOUKI T, DUVAL A, BEN ZINEB T. Finite Elementanalysis of a shape memory alloy actuator fora micropump [J]. Simulation Modelling Practice andTheory, 2012, 27: 112-126. [13] CHEMISKY Y, CHATZIGEORGIOU G, KUMAR P,et al. A constitutive model for cyclic actuation of hightemperatureshape memory alloys [J]. Mechanics ofMaterials, 2014, 68: 120-136. [14] GU X, ZAKI W, MORIN C, et al. Time integrationand assessment of a model for shape memory alloysconsidering multiaxial nonproportional loading cases[J]. International Journal of Solids and Structures,2015, 54: 82-99. [15] HAZAR S, ZAKI W, MOUMNI Z, et al. Modeling ofsteady-state crack growth in shape memory alloys usinga stationary method [J]. International Journal ofPlasticity, 2015, 67: 26-38. [16] PERAZA HERNANDEZ E A, KIEFER B, HARTL DJ, et al. Analytical investigation of structurally stableconfigurations in shape memory alloy-actuated plates[J]. International Journal of Solids and Structures,2015, 69/70: 442-458. [17] LONG X, PENG X, FU T, et al. A micro-macrodescription for pseudoelasticity of NiTi SMAs subjectedto nonproportional deformations [J]. InternationalJournal of Plasticity, 2017, 90: 44-65. [18] KANG Z T, ZHOU B, XUE S F. Finite element numericalsimulation on thermo-mechanical coupling behaviorin shape memory alloy pipe connection [J]. Journalof Mechanical Engineering, 2018, 54(18): 68-75 (inChinese). [19] ARMATTOE K M, BOUBY C, HABOUSSI M, et al.Modeling of latent heat effects on phase transformationin shape memory alloy thin structures [J]. InternationalJournal of Solids and Structures, 2016, 88/89:283-295. [20] WANG J, MOUMNI Z, ZHANG W, et al. A thermomechanicallycoupled finite deformation constitutivemodel for shape memory alloys based on Henckystrain [J]. International Journal of Engineering Science,2017, 117: 51-77. [21] LEI H S, WANG Z Q, ZHOU B, et al. Simulationand analysis of shape memory alloy fiber reinforcedcomposite based on cohesive zone model [J]. Materials& Design, 2012, 40: 138-147. [22] GU D, HE B. Finite element simulation and experimentalinvestigation of residual stresses in selectivelaser melted Ti-Ni shape memory alloy [J]. ComputationalMaterials Science, 2016, 117: 221-232. [23] ARMATTOE K M, HABOUSSI M, BEN ZINEB T.A 2D finite element based on a nonlocal constitutivemodel describing localization and propagation of phasetransformation in shape memory alloy thin structures[J]. International Journal of Solids and Structures,2014, 51(6): 1208-1220. [24] HASSANLI S, SAMALI B. Buckling analysis of laminatedcomposite curved panels reinforced with linearand non-linear distribution of Shape Memory Alloys[J]. Thin-Walled Structures, 2016, 106: 9-17. [25] HATEFI ARDAKANI S, AFSHAR A,MOHAMMADIS. Numerical study of thermo-mechanical coupling effectson crack tip fields of mixed-mode fracture in pseudoelasticshape memory alloys [J]. International Journalof Solids and Structures, 2016, 81: 160-178. [26] JIANG D J, BECHLE N J, LANDIS C M, et al. Bucklingand recovery of NiTi tubes under axial compression[J]. International Journal of Solids and Structures,2016, 80: 52-63. [27] KATANCHI B, CHOUPANI N, KHALIL-ALLAFI J,et al. Photostress analysis of stress-induced martensitephase transformation in superelastic NiTi [J]. MaterialsScience and Engineering: A, 2017, 688: 202-209. [28] ZHANG Y Q, JIANG S Y, ZHAO Y N, et al. Simulationof isothermal precision extrusion of NiTi shapememory alloy pipe coupling by combining finite elementmethod with cellular automaton [J]. Journal ofCentral South University, 2017, 24: 506-514. [29] YU C, KANG G Z, KAN Q H, et al. A micromechanicalconstitutive model based on crystal plasticity forthermo-mechanical cyclic deformation of NiTi shapememory alloys [J]. International Journal of Plasticity,2013, 44: 161-191. [30] YU C, KANG G Z, KAN Q H. A micromechanicalconstitutive model for anisotropic cyclic deformation ofsuper-elastic NiTi shape memory alloy single crystals[J]. Journal of the Mechanics and Physics of Solids,2015, 82: 97-136. [31] ASHRAFI M J, ARGHAVANI J, NAGHDABADI R,et al. Theoretical and numerical modeling of dense andporous shape memory alloys accounting for couplingeffects of plasticity and transformation [J]. InternationalJournal of Solids and Structures, 2016, 88/89:248-262. [32] PARANJAPE H M, MANCHIRAJU S, ANDERSONP M. A phase field - Finite element approach to modelthe interaction between phase transformations andplasticity in shape memory alloys [J]. InternationalJournal of Plasticity, 2016, 80: 1-18. [33] HU L, JIANG S, SHI L, et al. Prediction of grain scaleplasticity of NiTi shape memory alloy based on crystalplasticity finite element method [J]. Transactions ofNonferrous Metals Society of China, 2019, 29(4): 775-784. [34] CISS′E C, ZAKIW, GU X, et al. A nonlinear 3D modelfor iron-based shape memory alloys considering differentthermomechanical properties for austenite andmartensite and coupling between transformation andplasticity [J]. Mechanics of Materials, 2017, 107: 1-21. [35] WANG X M, XU B X, YUE Z F. Micromechanicalmodelling of the effect of plastic deformation on themechanical behaviour in pseudoelastic shape memoryalloys [J]. International Journal of Plasticity, 2008,24(8): 1307-1332. [36] ZHOU B. A macroscopic constitutive model of shapememory alloy considering plasticity [J]. Mechanics ofMaterials, 2012, 48: 71-81.
Options
Outlines

/

〈 〉