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A criterion for plane strain, fully plastic, quasi-steady crack growth

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Abstract

Plane strain fracture by hole growth in ordinary-sized parts of low-to-medium strength steels is essentially rigid-plastic, and may be approximated as non-hardening. Quasi-steady crack growth for such materials is predicted for crack-tip fields approximated by a pair of slip lines, such as unequally grooved specimens in tension and deep singly-face-cracked specimens under combined bending and tension. The crack growth increment Δa is given in terms of material parameters, far-field geometry, and loadings and their increments.

For the rigid-plastic, non-hardening approximation, stress and strain increment fields for growing cracks are identical to those for stationary cracks. For fields with a pair of symmetric slip-lines, the flanks of the decohering zone turn out to be rigid, and the decohering zone does not affect the crack-tip opening angle (CTOA), which then depends only on the micromechanisms of hole nucleation, growth and linkage by flow localization or fine cracking. These mechanisms are in turn approximately controlled by the near-field plasticity parameters: the angle of the slip plane θs, and the normal stress and displacement increment across the slip plane σs and Δus. Note the three-parameter characterization of the near-tip fields, in contrast to the one- or two-parameter characterization in elastic or nonlinear elastic fracture mechanics.

A sliding off and shear-cracking model for a growing crack, based on a hole growth equation, gives an approximate CTOA in terms of σs, θs, and material parameters. When hole nucleation strain is negligible, the estimated CTOA exhibits an inverse exponential dependence on σs and a higher order parabolic dependence on θs. For a given material, a series of fully plastic crack growth experiments is suggested to determine the approximate material parameters needed to characterize the dependence of CTOA on σs and θs, or from kinematics, of the shear strain behind the slip plane, γf, on σs.

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References

  1. W.J. Drugan, J.R. Rice and T.L. Sham, Journal of the Mechanics and Physics of Solids 30 (1982) 447–473.

    Google Scholar 

  2. L. Hermann and J.R. Rice, Metal Science 14 (1980) 285–291.

    Google Scholar 

  3. W.J. Drugan and X.Y. Chen, Journal of the Mechanics and Physics of Solids 37 (1989) 1–26.

    Google Scholar 

  4. X.Y. Chen and W.J. Drugan, Journal of the Mechanics and Physics of Solids 39 (1991) 895–925.

    Google Scholar 

  5. N. Liu and W.J. Drugan, International Journal of Fracture 59 (1993) 265–289.

    Google Scholar 

  6. P. Ponte Castañeda, Journal of the Mechanics and Physics of Solids 35 (1987) 227–268.

    Google Scholar 

  7. Y.C. Gao and K.C. Hwang, in Three-Dimensional Constitutive Relations and Ductile Fracture, S. Nemat-Nasser (ed.), North-Holland Publishing Company, Amsterdam (1981) 417–434.

    Google Scholar 

  8. P. Gudmundson, in Advances in Fracture Research: Proceedings of the 7th International Conference on Fracture Vol. 1, Pergamon, Oxford (1989) 315–322.

    Google Scholar 

  9. F. Nilsson and P. Stahle, Solid Mechanics Archives 13 (1988) 193–238.

    Google Scholar 

  10. F.A. McClintock, in Fracture, Vol. 3, H. Liebowitz (ed.), Academic Press, New York (1971) 47–225.

    Google Scholar 

  11. F.A. McClintock, International Journal of Fracture 42 (1990) 357–370.

    Google Scholar 

  12. G.A. Kardomateas, Mixed Mode I and II Fully Plastic Crack Growth From Simulated Weld Defects. Ph.D. thesis, Department of Mechanical Engineering, Massachusetts Institute of Technology (1985).

  13. F.A. McClintock, Journal of Applied Mechanics 25 (1958) 581–588.

    Google Scholar 

  14. F.A. McClintock, in Physics of Strength and Plasticity: Orowan Anniversary Volume, A.S. Argon (ed.), M.I.T. Press, Cambridge (1969) 307–326.

    Google Scholar 

  15. B. Dodd and Y. Bai, Ductile Fracture and Ductility, Academic Press, NY (1987).

    Google Scholar 

  16. F.A. McClintock, Journal of Applied Mechanics 35 (1968) 363–371.

    Google Scholar 

  17. F.A. McClintock, S.M. Kaplan and C.A. Berg, International Journal of Fracture Mechanics 17 (1966) 201–217.

    Google Scholar 

  18. J.R. Rice and D.M. Tracey, Journal of the Mechanics and Physics of Solids 17 (1969) 201–217.

    Google Scholar 

  19. B. Budiansky, J.W. Hutchinson and S. Slutsky, in Mechanics of Solids, The Rodney Hill 60th Anniversary Volume, H.G. Hopkins and M.J. Sewell (eds.), Pergamon Press, Oxford (1982) 13–45.

    Google Scholar 

  20. Y. Huang, J.W. Hutchinson and V. Tvergaard, Journal of the Mechanics and Physics of Solids 39 (1991) 223–241.

    Google Scholar 

  21. F.A. McClintock, in Ductility, American Society of Metals, Metals Park, Ohio (1968) 255–277.

    Google Scholar 

  22. V. Nagpal, F.A. McClintock, C.A. Berg and M. Subudhi, in International Symposium on the Foundations of Plasticity, A. Sawczuk (ed.), Noordhoff, Leiden (1972) 365–385.

    Google Scholar 

  23. P.F. Thomason, Ductile Fracture of Metals, Pergamon, Oxford (1990).

    Google Scholar 

  24. J. Koplik and A. Needleman, International Journal of Solids and Structures 24 (1988) 835–853.

    Google Scholar 

  25. V. Tvergaard, Engineering Fracture Mechanics 31 (1988) 421–436.

    Google Scholar 

  26. Courtesy of Dr. Walter Reuter of Idaho National Engineering Laboratory, Idaho Falls, Idaho.

  27. J.W. Carson, A Study of Plane Strain Ductile Fracture. Ph.D. thesis, Department of Mechanical Engineering, Massachusetts Institute of Technology (1970).

  28. V. Tvergaard and A. Needleman, Journal of the Mechanics and Physics of Solids 40 (1992) 447–471.

    Google Scholar 

  29. D.C. Drucker, in Structural Mechanics, E.H. Lee and P.S. Symonds (eds.), Pergamon Press, London (1960) 407–456.

    Google Scholar 

  30. D.J.F. Ewing and R. Hill, Journal of the Mechanics and Physics of Solids 15 (1967) 115–124.

    Google Scholar 

  31. J.R. Rice, in The Surface Crack: Physical Problems and Computational Solutions, J.L. Swedlow (ed.), American Society of Mechanical Engineers, New York (1972) 171–185.

    Google Scholar 

  32. C.S. White, R.O. Ritchie and D.M. Parks, in Elastic-Plastic Fracture: Second Symposium, Volume I-Inelastic Crack Analysis, ASTM STP 803, C.F. Shih and J.P. Gudas (eds.), Philadelphia (1983) 384–409.

  33. H.W. Huff, J.A. Joyce and F.A. McClintock, in Fracture: Proceedings of the 2nd International Conference on Fracture, Chapman and Hall, London (1969) 83–94.

    Google Scholar 

  34. A.P. Green and B.B. Hundy, Journal of the Mechanics and Physics of Solids 4 (1956) 128–144.

    Google Scholar 

  35. Y.J. Kim, F.A. McClintock and D.M. Parks, Journal of Applied Mechanics (1995) accepted.

  36. M. Shiratori and B. Dodd, International Journal of Mechanical Sciences 22 (1980) 127–131.

    Google Scholar 

  37. H. Lee and D.M. Parks, International Journal of Fracture 63 (1994) 329–349.

    Google Scholar 

  38. C. Betegón and J.W. Hancock, Journal of Applied Mechanics 58 (1991) 104–110.

    Google Scholar 

  39. N.P. O'Dowd and C.F. Shih, Journal of the Mechanics and Physics of Solids 40 (1992) 939–963.

    Google Scholar 

  40. Y.J. Kim, F.A. McClintock and D.M. Parks, Global Equilibrium of Least Upper Bound Circular Arcs and its Application to Fracture Mechanics. Manuscript in preparation (1995). See also [41].

  41. Y.J. Kim, Modeling Fully Plastic, Plane Strain Crack Growth. Ph.D. thesis, Department of Mechanical Engineering, Massachusetts Institute of Technology (1993).

  42. V. Tvergaard and J.W. Hutchinson, Journal of the Mechanics and Physics of Solids 40 (1992) 1377–1397.

    Google Scholar 

  43. G.A. Kardomateas and F.A. McClintock, International Journal of Fracture 40 (1989) 1–12.

    Google Scholar 

  44. A.S. Argon, J. Im and R. Safoglu, Metallurgical Transactions 6A (1975) 825–837.

    Google Scholar 

  45. F.A. McClintock and S.J. Wineman, International Journal of Fracture 33 (1987) 285–295.

    Google Scholar 

  46. J.W. Hancock, W.G. Reuter and D.M. Parks, in Constraint Effects in Fracture, ASTM STP 1171, E.M. Hackett, K.-H. Schwalbe and R.H. Dodds, Jr. (eds.), Philadelphia (1993) 21–40.

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  1. Department of Mechanical Engineering, Massachusetts Institute of Technology, 02139, Cambridge, MA, USA

    Frank A. McClintock, Yun-Jae Kim & David M. Parks

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  1. Frank A. McClintock
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  2. Yun-Jae Kim
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  3. David M. Parks
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McClintock, F.A., Kim, YJ. & Parks, D.M. A criterion for plane strain, fully plastic, quasi-steady crack growth. Int J Fract 72, 197–221 (1995). https://doi.org/10.1007/BF00037311

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