Volume 20, Issue 3 (March 2020)                   Modares Mechanical Engineering 2020, 20(3): 761-775 | Back to browse issues page

XML Persian Abstract Print


Download citation:
BibTeX | RIS | EndNote | Medlars | ProCite | Reference Manager | RefWorks
Send citation to:

Jalili M, Soltani B, Nayebi A. Multiscale Modeling Of Cyclic Plastic Deformation of Magnesium Alloy AZ31 Using Crystal Plasticity Finite Element Method and Computational Homogenization. Modares Mechanical Engineering 2020; 20 (3) :761-775
URL: http://mme.modares.ac.ir/article-15-28813-en.html
1- Mechanical Engineering Faculty, University of Kashan, Kashan, Iran
2- Mechanical Engineering Faculty, University of Kashan, Kashan, Iran , bsoltani@kashanu.ac.ir
3- Mechanical Engineering Faculty, Shiraz University, Shiraz, Iran
Abstract:   (5273 Views)
In the present research, a multiscale method based on crystal plasticity finite element method and computational homogenization is proposed to simulate monotonic and cyclic plastic deformation of a highly textured rolled magnesium alloy AZ31. All active deformation mechanisms including slip, twinning as well as detwinning have been simulated in the model through user material subroutine in ABAQUS (UMAT). All representative volume elements have been constructed, synthetically. Polycrystal laminate has been reproductive by representative volume element (RVE) and periodic boundary conditions have been applied on the RVE faces. For cyclic validations, uniaxial compression-tension along extrusion direction has been applied for 2 loading cycles and the problem at the macroscopic scale has been solved by the ABAQUS finite element solver. The results are in good accordance with the experimental curves and the proposed model can accurately predict all cyclic behavior characteristics like asymmetry in a stress-strain curve due to alternating twinning-detwinning, tensile and compressive peak stresses, twinning and detwinning.
Full-Text [PDF 1832 kb]   (1781 Downloads)    
Article Type: Original Research | Subject: Metal Forming
Received: 2018/12/31 | Accepted: 2019/07/18 | Published: 2020/03/1

References
1. Shaftel H, Jackson R, Callery S, Bailey D, editors. Global climate change: Vital signs of the planet, NASA Jet Propulsion Laboratory [Internet]. California: NASA's Jet Propulsion Laboratory; 2017 [Cited 2018 December 30]. Available from: https://climate.nasa.gov. [Link]
2. epa.gov [Internet]. Washington: United States Environmental Protection Agency; 2017 [Cited 2018 December 30]. Available from: https://www.epa.gov/climatechange/ghgemissions/inventoryexplorer/. [Link]
3. Natural Resources Canada. Learn the facts: Weight affects fuel consumption [Internet]. Canada: Natural Resources Canada; 2017 [Cited 2018 December 30]. Available from: http://www.nrcan.gc.ca/energy/efficiency/transportation/cars-lighttrucks/buying/16755. [Link]
4. Bishop JDK, Martin NPD, Boies AM. Cost-effectiveness of alternativepowertrains for reduced energy use and CO2 emissions in passenger vehicles. Applied Energy. 2014;124:44-61. [Link] [DOI:10.1016/j.apenergy.2014.02.019]
5. Fontaras G, Zacharof NG, Ciuffo B. Fuel consumption and CO2 emissions from passenger cars in Europe - Laboratory versus real-world emissions. Progress in Energy and Combustion Science. 2017;60:97-131. [Link] [DOI:10.1016/j.pecs.2016.12.004]
6. Taylor GI. Plastic Strain in Metals. Journal of the Institute of Metals.1938;(62):307-324. [Link]
7. Agnew SR, Ozgur D. Plastic anisotropy and the role of non-basal slip in magnesium alloy AZ31B. International Journal of Plasticity. 2005;21(6):1161-1193. [Link] [DOI:10.1016/j.ijplas.2004.05.018]
8. Houtte PV. Simulation of the rolling and shear texture of brass by the Taylor theory adapted for mechanical twinning. Acta Metallurgica. 1978;26(4):591-604. [Link] [DOI:10.1016/0001-6160(78)90111-6]
9. Kalidindi SR. Incorporation of deformation twinning in crystal plasticity models. Journal of the Mechanics and Physics of Solids. 1998;46(2):267-271. [Link] [DOI:10.1016/S0022-5096(97)00051-3]
10. Kalidindi SR, Bronkhorst CA, Anand L. Crystallographic texture evolution in bulk deformation processing of FCC metals. Journal of the Mechanics and Physics of Solids. 1992;40(3):537-569. [Link] [DOI:10.1016/0022-5096(92)80003-9]
11. Peirce D, Asaro RJ, Needleman A. An analysis of nonuniform and localized deformation in ductile single crystals. Acta Metallurgica. 1982;30(6):1087-1119. [Link] [DOI:10.1016/0001-6160(82)90005-0]
12. Peirce D, Asaro RJ, Needleman A. Material rate dependence and localized deformation in crystalline solids. Acta Metallurgica. 1983;31(12):1951-1976. [Link] [DOI:10.1016/0001-6160(83)90014-7]
13. Asaro JR. Micromechanics of crystals and polycrystals. Advances in Applied Mechanics. 1983;23:1-115. [Link] [DOI:10.1016/S0065-2156(08)70242-4]
14. Staroselsky A, Anand L. A constitutive model for hcp materials deforming by slip and twinning: Application to magnesium alloy AZ31B. International Journal of Plasticity. 2003;19(10):1843-1864. [Link] [DOI:10.1016/S0749-6419(03)00039-1]
15. Graff S, Brocks W, Steglich D. Yielding of magnesium: From single crystal to polycrystalline aggregates. International Journal of Plasticity. 2007;23(12):1957-1978. [Link] [DOI:10.1016/j.ijplas.2007.07.009]
16. Mayama T, Noda M, Chiba R, Kuroda M. Crystal plasticity analysis of texture development in magnesium alloy during extrusion. International Journal of Plasticity. 2011;27(12):1916-1935. [Link] [DOI:10.1016/j.ijplas.2011.02.007]
17. Fernandez A, Teresa Perez Prado M, Wei Y, Jerusalem A. Continuum modeling of the response of an mg alloy AZ31 rolled sheet during uniaxial deformation. International Journal of Plasticity. 2011;27(11):1739-1757. [Link] [DOI:10.1016/j.ijplas.2011.05.002]
18. Herrera-Solaz V, LLorca J, Dogan E, Karaman I, Segurado J. An inverse optimization strategy to determine single crystal mechanical behavior from polycrystal tests: Application to AZ31 Mg alloy. Journal of Plasticity. 2014;57:1-15. [Link] [DOI:10.1016/j.ijplas.2014.02.001]
19. Kothari M, Anand L. Elasto-Viscoplastic constitutive equations for polycrystalline metals: Application to tantalum. Journal of the Mechanics and Physics of Solids. 1998;46(1):51-83. [Link] [DOI:10.1016/S0022-5096(97)00037-9]
20. Segurado J, Lebensohn RA, LLorca J. Computational homogenization of polycrystals. Advances in Applied Mechanics. 2018;51:1-114. [Link] [DOI:10.1016/bs.aams.2018.07.001]
21. Matous K, Geers MGD, Kouznetsova VG, Gillman A. A review of predictive nonlinear theories for multiscale modeling of heterogeneous materials. Journal of Computational Physics. 2017;330:192-220. [Link] [DOI:10.1016/j.jcp.2016.10.070]
22. Hama T, Takuda H. Crystal-Plasticity finite-element analysis of inelastic behavior during unloading in a magnesium alloy sheet. International Journal of Plasticity. 2011;27(7):1072-1092. [Link] [DOI:10.1016/j.ijplas.2010.11.004]
23. Hama t, Takuda H. Crystal plasticity finite-element simulation of work-hardening behavior in a magnesium alloy sheet under biaxial tension. Computational Materials Science. 2012;51(1):156-164. [Link] [DOI:10.1016/j.commatsci.2011.07.026]
24. Hama T, Kitamura N, Takuda H. Effect of twinning and detwinning on inelastic behavior during unloading in a magnesium alloy sheet. Materials Science and Engineering: A. 2013;583:232-241. [Link] [DOI:10.1016/j.msea.2013.06.070]
25. Hama T, Nagao H, Kuchinomachi Y, Takuda H. Effect of pre-strain on work-hardening behavior of magnesium alloy sheets upon cyclic loading. Materials Science and Engineering: A. 2014;591:69-77. [Link] [DOI:10.1016/j.msea.2013.10.083]
26. Hama T, Tanaka Y, Uratani, M, Takuda H. Deformation behavior upon two-step loading in a magnesium alloy sheet. International Journal of Plasticity. 2016;82:283-304. [Link] [DOI:10.1016/j.ijplas.2016.03.009]
27. Yi N, Hama T, Kobuki A, Fujimoto H, Takuda H. Anisotropic deformation behavior under various strain paths in commercially pure titanium grade 1 and grade 2 sheets. Materials Science and Engineering: A. 2016;655:70-85. [Link] [DOI:10.1016/j.msea.2015.12.081]
28. Hama T, Kobuki A, Takuda H. Crystal plasticity finite element analysis of anisotropic deformation behavior in a commercially pure titanium grade 1 sheet. International Journal of Plasticity. 2017;91:77-108. [Link] [DOI:10.1016/j.ijplas.2016.12.005]
29. Hama T, Suzuki T, Hatakeyama Sh, Fujimoto H, Takuda H. Role of twinning on the stress and strain behaviors during reverse loading in rolled magnesium alloy sheets. Materials Science and Engineering: A. 2018;725:8-18. [Link] [DOI:10.1016/j.msea.2018.03.124]
30. Wang H, Wu PD, Wang J, Tome CN. A crystal plasticity model for hexagonal close packed (HCP) crystals including twinning and detwinning mechanisms. International Journal of Plasticity. 2013;49:36-52. [Link] [DOI:10.1016/j.ijplas.2013.02.016]
31. Asaro RJ, Needleman A. Overview no. 42 texture development and strain hardening in rate dependent polycrystals. Acta Metallurgica. 1985;33(6):923-953. [Link] [DOI:10.1016/0001-6160(85)90188-9]
32. Hutchinson JW. Bounds and self-consistent estimates for creep of polycrystalline materials. Proceedings of the Royal Society of London Series A: Mathematical and Physical Sciences1976;348(1652):101-127. [Link] [DOI:10.1098/rspa.1976.0027]
33. Zhang J, Joshi ShP. Phenomenological crystal plasticity modeling and detailed micromechanical investigations of pure magnesium. Journal of the Mechanics and Physics of Solids. 2012;60(5):945-972. [Link] [DOI:10.1016/j.jmps.2012.01.005]
34. Tadano Y, Yoshihara Y, Hagihara S. A Crystal plasticity modeling considering volume fraction of deformation twinning. International Journal of Plasticity. 2016;84:88-101. [Link] [DOI:10.1016/j.ijplas.2016.05.002]
35. Yu Q, Zhang J, Jiang Y. Direct observation of twinning-detwinning-retwinning on magnesium single crystal subjected to strain-controlled cyclic tension-compression in [0001] direction. Philosophical Magazine Letters. 211;91(12):757-765. [Link] [DOI:10.1080/09500839.2011.617713]
36. Hazeli K, Askari H, Cuadra J, Streller F, Carpick RW, Zbib HM, et al. Microstructure-Sensitive investigation of magnesium alloy fatigue. International Journal of Plasticity. 2015;68:55-76. [Link] [DOI:10.1016/j.ijplas.2014.10.010]
37. Xiong Y, Yu Q, Jiang Y. Multiaxial fatigue of extruded AZ31B magnesium alloy. Materials Science and Engineering: A. 2013;546:119-128. [Link] [DOI:10.1016/j.msea.2012.03.039]
38. Belytschko T, Kam Liu W, Moran B, Elkhodary Kh. Nonlinear Finite Elements for Continua and Structures. 2nd Edition. Hoboken: Wiley; 2014. [Link]
39. Jackson MA, Groeber MA, Uchic MD, Rowenhorst DJ, Graef MD. H5ebsd: An archival data format for electron back-scatter diffraction data sets. Integrating Materials and Manufacturing Innovation. 2014;3(1):44-55. [Link] [DOI:10.1186/2193-9772-3-4]
40. Lv L, Xin Y, Yu H, Hong R, Liu Q. The role of dislocations in strain hardening of an extension twinning predominant deformation. Materials Science and Engineering: A. 2015;636:389-395. [Link] [DOI:10.1016/j.msea.2015.04.007]
41. Fan H, Aubry S, Arsenlis A, EL-Awady J. The Role of twinning deformation on the hardening response of polycrystalline magnesium from discrete dislocation dynamics simulation. Acta Materialia. 2015;92:126-139. [Link] [DOI:10.1016/j.actamat.2015.03.039]
42. Hyuk Park S, Hong S, Yoon J, Soo Lee Ch. Influence of loading direction on the anisotropic fatigue properties of rolled magnesium alloy. International Journal of Fatigue. 2016;87:210-215. [Link] [DOI:10.1016/j.ijfatigue.2016.01.026]
43. Hong SG, Park SH, Lee ShS. Role of {10-12} twinning charactersitics in the deformation behavior of a polycrystalline magnesium alloy. Acta Materialia. 2010;58(18):5873-5885. [Link] [DOI:10.1016/j.actamat.2010.07.002]
44. Castro F, Jiang Y. Fatigue of extruded AZ31B magnesium alloy under stress- and strain-controlled conditions including step loading. Mechanics of Materials. 2017;108:77-86. [Link] [DOI:10.1016/j.mechmat.2017.03.002]
45. Xiong Y, Yu Q, Jiang Y. Cyclic deformation ANF fatigue of extruded AZ31B magnesium alloy under different strain rations. Materials Science and Engineering: A. 2016;649:93-103. [Link] [DOI:10.1016/j.msea.2015.09.084]
46. Roostaei AA, Jahed H. Multiaxial cyclic behavior and fatigue modelling of AM30 magnesium alloy extrusion. [Link]
47. Xiong Y. Microstructure damage evaluation associated with cyclic deformation for extruded AZ31B magnesium alloy. Materials Science and Engineering: A. 2016;675:171-180. [Link] [DOI:10.1016/j.msea.2016.08.043]
48. Wen B, Wang F, Jin L, Dong J. Fatigue damage development in extruded Mg-3Al-Zn magnesium alloy. Material Science and Engineering: A. 2016;667:171-178. [Link] [DOI:10.1016/j.msea.2016.05.009]
49. McDowell DL, Dunne FPE. Microstructure-Sensitive computational modeling of fatigue crack formation. International Journal of Fatigue. 2010;32(9):1521-1542. [Link] [DOI:10.1016/j.ijfatigue.2010.01.003]
50. Dunne FPE. Fatigue crack nucleation: Mechanistic modelling across the length scales. Current Opinion in Solid State and Materials Science. 2014;18(4):170-179. [Link] [DOI:10.1016/j.cossms.2014.02.005]
51. Catelluccio G, Musinski WD, McDowell D. Recent developments in assessing microstructure-sensitive early stage fatigue of polycrystals. Current Opinion in Solid State and Materials Science. 2014;18(4):180-187.International Journal of Fatigue. 2017;97:150-161. [Link] [DOI:10.1016/j.cossms.2014.03.001]
52. Zhang H, Jérusalem A, Salvati E, Papadaki C, Fong KS, Song X, et al. Multi-Scale Mechanisms of Twinning-Detwinning in Magnesium AZ31B Alloy Simulated by Crystal Plasticity Modeling and Validated via In Situ Synchrotron XRD and In Situ SEMEBSD. International Journal of Plasticity. 2019;119:43-56. [Link] [DOI:10.1016/j.ijplas.2019.02.018]

Add your comments about this article : Your username or Email:
CAPTCHA

Send email to the article author


Rights and permissions
Creative Commons License This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.