Skip to main content
SpringerLink
Log in

A hierarchical multi-physics model for design of high toughness steels

  • Published:
Journal of Computer-Aided Materials Design

Abstract

In support of the computational design of high toughness steels as hierarchically structured materials, a multiscale, multiphysics methodology is developed for a `ductile fracture simulator.' At the nanometer scale, the method unites continuum mechanics with quantum physics, using first-principles calculations to predict the force-distance laws for interfacial separation with both normal and plastic sliding components. The predicted adhesion behavior is applied to the description of interfacial decohesion for both micron-scale primary inclusions governing primary void formation and submicron-scale secondary particles governing microvoid-based shear localization that accelerates primary void coalescence. Fine scale deformation is described by a `Particle Dynamics' method that extends the framework of molecular dynamics to multi-atom aggregates. This is combined with other meshfree and finite-element methods in two-level cell modeling to provide a hierarchical constitutive model for crack advance, combining conventional plasticity, microstructural damage, strain gradient effects and transformation plasticity from dispersed metastable austenite. Detailed results of a parallel experimental study of a commercial steel are used to calibrate the model at multiple scales. An initial application provides a Toughness-Strength-Adhesion diagram defining the relation among alloy strength, inclusion adhesion energy and fracture toughness as an aid to microstructural design.

The analysis of this paper introduces an approach of creative steel design that can be stated as the exploration of the effective connections among the five key-components: elements selection, process design, micro/nanostructure optimization, desirable properties and industrial performance by virtue of innovations and inventions.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Cybersteel2020, ONR contract grant number: N00014-01-1-0953; PIs: Olson, G.B., Freeman, A., Liu, W.K. and Moran, B., Northwestern University.

  2. Olson, G.B., Science, 277 (1997) 1237.

    Article  CAS  Google Scholar 

  3. Thomas, L.H., Proc. Cambridge Phil. Soc., 23 (1927) 542.

    Article  CAS  Google Scholar 

  4. Fermi, E., Z. Physik, 48 (1928) 73.

  5. Hohenberg, P. and Kohn, W., Phys. Rev., 136 (1964) 864.

    Article  Google Scholar 

  6. Kohn, W. and Sham, L.J., Phys. Rev., 140 (1965) 1133.

    Article  Google Scholar 

  7. Krakauer, H. and Freeman, A.J., Phys. Rev., B19 (1979) 1706.

    Article  CAS  Google Scholar 

  8. NRL, DoD Plane Wave: A General Scalable Density Functional Code, 2002.

  9. Mehl, M.J. and Papaconstantopoulos, D.A. Phys. Rev., B54 (1996) 4519.

    CAS  Google Scholar 

  10. Papaconstantopoulos, D.A. and Mehl, M.J., J. Phase Equilibria, 18 (1997) 593.

    CAS  Google Scholar 

  11. Wimmer, E., Krakauer, H., Weinert, M. and Freeman, A.J., Phys. Rev., B24 (1981) 864.

    CAS  Google Scholar 

  12. Rose, J.H., Smith, J.R. and Ferrante, J., Phys. Rev., B28 (1983) 1835.

    CAS  Google Scholar 

  13. Rice, J.R., J. Mech. Phys. Solids, 40 (1992) 239.

    Article  CAS  Google Scholar 

  14. Weertman, J., Philosophical Magazine a-Physics of Condensed Matter Structure Defects and Mechanical Properties, 43 (1981) 1103.

    CAS  Google Scholar 

  15. Needleman, A., J. Appl. Mech., 54 (1987) 525.

    Article  Google Scholar 

  16. Argon, A.S., Im, J. and Safoglu, R., Metallurgical Trans., A6 (1975) 825.

    Google Scholar 

  17. Shishidou, T., Lee, J.H., Zhao, Y.J. and Freeman A., J. Appl. Phys., 93 (2003) 6876.

    Article  CAS  Google Scholar 

  18. Rice, J.R., In Thompson, A.W. and Bernstein, I.M. (Eds.) Effect of Hydrogen on Behavior of Materials, 1976, The Metallurgical Society of AIME: Warrendale, PA., p. 455.

    Google Scholar 

  19. Rice, J.R. and Wang, J.S.,Materials Science and Engineering a-Structural Materials Properties Microstructure and Processing, 107 (1989) 23.

    Google Scholar 

  20. Hirth, J.P. and Rice, J.R., Metallurgical Transactions a-Physical Metallurgy and Materials Science, 11 (1980) 1501.

    Google Scholar 

  21. Asaro, R.J., Philosophical Transactions of the Royal Society of London Series a-Mathematical Physical and Engineering Sciences, 295 (1980) 151.

    CAS  Google Scholar 

  22. Alber, I., Bassani, J.L., Khantha, M., Vitek, V. and Wang, G.J., Phil. Trans. Roy. Soc. Lond. A., 339 (1992) 555.

    Google Scholar 

  23. Hao, S., Liu, W.K. and Moran, B., in preparation, 2003.

  24. Daw, M.S. and Baskes, M.I., Phys. Rev., B29 (1984) 6443.

    Article  CAS  Google Scholar 

  25. Baskes, M.I., J. Metals, 40 (1988) 123.

  26. Liu, W.K., Jun, S. and Zhang, Y.F., Int. J. Num. Meth. Fluids, 20 (1995) 1081.

    Article  Google Scholar 

  27. Liu, W.K., Jun, S., Li, S., Adee, J. and Belytschko, T., Int. J. Num. Meth. Engng., 38 (1995) 1655.

    Article  Google Scholar 

  28. Moran, B. and J. Yoo, 2002.

  29. Hao, S., Liu, W.K. In: Moving Particle Finite Element Method with Global Superconvergence. The 5th World Congress on Computational Mechanics, 2002, Vienna, Austria.

  30. Hao, S., Liu, W.K. and Belytschko, T., Int. J. Num. Meth. Engng., 59 (2004) 1007.

    Article  Google Scholar 

  31. Belytschko, T., Lu, Y.Y. and Gu, L., Int. J. Num. Meth. Engng., 37 (1994) 229.

    Article  Google Scholar 

  32. Chen, J.S., S.P. Yoon and C.T. Wu, Int. J. Num. Meth. Engng., 53 (2002) 2587.

    Article  Google Scholar 

  33. Hughes, T.J.R., Comput. Meth. Appl. Mech. Engng., 127 (1995) 387.

    Article  Google Scholar 

  34. Liu, W.K., Uras, R.A. and Chen, Y., J. Appl. Mech., 64 (1997) 861.

    Google Scholar 

  35. Liu, W.K., Zhang, Y.F. and Ramirez, M.R., Int. J. Num. Meth. Engng., 32 (1991) 960.

    Article  Google Scholar 

  36. Hao, S., Park, H.S. and Liu, W.K., Int. J. Num. Meth. Engng., 53 (2002) 1937.

  37. Belytschko, T., Krongauz, Y., Organ, D., Fleming, M. and Krysl, P., Comput. Meth. Appl. Mech. Engng., 139 (1996) 3.

    Article  Google Scholar 

  38. Babuska, I., Banerjee, U. and Osborn, J.E., Acta Numerica, 2002 (to appear).

  39. Oh, D.J. and Johnson, R.A., J. Mat. Res., 3 (1988) 471.

    CAS  Google Scholar 

  40. Johnson, R.A. and Oh, D.J., J. Mat. Res., 4 (1989) 1195.

    CAS  Google Scholar 

  41. Horstemeyer, M.F. et al., Modelling and Simulation in Materials Science and Engineering, 11 (2003) 265.

    Article  CAS  Google Scholar 

  42. Ashcroft, N.W. and Mermin, N.D., Solid State Physics, 1976, Saunders College Publishing.

  43. Tadmor, E.B., Ortiz, M. and Phillips, R., Philosophical Magazine a-Physics of Condensed Matter Structure Defects and Mechanical Properties, 73 (1996) 1529.

    Google Scholar 

  44. Ortiz, M. et al., Mrs Bulletin, 26 (2001) 216.

    CAS  Google Scholar 

  45. Hao, S., Liu, W.K. and Qian, D., J. Appl. Mechanics-Transactions Asme, 67 (2000) 803.

    Article  Google Scholar 

  46. Wagner, G.J. and Liu, W.K., to be published in J. Compt. Phy., 2003.

  47. Belytschko, T., Liu, W.K. and Moran, B., Nonlinear finite elements for continua and structures, 2000, Chichester, New York, John Wiley, xvi, p. 650.

    Google Scholar 

  48. Zhang, P. et al., Int. J. Solids Struct., 39 (2002) 3893.

    Article  Google Scholar 

  49. Hughes, T.J.R., Franca, L.P. and Mallet, M., Comput. Meth. Appl. Mech. Engng., 54 (1986) 223.

    Article  Google Scholar 

  50. Germain, P., Nguyen, Q.S. and Suquet, P., J. Appl. Mech., ASME Trans., 50 (1983) 1010.

    Article  Google Scholar 

  51. Chaboche, J.L., Int. J. Plasticity, 5 (1989) 247.

    Article  Google Scholar 

  52. Horstemeyer, M.F. and Wang, P., to be published in 'Journal of Computer Aided Materials Design', 2003.

  53. Krauss, G., In: Shear fracture of ultrahigh strength low alloy steels. Innovations in Ultrahigh-strength steel technology, 1984, Lake George, NY.

  54. Freeman, A.J., J. Comput. Appl. Math., 149 (2002) 27.

    Google Scholar 

  55. Liu, W.K., Hao, S., Belytschko, T., Li, S.F. and Chang, C.T., Comput. Mat. Sci., 16 (1999) 197.

    Article  CAS  Google Scholar 

  56. Olson, G.B., Liu,W.K., Moran, B. and Hao, S., In: A multi-scale, multi-physics model in steel design. SRG Meeting 2002, 2002. Northwestern University, Evanston, IL, U.S.A.

    Google Scholar 

  57. Olson, G.B., In Olson, G.B., Azrin, M. and Wright, E.S. (Eds.) Innovations in Ultrahigh-Strength Steel Technology, 1987, Lake George, N.Y., p. 1.

  58. Argon, A.S., Im, J. and Needleman, A., Metallurgical Trans., A6 (1975) 815.

    Google Scholar 

  59. Jack, D.H. and Jack, K.H., Mat. Sci. Engng., 11 (1973) 1.

    Article  CAS  Google Scholar 

  60. Olson, G.B., In Bever, M.B. (Ed.) Encyclopedia of Mat. Sci. & Eng., 1986, Pergamon Press, p. 2929.

  61. Socrate, S. and Parks, D.M., 1995, MIT.

  62. Olson, G.B., Materials Science and Engineering a-Structural Materials Properties Microstructure and Processing, 275 (1999) 11.

    Google Scholar 

  63. Oden, J.T. and Vemaganti, K., Physica D, 133 (1999) 404.

    Article  Google Scholar 

  64. Belytschko, T. and Black, T., Int. J. Num. Meth. Engng., 45 (1999) 601.

    Article  Google Scholar 

  65. Belytschko, T., Gu, L. and Lu, Y.Y., Modelling and Simulation in Materials Science and Engineering, 2 (1994) 519.

    Article  Google Scholar 

  66. Armero, F. and Oller, S., Int. J. Solids Struct., 37 (2000) 7409.

    Article  Google Scholar 

  67. Needleman, A., Ultramicroscopy, 40 (1992) 203.

    Article  Google Scholar 

  68. Fish, J. and Belsky, V., In: AdaptiveMulti-grid Method for a Periodic Heterogeneous Medium, 1995, p. 243.

  69. Ladeveze, P., Computers & Structures, 44 (1992) 79.

    Article  Google Scholar 

  70. Evans, A.G. et al., Acta Metallurgica Et Materialia, 34 (1986) 1634.

    Google Scholar 

  71. Grosh, S., Lee, K. and Paghavan, P., Int. J. Solids Struct., 38 (2001) 2335.

    Article  Google Scholar 

  72. Shishidou, T., Zhao, Y.J., Lee, J.H. and Freeman, A.J., private discussion, 2002.

  73. Jhi, S.H., Ihm, J., Louie, S.G. and Cohen, M.L., Nature, 399 (1999) 132.

  74. Spencer, M.J.S. et al., Surface Science, 515 (2002) L464.

    Article  CAS  Google Scholar 

  75. Eshelby, J.D., In Sneddon, I.N. and Hill, R. (Eds.) Progress in Solid Mechanics, 1961, North-Holland, Amsterdam, p. 89.

  76. Hill, R., J. Mech. Phys. Solids, 13 (1965) 89.

    Article  CAS  Google Scholar 

  77. Hutchinson, J.W., Proceedings of the Royal Society of London Series a-Mathematical and Physical Sciences, 319 (1970) 247.

    CAS  Google Scholar 

  78. Bishop, J.F. and Hill, R., Phil. Mag., 42 (1951) 414.

    CAS  Google Scholar 

  79. Rice, J.R. and Tracey, D.M., J. Mech. Phys. Solids, 17 (1969) 2.

    Google Scholar 

  80. Gurson, A.L., J. Engng. Mat. Technol., 99 (1977) 2.

    Google Scholar 

  81. Tvergaard, V. and Hutchinson, J.W., Int. J. Fract., 18 (1982) 237.

    Google Scholar 

  82. Hutchinson, J.W., Proceedings of the Royal Society of London Series a-Mathematical Physical and Engineering Sciences, 348 (1976) 101.

    CAS  Google Scholar 

  83. Moran, B., Asaro, R.J. and Shih, C.F., Effects of material rate sensitivity and void nucleation on fracture initation in a circumferentially cracked bar, 22 (1991).

  84. Embury, J.D., Journal De Physique Iv, 3 (1993) 607.

    Google Scholar 

  85. Duva, J.M. and Hutchinson, J.W., J. Mech. Mater., 3 (1984) 41.

    Article  Google Scholar 

  86. Hao, S., Liu, W.K. and Chang, C.T., Comput. Meth. Appl. Mech. Engng., 187 (2000) 401.

    Article  Google Scholar 

  87. Olson, G.B. and Hsieh, K.C., Tech. Report. 2002, Dept. Mat. Sci. Engr., Northwestern University.

  88. Briant, C.L. et al., Void Nucleation in a Low Alloy Steel. TMS Meeting, 2002.

  89. Hao, S., Liu, W.K. and Klein, P., Multi-Scale Damage Model, 2000. Chicago, IL., U.S.A., IUTAM2000.

    Google Scholar 

  90. Hao, S. et al., A three-level multi-physics computational constitutive model for metal. In preparation, 2003.

  91. Vernerey. F. and Hao, S., Moran, B. and Liu, W.K., In preparation, 2003.

  92. Tvergaard, V. and Hutchinson J.W., Int. J. of Fracture Mechanics, 17 (1981) 389.

    Article  Google Scholar 

  93. Hao, S., Liu, W.K., Rosakis, A. and Klein, P., Modeling and Simulation of Intersonic Crack Growth. Northwestern University, ed. M. Engineering, 2001.

  94. Fleck, N.A., Muller, G.M., Ashby, M.F. and Hutchinson, J.W., Acta Metallurgica et Materialia, 42 (1994) 475.

    Article  CAS  Google Scholar 

  95. Gao, H., Huang, Y., Nix, W.D. and Hutchinson, J.W., J. Mech. Phys. Solids, 47 (1999) 1239.

    Article  Google Scholar 

  96. Tvergaard, V. and Needleman, A., J. Mech. Phys. Solids, 40 (1992) 447.

    Article  Google Scholar 

  97. Gao, H.J., Huang, Y., Nix, W.D. and Hutchinson, J.W., J. Mech. Phys. Solids, 47 (1999) 1239.

    Article  Google Scholar 

  98. Fleck, N.A. and Hutchinson, J.W., Adv. Appl. Mech., 33 (1997) 295.

    Article  Google Scholar 

  99. Hao, S. and Liu,W.K.,Moving particle finite element method with global superconvergence. Submitted for publication, 2002.

  100. Hao, S. and Brocks, W., Comput. Mech., 20 (1997) 34.

    Article  Google Scholar 

  101. Moran, B. and Shih, F., Eng. Fract. Mech, 27 (1987) 615.

    Article  Google Scholar 

  102. Moran, B. and Shih, F., Int. J. Fracture, 35 (1987) 295.

    Article  Google Scholar 

  103. Gaspar, R., Acta Phys. Acad. Sci. Hung., 3 (1954) 263.

    Article  Google Scholar 

  104. Heidin, L. and S.J. Lundqvist, Phys. (France), 33 (1972) C3.

    Google Scholar 

  105. Hughes, T.J.R. and Winget, J., Int. J. Num. Meth. Engng., 15 (1980) 1862.

    Article  Google Scholar 

  106. Horstemeyer, M.F. and Baskes, M.I., J. Engng. Mat. Technol.-Trans. Asme, 121 (1999) 114.

    Google Scholar 

  107. Khan, A.S. and Su, X.M., Int. J. Plasticity, 10 (1994) 807.

    Article  Google Scholar 

  108. Khan, A.S. and Parikh, Y., Int. J. Plasticity, 2 (1986) 379.

    Article  CAS  Google Scholar 

  109. Deng, D., Argon, A.S. and Yip, S., Philosophical Transactions of the Royal Society of London Series a-Mathematical Physical and Engineering Sciences, 329 (1989) 613.

    CAS  Google Scholar 

  110. Tang, M.J. and Yip, S., Phys. Rev. Lett., 75 (1995) 2738.

    Article  CAS  Google Scholar 

  111. Yip, S., Li, J., Tang, M.J. and Wang, J.G., Materials Science and Engineering a-Structural Materials Properties Microstructure and Processing, 317 (2001) 236.

    Google Scholar 

  112. Needleman, A., Acta Materialia, 48 (2000) 105.

    Article  CAS  Google Scholar 

  113. Curtin, W.A. and Miller, R.E., Modelling and Simulation in Materials Science and Engineering, 11 (2003) R33.

    Article  CAS  Google Scholar 

  114. Weinert, M., J. Math. Phys., 22 (1981) 2433.

    Article  CAS  Google Scholar 

  115. Gurtin, M., J. Mech. Phys. Solids, 48 (2000) 898.

    Google Scholar 

  116. Gurtin, M., Physica, D92 (1996) 178.

    CAS  Google Scholar 

  117. Jansen, H.J.F. and Freeman, A.J., Phys. Rev. B30 (1984) 561.

    Article  CAS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Materials Technology Laboratory, Northwestern University, 2145 Sheridan Road, Evanston, Illinois, 60208, U.S.A

    Su Hao, Brian Moran, Wing Kam Liu & Gregory B. Olson

Authors
  1. Su Hao
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Brian Moran
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Wing Kam Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Gregory B. Olson
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Hao, S., Moran, B., Kam Liu, W. et al. A hierarchical multi-physics model for design of high toughness steels. Journal of Computer-Aided Materials Design 10, 99–142 (2003). https://doi.org/10.1023/B:JCAD.0000036813.66891.41

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/B:JCAD.0000036813.66891.41

Keywords

Search

Navigation