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Multiscale Constitutive Modelling of the Influence of Anisotropy E?ects on Fracture Phenomena in Inelastic Solids

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EN
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The main objective of the present paper is the consistent development of the thermodynamical theory of elasto-viscoplasticity within the framework of a unique constitutive materialstructure. The focus of attention on the description of the influence of anisotropy effects on fracture phenomena is proposed. In the first part a general principle of determinism is formulated and a unique constitutive material structure is developed. The original conception of the intrinsic state of a particle X during motion of a body B has been assumed. A notion of the method of preparation of the deformation-temperature con?guration of a particle X has been proposed as a simple way of the gathering information for the description of the internal dissipation. As the basis of the thermodynamical requirements the dissipation principle in the form of the Clausius-Duhem inequality is assumed. By particular assumption of the method of preparation space for a unique constitutive material structure the internal state variable material structure has been constructed. In the second part the thermodynamical theory of elasto-viscoplasticity within the framework of the internal state variable material structure is formulated. Introduction of a finite set of the internal state variables is based on multiscale considerations in analysis of the physical foundations of inelastic solids and experimental observation results. Particular attention is focused on the determination of the evolution laws for the introduced internal state variables. Fracture criterion based on the evolution of the anisotropic intrinsic microdamage is proposed.
Rocznik
Strony
225--225
Opis fizyczny
–-284, Bibliogr. 119 poz., rys., tab., wykr.
Twórcy
  • Institute of Fundamental Technological Research Polish Academy of Sciences Pawińskiego 5B, 02-106 Warszawa, Poland, pperzyna@ippt.pan.pl
Bibliografia
  • 1. Abraham R., Marsden J.E., Foundations of Mechanics, Second Edition, AddisonWesley, Reading Mass., 1978.
  • 2. Abraham R., Marsden, J.E., Ratiu T., Manifolds, Tensor Analysis and Applications, Springer, Berlin, 1988.
  • 3. Barbee T.W., Seaman L., Crewdson R., Curran D., Dynamic fracture criteria for ductile and brittle metals, J. Mater., 7, 393–401, 1972.
  • 4. Bernstein B., Proof of Caratheodory’s local theorem and its global application to thermostatics, J. Math. Phys., 1, 222–224, 1960.
  • 5. Boehler J.P. (Ed.), Yielding, Damage, and Failure of Anisotropic Solids, Proc. IUTAM/ICM Symposium, Villard-de Lans, 24–28 August 1987, Mech. Eng. Public. Limited, London, 1990.
  • 6. Born M., Kritische Betrachtungen zur traditionellen Darstelllung der Thermodynamik, Physik. Zeitschr., 22, 218–224, 249–254, 282–286, 1921.
  • 7. Boyling J.B., Caratheodory’s principle and the existence of global integrating, Commun. Math. Phys., 10, 52–68, 1968.
  • 8. Boyling J.B., An axiomatic approach to classical thermodynamics, Proc. Royal Soc. London, A329, 35–70, 1972.
  • 9. Bridgman P.W., The termodynamics of plastic deformation and generalized entropy, Rev. Modern Phys., 22, 56–63, 1950.
  • 10. Buchdahl H.A., A formal treatment of the consequences of the second law of thermodynamics in Caratheodory’s formulation, Zeitschrift Phys., 152, 425–439, 1958.
  • 11. Buchdahl H.A., Entropy concept and ordering of states, I, Zeitschrift Phys., 168, 316– 321, 1962.
  • 12. Buchdahl H.A., Greve W., Entropy concept and ordering of states, II, Zeitschrift Phys., 168, 386–391, 1962.
  • 13. Campbell J.D., Ferguson W.G., The temperature and strain-rate dependence of the shear strength of mild steel, Phil. Mag., 81, 63–82, 1970.
  • 14. Caratheodory C., (1909), Untersuchungen ¨uber die Grundlagen der Thermodynamik. Math. Annalen, 67, 355–386.
  • 15. Chakrabarti A.K., Spretnak J.W., (1975), “Instability of plastic flow in the direction of pure shear”, Metallurgical Transactions, 6A, 733–747.
  • 16. Coleman B.D., Thermodynamics of materials with memory, Arch. Rat. Mech. Anal., 17, 1–46, 1964.
  • 17. Coleman B.D., Gurtin M.E., Thermodynamics with internal state variables, J. Chem. Phys., 47, 597–613, 1967.
  • 18. Coleman B.D., Mizel V.J., A general theory of dissipation in materials with memory, Arch. Rat. Mech. Anal., 27, 255–274, 1968.
  • 19. Coleman B.D., Noll W., The thermodynamics of elastic materials with heat conduction and viscosity, Arch. Rational Mech. Anal., 13, 167–178, 1963.
  • 20. Coleman B.D., Owen D.R., On the thermodynamics of materials with memory, Arch. Rat. Mech. Anal., 36, 245–269, 1970.
  • 21. Coleman B.D., Owen D.R., A mathematical foundations for thermodynamics, Arch. Rat. Mech. Anal., 54, 1–104, 1974.
  • 22. Cooper J.L.B., The foundations of thermodynamics, J. Math. Anal. Appls., 17, 172–193, 1967.
  • 23. Curran D.R., Seaman L., Shockey D.A., Dynamic failure in solids, Physics Today, January, 46–55, 1977.
  • 24. Curran D.R., Seaman L., Shockey D.A., Linking dynamic fracture to microstructural processes, in: Shock Waves and High-Strain Rate Phenomena in Metals: Concepts and Applications, M.A. Meyers and L.E. Murr [Eds.], Plenum Press, New York, pp. 129–167 1981.
  • 25. Curran D.R., Seaman L., Shockey D.A., Dynamic failure of solids, Physics Reports, 147, 253–388, 1987.
  • 26. Dafalias Y.F., Corotational rates for kinematic hardening at large plastic deformations, J. Appl. Mech., 50, 561–565, 1983.
  • 27. Dornowski W., Perzyna P., Constitutive modelling of inelastic solids for plastic flow processes under cyclic dynamic loadings, Transaction of the ASME, J. Eng. Materials and Technology, 121, 210–220, 1999.
  • 28. Dornowski W., Perzyna P., Localization phenomena in thermo-viscoplastic flow processes under cyclic dynamic loadings, Computer Assisted Mechanics and Engineering Sciences, 7, 117–160, 2000.
  • 29. Dowling A.R., Harding J., Campbell D.J., The dynamic punching of metals, J. Inst. of Metals, 98, 215–224, 1970.
  • 30. Duszek M.K., Perzyna P., On combined isotropic and kinematic hardening effects in plastic flow processes, Int. J. Plasticity, 7, 351–363, 1991.
  • 31. Duszek M.K., Perzyna P., The localization of plastic deformation in thermoplastic solids, Int. J. Solids Structures, 27, 1419–1443, 1991.
  • 32. Duszek-Perzyna M.K., Perzyna P., Analysis of the influence of different effects on criteria for adiabatic shear band localization in inelastic solids, in: Material Instabilities: Theory and Applications, ASME Congress, Chicago, 9–11 November 1994, R.C. Batra and H.M. Zbib [Eds.], AMD-Vol. 183/MD-Vol.50, ASME, New York, pp. 59–85, 1994.
  • 33. Duszek-Perzyna M.K., Perzyna P., Analysis of anisotropy and plastic spin effects on localization phenomena, Arch. Appl. Mechanics, 68, 352–374, 1998.
  • 34. Eckart C., The thermodynamics of irreversible processes, Phys. Review, 58, 267–269. 369–275, 919–924, 1940; 73, 373–382, 1948.
  • 35. Engelking R., General Topology, Polish Scientific Publishers, Warsaw, 1977.
  • 36. Falk G., Jung H., Axiomatik der Thermodynamik, Handbuch der Physik, III/2, Springer, pp. 119–175, 1959.
  • 37. Feynman R.P., Leighton R.B., Sands M., The Feynman Lectures on Physics, I, II, III, Addison-Wesley, New York, 65, 1963.
  • 38. Follansbee P.S., Metallurgical Applications of Shock-Wave and High-Strain-Rate Phenomena, (Murr LE, Staudhammer KP, Meyeres MA, eds.), pp.451–480, Marcel Dekker, New York, 1986.
  • 39. Giles R., Mathematical Foundations of Thermodynamics, Pergamon Press, Oxford 1964.
  • 40. Glema A., Łodygowski T., Nowak Z., Perzyna P., Voyiadjis G.Z., Thermo-elasto-viscoplastic model of a material with non-local and anisotropic intinsic microdamage, McMat 2005, Mechanics and Materials Conference, Baton Rouge, LA, USA, June 1–3, 2005.
  • 41. Glema A., Łodygowski T., Perzyna P., Interacton of deformation waves and localization phenomena in inelastic solids, Computer Methods in Applied Mechanics and Engineering, 183, 123–140, 2000.
  • 42. Glema A., Łodygowski T., Perzyna P., The role of dispersion for the description of strain localization in materials under impact loading, European Conference on Computational Mechanics, June 26–29, Cracow, Poland, 2001.
  • 43. Glema A., Łodygowski T., Perzyna P., Localization of plastic deformations as a result of wave interaction, CAM&ES, 3, 81–91, 2003.
  • 44. Glema A., Łodygowski T., Perzyna P., Numerical investigations of dynamic shear bands in inelastic solids as a problem of mesomechanics, Comput. Mech., 41, 219–229, 2008.
  • 45. Grebe H.A., Pak H.R., Meyers M.A., Adiabatic shear band localization in titanium and Ti-6PctAl-4PctV alloy, Met. Trans., 16A, 761-775, 1985.
  • 46. Jaumann G., Geschlossenes System physikalischer und chemischer Differentialgesetze, Sitzgsber. Akad. Wiss. Wien (IIa), 120, 385–530, 1911.
  • 47. Johnson J.N., Dynamic fracture and spallation in ductile solids, J. Appl. Phys., 52, 2812–2825, 1981.
  • 48. Kelley J.L., General topology, Van Nostrand., New York, 1955.
  • 49. Kosiński W., Perzyna P., The unique material structure, Bull. Acad. Polon. Sci., Ser. Sci. Techn., 21, 655–662, 1973.
  • 50. Kosiński W., Wojno W., Remarks on internal variable and history descriptions of material, Arch. Mech., 25, 709–713, 1973.
  • 51. Kumar A., Kumble R.Gg., Viscous drag on dislocations at high strain rates in copper, J. Appl. Physics, 40, 3475–3480, 1969.
  • 52. Landsberg P.T., Foundations of thermodynamics, Rev. Modern Phys., 28, 363–392, 1956.
  • 53. Landsberg P.T., Main ideas in the axiomatics of thermodynamics, Pure and Applied Chemistry, 22, 215–227, 1970.
  • 54. Landsberg P.T., Time in statistical physics and special relativity, Studium Generale, 23, 1108–1158, 1970.
  • 55. Lederman L.M., Hill Ch.T., Symmetry and the Beautiful Universe, Prometheus Books, Amherst, 2004.
  • 56. Leitman M.J., Mizel V.J., On fading memory space and hereditary integral equations, Arch. Rat. Mech. Anal., 55, 18–51, 1974.
  • 57. Loret B., On the effects of plastic rotation in the finite deformation of anisotropic elastoplastic materials, Mech. Mater., 2, 287–304, 1983.
  • 58. Marsden J.E., Hughes T.J.R., Mathematical Foundations of Elasticity, Prentice-Hall, Englewood Cliffs, New York, 1983.
  • 59. Meyers H.C., Dynamic Behaviour of Materials, John Wiley, New York, 1994.
  • 60. Meyers M.A., Aimone C.T., Dynamic fracture (spalling) of metals, Prog. Mater. Sci., 28, 1–96, 1983.
  • 61. Nagel E., The Structure of Science, Harcourt, Brace World, Inc., New York 1961.
  • 62. Nemat-Nasser S., Phenomenological theories of elastoplasticity and strain localization at high strain rates, Appl. Mech. Rev., 45, S19–S45, 1992.
  • 63. Noether E., Invariante Variationsprobleme,Goett. Nachr., 1918, 235–257, 1918.
  • 64. Noll W., A new mathematical theory of simple materials, Arch. Rat. Mech. Anal., 48, 1–50, 1972.
  • 65. Noll W., Lectures on the foundations of continuum mechanics and thermodynamics, Arch. Rat. Mech. Anal., 52, 62–92, 1973.
  • 66. Nowacki W.K., Nowak Z., Perzyna P., Pęcherski R.B., Effect of strain rate on ductile fracture. A new methodology, Jour. Theoretical and Applied Mechanics, 48, 1003– 1026, 2010.
  • 67. Nowak Z., Perzyna P., Pęcherski R.B., Description of viscoplastic flow accounting for shear banding, Arch. of Metallurgy and Materials, 52, 217–222, 2007.
  • 68. Oldroyd J., On the formulation of rheological equations of state, Proc. R. Soc. Lond., A200, 523–541, 1950.
  • 69. Penrose R., The Road to Reality, A Complete Guide to the Laws of the Universe, A.A. Knopf, New York 2005.
  • 70. Perzyna P., The constitutive equations for rate sensitive plastic materials, Quart. Appl. Math., 20, 321–332, 1963.
  • 71. Perzyna P., Fundamental problems in viscoplasticity, Advances in Applied Mechanics, 9, 343–377, 1966.
  • 72. Perzyna P., Thermodynamic theory of viscoplasticity, Advances in Applied Mechanics, 11, 313–354, 1971.
  • 73. Perzyna P., A gradient theory of rheological materials with internal structural changes, Arch. Mech., 23, 845–850, 1971.
  • 74. Perzyna P., Internal variable description of plasticity, International Symposium on Foundation of Plasticity, Warsaw, Poland, August 30–September 2 1972 , in: Problems of plasticity, A. Sawczuk [Ed.], Nordhoof Publishing, Leyden, 1974, pp. 145–176, 1972.
  • 75. Perzyna P., Thermodynamics theory of rheological materials with internal changes, Symposium franco-polonais, Problemes de la Rh´eologie, Varsovie 1971, PWN, Varsovie, 1973,pp. 277–306.
  • 76. Perzyna P., Physical theory of viscoplasticity, Bull. Acad. Polon. Sci., Serie Sci. Tech., 21, 123–139, 1973.
  • 77. Perzyna P., Thermodynamics of a unique material structure, Arch. Mechanics, 27, 791– 806, 1975.
  • 78. Perzyna P., On material isomorphism in description of dynamics plasticity, Arch. Mech., 27, 473–484, 1975.
  • 79. Perzyna P., Coupling of dissipative mechanisms of viscoplastic flow, Arch. Mechanics, 29, 607–624, 1977.
  • 80. Perzyna P., Modified theory of viscoplasticity. Application to advanced flow and instability phenomena, Arch. Mechanics, 32, 403–420, 1980.
  • 81. Perzyna P., Thermodynamics of dissipative materials, in Recent Developments in Thermodynamics of Solids, G. Lebon and P. Perzyna [Eds.], Springer-Verlag, Wien, New York, pp. 95–220, 1980.
  • 82. Perzyna P., Constitutive modelling of dissipative solids for postcritical behaviour and fracture, ASME J. Eng. Materials and Technology, 106, 410–419, 1984.
  • 83. Perzyna P., Internal state variable description of dynamic fracture of ductile solids, Int. J. Solids Structures, 22, 797–818, 1986.
  • 84. Perzyna P., Constitutive modelling for brittle dynamic fracture in dissipative solids, Arch. Mechanics, 38, 725–738, 1986.
  • 85. Perzyna P., Temperature and rate dependent theory of plasticity of crystalline solids, Revue Phys. Appl., 23, 445–459, 1988.
  • 86. Perzyna P., Instability phenomena and adiabatic shear band localization in thermoplastic flow processes, Acta Mechanica, 106, 173–205, (1994).
  • 87. Perzyna P., Interactions of elastic-viscoplastic waves and localization phenomena in solids, IUTAM Symposium on Nonlinear Waves in Solids, August 15–20, 1993, Victoria, Canada, J.L. Wegner and F.R. Norwood [Eds.], ASME, pp. 114–121, 1995.
  • 88. Perzyna P., Constitutive modelling of dissipative solids for localization and fracture. In: Localization and Fracture Phenomena in Inelastic Solids P. Perzyna [Ed.], Springer, Wien, New York, pp. 99–242, 1998.
  • 89. Perzyna P., Thermo-elasto-viscoplasticity and damage, In: Handbook of Materials Behaviour Models, J. Lemaitre [Ed.], Academic Press, New York, pp. 821–834, 2001.
  • 90. Perzyna P., Thermodynamical theory of inelastic single crystals, Engineering Transactions, 50, 107–164, (2002).
  • 91. Perzyna P., The thermodynamical theory of elasto-viscoplasticity, Engineering Transactions, 53, 235–316, (2005).
  • 92. Perzyna P., The thermodynamical theory of elasto-viscoplasticity accounting for microshear banding and induced anisotropy effects, Mechanics, 27, 25–42, (2008).
  • 93. Perzyna P., The thermodynamical theory of elasto-viscoplasticity for description of nanocrystalline metals, Engng. Trans., 58, 15–74, (2010).
  • 94. Perzyna P., Micromechanics of localized fracture phenomena in inelastic solids generated by impactg loaded adiabatic processes, Engng. Trans., 59, 299–348, (2011).
  • 95. Perzyna P., Drabik A., Description of micro-damage process by porosity parameter for nonlinear viscoplasticity, Arch. Mechanics, 41, 895–908, (1989).
  • 96. Perzyna P., Kosiński W., (1973), A mathematical theory of materials, Bull. Acad. Polon. Sci., Ser. Sci. Tech., 21, 647–654.
  • 97. Perzyna P., Voyiadjis G.Z., (2005), Thermodynamic theory of elasto-viscoplasticity for induced anisotropy effects, McMat 2005, Mechanics and Materials Conference, June 1–3, 2005, Baton Rouge, LA, USA.
  • 98. Perzyna P., Wojno W., Thermodynamics of a rate sensitive plastic material, Arch. Mech., 20, 499–511, (1968).
  • 99. Perzyna P., Wojno W., Unified constitutive equations for elastic-viscoplastic material, Bull. Acad. Polon. Sci., Ser. Sci. Tech., 24, 85–94, (1976).
  • 100. Pęcherski R.B., Macroscopic effects of microshear banding in plasticity of metals, Acta Mechanica, 131, 203–224, (1998).
  • 101. Planck M., Uber das Prinzip der Vermehrung der Entropie ¨ , Wied. Ann., 30, 562–582; 31, 189–203; 32, 462–503, (1887).
  • 102. Planck M., Vorlesungen ¨uber Thermodynamic, Elfte Auflage, Berlin 1964 (Erste Auflage 1897).
  • 103. Planck M., Die Einheit des Physikalishen Weltbildes, Vortrag gehalten 9.12.1908 in Leiden, Phys. Zeitschr., 10, 62–75, (1909).
  • 104. Popper K.R., The Logic of Scientific Discovery, Hutchinson Publishing Group Ltd., London. 1974.
  • 105. Rastall P., Classical thermodynamics simplified, J. Math. Phys., 11, 2955–2965, 1970.
  • 106. Rosenfield A.R., Hahn G.T., (1966), Numerical decsription of the ambient lowtemperature, and high-strain rate flow and fracture behaviour of plain carbon steel, Trans. Am. Soc. Metals, 59, 962–980.
  • 107. Seaman L., Curran D.R., Shockey D.A., Computational models for ductile and brittle fracture, J. Appl. Phys., 47, 4814–4826, 1976.
  • 108. Seeger A., The temperature dependence of the critical shear stress and of work– hardening of metal crystals, Phil. Mag., 745, 771–773, 1954.
  • 109. 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, 1955.
  • 110. Seeger A., Kristalplastizitat, Handbuch der Physik VII/2, S. Flugge [Ed.], pp.1–208, Springer-Verlag, 1958.
  • 111. Shockey D.A., Seaman L., Curran D.R., In: Metallurgical Effects at High Strain Rates, R.W. Rohde, B.M. Butcher, J.R. Holland, and C.H. Karnes [Eds.], Plenum Press, New York, p. 473, 1973.
  • 112. Shockey D.A., Seaman L., Curran D.R., The microstatistical fracture mechanics approach to dynamic fracture problem, Int. J. Fracture, 27, 145–157, 1985.
  • 113. Teodosiu C., Sidoroff F., A theory of finite elastoplasticity of single crystals, Int. J. Engng. Sci., 14, 165–176, 1976.
  • 114. Truesdell C., Rational thermodynamics, McGraw-Hill, New York, 1969.
  • 115. Truesdell C., Noll W., The Non-Linear Field Theories of Mechanics, in: Handbuch der Physik III/3, S. Flugge ˝ [Ed.], Springer-Verlag, Berlin 1965.
  • 116. Valanis K.C., Unified theory of thermodynamical behaviour of viscoplastic materials, Symp. Mech. Behav. Mater. Dyn. Loads, San Anotnio 1967, Springer, pp. 343–364, New York, 1968.
  • 117. Van der Giessen E., Micromechanical and thermodynamic aspects of the plastic spin, Int. J. Plasticity, 7, 365–386, 1991.
  • 118. Zaremba S., Sur une forme perfectionn´ee de la th´eorie de la relaxation, Bull. Int. Acad. Sci. Cracovie, 594–614, 1903.
  • 119. Zaremba S., Le principe des mouvements relatifs et les ´equations de la m´ecanique physique, Bull. Int. Acad. Sci. Cracovie, 614–621, 1903.
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