Transactions of the Korean Society of Mechanical Engineers A (대한기계학회논문집A)

The Korean Society of Mechanical Engineers (대한기계학회)
권호 표지
DOI QR코드

DOI QR Code

Limit Load and Fully Plastic Stress Analysis for Circular Notched Plates and Bars Using Fully Plastic Analysis

완전소성해석을 이용한 원형노치 인장시편의 한계하중 및 완전소성응력장 해석

  • 오창균 (고려대학교 대학원 기계공학과) ;
  • 명만식 (고려대학교 대학원 기계공학과) ;
  • 김윤재 (고려대학교 기계공학과) ;
  • 박진무 (고려대학교 기계공학과)
  • Published : 2005.12.01
Download PDF
⟨ Previous Next ⟩

Abstract

For the last four decades, tension test of notched bars has been performed to investigate the effect of stress triaxiality on ductile fracture. To quantify the effect of the notch radius on stress triaxiality, the Bridgman equation is typically used. However, recent works based on detailed finite element analysis have shown that the Bridgman equation is not correct, possibly due to his assumption that strain is constant in the necked ligament. Up to present, no systematic work has been performed on fully plastic stress fields for notched bars in tension. This paper presents fully plastic results for tension of notched bars and plates in plane strain, via finite element limit analysis. The notch radius is systematically varied, covering both un-cracked and cracked cases. Comparison of plastic limit loads with existing solutions shows that existing solutions are accurate for notched plates, but not for notched bars. Accordingly new limit load solutions are given for notched bars. Variations of stress triaxiality with the notch radius and depth are also given, which again indicates that the Bridgman solution for notched bars is not correct and inaccuracy depends on the notch radius and depth.

Keywords

References

  1. Clausing, D. P., 1970, 'Effect of Plastic Strain on Ductility and Toughness,' International Journal of Fracture Mechanics, Vol. 6, pp. 71-85 https://doi.org/10.1007/BF00183662
  2. McClintock, F. A., 1968, 'A Criterion for Ductile Fracture by the Growth of Holes,' Journal of Applied Mechanics, Vol. 35(20), pp. 363-371 https://doi.org/10.1115/1.3601204
  3. Rice, J. R. and Tracey, D. M., 1969, 'On the Ductile Enlargement of Voids in Triaxial Stress Fields,' Journal of the Mechanics and Physics of Solids, Vol. 17pp.201-217 https://doi.org/10.1016/0022-5096(69)90033-7
  4. McClintock, F. A., 1971, Plasticity aspects of fracture. In: Fracture: An Advanced Treatise, Vol. 3, Academic Press, New York, pp. 47-225
  5. Hancock, J. and Brown, D., 1983, 'On the Role of Strain and Stress State in Ductile Fracture,' Journal of the Mechanics and Physics of Solids, Vol. 31, pp. 1-24 https://doi.org/10.1016/0022-5096(83)90017-0
  6. Garrison, W. M. Jr. and Moody, N. R., 1987, 'Ductile Fracture,' Journal of the Physics and Chemistry of Solids, Vol. 48, pp. 1035-1074 https://doi.org/10.1016/0022-3697(87)90118-1
  7. Thomason, P. F., 1990, Ductile fracture of metals, Oxford: Pergamon Press.
  8. Kachanov, L. M., 1971, Foundations of the Theory of Plasticity, North-Holland Publishing Company
  9. Bridgman, P., 1952, Studies in Large Plastic Flow and Fracture, New York: McGraw-Hill Book Company
  10. Alves, M. and Jones, N., 1999, 'Influence of Hydrostatic Stress on Failure of Axisymmetric Notched Specimens,' Journal of Mechanics and Physics of Solids, Vol. 47, pp. 643-667 https://doi.org/10.1016/S0022-5096(98)00060-X
  11. Bao, Y., 2005, 'Dependence of Ductile Crack Formation in Tensile Tests and Stress Triaxiality, Stress and Strain Ratios,' Engineering Fracture Mechanics, Vol. 72, pp. 505-522 https://doi.org/10.1016/j.engfracmech.2004.04.012
  12. Bao, Y. and Wierzbicki, T., 2004, 'On Fracture Locus in the Equivalent Strain and Stress Triaxiality Space,' International Journal of Mechanical Science, Vol. 46, pp. 81-98 https://doi.org/10.1016/j.ijmecsci.2004.02.006
  13. Miller, A. G., 1988, 'Review of Limit Loads of Structures Containing Defects,' Int Jnl of Pressure Vessels and Piping, Vol. 32, pp. 191-327 https://doi.org/10.1016/0308-0161(88)90073-7
  14. ABAQUS Version 6.4, 2005, User's manual. Hibbitt, Karlson & Sorensen, Inc, RI.
  15. Ewing, D. J. F. and Hill, R., 1967, 'The Plastic Constraint of V-Notched Tension Bars,' Journal of the Mechanics and Physics of Solids, Vol. 15, pp. 115-124 https://doi.org/10.1016/0022-5096(67)90021-X
  16. Scibetta, M., Chaouadi, R. and Van Walle, E., 2000, 'Fracture Toughness Analysis of Circumferentially-Cracked Round Bars,' International Journal of Fracture, Vol. 104, pp. 145-168 https://doi.org/10.1023/A:1007625612644
  17. Penny, R. K. and Marriot, D. L., 1995, Design for Creep, Chapman & Hall
  18. Webster, G. A., Ainsworth, R. A., 1994, High Temperature Component Life Assessment, London: Chapman & Hall