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Evaluation of plastic flow curve of pure titanium sheet using hydraulic bulge test

유압벌지실험을 이용한 순 티탄늄 판재의 소성유동곡선 평가(제2보)

  • Received : 2016.03.16
  • Accepted : 2016.04.07
  • Published : 2016.04.30

Abstract

In this study, the plastic flow curve of commercially pure titanium sheet (CP Ti) actively used in the plate heat exchanger etc., was evaluated. The plastic flow curve known as hardening curve is a key factor needed in conducting finite element analyses (FEA) for the forming process of a sheet material. A hydraulic bulge test was performed on the CP Ti sheet and the strain in this test was measured using the DIC method and ARAMIS system. The measured true stress-true strain curve from the hydraulic bulge test (HBT) was compared with that from the tensile test. The measured true stress-true strain curve from the hydraulic bulge test showed stable plastic flow curve over the strain range of 0.7 which cannot be obtained in the case of the uniaxial tensile test. The measured true stress-true strain curve from the hydraulic bulge test can be fitted well by the hardening equation known as the Kim-Tuan model.

본 논문에서는 대형 선박의 판형 열교환기 등에 널리 이용되고 있는 순 티타늄 판재의 소성변형을 유한요소해석하기 위한 기초 데이터로서 순 티타늄 판재의 유동곡선을 평가하였다. 순 티타늄 판재의 프레스 가공 시에 판재에는 국부적으로 큰 소성변형이 발생하고 있다. 그러나 기존의 단축 인장실험에서 얻을 수 있는 소성변형률이 낮아서 티타늄 판재의 가공공정 설계를 위한 유한요소해석의 정밀도를 떨어뜨리는 경우가 있다. 본 연구에서는 큰 소성변형률 까지 안정적으로 성형이 가능한 유압벌지실험을 수행하여 재료의 소성변형에서 가공경화특성을 나타내는 유동곡선으로써 진응력-진변형률 선도를 구하였고 그 결과를 인장실험 결과와 비교하였다. 순 티타늄 판재의 유압벌지실험에서 재료의 변형률은 3D 디지털 영상상관법을 이용한 ARAMIS 시스템으로 실시간 측정된다. 이 유압벌지실험으로부터는 소성 변형률이 0.65 이상 까지도 안정적으로 재료의 소성유동곡선을 얻을 수 있었으며 그 결과는 Kim-Tuan 이 문헌 17[Y.S. Kim, J.H. In, Korean Acadmia-Ind. Coop. Soc.,(be in print), 2016] 의 연구에서 제안한 가공경화식으로 잘 핏팅됨을 알 수 있었다.

Keywords

References

  1. J.H.Park, Characteristics and Applications of Plate Type Heat Exchanger, J. Korean Soc. Marine Engng., 33(6), 801-811, 2009 DOI: http://dx.doi.org/10.5916/jkosme.2009.33.6.801
  2. A. Fujita, Y. Itsumi, T. Nakamoto, K. Yamamoto, Pre-coated titanium sheet with excellent press formability, Kobelco Tech. Review, 30, pp.19-23, 2011.
  3. M. Usuda, Press formability of commercially pure titanium sheets, Nippon Steel Technical Report, 85(1), pp.24-30, 2002
  4. S. Ishiyama, S. Hanada, O. Izumi, Orientation dependence of twining in commercially pure titanium, The Japan Inst. Metals, 54(9), pp.976-994, 1990 https://doi.org/10.2320/jinstmet1952.54.9_976
  5. M. Ishiki, T. Kutabara, Y. Hayashida, Measurement and analysis of differential work hardening behavior of pure titanium sheet using spline function, Int. J. Form., 4 pp.193-204, 2011. DOI: http://dx.doi.org/10.1007/s12289-010-1024-5
  6. A. L. Port, F. Toussaint, R. Arrieux, Finite element study and sensitive analysis of the deep-drawing formability of commercially pure titanium, Int. J. Mater. Form., 2(2), pp..121-129, 2009.
  7. Y.S. Kim, Engineering plasticity and its application, Sigma Press, Korea, pp.532-574, 2014.
  8. Q. Cao, Q. Zhang, X, Zhang, Anisotropy of mechanical behavior in commercially pure titanium sheets, J. Harbin Inst. Tech., 22(1), pp.63-67, 2015
  9. S. Coppieters, D. Yanaga, K. Denys, T. Kuwabara, Identification of post-necking strain hardening behavior of pure titanium sheet, Proc. SEM 2015 Annual Conf. Soc. Exp. Mech. Series, Costa Mesa, USA, pp 59-64. 2015
  10. R. Hill,. A theory of plastic bulging of a metal diaphragm by lateral pressure. Philosophical Magazine 41(322), pp.1133-1142 , 1950 DOI: http://dx.doi.org/10.1080/14786445008561154
  11. J. Chakrabarty, J.M. Alexander, Hydrostatic bulging of circular diaphragms, J. Strain Analysis, 5, pp.155-161, 1970. DOI: http://dx.doi.org/10.1243/03093247V053155
  12. R.F. Young, J.E. Bird, J.L. Duncan, An automated hydraulic bulge tester, J. Appl. Metal Work. 2(1-11), pp. 11-18, 1981. https://doi.org/10.1007/BF02833994
  13. C. Vial, W.F. Hosford, Yield loci of anisotropic sheet metals, Int. J. Mech. Sci., 25(12), pp.899-915, 1983. DOI: http://dx.doi.org/10.1016/0020-7403(83)90020-6
  14. M. Atkinson, Accurate determination of biaxial stressstrain relationships from hydraulic bulging test of sheet metal, Int. J. Mech. Sci.., 39, pp.761-769, 1997 DOI: http://dx.doi.org/10.1016/S0020-7403(96)00093-8
  15. G. Gutscher, H-C. Wu, G. Ngaile, T. Altan, Determination of flow stress for sheet metal forming using the viscous pressure bulge (VPB) test, J. Mater. Proc. Technol., 146, pp.1-7, 2004. DOI: http://dx.doi.org/10.1016/S0924-0136(03)00838-0
  16. M. Sigvant, K. Mattiasson, H. Vegter, P. Thilderkvist, A viscous pressure bulge test for the determination of a plastic hardening curve and equibiaxial material data, Int J. Mater. Form. 2, pp.235-242, 2009. DOI: http://dx.doi.org/10.1007/s12289-009-0407-y
  17. Y.S. Kim, J.H. In, Evaluation of press formability of pure titanium sheet (I), Korean Acadmia-Ind. Coop. Soc.,(be in print), 2016.
  18. J. Tyson1, J. Psilopoulos1, E. Schwartz1, K. Galanulis, Advanced material properties measurements with optical metrology,http://www.trilion.com/wp-content/uploads/2012/ 09/Advanced-Materials-Measurements.pdf
  19. http://www.gom.com/3d-software/gom-system-software.html
  20. B. Pan, K. Qian, H. Xie, A. Asundi, Two-dimensional digital image correlation for in-plane dispalcement and starin measurement: A review, Measure. Sci. Technol., 20 (6), Paper no. 062001, 2009 https://doi.org/10.1088/0957-0233/20/6/062001
  21. I.Y. Choi, Y.J. Kang, K.M. Hong, H.S. Lee, S.J. Kim, Study on the development of the displacement and strain distribution measurement algorithm to the open hole tension test by using the digital image correlation, J. Korean Soc. Precis. Eng., 33 (2), pp.121-128, 1026 https://doi.org/10.7736/KSPE.2016.33.2.121