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Fully Plastic Analyses of Unequally Notched Specimens in Bending Moment

굽힘 하중이 작용하는 비대칭노치시편의 완전소성해석

  • Published : 2006.03.01

Abstract

This paper proposes slip line fields for bending of unequally notched specimens in plane strain that have a sharp crack in one side and a sharp V-notch in the other side. Depending on the back angle, two slip line fields are proposed, from which the limit moment and crack tip stress fields are obtained as a function of the back angle. Excellent agreement between slip line field solutions with those from detailed finite element limit analysis based on non-hardening plasticity provides confidence in the proposed slip line fields. One interesting point is that, for the unequally notched specimen, the difference between the crack tip triaxial stress for tension and that for bending increases significantly with increasing the back angle. This suggests that such a specimen could be potentially useful to investigate the crack tip constraint effect on fracture toughness of materials. In this respect, the possibility of designing a new toughness testing specimen with varying crack tip constraint is discussed.

Keywords

References

  1. O'Dowd, N. P. and Shih, C. F., 1991, 'A Family of Crack Tip Fields Characterised by a Triaxiality Parameter,' Journal of Mechanics and Physics of Solids, Vol. 39, pp. 989-1015 https://doi.org/10.1016/0022-5096(91)90049-T
  2. Hancock, J. W., Reuter, W. G. and Parks, D. M., 1993, 'Constraint and Toughness Parameterised by T,' Constraint Effect in Fracture, ASTM STP 1171, Hackett E M, Schwalbe K-H, and Dodds R-H (editors), American Society for Testing and Materials, Philadelphia, pp. 21-40
  3. Joyce, J A., Hackett, E. M. and Roe, C, 1993, 'Effects of Crack Depth and Mode of Loading on the J-R Curve Behaviour of a High-Strength Steel,' Constraint Effect in Fracture, ASTM STP 1171, Hackett E M, Schwalbe K-H, and Dodds R-H (editors), American Society for Testing and Materials, Philadelphia, pp. 239-263
  4. Roos, E., Eisele, U. and Silcher, H., 1993, 'Effect of Stress State on the Ductile Fracture Behaviour of Large-Scale Specimens,' Constraint Effect in Fracture, ASTM STP 1171, Hackett E M, Schwalbe K-H, and Dodds R-H (editors), American Society for Testing and Materials, Philadelphia, pp. 41-63
  5. Kirk, M. T. and Dodds, R-H Jr., 1993, 'J and CTOD Estimation Equations for Shallow Cracks in Single Edge Notch Bend Specimens,' Journal of Testing and Evaluation, Vol. 21, pp. 228-238 https://doi.org/10.1520/JTE11948J
  6. Schwalbe, K-H., Neale, B K. and Heerens, J., 1994, 'The GKSS Testing Procedure for Determining the Fracture Behaviour of Materials: EFAM GTP 94,' GKSS Report GKSS/94/E/60. GKSS Froschungszentrum, Geesthacht, Germany
  7. Kim, Y. J. and Budden, P. J., 2001, 'Plastic Factors of Homogeneous and Bi-Material SE(T) Specimens for Toughness and Creep Crack Growth Testing,' Fatigue and Fracture of Engineering Materials and Structures, Vol. 24, pp. 751-760 https://doi.org/10.1046/j.1460-2695.2001.00436.x
  8. Kim, Y. J, 2002, 'Experimental J Estimation Equations for Single Edge Cracked Bars in Four-Point Bend: Homogeneous and Bi-Material Specimens,' Engineering Fracture Mechanics, Vol. 69, pp. 793-811 https://doi.org/10.1016/S0013-7944(01)00125-4
  9. Kim, Y. J., Sohn, B. G and Kim, Y. J, 2004,'Elastic-Plastic Finite Element Analysis for Double-Edge-Cracked Tension Plates,' Engineering Fracture Mechanics, Vol. 71, pp. 945-966 https://doi.org/10.1016/S0013-7944(03)00157-7
  10. Jin-Su Kim, Soo-Man Cho, Yun-Jae Kim and Young-Jin Kim, 2003, 'Specimen Thickness and Crack Depth Effects on J Testing and Crack Tip Constraint for Non-Standard Specimen,' Trans. Of the KSME, A, ?Vol. 27, No.9, pp. 1531-1538
  11. ASTM Standard, E 1739-96, Standard Test Method for J Integral Characterisation of Fracture Toughness, Annual Book of ASTM Standards, Section 3, Vol. 03.01, pp. 957-980
  12. McClintock, F.A., 1971, Plasticity aspects of fracture, In H. Liebowitz (ed.), Fracture Vol. 3. Academic Press, New York, 1971, pp. 47-225
  13. Green, A.P. and Hundy B.B., '1956, Initial Plastic Yielding in Notched Bend Tests,'Journal of the Mechanics and Physics of Solids, Vol. 4, pp. 128-144 https://doi.org/10.1016/0022-5096(56)90085-0
  14. Ewing, D.G.F., 1968, 'Calculations on the Bending of Rigid/Plastic Notched Bars,' Journal of the Mechanics and Physics of Solids, Vol. 16, pp. 205-213 https://doi.org/10.1016/0022-5096(68)90029-X
  15. Hill, R., 1956, The Mathematical Theory of ?Plasticity, Oxford University Press, Oxford
  16. Kachanov, L. M., 1971, Foundation of the Theory of Plasticity, North-Holland, Amsterdam
  17. ABAQUS User's Manual. version 6.3, Hibbit, Karlsson and Sorensen, Inc., Providence, RI, 2003
  18. Lee, H. and Parks, D.M., 1993, 'Fully Plastic Analyses of Plane Strain Single Edge Cracked Specimens Subject to Combined Tension and Bending,' International Journal of Fracture, Vol. 63, pp.329-349 https://doi.org/10.1007/BF00013042
  19. Ainsworth, R. A., Sattari-Far, I., Sherry, A. H., Hooton, D G. and Hadley, I., 2000, 'Methods for Including Constraint Effects Within the SINTAP Procedures,' Engineering Fracture Mechanics, Vol. 67, pp. 563-572 https://doi.org/10.1016/S0013-7944(00)00074-6