Structural Engineering and Mechanics

  • 제44권3호
  • /
  • Pages.289-303
  • /
  • 2012
  • /
  • 1225-4568(pISSN)
  • /
  • 1598-6217(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

Influence of pressure-dependency of the yield criterion and temperature on residual stresses and strains in a thin disk

  • Alexandrov, S. (Department of Mechanical Engineering and Advanced Institute for Manufacturing with High-tech Innovations, National Chung Cheng University) ;
  • Jeng, Y.R. (Department of Mechanical Engineering and Advanced Institute for Manufacturing with High-tech Innovations, National Chung Cheng University) ;
  • Lyamina, E. (A.Yu Ishlinsky Institute for Problems in Mechanics, Russian Academy of Sciences)
  • 투고 : 2011.10.12
  • 심사 : 2012.09.28
  • 발행 : 2012.11.10
⟨ 이전 논문 다음 논문 ⟩

초록

Existing plane stress solutions for thin plates and disks have shown several qualitative features which are difficult to handle with the use of commercial numerical codes (non-existence of solutions, singular solutions, rapid growth of the plastic zone with a loading parameter). In order to understand the effect of temperature and pressure-dependency of the yield criterion on some of such features as well as on the distribution of residual stresses and strains, a semi-analytic solution for a thin hollow disk fixed to a rigid container and subject to thermal loading and subsequent unloading is derived. The material model is elastic-perfectly/plastic. The Drucker-Prager pressure-dependent yield criterion and the equation of incompressibity for plastic strains are adopted. The distribution of residual stresses and strains is illustrated for a wide range of the parameter which controls pressure-dependency of the yield criterion.

키워드

참고문헌

  1. Alexandrov, S. and Alexandrova, N. (2001), "Thermal effects on the development of plastic zones in thin axisymmetric plates", J. Strain Anal. Eng. Design., 36(2), 169-176. https://doi.org/10.1243/0309324011512720
  2. Alexandrov, S.E., Lomakin, E.V. and Jeng, Y.R. (2010), "Effect of the pressure dependency of the yield condition on the stress distibution in a rotating disk", Doklady-Physics, 55(12), 606-608. https://doi.org/10.1134/S1028335810120050
  3. Alexandrov, S., Jeng, Y.-R. and Lomakin, E. (2011a), "Effect of pressure-dependency of the yield criterion on the development of plastic zones and the distribution of residual stresses in thin annular dsks" Trans. ASME J. Appl. Mech., 78(3), 031012. https://doi.org/10.1115/1.4003361
  4. Alexandrov, S., Jeng, Y.R. and Lyamina, E. (2011b), "Influence of pressure-dependence of yield criterion and temperature on the development of plastic zones in thin plates", Proceedings of 2011 World Congress Advances in Structural Engineering and Mechanics, ASEM'11, Seuol, September.
  5. Alexandrova, N. and Alexandrov, S. (2004a), "Elastic-plastic stress distribution in a rotating annular disk", Mech. Base. Des. Struct. Mach., 32(1), 1-15. https://doi.org/10.1081/SME-120026587
  6. Alexandrova, N. and Alexandrov, S. (2004b), "Elastic-plastic stress distribution in a plastically anisotropic rotating disk", Trans. ASME J. Appl. Mech., 71(3), 427-429. https://doi.org/10.1115/1.1751183
  7. Alexandrova, N., Alexandrov, S. and Vila Real, P. (2004), "Displacement field and strain distribution in a rotating annular disk", Mech. Base. Des. Struct. Mach., 32(4), 441-457. https://doi.org/10.1081/SME-200034151
  8. Ball, D.L. (1995), "Elastic-plastic stress analysis of cold expanded fastener holes", Fat. Fract. Eng. Mater. Struct., 18, 47-63. https://doi.org/10.1111/j.1460-2695.1995.tb00141.x
  9. Bengeri, M. and Mack, W. (1994), "The influence of the temperature dependence of the yield stress on the stress distribution in a thermally assembled elastic-plastic shrink fit", Acta Mech., 103, 243-257. https://doi.org/10.1007/BF01180229
  10. Chakherlou, T.N. and Yaghoobi, A. (2010), "Numerical simulation of residual stress relaxation around a coldexpanded fastener hole under longitudinal cyclic loading using different kinematic hardening models", Fat Fract. Eng. Mater. Struct., 33, 740-751.
  11. Cohen, T., Masri, R. and Durban, D. (2009), "Analysis of circular hole expansion with generalized yield criteria", Int. J. Solids Struct., 46, 3643-3650. https://doi.org/10.1016/j.ijsolstr.2009.06.013
  12. Debski, R. and Zyczkowski, M. (2002), "On decohesive carrying capacity of variable-thickness annular perfectly plastic disks", Z. Angew. Math. Mech (ZAMM), 82(10), 655-669. https://doi.org/10.1002/1521-4001(200210)82:10<655::AID-ZAMM655>3.0.CO;2-V
  13. Deepak, D., Gupta, V.K. and Dham, A.K. (2009), "Impact of stress exponent on steady state creep in a rotating composite disc", J. Strain Anal. Eng. Des., 44, 127-135. https://doi.org/10.1243/03093247JSA466
  14. Drucker, D.C. and Prager, W. (1952), "Soil mechanics and plastic analysis for limit design", Q. Appl. Math., 10, 157-165. https://doi.org/10.1090/qam/48291
  15. Durban, D. and Fleck, N.A. (1997), "Spherical cavity expansion in a Drucker-Prager solid", Trans. ASME J. Appl. Mech., 64, 743-750. https://doi.org/10.1115/1.2788978
  16. Durban, D. and Birman, V. (1982), "On the elastic-plastic stress concentration at a circular hole in an anisotropic sheet", Acta Mech., 43, 73-84. https://doi.org/10.1007/BF01175817
  17. Dutta, N. and Rasty, J. (2010), "Prediction of elastic-plastic boundary around cold-expanded holes using elastic strain measurement", Trans. ASME J. Eng. Mater. Technol., 132, 031009. https://doi.org/10.1115/1.4001591
  18. Gamer, U. (1992), "A concise treatment of the shrink fit with elastic-plastic hub", Int. J. Solids Struct., 29, 2463-2469. https://doi.org/10.1016/0020-7683(92)90003-C
  19. Gupta, V.K., Singh, S.B., Chandrawat, H.N. and Ray, S. (2005), "Modeling of creep behavior of a rotating disc in the presence of both composition and thermal gradients", Trans. ASME J. Eng. Mater. Technol., 127, 97-105. https://doi.org/10.1115/1.1839187
  20. Guven, U. (1992), "Elastic-plastic annular disk with variable thickness subjected to external pressure", Acta Mech., 92, 29-34. https://doi.org/10.1007/BF01174165
  21. Hsu, Y.C. and Forman, R.G. (1975), "Elastic-plastic analysis of an infinite sheet having a circular hole under pressure", Trans. ASME, J. Appl. Mech., 42, 347-352. https://doi.org/10.1115/1.3423579
  22. Jang, J.S. and Kim, D.W. (2008), "Re-cold expansion process simulation to impart the residual stresses around fastener holes in 6061 A-T6 aluminium alloy", Proc. IMechE Part B, J. Eng. Manufact., 222, 1325-1332. https://doi.org/10.1243/09544054JEM1061
  23. Kao, A.S., Kuhn, H.A., Spitzig, W.A. and Richmond, O. (1990), "Influence of superimposed hydrostatic pressure on bending fracture and formability of a low carbon steel containing globular sulfides", ASME J. Eng. Mater. Technol., 112, 26-30. https://doi.org/10.1115/1.2903182
  24. Kleiber, M. and Kowalczyk, P. (1996), "Sensitivity analysis in plane stress elasto - plasticity and elasto - viscoplasticity", Comput. Meth. Appl. Mech. Eng., 137, 395-409. https://doi.org/10.1016/S0045-7825(96)01072-9
  25. Lippmann, H. (1992), "The effect of a temperature cycle on the stress distribution in a shrink fit", Int. J. Plasticity, 8, 567-582. https://doi.org/10.1016/0749-6419(92)90031-7
  26. Liu, P.S. (2006), "Mechanical behaviors of porous metals under biaxial tensile loads", Mater. Sci. Eng., A422, 176-183.
  27. Mack, W. (1993), "Thermal assembly of an elastic-plastic hub and a solid shaft", Arch. Appl. Mech., 63, 42-50. https://doi.org/10.1007/BF00787908
  28. Mack, W. and Bengeri, M. (1994), "Thermal assembly of an elastic-plastic shrink fit with solid inclusion", Int. J. Mech. Sci., 36, 699-705. https://doi.org/10.1016/0020-7403(94)90086-8
  29. Masri, R., Cohen, T. and Durban, D. (2010), "Enlargement of a circular hole in a thin plastic sheet: Taylor-Bethe controversy in retrospect Q.", J. Mech. Appl. Math., 63(4), 589-616. https://doi.org/10.1093/qjmam/hbq013
  30. Poussard C., Pavier, M.Y. and Smith, D.J. (1995), "Analytical and finite element predictions of residual stresses in cold worked fastener holes", J. Strain Anal. Eng. Des., 30, 291-304. https://doi.org/10.1243/03093247V304291
  31. Spitzig, W.A. (1979), "Effect of hydrostatic pressure on plastic-flow properties of iron single crystals", Acta Metall., 27, 523-534. https://doi.org/10.1016/0001-6160(79)90004-X
  32. Spitzig, W.A., Sober, R.J. and Richmond, O. (1976), "The effect of hydrostatic pressure on the deformation behavior of maraging and HY-80 steels and its implications for plasticity theory", Metallurg. Trans., 7A, 1703-1710.
  33. Wilson, C.D. (2002), "A critical reexamination of classical metal plasticity", ASME J. Appl. Mech., 69(1), 63-68. https://doi.org/10.1115/1.1412239
  34. Yoshida, S., Oguchi, A. and Nobuki, M. (1971), "Influence of high hydrostatic pressure on the flow stress of copper polycrystals", Trans. Jpn. Inst. Met., 12, 238-242. https://doi.org/10.2320/matertrans1960.12.238
  35. You, L.H., You, X.Y., Zhang, J.J. and Li, J. (2007), "On rotating circular disks with varying material properties", Z. Angew. Math. Phys., 58, 1068-1084. https://doi.org/10.1007/s00033-007-5094-2

피인용 문헌

  1. Stress-strain state in an elastoplastic cylindrical tube with free ends. I. General solution vol.48, pp.5, 2013, https://doi.org/10.3103/S0025654413050099
  2. An exact semi-analytic solution for residual stresses and strains within a thin hollow disc of pressure-sensitive material subject to thermal loading vol.49, pp.4, 2014, https://doi.org/10.1007/s11012-013-9826-4
  3. Effect of temperature-dependent mechanical properties of plastic collapse of thin discs vol.228, pp.14, 2014, https://doi.org/10.1177/0954406213519757
  4. Effects of thickness variations on the thermal elastoplastic behavior of annular discs vol.47, pp.6, 2013, https://doi.org/10.12989/sem.2013.47.6.839
  5. Elastic-Plastic Stresses and Strains in Thin Discs with Temperature-Dependent Properties Subject to Thermal Loading vol.37, pp.4, 2014, https://doi.org/10.1080/01495739.2013.870864
  6. Enlargement of a circular hole in a disc of plastically compressible material vol.224, pp.12, 2013, https://doi.org/10.1007/s00707-013-0916-0