DOI QR코드

DOI QR Code

Forming Limit Diagrams of Zircaloy-4 and Zirlo Sheets for Stamping of Spacer Grids of Nuclear Fuel Rods

핵연료 지지격자 성형을 위한 Zircaloy-4와 Zirlo 판재의 성형한계도 예측

  • Received : 2010.12.17
  • Accepted : 2011.06.09
  • Published : 2011.08.01

Abstract

In this work, we investigated the theoretical forming limit models for Zircaloy-4 and Zirlo used for spacer grid of nuclear fuel rods. Tensile and anisotropy tests were performed to obtain stress-strain curves and anisotropic coefficients. The experimental forming limit diagrams (FLD) for two materials were obtained by dome stretching tests following NUMISHEET 96. Theoretical FLD depends on FL models and yield criteria. To obtain the right hand side (RHS) of FLD, we applied the FL models (Swift's diffuse necking, M-K theory, S-R vertex theory) to Zircaloy-4 and Zirlo sheets. Hill's local necking theory was adopted for the left hand side (LHS) of FLD. To consider the anisotropy of sheets, the yield criteria of Hill and Hosford were applied. Comparing the predicted curves with the experimental data, we found that the RHS of FLD for Zircaloy-4 can be described by the Swift model (with the Hill's criterion), while the LHS of the FLD can be explained by Hill model. The FLD for Zirlo can be explained by the S-R model and the Hosford's criterion (a = 8).

본 연구에서는 핵연료 지지격자체의 재료인 Zircaloy-4 와 Zirlo 판재의 이론적 성형한계 예측모델을 제시했다. 먼저 인장시험 및 이방성시험으로 응력-변형률곡선과 이방성계수를 획득했으며, NUMISHEET 96을 따르는 돔장출시험으로 두 재료의 실험적 성형한계도들을 얻었다. 이론적 성형한계도는 성형한계모델과 항복조건의 영향을 받는다. Swift 확산네킹이론, Marciniak-Kuczynski 의 재료결함 모델, Storen-Rice 의 정점이론을 이용해 부변형률이 양인 구간에서의 성형한계 곡선을 구했으며, 부변형률이 음인 구간에는 Hill 의 국부네킹 이론을 적용했다. 또한 재료이방성을 고려하기 위해 Hill 48, Hosford 79 항복조건을 사용 했다. Swift 확산네킹모델 (Hill 48 항복조건 적용)과 Hill 모델은 각각 변형률비가 양과 음인 영역에 대해 Zircaloy-4의 성형한계도를 비교적 정확히 예측하며, Zirlo의 성형한계도는 Hosford 79 항복조건 (a = 8)을 적용한 Storen-Rice 모델로 나타낼 수 있다.

Keywords

Acknowledgement

Supported by : 한국연구재단

References

  1. Keeler, S. P. and Backofen, W. A., 1963, "Plastic Instability and Fracture in Sheets Stretched over Rigid Punches," ASM Transaction Quarterly, Vol. 54, pp. 25-48.
  2. Goodwin, G. M., 1968, "Application of Strain Analysis to Sheet Metal Forming Problems in the Press Shop," Transaction Society of Automotive Engineering, pp. 380-387.
  3. Swift, H. W., 1952, "Plastic Instability under Plane Stress," Journal of the Mechanics and Physics of Solids, Vol. 1, pp. 1-16. https://doi.org/10.1016/0022-5096(52)90002-1
  4. Hill, R., 1948, "A Theory of the Yielding and Plastic Flow of Anisotropic Metals," Proceedings of Royal Society of London, Vol. 193, pp. 281-297. https://doi.org/10.1098/rspa.1948.0045
  5. Hill, R., 1952, "On Discontinuous Plastic State, with Special Reference to Localized Necking in Thin Sheets," Journal of the Mechanics and Physics of Solids, Vol. 1, pp. 19-30. https://doi.org/10.1016/0022-5096(52)90003-3
  6. Marciniak, Z. and Kuczynski, K., 1967, "Limits Strains in the Processes of Stretch-forming Sheet Metal," International Journal of Mechanical Sciences, Vol. 9, pp. 609-620. https://doi.org/10.1016/0020-7403(67)90066-5
  7. Storen, S. and Rice, J. R., 1975, "Localized Necking in Thin Sheets," Journal of the Mechanics and Physics of Solids, Vol. 23, pp. 421-441. https://doi.org/10.1016/0022-5096(75)90004-6
  8. Hill, R., 1948, "A Theory of the Yielding and Plastic Flow of Anisotropic Metals," Proceedings of Royal Society of London, Vol. 193, pp. 281-297. https://doi.org/10.1098/rspa.1948.0045
  9. Hosford, W. F., 1979, "On Yield Loci of Anisotropic Cubic Metals," Seventh North American Metalworking Research Conference, Dearborn, Michigan, pp. 191-196.
  10. Lee, J. K., Kinzel, G. L. and Wagoner, R. H. (Eds), 1996, NUMISHEET 96 3rd International Conference on Numerical Simulation of 3D Sheet Metal Forming Processes-Verification of Simulation with Experiments, Dearborn, Michigan, pp. 427-608.

Cited by

  1. Enhancement of Dimple Formability in Sheet Metals by 2-Step Forming vol.37, pp.7, 2013, https://doi.org/10.3795/KSME-A.2013.37.7.841
  2. Measurement of Surface Strain on Soft Biological Tissues Using Irregular Grid Pattern vol.37, pp.8, 2013, https://doi.org/10.3795/KSME-A.2013.37.8.1051
  3. Numerical approach to the evaluation of forming limit curves for zircaloy-4 sheet vol.30, pp.21, 2015, https://doi.org/10.1557/jmr.2015.293
  4. Back-propagation neural network-based approximate analysis of true stress-strain behaviors of high-strength metallic material vol.30, pp.3, 2016, https://doi.org/10.1007/s12206-016-0227-1