DOI QR코드

DOI QR Code

Crack tip plastic zone under Mode I, Mode II and mixed mode (I+II) conditions

  • Ayatollahi, M.R. (Fatigue and Fracture Laboratory, Center of Excellence in Experimental Solid Mechanics and Dynamics, Department of Mechanical Engineering, Iran University of Science and Technology) ;
  • Sedighiani, Karo (Fatigue and Fracture Laboratory, Center of Excellence in Experimental Solid Mechanics and Dynamics, Department of Mechanical Engineering, Iran University of Science and Technology)
  • 투고 : 2009.12.20
  • 심사 : 2010.07.30
  • 발행 : 2010.11.30

초록

The shape and size of the plastic zone around the crack tip are analyzed under pure mode I, pure mode II and mixed mode (I+II) loading for small scale yielding and for both plane stress and plane strain conditions. A new analytical formulation is presented to determine the radius of the plastic zone in a non-dimensional form. In particular, the effect of T-stress on the plastic zone around the crack tip is studied. The results of this investigation indicate that the stress field with a T-stress always yields a larger plastic zone than the field without a T-stress. It is found that under predominantly mode I loading, the effect of a negative T-stress on the size of the plastic zone is more dramatic than a positive T-stress. However, when mode II portion of loading is dominating the effect of both positive and negative T-stresses on the size of the plastic zone is almost equal. For validating the analytical results, several finite element analyses were performed. It is shown that the results obtained by the proposed analytical formulation are in very good agreements with those obtained from the finite element analyses.

키워드

참고문헌

  1. Al-Ani, A.M. and Hancock, J.W. (1991), "J-dominance of short cracks in tension and bending", J. Mech. Phys. Solids, 39, 23-43. https://doi.org/10.1016/0022-5096(91)90029-N
  2. Alshoaibi, A.M. (2010) "Finite element procedures for the numerical simulation of fatigue crack propagation under mixed mode loading", Struct. Eng. Mech., 35(3).
  3. Anderson, T.L. (1995), Fracture Mechanics: Fundamentals and Applications, Second Edition, CRC Press.
  4. Arun Roy, Y. and Narasimhan, R. (1997), "J-dominance in mixed mode ductile fracture specimens", Int. J. Fract., 88, 259-279. https://doi.org/10.1023/A:1007475708898
  5. Ayatollahi, M.R. and Aliha, M.R.M. (2009), "Mixed mode fracture in soda lime glass analyzed by using the generalized MTS criterion", Int. J. Solids Struct., 46, 311-321. https://doi.org/10.1016/j.ijsolstr.2008.08.035
  6. Ayatollahi, M.R., Aliha, M.R.M. and Hassani, M.M. (2006), "Mixed mode brittle fracture in PMMA-An experimental study using SCB specimens", Mater. Sci. Eng., 417, 348-356. https://doi.org/10.1016/j.msea.2005.11.002
  7. Ayatollahi, M.R., Pavier, M.J. and Smith, D.J. (1996), "On mixed mode loading of a single edge notched specimen", Int. J. Fract., 82, R61-R66. https://doi.org/10.1007/BF00013242
  8. Ayatollahi, M.R., Pavier, M.J. and Smith, D.J. (1998), "Determination of T-stress from finite element analysis for mode I and mixed mode I/II loading", Int. J. Fract., 91, 283-298. https://doi.org/10.1023/A:1007581125618
  9. Ayatollahi, M.R., Pavier, M.J. and Smith, D.J. (2002a), "A New Specimen for Mode II Fracture tests", ECF14, Poland, 1, 161-168.
  10. Ayatollahi, M.R., Pavier, M.J. and Smith, D.J. (2002b), "Crack-tip constraint in mode II deformation", Int. J. Fract., 113, 153-173. https://doi.org/10.1023/A:1015504414612
  11. Banks, T.M. and Garlick, A. (1984), "The form of crack tip plastic zones", Eng. Fract. Mech., 19, 571-581. https://doi.org/10.1016/0013-7944(84)90012-2
  12. Benrahou, K.H., Benguediab, M., Belhouari, M., Nait-Abdelaziz, M. and Imad, A. (2007), "Estimation of the plastic zone by finite element method under mixed mode (I and II) loading", Comput. Mater. Sci., 38, 595-601. https://doi.org/10.1016/j.commatsci.2006.04.001
  13. Betegon, C. and Hancock, J.W. (1991), "Two-parameter characterization of elastic-plastic crack-tip fields", J. Appl. Mech., 58, 104-110. https://doi.org/10.1115/1.2897135
  14. Bian, L.C. (2007), "Material plasticity dependence of mixed mode fatigue crack growth in commonly used engineering materials", Int. J. Solids Struct., 44, 8440-8456. https://doi.org/10.1016/j.ijsolstr.2007.06.021
  15. Bian, L.C. and Kim, K.S. (2004), "The minimum plastic zone radius criterion for crack initiation direction applied to surface cracks and through-cracks under mixed mode loading", Int. J. Fatigue, 26, 1169-1178. https://doi.org/10.1016/j.ijfatigue.2004.04.006
  16. Bilby, B.A., Carden, G.E., Goldthorpe, M.R. and Howard, I.C. (1986), Size Effect in Fracture, Mechanical Engineering Publications, London.
  17. Broek, D. (1982), Elementary Engineering Fracture Mechanics, Martinus Nijhoff Publishers.
  18. Chen, C., Fleck, N.A. and Lu, T.J. (2001), "The mode I crack growth resistance of metallic foams", J. Mech. Phys. Solids, 49, 231-259. https://doi.org/10.1016/S0022-5096(00)00039-9
  19. Du, Z.Z. and Hancock, J.W. (1991), "The effect of non-singular stresses on crack tip constraint", J. Mech. Phys. Solids, 39, 555-567. https://doi.org/10.1016/0022-5096(91)90041-L
  20. Edmunds, T.M. and Willis, J.R. (1977), "Matched asymptotic expansions in nonlinear fracture mechanics-III. Inplane loading of an elastic perfectly-plastic symmetric specimen", J. Mech. Phys. Solids, 25, 423-455. https://doi.org/10.1016/0022-5096(77)90028-X
  21. Erdogan, F. and Sih, G.C. (1963), "On the crack extension in plates under plane loading and transverse shear", J. Basic Eng., 85, 519-525. https://doi.org/10.1115/1.3656897
  22. Fett, T. (2001), "Stress intensity factors and T-stress for internally cracked circular disks under various boundary conditions", Eng. Fract. Mech., 68, 1119-1136. https://doi.org/10.1016/S0013-7944(01)00025-X
  23. Gomez, F.J., Elices, M. and Planas J. (2005), "The cohesive crack concept: application to PMMA at 60C", Eng. Fract. Mech., 72, 1268-1285. https://doi.org/10.1016/j.engfracmech.2004.09.005
  24. Haefele, P.M. and Lee, J.D. (1995), "The constant stress term", Eng. Fract. Mech., 50, 869-882. https://doi.org/10.1016/0013-7944(94)E0064-N
  25. Harmain, G.A. and Provan, J.W. (1997), "Fatigue crack-tip plasticity revisited - The issue of shape addressed", Theor. Appl. Fract. Mec., 26, 63-79. https://doi.org/10.1016/S0167-8442(96)00036-5
  26. Irwin, G.R. (1948), Fracture Dynamics. Fracturing of Metals, ASM, Cleveland, Chio.
  27. Jing, P.H. and Khraishi, T. (2004), "Analytical solutions for crack tip plastic zone shape using the von mises and tresca yield criteria: Effects of crack mode and stress condition", J. Mech., 20, 199-210. https://doi.org/10.1017/S1727719100003415
  28. Jing, P., Khraishi, T. and Gorbatikh, L. (2003), "Closed-form solutions for the mode II crack tip plastic zone shape", Int. J. Fract., 122, L137-142. https://doi.org/10.1023/B:FRAC.0000005806.28267.f6
  29. Khan, S.M.A. and Khraisheh, K. (2004), "A new criterion for mixed mode fracture initiation based on the crack tip plastic core region", Int. J. Plast., 20, 55-84. https://doi.org/10.1016/S0749-6419(03)00011-1
  30. Khan, S.M.A. and Khraisheh, M.K. (2000), "Analysis of mixed mode crack initiation angles under various loading conditions", Eng. Fract. Mech., 67, 397-419. https://doi.org/10.1016/S0013-7944(00)00068-0
  31. Kim, Y., Zhu, X.K. and Chao, Y.J. (2001), "Quantification of constraint on elastic plastic 3D crack front by the J-A2 three-term solution", Eng. Fract. Mech., 68, 895-914. https://doi.org/10.1016/S0013-7944(00)00134-X
  32. Kong, X.M., Schluter, N. and Dahl, W. (1995), "Effect of triaxial stress on mixed-mode fracture", Eng. Fract. Mech., 52, 379-388. https://doi.org/10.1016/0013-7944(94)00228-A
  33. Larsson, S.G. and Carlsson, A.J. (1973), "Influence of non-singular stress and specimen geometry on small-scale yielding at each tip in elastic-plastic materials", J. Mech. Phys. Solids, 21, 263-277. https://doi.org/10.1016/0022-5096(73)90024-0
  34. Mishra, S.C. and Parida, B.K. (1985), "Determination of the size of crack-tip plastic zone in a thin sheet under uniaxial loading", Eng. Fract. Mech., 22, 351-357. https://doi.org/10.1016/0013-7944(85)90136-5
  35. O'Dowd, N.P. and Shih, C.F. (1991), "Family of crack-tip fields characterized by a triaxiality parameter-I. Structure of fields", J. Mech. Phys. Solids, 39, 989-1015. https://doi.org/10.1016/0022-5096(91)90049-T
  36. Rice, J.R. (1968), A Mathematical Theory of Fracture, In: Fracture, Academic press, New York.
  37. Rice, J.R. (1974), "Limitations to the small scale yielding for crack-tip plasticity", J. Mech. Phys. Solids, 22, 17-26. https://doi.org/10.1016/0022-5096(74)90010-6
  38. Shih, C.F., O'Dowd, P.N. and Kirt, M.T. (1993), "A framework for quantifying crack tip constraint", ASTM STP, 1171, 2-20.
  39. Sih, G.C. (1973), "Some basic problems in fracture mechanics and new concepts", Eng. Fract. Mech., 5, 365-377. https://doi.org/10.1016/0013-7944(73)90027-1
  40. Sih, G.C. (1974), "Strain-energy-density factor applied to mixed mode crack problems", Int. J. Fract., 10, 305-321. https://doi.org/10.1007/BF00035493
  41. Smith, D.J., Ayatollahi, M.R. and Pavier, M.J. (2001), "The role of T-stress in brittle fracture for linear elastic materials under mixed-mode loading", Fatigue Fract. Eng. Mater. Struct., 24, 137-150. https://doi.org/10.1046/j.1460-2695.2001.00377.x
  42. Theocaris, P.S. and Andrianopoulos, N.P. (1982), "The Mises elastic-plastic boundary as the core region in fracture criteria", Eng. Fract. Mech., 16, 425-432. https://doi.org/10.1016/0013-7944(82)90120-5
  43. Theocaris, P.S., Kardomateas, G.A. and Andrianopoulos, N.P. (1983), "Experimental study of the T-criterion in ductile fracture", Eng. Fract. Mech., 17, 439-447. https://doi.org/10.1016/0013-7944(83)90040-1
  44. Tvergaard, V. and Hutchinson, J.W. (1992), "The relation between crack growth resistance and fracture process parameters in elastic-plastic solids", J. Mech. Phys. Solids, 40, 1377-1397. https://doi.org/10.1016/0022-5096(92)90020-3
  45. Tvergaard, V. and Hutchinson, J.W. (1994), "Effect of T-stress on mode-I crack growth resistance in a ductile solid", Int. J. Solids Struct., 31, 823-833. https://doi.org/10.1016/0020-7683(94)90080-9
  46. Ukadgaonker, V.G. and Awasare, P.J. (1995), "A new criterion for fracture initiation", Eng. Fract. Mech., 51, 265-274. https://doi.org/10.1016/0013-7944(94)00265-J
  47. Wang, Y.Y. (1993), "On the two-parameter characterization of elastic-plastic front field in surface crack cracked plates", ASTM Special Technical Publication, 1171, 120-138.
  48. Williams, M.L. (1957), "Stress singularities resulting from various boundary conditions insingular corners of plates in extension", J. Appl. Mech., 19, 526-528.
  49. Yuan, H. and Broeks, W. (1998), "Quantification of constraint effects in elastic plastic crack front field", J. Mech. Phys. Solids, 46, 219-241. https://doi.org/10.1016/S0022-5096(97)00068-9
  50. Zhang, J.P. and Venugopalan, D. (1987), "Effects of notch radius and anisotropy on the crack tip plastic zone", Eng. Fract. Mech., 26, 913-925. https://doi.org/10.1016/0013-7944(87)90038-5

피인용 문헌

  1. A T-stress controlled specimen for mixed mode fracture experiments on brittle materials vol.36, 2012, https://doi.org/10.1016/j.euromechsol.2012.02.008
  2. A review of T-stress and its effects in fracture mechanics vol.134, 2015, https://doi.org/10.1016/j.engfracmech.2014.10.013
  3. The Influence of Specimen Type on Tensile Fracture Toughness of Rock Materials vol.174, pp.3, 2017, https://doi.org/10.1007/s00024-016-1458-x
  4. Mode I Fracture Analysis of Polymethylmetacrylate Using Modified Energy-Based Models vol.18, pp.4, 2015, https://doi.org/10.1134/S1029959915040050
  5. Fracture analysis of a semi-elliptical crack in a nozzle–vessel junction under external loads vol.226, pp.4, 2012, https://doi.org/10.1177/0954406211419434
  6. The effect of T-stress on the brittle fracture under mixed mode loading vol.10, 2011, https://doi.org/10.1016/j.proeng.2011.04.128
  7. Evaluating fracture behavior of brittle polymeric materials using an IASCB specimen vol.32, pp.1, 2013, https://doi.org/10.1016/j.polymertesting.2012.09.013
  8. Calculation of the influence of plastic deformation on the evolution of crack stress intensity factors in a body-centered cubic crystal vol.57, pp.3, 2015, https://doi.org/10.1134/S1063783415030105
  9. Three-dimensional finite element analyses of T -stress for different experimental specimens vol.91, 2017, https://doi.org/10.1016/j.tafmec.2017.04.018
  10. Geometry effects on fracture trajectory of PMMA samples under pure mode-I loading vol.163, 2016, https://doi.org/10.1016/j.engfracmech.2016.05.014
  11. Mode I fracture initiation in limestone by strain energy density criterion vol.57, pp.1, 2012, https://doi.org/10.1016/j.tafmec.2011.12.003
  12. Statistical Analysis of Rock Fracture Toughness Data Obtained from Different Chevron Notched and Straight Cracked Mode I Specimens vol.51, pp.7, 2018, https://doi.org/10.1007/s00603-018-1454-9
  13. Tensile and fracture characterization using a simplified digital image correlation test set-up vol.69, pp.4, 2010, https://doi.org/10.12989/sem.2019.69.4.467