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A Coupled Crystal Plasticity and Anisotropic Yield Function Model to Identify the Anisotropic Plastic Properties and Friction Behavior of an AA 3003 Alloy

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Abstract

A multi-scale simulation of the tip test, developed to determine the tribological characteristics of the back-extrusion process, was conducted on an AA 3003 alloy. A microstructure-level simulation, coupled with crystal plasticity finite element (CPFE) analysis, was utilized to characterize the macro-mechanical properties of the AA 3003. Owing to the limited size of the material provided, we performed CPFE analyses rather than multiple mechanical tests to determine the plastic anisotropy characteristics of the AA 3003 alloy. A three-dimensional finite element (FE) model of the tip test was developed using two different yield functions, namely the generalized von Mises yield function and Hill’s (1948) yield function, with material parameters identified from the CPFE analyses. The results revealed the following: 1. The directionality observed during the tip test is governed by the plastic anisotropy, rather than the frictional conditions. 2. The plastic anisotropy results in different Coulomb friction values. Therefore, the anisotropy should be carefully addressed in the tip test.

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Notes

  1. The material investigated in this study, rolled AA 3003, was an example of this limitation. Indeed, AA 3003 showed pronounced earing behavior following the tip test; however, the amount of material available limited its use for multiple mechanical tests.

  2. The main purpose of the current study is to focus on the effect of plastic anisotropy during the tip test. The effect of temperature in the experiment was ignored for the sake of simplicity.

  3. Although there is a discrepancy with regard to the small strain region between the experimental results and the H/V fits, the flow stress under this small strain range is not of significant importance considering the large amount of deformation that occurs during the tip test.

  4. To estimate the number of FEs (or Euler angles) required to accurately represent the macroscopic behavior of Al 3003, CPFE simulations with various number of FEs, such as 126, 225, 343, 512, 1000, 3375, 8000, and 27000, were conducted to predict r-value in uniaxial tension along the RD. The results revealed that the relative error of the predicted r-value becomes less than 2 pct when over 1000 FEs were used. Therefore, we decided to use the FE model with 1000 FEs (or 1000 Euler angles) for subsequent CPFE simulations.

  5. The force ratio of 1/2 was imposed for the plane-strain tension along the TD.

  6. To compensate for test-to-test scattering caused by machining errors and the thickness of the paint (in the case of the DIC measurement), the tip height value at the origin was brought to the same value in representative tests.

  7. The methodology used to measure the radial tip distance is detailed elsewhere.[11]

  8. Although the radial tip distance also showed directionality, the average value of the measured radial tip distances at four different points was used for simplicity. This is a reasonable assumption considering the conclusion in Section VI–B, in which the friction does not influence the directionality of the radial tip distance but only changes the overall value.

  9. It should be noted that the earing in the tip test should be distinguished from the earing in the sheet metal forming, in particular, the earing in the cup drawing of sheet metals. The earing in the cup drawing is mostly induced by the planar anisotropy under uniaxial tensile stress state in the flange region. In contrast, the material undergoes compression (States Ι and ΙΙ) and plane-strain tension (State ΙΙΙ) modes in the tip test. Therefore, unlike the cup drawing case, the earing in the tip test is not solely dependent on the planar anisotropy.

References

  1. H. Kudo: Int. J. Mech. Sci. 1960, vol. 2, pp. 102-27.

    Article  Google Scholar 

  2. J. B. Hawkyard and W. Johnson: Int. J. Mech. Sci., 1967, vol. 9, pp. 163-82.

    Article  Google Scholar 

  3. T. Robinson, H. Ou, and C. G. Armstrong: J. Mater. Process. Technol., 2004, vol. 153–154, pp. 54-59.

    Article  Google Scholar 

  4. S. J. Mirahmadi, M. Hamedi, and M. Cheraghzadeh: Tribol. Trans., 2015, vol. 58, pp. 778-85.

    Article  Google Scholar 

  5. M. Dehghan, F. Qods, M. Gerdooei, and J. Doai: Appl. Mech. Mater., 2012, vol. 249–250, pp. 663-66.

    Article  Google Scholar 

  6. Y. T. Im, O. Vardan, G. Shen, and T. Altan: CIRP Ann. - Manuf. Technol., 1988, vol. 37, 225-30.

    Article  Google Scholar 

  7. T. Nakamura, N. Bay, and Z.-L. Zhang: J. Tribol., 1997, vol. 119, pp. 501-06.

    Article  Google Scholar 

  8. T. Nakamura, N. Bay, and Z.-L. Zhang: J. Tribol., 1998, vol. 120, pp. 716-23.

    Article  Google Scholar 

  9. A. Buschhausen, K. Weinmann, J. Y. Lee, and T. Altan: J. Mater. Process. Technol., 1992, vol. 33, pp. 95-108.

    Article  Google Scholar 

  10. T. Nishimura, T. Sato, and Y. Tada, J: Mater. Process. Technol., 1995, vol. 53, pp. 726-35.

    Article  Google Scholar 

  11. Y.-T. Im, J.-S. Cheon, and S.-H. Kang: J. Manuf. Sci. Eng., 2002, vol. 124, pp. 409-15.

    Article  Google Scholar 

  12. P. Chauviere, K. H. Jung, D. K. Kim, H. C. Lee, S. H. Kang, and Y. T. Im: J. Mech. Sci. Technol., 2008, vol. 22, pp. 924-30.

    Article  Google Scholar 

  13. Y.-T. Im, S.-H. Kang, and J.-S. Cheon: J. Manuf. Sci. Eng., 2003, vol. 125, pp. 378-83.

    Article  Google Scholar 

  14. S.-H. Kang, J.-H. Lee, J.-S. Cheon, and Y.-T. Im: Int. J. Mech. Sci., 2004, vol. 46, pp. 855-69.

    Article  Google Scholar 

  15. H. J. Bong, D. Leem, J. H. Kim, Y. T. Im: and M. G. Lee, Met. Mater. Int. 2016, vol. 22, pp. 356-63.

    Article  Google Scholar 

  16. K. H. Jung, H. C. Lee, D. K. Kim, S. H. Kang, and Y. T. Im: Wear, 2012, vol. 286–287, pp. 19-26.

    Article  Google Scholar 

  17. K.-H. Jung, H.-C. Lee, J. S. Ajiboye, S.-H. Kang, and Y.-T. Im: J. Tribol., 2009, vol. 132, pp. 11601.

    Article  Google Scholar 

  18. K. H. Jung, H. C. Lee, J. S. Ajiboye, and Y. T. Im: Tribol. Lett., 2009, vol. 37, 353-59.

    Article  Google Scholar 

  19. F. Barlat and H. Bong: in 60 Excell. Invent. Met. Form. SE - 7, A.E. Tekkaya, W. Homberg, and A. Brosius, eds., Springer, Berlin, 2015, pp. 43–48.

  20. H. J. Bong, F. Barlat, D. C. Ahn, H.-Y. Kim: and M.-G. Lee, Int. J. Mech. Sci., 2013, vol. 75, 94-109.

    Article  Google Scholar 

  21. H. J. Bong, F. Barlat, M.-G. Lee, and D. C. Ahn: Int. J. Mech. Sci., 2012, vol. 64, 1-10.

    Article  Google Scholar 

  22. M. G. Lee, J. W. Lee, J. J. Gracio, G. Vincze, E. F. Rauch, and F. Barlat: Comput. Mater. Sci., 2013, vol. 79, 570-83.

    Article  Google Scholar 

  23. M. Liu, K.A. Tieu, K. Zhou, C.-T. Peng: Metall. Mater. Trans. A. 2016, vol. 47 pp. 2717–25.

    Article  Google Scholar 

  24. J.-H. Jung, Y.-S. Na, K.-M. Cho, D.M. Dimiduk, Y.S. Choi: Metall. Mater. Trans. A, 2015, vol. 46, 4834–40.

    Article  Google Scholar 

  25. S. F. Choudhury, L. Ladani: Metall. Mater. Trans. A, 2014, vol. 46A, pp. 1108-18.

    Google Scholar 

  26. K. Zhang and B. Holmedal and O. S. Hopperstad and S. Dumoulin: Model. Simul. Mater. Sci. Eng., 2014, vol. 22, pp. 75015.

    Article  Google Scholar 

  27. R. K. Verma, P. Biswas, T. Kuwabara, and K. Chung: Mater. Sci. Eng. A, 2014, vol. 604, pp. 98-102.

    Article  Google Scholar 

  28. K. Inal, R. K. Mishra, and O. Cazacu: Int. J. Solids Struct., 2010, vol. 47, pp. 2223-33.

    Article  Google Scholar 

  29. H. Lim, R. Dingreville, L. A. Deibler, T. E. Buchheit, and C. C. Battaile: Comput. Mater. Sci. 2016, vol. 117, pp. 437-44.

    Article  Google Scholar 

  30. B. Klusemann, B. Svendsen, and H. Vehoff: Comput. Mater. Sci., 2012, vol. 52, pp. 25-32.

    Article  Google Scholar 

  31. M. Knezevic and S. R. Kalidindi: Comput. Mater. Sci., 2007, vol. 39, pp. 643-48.

    Article  Google Scholar 

  32. H. Lim, J. D. Carroll, C. C. Battaile, T. E. Buchheit, B. L. Boyce, and C. R. Weinberger: Int. J. Plast., 2014, vol. 60, pp. 1-18.

    Article  Google Scholar 

  33. F. Meier, C. Schwarz, and E. Werner: Comput. Mater. Sci., 2014, vol. 94, pp. 122-31.

    Article  Google Scholar 

  34. J. Jung, J. I. Yoon, J. H. Moon, H. K. Park, and H. S. Kim: Comput. Mater. Sci., 2017, vol. 126, pp. 121-31.

    Article  Google Scholar 

  35. A. Khajezade, M.H. Parsa, H. Mirzadeh: Metall. Mater. Trans. A, 2016, vol. 47 pp. 941–48.

    Article  Google Scholar 

  36. M.I. Latypov, M.-G. Lee, Y. Beygelzimer, D. Prilepo, Y. Gusar, H.S. Kim: Metall. Mater. Trans. A, 2016, vol. 47, 1248–60

    Article  Google Scholar 

  37. Y.S. Choi, M.A. Groeber, P.A. Shade, T.J. Turner, J.C. Schuren, D.M. Dimiduk, M.D. Uchic, A.D. Rollett: Metall. Mater. Trans. A, 2014, vol. 45, pp. 6352–59.

    Article  Google Scholar 

  38. F. Barlat and O. Richmond: Mater. Sci. Eng., 1987, vol. 95, 15-29.

    Article  Google Scholar 

  39. M. Kuroda: in AIP Conf. Proc., 2005, vol. 778, pp. 445–50.

  40. F. Khakbaz and M. Kazeminezhad: Mater. Sci. Eng. A, 2012, vol. 532, pp. 26-30.

    Article  Google Scholar 

  41. R. Fournier and S. Fournier: Sheet Metal Handbook, HP Books, 1989, p. 143.

  42. S. Lim, H. Huh: Int. J. Automot. Technol. 2017, vol. 18, pp. 719-27.

    Article  Google Scholar 

  43. J. H. Sung, J. H. Kim, and R. H. Wagoner: Int. J. Plast., 2010, vol. 26, pp. 1746-71.

    Article  Google Scholar 

  44. A. Smith, Z. Chen, J. J. Y. Lee, M. G. Lee, and R. Wagoner, Int. J. Plast. 2014, vol. 58, pp. 100-19

    Article  Google Scholar 

  45. W.F. Hosford and R.M. Caddel: Metal Forming: Mechanics and Metallurgy, Cambridge University Press, 1983.

  46. R. Hielscher and H. Schaeben: J. Appl. Crystallogr., 2008, vol. 41, pp. 1024-37.

    Article  Google Scholar 

  47. H. Huh, C.G. Park, C.S. Lee, and Y.T. Keum: in Proc. 9th AEPA 2008 (World Scientific, Daejeon, Korea, 2009), pp. 527–28.

  48. S. Akramove, M. G. Lee, I. Kim, D. Y. Sung, B. H. Park, and I. Kim, Mater. Sci. Forum, 2005, vol. 495–497, pp. 803-8.

    Article  Google Scholar 

  49. R. J. Asaro and J. R. Rice: J. Mech. Phys. Solids, 1977, vol. 25, pp. 309-38.

    Article  Google Scholar 

  50. E. H. Lee: J. Appl. Mech., 1969, vol. 36, pp. 1-6.

    Article  Google Scholar 

  51. R. Hill and J. R. Rice: J. Mech. Phys. Solids, 1972, vol. 20, pp. 401-13.

    Article  Google Scholar 

  52. D. Peirce, R. J. Asaro, and A. Needleman: Acta Metall., 1982, vol. 30, pp. 1087-1119.

    Article  Google Scholar 

  53. M. G. Lee, H. Lim, B. L. Adams, J. P. Hirth, and R. H. Wagoner: Int. J. Plast., 2010, vol. 26, pp. 925-38.

    Article  Google Scholar 

  54. J. R. Rice: J. Mech. Phys. Solids, 1971, vol. 19, pp. 433-55.

    Article  Google Scholar 

  55. J.W. Hutchinson: in Proc. R. Soc. Lond., 1976 vol. A 348, pp. 101–27.

  56. C. A. Bronkhorst, S. R. Kalidindi, and L. Anand: The Royal Society, 1992, vol. 341, pp. 443–477.

    Google Scholar 

  57. S. R. Kalidindi, C. A. Bronkhorst, and L. Anand: J. Mech. Phys. Solids, 1992, vol. 40, pp. 537-69.

    Article  Google Scholar 

  58. J. Gubicza, N. Q. Chinh, J. L. Lábár, S. Dobatkin, Z. Hegedűs, and T. G. Langdon, J. Alloys Compd, 2009, vol. 483, pp. 271-74.

    Article  Google Scholar 

  59. H. Wiedersich, JOM, 1964, vol. 16(5), pp. 425-30.

    Article  Google Scholar 

  60. G. Schoeck and R. Frydman, Phys. Status Solidi, 1972, vol. 53, pp. 661-73.

    Article  Google Scholar 

  61. M. Kassner, J. Mater. Sci, 1990, vol. 25(4), pp. 1997-2003.

    Article  Google Scholar 

  62. U.F. Kocks: J. Eng. Mater. Technol. Trans. ASME, 1976, vol. 98 Ser H, pp. 76–85.

  63. S.R. Kalidindi: Ph.D. Thesis, Polycrystal Plasticity: Constitutive Modeling and Deformation Processing, Massachusetts Institute of Technology, 1992.

  64. R. Hill: Proc. R. Soc. London A Math. Phys. Eng. Sci., 1948, vol. 193, pp. 281-97.

    Article  Google Scholar 

  65. K. Zhang, B. Holmedal, O. S. S. Hopperstad, S. Dumoulin, J. Gawad, A. Van Bael, and P. Van Houtte, Int. J. Plast, 2015, vol. 66, pp. 3-30.

    Article  Google Scholar 

  66. Y. Hanabusa, H. Takizawa, and T. Kuwabara, J. Mater. Process. Technol, 2013, vol. 213, pp. 961-70.

    Article  Google Scholar 

  67. F. Barlat, H. Aretz, J. W. Yoon, M. E. Karabin, J. C. Brem, and R. E. Dick, Int. J. Plast. 2005, vol. 21, pp. 1009-39.

    Article  Google Scholar 

  68. J. C. Pierret, A. Rassili, G. Vaneetveld, R. Bigot, and J. Lecomte-Beckers, Int. J. Mater. Form, 2010, vol. 3, 763-66.

    Article  Google Scholar 

  69. T. J. Shin, Y. H. Lee, J. T. Yeom, S. H. Chung, S. S. Hong, I. O. Shim, N. K. Park, C. S. Lee, and S. M. Hwang, Comput. Methods Appl. Mech. Eng, 2005, vol. 194, 3838-69.

    Article  Google Scholar 

  70. H. Bašić, I. Demirdžić, and S. Muzaferija, Int. J. Numer. Methods Eng, 2005, vol. 62, pp. 475-94.

    Article  Google Scholar 

  71. J.-H. Cheng: Int. J. Numer. Methods Eng., 1988, vol. 26, pp. 1-18.

    Article  Google Scholar 

  72. W. K. Liu, T. Belytschko, and H. Chang: Comput. Methods Appl. Mech. Eng., 1986, vol. 58, pp. 227-45.

    Article  Google Scholar 

  73. D. J. Benson: Comput. Methods Appl. Mech. Eng. 1989, vol. 72, pp. 305-50.

    Article  Google Scholar 

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Acknowledgments

The authors acknowledge H.G. Kim for the XRD measurement. H.M. Back and Dr. D.K. Kim kindly helped for the tip-test experiments at KAIST. J. Lee appreciates the support by the Fundamental Research Program of the Korea Institute of Materials Science (KIMS). MGL appreciates supports from National Research Foundation of Korea (NRF) (2017R1A2A2A05069619) and Engineering Research Center (2012R1A5A1051500).

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Authors and Affiliations

  1. Department of Materials Science and Engineering, The Ohio State University, Columbus, OH, 43210, USA

    Hyuk Jong Bong

  2. Department of Mechanical Engineering, Northwestern University, 2145 Sheridan road, Evanston, IL, 60208, USA

    Dohyun Leem

  3. Materials Deformation Department, Korean Institute of Materials Science (KIMS), Changwon, Gyeongnam, 51508, South Korea

    Jinwoo Lee

  4. Department of Mechanical Engineering, University of New Hampshire, 33 Academic Way, Durham, NH, 03824, USA

    Jinjin Ha

  5. Department of Materials Science and Engineering, Korea University, Seoul, 02841, South Korea

    Myoung-Gyu Lee

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  1. Hyuk Jong Bong
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Manuscript submitted January 2, 2017.

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Bong, H.J., Leem, D., Lee, J. et al. A Coupled Crystal Plasticity and Anisotropic Yield Function Model to Identify the Anisotropic Plastic Properties and Friction Behavior of an AA 3003 Alloy. Metall Mater Trans A 49, 282–294 (2018). https://doi.org/10.1007/s11661-017-4406-1

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