Structural Engineering and Mechanics

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

J-integral and fatigue life computations in the incremental plasticity analysis of large scale yielding by p-version of F.E.M.

  • Woo, Kwang S. (Department of Civil Engineering, Yeungnam University) ;
  • Hong, Chong H. (Department of Civil Engineering, Tamna University) ;
  • Basu, Prodyot K. (Department of Civil Engineering, Vanderbilt University)
  • Received : 2003.04.17
  • Accepted : 2003.09.24
  • Published : 2004.01.25
⟨ Previous Next ⟩

Abstract

Since the linear elastic fracture analysis has been proved to be insufficient in predicting the failure of strain hardening materials, a number of fracture concepts have been studied which remain applicable in the presence of plasticity near a crack tip. This work thereby presents a new finite element model to predict the elastic-plastic crack-tip field and fatigue life of center-cracked panels(CCP) with ductile fracture under large-scale yielding conditions. Also, this study has been carried out to investigate the path-dependence of J-integral within the plastic zone for elastic-perfectly plastic, bilinear elastic-plastic, and nonlinear elastic-plastic materials. Based on the incremental theory of plasticity, the p-version finite element is employed to account for the accurate values of J-integral, the most dominant fracture parameter, and the shape of plastic zone near a crack tip by using the J-integral method. To predict the fatigue life, the conventional Paris law has been modified by substituting the range of J-value denoted by ${\Delta}J$ for ${\Delta}K$. The experimental fatigue test is conducted with five CCP specimens to validate the accuracy of the proposed model. It is noted that the relationship between the crack length a and ${\Delta}K$ in LEFM analysis shows a strong linearity, on the other hand, the nonlinear relationship between a and ${\Delta}J$ is detected in EPFM analysis. Therefore, this trend will be depended especially in the case of large scale yielding. The numerical results by the proposed model are compared with the theoretical solutions in literatures, experimental results, and the numerical solutions by the conventional h-version of the finite element method.

Keywords

References

  1. Babuska, I. and Szabo, B. (1982), "On the rates of convergence of the finite element method", Numer. Meth. Engng., 18, 323-341. https://doi.org/10.1002/nme.1620180302
  2. Basu, P.K. and Lamprecht, R.M. (1979), "Some trends in computerized stress analysis", Proc. of the Seventh ASCE Conf. in Electronic Computation, Washington University, St. Louis, MO.
  3. Dadkhah, M.S. and Kobayashi, A.S. (1989), "HRR field of a moving crack, an experimental analysis", Engng. Fracture Mech., 34, 253-262. https://doi.org/10.1016/0013-7944(89)90258-0
  4. Dowling, N.E. and Begley, J.A. (1976), "Fatigue crack growth during gross plasticity and J-integral. Mechanics of crack growth, cracks and fracture", ASTM STP, 590, 82-103.
  5. Dugdale, D.S. (1960), "Yielding of steel sheets containing slits", Mech. Phys. Solids, 8, 100-108. https://doi.org/10.1016/0022-5096(60)90013-2
  6. Feng, D.Z. and Zhang, K.D. (1993), "Finite element numerical evaluation of J-integral for cracked ductile cylinders", Engng. Fracture Mech., 46, 481-489. https://doi.org/10.1016/0013-7944(93)90240-S
  7. Gdoutos, E.E. and Papakaliatakis, G. (1986), "The effect of load biaxiality on crack growth in non-linear materials", Theoretical and Applied Fracture Mechanics, 5, 141-156.
  8. Hutchinson, J.W. (1968), "Plastic stress and strain fields at a crack tip", J. Mech. Phys. Solids, 16, 337-347. https://doi.org/10.1016/0022-5096(68)90021-5
  9. Hutchinson, J.W. (1968), "Singular behavior at the end of a tensile crack in a hardening material", J. Mech. Phys. Solids, 16, 13-31. https://doi.org/10.1016/0022-5096(68)90014-8
  10. Irwin, G.R. (1971), "Plastic zone near a crack and fracture toughness", Proc. 7th Sagamore Conf., IV-63.
  11. Kim, K.S. and Orange, T.W. (1988), "A review of path-independent integrals in elastic-plastic fracture mechanics", ASTM STP, 945, 713-729.
  12. Kuang, J.H. and Chen, Y.C. (1996), "The values of J-integral within the plastic zone", Engng. Fracture Mech., 55, 869-881. https://doi.org/10.1016/S0013-7944(96)00077-X
  13. McMeeking, R.M. (1977), "Finite deformation analysis of crack-tip opening in elastic-plastic materials", J. Mech. Phys. Solids, 25, 357-381. https://doi.org/10.1016/0022-5096(77)90003-5
  14. Miller, K.J. and Kfouri, A.P. (1974), "An elastic-plastic finite element analysis of crack tip fields under biaxial loadings", Int. J. Fracture, 10, 393-404. https://doi.org/10.1007/BF00035500
  15. Owen, D.R.J. and Fawkes, A.J. (1983), Engineering Fracture Mechanics: Numericak Methods and Applications, Pineridge Press Ltd., Swansea, U.K.
  16. Paris, P.C. and Erdogan, F. (1963), "A critical analysis of crack propagation laws", Trans. ASME, J. Basic Engng, 55, 528-534.
  17. Rahman, S. (2001), "Probabilistic fracture mechanics: J-estimation and finite element methods", Engng. Fracture Mech., 68, 107-125. https://doi.org/10.1016/S0013-7944(00)00092-8
  18. Rice, J.R. (1968), "A path independent integral and the approximate analysis of concentration by notches and cracks", J. Appl. Mech., 35, 379-386. https://doi.org/10.1115/1.3601206
  19. Rice, J.R. and Rosengren, G.F. (1968), "Plane strain deformation near a crack tip in a power-law hardening material", J. Mech. Phys. Solids, 16, 1-12. https://doi.org/10.1016/0022-5096(68)90013-6
  20. Schmitt, W. and Kienzler, R. (1989), "The J-integral concept for elastic-plastic material behavior", Engng. Fracture Mech., 32, 409-418. https://doi.org/10.1016/0013-7944(89)90313-5
  21. Sivaneri, N.T., Xie, Y.P. and Kang, B.S. (1991), "Elastic-plastic crack-tip-field numerical analysis integrated with Moire' interferometry", Engng. Fracture Mech., 49, 291-303.
  22. Srivastava, Y.P. and Garg, S.B.L. (1988), "Study on modified J-integral range and its correlation with fatigue crack growth", Engng. Fracture Mech., 30, 119-133. https://doi.org/10.1016/0013-7944(88)90217-2
  23. Stump, D.M. and Zywicz, E. (1993), "J-integral computations in the incremental and deformation plasticity analysis of small-scale yielding", Engng. Fracture. Mech., 45, 61-77. https://doi.org/10.1016/0013-7944(93)90008-G
  24. Wei, Y. and Wang, T. (1995), "Characterization of elastic-plastic fields near stationary crack tip and fracture criterion", Engng. Fracture Mech., 51, 547-553. https://doi.org/10.1016/0013-7944(94)00316-A
  25. Woo, K.S. (1993), "Robustness of hierarchical elements formulated by integrals of Legendre polynomials", Comput. & Struct., 49(3), 421-426. https://doi.org/10.1016/0045-7949(93)90043-D
  26. Woo, K.S. and Jung, W.S. (1994), "Stress intensity factors for 3-D axisymmetric bodies containing cracks by pversion of F.E.M.", Structural Engineering Mechanics, 2(3), 245-256. https://doi.org/10.12989/sem.1994.2.3.245
  27. Woo, K.S. and Lee, C.G. (1995), "p-Version finite element approximations of stress intensity factors for cracked plates including shear deformation", Engng. Fracture. Mech., 52(3), 493-502. https://doi.org/10.1016/0013-7944(95)00019-R
  28. Woo, K.S., Hong, C.H. and Shin, Y.S. (1998), "An extended equivalent domain integral method for mixed mode fracture problems by the p-version of FEM", Numer. Meth. Engng., 42, 857-884. https://doi.org/10.1002/(SICI)1097-0207(19980715)42:5<857::AID-NME390>3.0.CO;2-#

Cited by

  1. Strength and ductility of fillet welds with transverse root notch vol.65, pp.4, 2009, https://doi.org/10.1016/j.jcsr.2008.05.001
  2. Seismic performance of RC bridge piers subjected to moderate earthquakes vol.24, pp.4, 2006, https://doi.org/10.12989/sem.2006.24.4.429
  3. Fatigue life prediction of horizontally curved thin walled box girder steel bridges vol.28, pp.4, 2008, https://doi.org/10.12989/sem.2008.28.4.387