Journal of the Korean Society for Industrial and Applied Mathematics

Korean Society for Industrial and Applied Mathematics (한국산업응용수학회)
권호 표지
DOI QR코드

DOI QR Code

DEVELOPMENT OF THE HANSEL-SPITTEL CONSTITUTIVE MODEL GAZED FROM A PROBABILISTIC PERSPECTIVE

  • LEE, KYUNGHOON (DEPARTMENT OF AEROSPACE ENGINEERING, PUSAN NATIONAL UNIVERSITY) ;
  • KIM, JI HOON (SCHOOL OF MECHANICAL ENGINEERING, PUSAN NATIONAL UNIVERSITY) ;
  • KANG, BEOM-SOO (DEPARTMENT OF AEROSPACE ENGINEERING, PUSAN NATIONAL UNIVERSITY)
  • Received : 2017.06.14
  • Accepted : 2017.07.19
  • Published : 2017.09.25
Download PDF
⟨ Previous Next ⟩

Abstract

The Hansel-Spittel constitutive model requires a total of nine parameters for flow stress prediction. Typically, the parameters are estimated by least squares methods for given tensile test measurements from a deterministic perspective. In this research we took a different approach, a probabilistic viewpoint, to see through the development of the Hansel-Spittel constitutive model. This perspective change showed that deterministic least squares methods are closely related to statistical maximum likelihood methods via Gaussian noise assumption. More intriguingly, this perspective shift revealed that the Hansel-Spittel constitutive model may leave out deterministic trends in residuals despite nearly perfect agreement with measurements. With tensile test measurements of AA1070 aluminum alloy, we demonstrated this deficiency of the Hansel-Spittel constitutive model, suggesting room for improvement.

Keywords

References

  1. G.R. Johnson andW.H. Cook, A constitutive model and data for metals subjected to large strains, high strain rates and high temperatures, Proceedings of the 7th International Symposium on Ballistics, 21 (1983) 541-547.
  2. F.J. Zerilli and R.W. Armstrong, Dislocation-mechanics-based constitutive relations for material dynamics calculations, Journal of Applied Physics 61 (1987) 1816-1825. https://doi.org/10.1063/1.338024
  3. D.J. Steinberg, S.G. Cochran, and M.W. Guinan, A constitutive model for metals applicable at high-strain rate, Journal of Applied Physics 51 (1980) 1498-1504. https://doi.org/10.1063/1.327799
  4. P.S. Follansbee and U.F. Kocks, A constitutive description of the deformation of copper based on the use of the mechanical threshold stress as an internal state variable, Acta Metallurgica 36 (1988) 81-93. https://doi.org/10.1016/0001-6160(88)90030-2
  5. D.L. Preston, D.L. Tonks, and D.C. Wallace, Model of plastic deformation for extreme loading conditions, Journal of Applied Physics 93 (2003) 211-220. https://doi.org/10.1063/1.1524706
  6. A. Hensel and T. Spittel, Kraft-und Arbeitsbedarf bildsamer Formgebungsverfahren, VEB Deutscher Verlag fur Grundstoffindustrie, Leipzig, 1st edition, 1978.
  7. T. Strutz, Data Fitting and Uncertainty, Springer Vieweg, 1st edition, 2016.
  8. M.K. Jo, E. An, I.W. Park, I.S. Song, H.Y. Kim, D. Kim, Y.H. Moon, and J.H. Kim, Effect of Process Parameters on Rectangular Cup Impact Extrusion of an AA1070 Aluminum Alloy, Transactions of Materials Processing 24 (2015) 323-331. https://doi.org/10.5228/KSTP.24.5.323