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Numerical Simulations of Thermo-Viscoplastic Flow Processes under Cyclic Dynamic Loadings

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Inelastic Analysis of Structures under Variable Loads

Part of the book series: Solid Mechanics and Its Applications ((SMIA,volume 83))

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Abstract

The main objective of the paper is the description of the behaviour and fatigue damage of inelastic solids in plastic flow processes under dynamic cyclic loadings.

A general constitutive model of elasto-viscoplastic damaged polycrystalline solids is developed within the thermodynamic framework of the rate type covariance structure with a finite set of the internal state variables. A set of the internal state variables is assumed and interpreted such that the theory developed takes account of the effects as follows: (i) plastic non-normality; (ii) plastic strain induced anisotropy (kinematic hardening); (iii) softening generated by microdamage mechanisms; (iv) thermomechanical coupling (thermal plastic softening and thermal expansion); (v) rate sensitivity.

To describe suitably the time and temperature dependent effects observed experimentally and the accumulation of the plastic deformation and damage during dynamic cyclic loading process the kinetics of microdamage and the kinematic hardening law have been modified. The relaxation time is used as a regularization parameter. The viscoplastic regularization procedure assures the stable integration algorithm by using the finite difference method. Particular attention is focused on the well-posedness of the evolution problem (the initial-boundary value problem) as well as on its numerical solutions. Convergence, consistency, and stability of the discretised problem are discussed. The Lax-Richtmyer equivalence theorem is formulated and conditions under which this theory is valid are examined. Utilizing the finite difference method for regularized elasto-viscoplastic model, the numerical investigation of the three-dimensional dynamic adiabatic deformation in a particular body under cyclic loading condition is presented. Particular examples have been considered, namely a dynamic, adiabatic and isothermal, cyclic loading processes for a smooth cylindrical tensile bar. The problem is assumed as axisymmetrical. The accumulation of damage and equivalent plastic deformation on each considered cycle has been obtained. It has been found that this accumulation of microdamage distinctly depends on the wave shape of the assumed loading cycle.

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References

  1. Abraham, R., Marsden, J.E. and Ratiu, T. (1988) Manifolds, Tensor Analysis and Applications, Springer, Berlin.

    Book  MATH  Google Scholar 

  2. Agah-Tehrani, A., Lee, E.H., Malett, R.L. and Onat, E.T. (1987) The theory of elastic-plastic deformation at finite strain with induced anisotropy modelled isotropic-kinematic hardening, J. Mech. Phys. Solids 35, 43–60.

    Article  Google Scholar 

  3. Armstrong, P.J. and Frederick, C.O. (1966) A mathematical representation of the multiaxial Baushinger effect, CEGB Report RD/B/N731, Central Electricity Generating Board.

    Google Scholar 

  4. Auricchio, F. and Taylor, R.L. (1995) Two material models for cyclic plasticity models: Nonlinear kinematic hardening and generalized plasticity, Int. J. Plasticity 11, 65–98.

    Article  MATH  Google Scholar 

  5. Auricchio, F., Taylor, R.L. and Lubliner, J. (1992) Application of a return map algorithm to plasticity models, in D.R.J. Owen and E. Onate (eds.), COMPLAS Computational Plasticity: Fundamentals and Applications, Barcelona, pp. 2229–2248.

    Google Scholar 

  6. Chaboche, J.L. (1986) Time - independent constitutive theories for cyclic plasticity, Int. J. Plasticity 2, 149–188.

    Article  MATH  Google Scholar 

  7. Coleman, B.D. and Noll, W. (1963) The thermodynamics of elastic materials with heat conduction and viscosity, Arch. Rational Mech. Anal. 13, 167–178.

    Article  MathSciNet  MATH  Google Scholar 

  8. Curran, D.R., Seaman, L. and Shockey, D.A. (1987) Dynamic failure of solids, Physics Reports 147, 253–388.

    Article  Google Scholar 

  9. Dafalias, Y.F. and Popov, E.P. (1976) Plastic internal variable formalism of cyclic plasticity, J. Appl Mech. 43, 645–651.

    Article  MATH  Google Scholar 

  10. Dautray, R. and Lions, J.-L. (1993) Mathematical Analysis and Numerical Methods for Science and Technology, Vol. 6. Evolution Problems I I, Springer, Berlin.

    Book  Google Scholar 

  11. Dornowski, W. (1998) The influence of finite deformation on the mechanism of microdamage in structural metals, Biuletyn WAT (in print).

    Google Scholar 

  12. Duszek, M.K. and Perzyna, P. (1991a) On combined isotropic and kinematic hardening effects in plastic flow processes, Int. J. Plasticity 7, 351–363.

    Article  MATH  Google Scholar 

  13. Duszek, M.K. and Perzyna, P. (1991b) The localization of plastic deformation in thermoplastic solids, Int. J. Solids Structures 27, 1419–1443.

    Article  MATH  Google Scholar 

  14. Duszek-Perzyna, M.K. and Perzyna, P. (1994) Analysis of the influence of different effects on criteria for adiabatic shear band localization in inelastic solids, in R.C. Batra and H.M. Zbib (eds.), Material Instabilities: Theory and Applications, ASME Congress, Chicago, 9–11 November 1994, AMD-Vol. 183/MD-Vol.50, ASME, New York, pp. 59–85.

    Google Scholar 

  15. Gustafsson, B., Kreiss, H.O. and Oliger, J. (1995) Time Dependent Problems and Difference Methods, John Wiley, New York.

    MATH  Google Scholar 

  16. Hughes T.J.R., Kato T. and Marsden J.E. (1977) Well-posed quasilinear second order hyperbolic system with application to nonlinear elastodynamics and general relativity, Arch. Rat. Mech. Anal. 63, 273–294.

    Article  MathSciNet  MATH  Google Scholar 

  17. Ionescu, I.R. and Sofonea, M. (1993) Functional and Numerical Methods in Viscoplasticity, Oxford.

    Google Scholar 

  18. Johnson, J.N. (1981) Dynamic fracture and spallation in ductile solids, J. Appl. Phys. 52, 2812–2825.

    Article  Google Scholar 

  19. Lodygowski, T. and Perzyna, P. (1997) Localized fracture of inelastic poly crystalline solids under dynamic loading processes, Int. J. Damage Mechanics 6, 364–407.

    Article  Google Scholar 

  20. Marsden, J.E. and Hughes, T.J.R. (1983) Mathematical Foundations of Elasticity, Prentice-Hall, Englewood Cliffs, New York.

    MATH  Google Scholar 

  21. Mróz, Z. (1967) On the description of anisotropic workhardening, J. Mech. Phys. Solids 15, 163–175.

    Article  Google Scholar 

  22. Nemes, J. A. and Eftis, J. (1993) Constitutive modelling on the dynamic fracture of smooth tensile bars, Int. J. Plasticity 9, 243–270.

    Article  MATH  Google Scholar 

  23. Oldroyd, J. (1950) On the formulation of rheological equations of state, Proc. Roy. Soc. (London) A 200, 523–541.

    Google Scholar 

  24. Perzyna, P. (1963) The constitutive equations for rate sensitive plastic materials, Quart Appl. Math., 20, 321–332.

    MathSciNet  MATH  Google Scholar 

  25. Perzyna, P. (1971) Thermodynamic theory of viscoplasticity, Advances in Applied Mechanics 11, 313–354.

    Article  Google Scholar 

  26. Perzyna, P. (1984) Constitutive modelling of dissipative solids for postcritical behaviour and fracture, ASME J. Eng. Materials and Technology 106, 410–419.

    Article  Google Scholar 

  27. Perzyna, P. (1986a) Internal state variable description of dynamic fracture of ductile solids, Int. J. Solids Structures 22, 797–818.

    Article  Google Scholar 

  28. Perzyna, P. (1986b) Constitutive modelling for brittle dynamic fracture in dissipative solids, Arch. Mechanics 38, 725–738.

    MathSciNet  MATH  Google Scholar 

  29. Perzyna, P. (1995) Interactions of elastic-viscoplastic waves and localization phenomena in solids, in L.J. Wegner and F.R. Norwood (eds.), Nonlinear Waves in Solids, Proc. IUTAM Symposium, August 15–20, 1993, Victoria, Canada, ASME Book No AMR 137, pp. 114–121.

    Google Scholar 

  30. Perzyna, P. and Drabik, A. (1989) Description of micro-damage process by porosity parameter for nonlinear viscoplasticity, Arch. Mechanics 41, 895–908.

    Google Scholar 

  31. Perzyna, P. and Drabik, A. (1999) Micro-damage mechanism in adiabatic processes, Int. J. Plasticity (submitted for publication).

    Google Scholar 

  32. Prager, W. (1955) The theory of plasticity: A survey of recent achievements, (J. Clayton Lecture), Proc. Inst. Mech. Eng. 169, 41–57.

    Article  MathSciNet  Google Scholar 

  33. Richtmyer, R.D. (1978) Principles of Advance Mathematical Physics, Vol. I, Springer, New York.

    Google Scholar 

  34. Richtmyer, R.D. and Morton, K.W. (1967) Difference Methods for Initial-Value Problems, John Wiley, New York.

    MATH  Google Scholar 

  35. Ristinmaa, M. (1995) Cyclic plasticity model using one yield surface only, Int. J. Plasticity 11, 163–181.

    Article  MATH  Google Scholar 

  36. Shima, S. and Oyane, M. (1976) Plasticity for porous solids, Int. J. Mech. Sci. 18, 285–291.

    Article  Google Scholar 

  37. Shockey, D.A., Seaman, L. and Curran, D.R. (1985) The microstatistical fracture mechanics approach to dynamic fracture problem, Int. J. Fracture 27, 145–157.

    Article  Google Scholar 

  38. Sidey, D. and Coffin, L.F. (1979) Low-cycle fatigue damage mechemism at high temperature, in J.T. Fong (ed.), Fatigue Mechanism, Proc. ASTM STP 675 Symposium, Kansas City, Mo., May 1978, Baltimore, pp. 528–568.

    Google Scholar 

  39. Strang, G. and Fix, G.J. (1973) An Analysis of the Finite Element Method, Prentice-Hall, Englewood Cliffs.

    MATH  Google Scholar 

  40. Truesdell C. and Noll W. (1965) The nonlinear field theories, Handbuch der Physik, Band III/3, Springer, Berlin, pp. 1–579.

    Google Scholar 

  41. Van der Giessen, E. (1989) Continuum models of large deformation plasticity, Part I: Large deformation plasticity and the concept of a natural reference state, Eur. J. Mech., A/Solids 8, 15.

    MATH  Google Scholar 

  42. Van der Giessen, E. (1989) Continuum models of large deformation plasticity, Part II: A kinematic hardening model and the concept of a plastically induced orientational structure, Eur. J. Mech., A/Solids 8, 89.

    MATH  Google Scholar 

  43. Wang, J.-D. and Ohno, N. (1991) Two equivalent forms of nonlinear kinematic hardening: application to nonisothermal plasticity, Int. J. Plasticity 7, 637–650.

    Article  Google Scholar 

  44. Ziegler, H. (1959) A modification of Prager’s hardening rule, Quart. Appl. Math. 17, 55–65.

    MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Military University of Technology, Kaliskiego 2, 01-489, Warsaw, Poland

    W. Dornowski

  2. Institute of Fundamental Technological Research, Polish Academy of Sciences, Świętokrzyska 21, 00-049, Warsaw, Poland

    P. Perzyna

Authors
  1. W. Dornowski
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  2. P. Perzyna
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Editors and Affiliations

  1. Institut für allgemeine Mechanik, Rheinisch-Westfälische Technische Hochschule Aachen, Germany

    Dieter Weichert

  2. Department of Structural Engineering, Technical University (Politecnico) of Milan, Italy

    Giulio Maier

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© 2000 Kluwer Academic Publishers

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Dornowski, W., Perzyna, P. (2000). Numerical Simulations of Thermo-Viscoplastic Flow Processes under Cyclic Dynamic Loadings. In: Weichert, D., Maier, G. (eds) Inelastic Analysis of Structures under Variable Loads. Solid Mechanics and Its Applications, vol 83. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-9421-4_5

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  • DOI: https://doi.org/10.1007/978-94-010-9421-4_5

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-1-4020-0382-0

  • Online ISBN: 978-94-010-9421-4

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