Constitutive Equations for Thermoinelasticity and Instability Phenomena in Thermodynamic Flow Processes

  • P. Perzyna
Part of the International Centre for Mechanical Sciences book series (CISM, volume 321)


In recent years it has been observed active research work in the field of the instability phenomena of plastic flow processes. Particularly the localization of plastic deformation along a shear band treated as a prelude to failure initation has been a matter of a great interest.


Constitutive Equation Shear Band Adiabatic Process Internal State Variable Kirchhoff Stress Tensor 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Abraham, R., Marsden, J.E., Foundations of Mechanics, Second Edition, Addison-Wesley, Reading Mass., 1978zbMATHGoogle Scholar
  2. 2.
    Abraham, R., Marsden, J.E., Ratiu, T., Manifolds, Tensor analysis and Applications, Addison-Wessley, Reading, MA, 1983zbMATHGoogle Scholar
  3. 3.
    Agah-Tehrani, A., Lee, E.H., Mallett, R.L., Onat, E.H., The theory of elastic-plastic deformation at finite strain with induced anisotropy modelled as combined isotropic-kinematic hardening, J.Mech.Phys.Solids, 35, 519–539, 1987zbMATHGoogle Scholar
  4. 4.
    Anand, L., Spitzig, W.A., Initiation of localized shear band in plane strain, J.Mech.Phys. Solids, 28, 113–128, 1980Google Scholar
  5. 5.
    Asaro, R.J., Crystal plasticity, ASME, 50, 921–934, 1983zbMATHGoogle Scholar
  6. 6.
    Asaro, R.J., Micromechanics of crystals and policrystals, Advances in Applied Mechanics, 23, 1–115, 1983Google Scholar
  7. 7.
    Asaro, R.J., Needleman, A., Texture development and strain hardening in rate dependent policrystals, Acta Metall., 33, 923–953, 1985Google Scholar
  8. 8.
    Asaro, R.J., Rice, R.J., Strain localization in ductile single crystals, J.Mech.Phys.Solids, 25, 309–338, 1977zbMATHGoogle Scholar
  9. 9.
    Ashby, M.F., Frost, H.J., in Constitutive Equation in Plasticity (ed. A.S.Argon),MIT Press, Cambridge, Mass., 1975Google Scholar
  10. 10.
    Bingham, E.C., Fluidity and Plasticity, McGraw Hill, New York, 1922Google Scholar
  11. 11.
    Campbell, J.D., Dynamic plasticity macroscopic and microscopic aspects, Material Sci.Engng., 12, 3–12, 1973Google Scholar
  12. 12.
    Campbell, J.D., Ferguson, W.G., The temperature and strain-rate dependence of the shear strength of mild steel, Phil.Mag., 81, 63–82, 1970Google Scholar
  13. 13.
    Chang, Y.W., Asaro, R.J., An experimental study of shear localization in aluminum-copper single crystals, Acta Metall., 29, 241–257, 1981Google Scholar
  14. 14.
    Chang, Y.W., Asaro, R.J., Lattice rotations and localized shearing in single crystals, Arch.Mechanics, 32, 369–401, 1980Google Scholar
  15. 15.
    Cho, K., Chi, Y.C., Duffy, J., Microscopic obserwations of adiabatic shear bands in three different steels, Brown University Report, Sept. 1988Google Scholar
  16. 16.
    Cox, T.B., Low, J.R. An investigation of the plastic fracture of AISI 4340 and 18 Nickel-200 grade maraging steels, Met. Trans., 5, 1457–1470, 1974Google Scholar
  17. 17.
    Dowling, A.R., Harding, J., Campbell, J.D., The dynamic punching of metals, J.Inst. of Metals, 98, 215–224, 1970Google Scholar
  18. 18.
    Duszek, M.K., Perzyna, P., Influence of the kinematic harden-ing on the plastic flow localization in damaged solids, Arch. Mechanics, 40, 595–609, 1988zbMATHGoogle Scholar
  19. 19.
    Duszek, M.K., Perzyna, P., On combined isotropic and kinematic hardening effects in plastic flow processes, Int. J. Plasticity 1991 (in print)Google Scholar
  20. 20.
    Duszek, M.K., Perzyna, P., Plasticity of damaged solid and shear band localization, Ing.-Archiv, 58, 380–392, 1988zbMATHGoogle Scholar
  21. 21.
    Duszek, M.K., Perzyna, P., T.he localization of plastic deformation in thermoplastic solids, Int.J.Solids and Structures, 27, 1419–1443, 1991zbMATHGoogle Scholar
  22. 22.
    Duszek-Perzyna, M. Perzyna, P., Stein, E., Adiabatic shear band localization in elastic-plastic damaged solids,The Second Int. Symposium on Plasticity and its current Applications, July 31- August 4, 1989, Mie University; Int.J. Plasticity (in print)Google Scholar
  23. 23.
    Duszek, M.K., Perzyna, P., Adiabatic shear band localization in elastic-plastic crystals, 1991 (in preparation to publication)Google Scholar
  24. 24.
    Evans, A.G., Rawlings, R.D., The thermally activated deformation of crystalline materials, Phys.Stat.Sol., 34, 9–31, 1969Google Scholar
  25. 25.
    Gilbert, J.E., Knops, R.J., Stability of general systems, Arch.Rat.Mech.Anal., 25, 271–284, 1967MathSciNetzbMATHGoogle Scholar
  26. 26.
    Green, A.E., Naghdi, P.M., Some remarks on elastic-plastic deformation at finite strain, Int.J.Engng.Sci., 9, 1219–1229, 1971zbMATHGoogle Scholar
  27. 27.
    Green, A.S., Naghdi, P.M., A general theory of an elastic-plastic continuum, Arch. Rat. Mech. Anal., 18, 1964Google Scholar
  28. 28.
    Gurson, A.L., Continuum theory of ductile rupture by void nucleation and growth, Part I. Yield criteria and flow rules for porous ductile media, J.Eng.Mater.Technol., 99, 2–15, 1977Google Scholar
  29. 29.
    Gurtin, M.E., Thermodynamics and stability, Arch. Rat. Mech. Anal., 59, 63–96, 1975MathSciNetzbMATHGoogle Scholar
  30. 30.
    Gurtin, M.E., Thermodynamics and the energy criterion for stability, Arch.Rat. Mech.Anal., 52, 93–103, 1973MathSciNetGoogle Scholar
  31. 31.
    Hadamard, J., Lecons sur la propagation des ondes et les equations de l’hydrodynamique, chap.6, Paris, 1903Google Scholar
  32. 32.
    Hartley, K.A., Duffy, J., Hawley, R.H., Measurement of the temperature profile during shear band formation in steels deforming at high strain rates, J.Mech.Phys.Solids, 35, 283–301, 1987Google Scholar
  33. 33.
    Hauser, F.E., Simmons, J.A., Dorn, J.E., Strain rate effects in plastic wave propagation, in Response of Metals to High Velocity Deformation, Wiley (Interscience) New York, 93–114, 1961Google Scholar
  34. 34.
    Hill, R., Acceleration wave in Solids, J.Mech.Phys.Solids, 10, 1–16, 1962MathSciNetzbMATHGoogle Scholar
  35. 35.
    Hill, R., Aspects of invariance in solids mechanics, Adv.Appl.Mech., 18, 1–75, 1987Google Scholar
  36. 36.
    Hill, R., The essential structure of constitutive laws for metal composites and policrystals, J.Mech.Phys.Solids, 15, 255–262, 1967Google Scholar
  37. 37.
    Hill, R., Rice, J.R., Constitutive analysis of elastic-plastic crystals at arbitrary strain, J.Mech.Phys.Solids, 20, 401–413, 1972zbMATHGoogle Scholar
  38. 38.
    Hill, R., Rice, J.R., Elastic potentials and the structure of enelastic constitutive laws, SIAM J.Appl.Math., 25, 448–461, 1973MathSciNetzbMATHGoogle Scholar
  39. 39.
    Hohenemser, K., Prager, W., Uber die Ansatze der Mechanik isotroper Kontinua, ZAMM, 12, 216–226, 1932Google Scholar
  40. 40.
    Hutchinson, J.W., Bounds and self-consistent estimates for creep of polycrystalline materials, Proc.Royal Soc. London, Sec.A 348, 101–127, 1976zbMATHGoogle Scholar
  41. 41.
    Iwakuma, T., Nemat-Nasser, S., Finite elastic-plastic deformation of polycrystalline metals, Proc.Royal Soc. London, A 394, 87–119, 1984zbMATHGoogle Scholar
  42. 42.
    Knops, R.J., Wilkes, E.W., Theory of elastic stability, Handbuch der Physik, VI a/3, Berlin, Heidelberg, New York, Springer, 1973Google Scholar
  43. 43.
    Kocks, U.F., Argon, A.S., Ashby, M.F., Thermodynamics and Kinetics of Slip, Pergamon Press, 1975Google Scholar
  44. 44.
    Kumar, A., Hauser, F.E., Dorn, J.E., Viscous drag on dislocations in aluminum at high strain rates, Acta Metall., 16, 1189–1197, 1968Google Scholar
  45. 45.
    Kumar, A., Kumble, R.G., Viscous drag on dislocations at high strain rates in copper, J.Appl.Physics, 40, 3475–3480, 1969Google Scholar
  46. 46.
    Le Roy, G., Embury, J.D., Edward, G., Ashby, M.F., A model of ductile fracture based on the nucleation and growth of voids, Acta Metall., 29, 1509–1522, 1981Google Scholar
  47. 47.
    Lee, E.H., Elastic-plastic deformations at finite strains, J. Appl. Mech., 36, 1–6, 1969zbMATHGoogle Scholar
  48. 48.
    Lindholm, U.S., Some experiments with the split Hopkinson pressure bar, J.Mech.Phys.Solids, 12, 317–335, 1964Google Scholar
  49. 49.
    Lindholm, U.S., in: Mechanical Behaviour of Materials under Dynamic Loads, (ed. U.S.Lindholm), Springer Verlag, 77–95, 1968Google Scholar
  50. 50.
    Lippmann, H., Velocity field equations and strain localization, Int.J.Solids Structure, 22, 1399–1409, 1986zbMATHGoogle Scholar
  51. 51..
    Malvern, L.E., The propagation of longitudinal waves of plastic deformation in a bar of material exhibiting, a strain-rate effects, J.Appl.Mech., 18, 203–208, 1951MathSciNetGoogle Scholar
  52. 52.
    Mandel, J., Conditions de stabilite et postulat de Drucker, in: Rheology and Soil Mechanics, eds. J.Kravtchenko and P.M.Sirieys, Springer-Verlag, 58–68, 1966Google Scholar
  53. 53.
    Marchand, A., Cho, K., Duffy, J., The formation of adiabatic shear bands in an AISI 1018 cold-rolled steel, Brown University Report, September 1988Google Scholar
  54. 54.
    Marchand, A., Duffy, J., An experimental study of the formation process of adiabatic shear bands in a structural steel, J.Mech.Phys.Solids, 36, 251–283, 1988Google Scholar
  55. 55.
    Marsden, J.E., Hughes, T.J.R., Mathematical Foundations of Elasticity, Prentice-Hall, Englewood Cliffs, NJ, 1983zbMATHGoogle Scholar
  56. 56.
    Mear, M.E., Hutchinson, J.W. Influence of yield surface curvature on flow localization in dillatant plasticity, Mechanics and Materials, 4, 395–407, 1985Google Scholar
  57. 57.
    Mehrabadi, M.M., Nemat-Nasser, S., Some basic kinematical relations for finite deformations of continua, Mechanics of Materials, 6, 127–138, 1987Google Scholar
  58. 58.
    Meyers, M.A., Aimone, C.T., Dynamic fracture (spalling) of metals, Prog. Mater. Sci., 28, 1–96, 1983Google Scholar
  59. 59.
    Nabarro, F.R.N., Theory of crystal dislocations, Oxford, 1967Google Scholar
  60. 60.
    Naghdi, P.M., A critical review of the state of finite plasticity, ZAMP, 41, 315–394, 1990MathSciNetzbMATHGoogle Scholar
  61. 61.
    Needleman, A., Rice, J.R., Limits to ductility set by plastic flow localization, in: Mechanics of Sheet Metal Forming (ed. Koistinen, D.P. and Wang, N.-M.), Plenum, New York, 237–267, 1978Google Scholar
  62. 62.
    Needleman, A., Tvergaard, V., Limits to formability in, rate sensitive metal sheets, Mechanical Behaviour of Materials-IV (ed.J.Carlsson and N.G.Ohlson), 51–65, 1984Google Scholar
  63. 63.
    Nemat-Nasser, S., Decomposition of strain measures and their rates in finite deformation elastoplasticity, Int.J.Solids Structures, 15, 155–166, 1979zbMATHGoogle Scholar
  64. 64.
    Neurat-Nasser, S., Chung, D.-T., Taylor, L.M., Phenomenological modelling of rate-dependent plasticity for high strain rate problems, Mechanics of Materials, 7, 319–344, 1989Google Scholar
  65. 65.
    Nemat-Nasser, S., Obata, M., Rate dependent, finite elasto-plastic deformation of polycrystals, Proc.Royal Soc. London, A 407, 343–375, 1986Google Scholar
  66. 66.
    Nemes, J.A., Eftis, J., Randles, P.W., Viscoplastic constitutive modeling of high strain-rate deformation, material damage and spall fracture, ASME J.Appl.Mech., 57, 282–291, 1990Google Scholar
  67. 67.
    Oldroyd, J., On the formulation of rheological equations of state, Proc.Roy.Soc. (London), Ser. A 200, 523–541, 1950MathSciNetzbMATHGoogle Scholar
  68. 68.
    Pan, J., Rice, J.R., Rate sensitivity of plastic flow and implications for yield surface vertices, Int. J. Solids Structures, 19, 973–987, 1983zbMATHGoogle Scholar
  69. 69.
    Pan, J., Saje, M., Needleman, A., Localization of deformation in rate sensitive porous plastic solids, Int.J.Fracture, 21, 261–278, 1983Google Scholar
  70. 70.
    Peirce, D., Asaro, R.J., Needleman, A., An analysis of non-uniform and localized deformation in ductile single crystals, Acta Metall., 30, 1087–1119, 1982Google Scholar
  71. 71.
    Peirce, D., Asaro, R.J., Needleman, A., Material rate dependence and localized deformation in crystalline solids, Acta Metall., 31, 1951–1976, 1983Google Scholar
  72. 72.
    Perzyna, P., The constitutive equations for rate sensitive plastic materials, Quart. Appl. Math., 20, 321–332, 1963MathSciNetzbMATHGoogle Scholar
  73. 73.
    Perzyna, P., Fundamental problems in viscoplasticity, Advances in Applied Mechanics, vol. 9, 243–377, 1966Google Scholar
  74. 74.
    Perzyna, P., Thermodynamic theory of viscoplasticity, Advances in Applied Mechanics, vol. 11 313–354, 1971Google Scholar
  75. 75.
    Perzyna, P., Coupling of dissipative mechanisms of viscoplastic flow, Arch. Mechanics, 29, 607–624, 1977MathSciNetzbMATHGoogle Scholar
  76. 76.
    Perzyna, P., Modified theory of viscoplastcity. Application to advanced flow and instability phenomena, Arch. Mechanics, 32, 403–420, 1980zbMATHGoogle Scholar
  77. 77.
    Perzyna, P., Thermodynamics of dissipative materials, in Recent Developments in Thermodynamics of Solids,Eds. Lebon, G. and Perzyna, P., Springer, Wien 1980, 95–220, 1980Google Scholar
  78. 78.
    Perzyna, P., Stability phenomena of dissipative solids with internal defects and imperfections, XV-th IUTAM Congress, Toronto, August 1980, Theoretical and Applied Mechanics, Proc. ed. F.P.J. Rimrott and B. Tabarrok, North-Holland, pp. 369–376, Amsterdam 1981Google Scholar
  79. 79.
    Perzyna, P., Stability problems for inelastic solids with defects and imperfections, Arch.Mech., 33, 587–602, 1981MathSciNetzbMATHGoogle Scholar
  80. 80.
    Perzyna, P., Application of dynamical system methods to flow processes of dissipative solids, Arch.Mech., 34, 523–539, 1982MathSciNetzbMATHGoogle Scholar
  81. 81.
    Perzyna, P., Stability of flow processes for dissipative solids with internal imperfections, ZAMP, 35, 848–867, 1984zbMATHGoogle Scholar
  82. 82.
    Perzyna, P., Constitutive modelling for brittle dynamic fracture in dissipative solids, Arch. Mechanics, 38, 725–738, 1986MathSciNetzbMATHGoogle Scholar
  83. 83.
    Perzyna, P., Constitutive equations of dynamic plasticity, Post Symposium Short Course, August 4–5,1989, Nagoya,JapanGoogle Scholar
  84. 84.
    Perzyna, P., Temperature and rate dependent theory of plasticity of polycrystalline solids, The Second Int. Symposium on Plasticity and its current Applications, July 31- August 4, 1989, Mie University, Tsu, JapanGoogle Scholar
  85. 85.
    Perzyna, P., Duszek-Perzyna, M.K., Stein, E., Analysis of the influence of different effects on ciiteria for shear band localization,28th Polish Solids Mech.Conf., Kozubnik, 1990Google Scholar
  86. 86.
    Perzyna, P., Adiabatic shear band localization in rate dependent plastic solids,1991 (in preparation to publication)Google Scholar
  87. 87.
    Prager, W., Introduction to Mechanics of Continua, Gin and Co., New York, 1961zbMATHGoogle Scholar
  88. 88.
    Rice, J., Plasticity of soil mechanics, in Proc. of the Symposium of the Role of Plasticity in Soil Mechanics, Cambridge, England 1973, ed. by Palmer, A.C., 263–275, 1973Google Scholar
  89. 89.
    Rice, J.R., Continuum mechanics and thermodynamics of plasticity in relation to microscale deformation mechanisms, in Constitutive Equations in Plasticity,(ed.A.S.Argon), The MIT Press, Cambridge, 23–75, 1975Google Scholar
  90. 90.
    Rice, J.R., Inelastic constitutive relations for solids: an internal variable theory and its application to metal plasticity, J.Mech.Phys.Solids, 19, 433–455, 1971zbMATHGoogle Scholar
  91. 91.
    Rice, J.R., On the structure of stress-strain relation for time-dependent plastic deformation in metals, J.Appl.Mech., 37, 728–737, 1970Google Scholar
  92. 92.
    Rice, J.R., The localization of plastic deformation, Theoretical and Applied Mechanics, ed. Koiter, W.T., North-Roland, 207–220, 1976Google Scholar
  93. 93.
    Rice, J.R., Rudnicki, J.W., A note on some features of the theory of localization of deformation, Int.J.Solids Structure, 16, 597–605, 1980MathSciNetzbMATHGoogle Scholar
  94. 94.
    Rudnicki, J.W., Rice, J.R., Conditions for the localization of deformation in pressure-sensitive dilatant materials, J. Mech. Phys. Solids, 23, 371–394, 1975Google Scholar
  95. 95.
    Seeger, A., The generation of lattice defects by moving dislocations and its application to the temperature dependence of the flow-stress of f.c.c. crystals, Phil.Mag., 46, 1194–1217, 1955Google Scholar
  96. 96.
    Shima, S., Oyane, M., Plasticity theory for porous solids, Int.J.Mech.Sci., 18, 285–291, 1976Google Scholar
  97. 97.
    Shioiri, J., Satoh, K., Nishimura, K., in High Velocity Deformation in Solids, IUTAM Symp.Proc. (ed.K.Kawata and J.Shioiri), Springer, 50–66, 1979Google Scholar
  98. 98.
    Shockey, D.A., Seaman, L., Curran, D.R., The microstatistical fracture mechanics approach to dynamic fracture problems, Int. J. Fracture, 27, 145–157, 1985Google Scholar
  99. 99.
    Simo, J.C., A framework for finite strain elasto-plasticity based on maximum plastic dissipation and the multiplicative decomposition: Part II, Computational aspects, Comput.Meths.Appl.Mech.Engng., 68, 1–31, 1988zbMATHGoogle Scholar
  100. 100.
    Simo, J.C., A framework for finite strain elastoplasticity based on maximum plastic dissipation and the multiplicative decomposition: Part I. Continuum formulation, Comput. Meth. Appl. Mech. Engng., 66, 199–219, 1988MathSciNetzbMATHGoogle Scholar
  101. 101.
    Spitzig, W.A., Deformation behaviour of nitrogenated Fe-Ti-Mn and Fe-Ti single crystals, Acta Metall., 29, 1359–1377, 1981Google Scholar
  102. 102.
    Stein, E., Duszek-Perzyna, M.K., Perzyna, P., Influence of thermal effects on shear band localization in elastic-plastic damaged solids, Proc. Euromech Colloquium 255,Paderborn,1989Google Scholar
  103. 103.
    Teodosiu, C., Sidoroff, F., A theory of finite elastoplasticity of single crystals, Int.J.Engng.Sci., 14, 165–176, 1976zbMATHGoogle Scholar
  104. 104.
    Thomas, T.Y., Plastic Flow and Fracture in Solids, New York, Academic Press, 1961zbMATHGoogle Scholar
  105. 105.
    Truesdell, C., Noll, W., The nonlinear field theories, in: Handbuch der Physik, Band III/3, Springer, Berlin, 1965Google Scholar
  106. 106.
    Tvergaard, V., Effects of yield surface curvature and void nucleation on plastic flow localization, J.Mech.Phys.Solids, 35, 43–60, 1987Google Scholar
  107. 107.
    Tvergaard, V., Needleman, A., Effect of material rate sensitivity on failure modes in the Charpy V-notch test, J. Mech. Phys. Solids, 34, 213–241, 1986Google Scholar
  108. 108.
    Willems, J.C., Dissipative dynamical systems, Part I: General Theory, Part II: Linear systems with quadratic supply rates, Arch.Rat.Mech.Anal., 45, 321–393, 1972MathSciNetzbMATHGoogle Scholar
  109. 109.
    Ziegler, H., A modification of Prager’s hardening rule, Quart. Appl. Math., 17, 55–65, 1959zbMATHGoogle Scholar

Copyright information

© Springer-Verlag Wien 1993

Authors and Affiliations

  • P. Perzyna
    • 1
  1. 1.Polish Academy of SciencesWarsawPoland

Personalised recommendations