DOI QR코드

DOI QR Code

Non-Local Analysis of Forming Limits of Ductile Material Considering Damage Growth

보이드 성장을 고려한 재료의 성형한계에 대한 비 국소 해석

  • 김영석 (경북대학교 기계공학부) ;
  • 원성연 (경북대학교 대학원 기계공학과)
  • Published : 2003.06.01

Abstract

In this paper, the strain localization of voided ductile material has been analyzed by nonlocal plasticity formulation in which the yield strength not only depends on an equivalent plastic strain measure (hardening parameter), but also on the Laplacian thereof. The gradient terms in yield criterion show an important role on modeling strain-softening phenomena of material. The influence of the mesh size on the elastic -plastic deformation behavior and the effect of the characteristic length parameter for localization prediction are also investigated. The proposed nonlocal plasticity shows that the load -strain curves converge to one curve. Results using nonlocal plasticity also exhibit the dependence of mesh size is much less sensitivity than that for a corresponding local plasticity formulation.

Keywords

References

  1. Needleman, A., 1988, 'Material Rate Dependence and Mesh Sensitivity on Localization Problems,' Comp. Meth. Appl. Mech. Engng., Vol. 67, pp. 69-86 https://doi.org/10.1016/0045-7825(88)90069-2
  2. Tomita, Y., 1995, 'Computational Simulation of Flow Localization Behavior,' JSME Int. J., Vol. 38, pp. 145-154
  3. Hong, S.I, Hwang, D.S., and Lee, B.S., 2000, 'A Study of Localization with Material Properties using Numerical Method,' Trans. Mat. Proc., Vol. 9, No.4, pp.395-403
  4. Pijaudier-Cabot, G, and Bazant, Z.P., 1987, 'Nonlocal Damage Theory,' J. Engng. Mech. ASCE, Vol. 113, pp. 1512-1533 https://doi.org/10.1061/(ASCE)0733-9399(1987)113:10(1512)
  5. Leblond, J.B., Perrin, G, and Devaux, J., 1994, 'Bifurcation Effects in Ductile Metals with Nonlocal Damage,' J. Appl. Mech. ASME, Vol. 61, pp. 236-242 https://doi.org/10.1115/1.2901435
  6. Tvergaard, V. and Needleman, A., 1995, 'Effects of Nonlocal Damage in Porous Plastic Solids,' Int. J. Solids Struct., Vol. 32, pp. 1063-1077 https://doi.org/10.1016/0020-7683(94)00185-Y
  7. Mindlin,R.D., 1963, 'Influence of Couple-Stresses on Stress Concentrations,' Exp. Mech., Vol. 3, pp. 1-7 https://doi.org/10.1007/BF02327098
  8. Aifantis,E.C., 1984, 'On the Microstructural Origin of Certain Inelastic Models,' Trans. ASME, J. Eng. Mater. Technol., Vol. 106, pp. 326-330 https://doi.org/10.1115/1.3225725
  9. Zbib,H., and Aifantis,E.C., 1989, 'On the Localization and Postiocalization Behavior of Plastic Deformation. Part I. On the Initiation of Shear-Bands; Part II. On the Evolution and Thickness of Shear Bands. Part III. On the Structure and Velocity of Protevin-Le Chatelier Bands,' Res. Mech., pp. 261-277,279-292, and 293-305
  10. Zbib,H., and Aifantis,E.C., 1989, 'On the Localization and Postiocalization Behavior of Plastic Deformation. Part I. On the Initiation of Shear-Bands; Part II. On the Evolution and Thickness of Shear Bands. Part III. On the Structure and Velocity of Protevin-Le Chatelier Bands,' Res. Mech., pp. 261-277,279-292, and 293-305
  11. Zbib,H., and Aifantis,E.C., 1989, 'On the Localization and Postiocalization Behavior of Plastic Deformation. Part I. On the Initiation of Shear-Bands; Part II. On the Evolution and Thickness of Shear Bands. Part III. On the Structure and Velocity of Protevin-Le Chatelier Bands,' Res. Mech., pp. 261-277,279-292, and 293-305
  12. Muhlhaus,H.B., and Aifantis,E.C., 1991, 'A Variational Principle for Gradient Plasticity,' Int. J. Solids Struct., Vol. 28(7), pp. 845-857 https://doi.org/10.1016/0020-7683(91)90004-Y
  13. de Borst.R, and Muhlhaus.H.B, 1992, 'Gradient-Dependent Plasticity : Formulation and Algorithm Aspects,' Int. J. Num. Methods Eng., Vol. 35, pp. 521-539 https://doi.org/10.1002/nme.1620350307
  14. Hutchinson, J.W., 2000, 'Plasticity at the Micron Scale,' Int. J. Solids and Structures, Vol. 37, pp. 225-238 https://doi.org/10.1016/S0020-7683(99)00090-6
  15. Bazant,Z.P., and Chang,T.P., 1984, 'Instability of Nonlocal Continum and Strain Averaging,' J. Engng. Mech., Vol. 110, pp. 1441-1450 https://doi.org/10.1061/(ASCE)0733-9399(1984)110:10(1441)
  16. Gurson, A.L., 1977, 'Continuum Theory of Ductile Rupture by Void Nucleation and Growth ; Part I Yield Criterion and Flow Rules for Porous Ductile Materials,' J. Engng. Mat. Tech., Vol. 99, pp. 2-15 https://doi.org/10.1115/1.3443401
  17. Needleman, A. and Tvergaard, V., 1978, 'Void Growth and Local Necking in Biaxially Stretched Sheets,' J. Eng. Mat. Tech., Vol. 100, pp. 164-169 https://doi.org/10.1115/1.3443466
  18. Hutchinson, J.W., and Tvergaard, V., 1981, 'Shear Band Formation in Plane Strain,' Int. J. Solids Struct., Vol. 17, pp. 451-470 https://doi.org/10.1016/0020-7683(81)90053-6
  19. Kim, Y.S., 2001, 'Theory of Engineering Plasticity,' Sigma Press, Seoul, Korea
  20. Mikkelsen, L.P., 1997, 'Post Necking Behavior Modeled by a Gradient Dependent Plasticity Theory,' Int. J. Solids Strut., Vol. 34, pp. 4531-4546 https://doi.org/10.1016/S0020-7683(97)00039-5
  21. Tomita, Y., and Kim, Y.S., 1984, 'Development of FEM Code for Elastic - Plastic Large Strain Analysis (EPLAN),' Kobe university, Kobe, Japan
  22. Hill, R., 1950, 'The Mathematical Theory of Plasticity,' Oxford University Press, Oxford, UK