Localization of plastic deformations as a result of wave interaction

• Autorzy: Glema A. , Łodygowski T. , Perzyna P.
• Języki publikacji: EN

Abstrakty

EN

The main objective of the paper is the investigation of the interaction and reflection of elastic-viscoplastic waves which can lead to localization phenomena in solids. The rate type constitutive structure for an elastic-viscoplastic material with thermomechanical coupling is used. An adiabatic inelastic flow process is considered. Discussion of some features of rate dependent plastic medium is presented. This medium has dissipative and dispersive properties. In the evolution problem considered in such dissipative and dispersive medium the stress and deformation due to wave reflections and interactions are not uniformly distributed, and this kind of heterogeneity can lead to strain localization in the absence of geometrical or material imperfections. Numerical examples are presented for a 2D specimens subjected to tension, with the controlled displacements imposed at one side with different velocities. The initial-boundary conditions which are considered reflect the asymmetric (single side) tension of the specimen with the opposite side fixed, which leads to non-symmetric deformation. The influence of the constitutive parameter (relaxation time of mechanical perturbances) is also studied in the examples. The attention is focused on the investigation of the interactions and reflections of waves and on the location of localization of plastic deformations.

Słowa kluczowe

EN

plastic deformation; ware propagation

PL

deformacja plastyczna; propagacja fali

• Wydawca: Instytut Podstawowych Problemów Techniki PAN
• Czasopismo: Computer Assisted Mechanics and Engineering Sciences
• Rocznik: 2003
• Tom: Vol. 10, No. 1
• Strony: 81--91
• Opis fizyczny: Bibliogr. 37 poz., rys., wykr

Twórcy

autor

Glema A.

• Politechnika Poznańska, Instytut Konstrukcji Budowlanych, ul. Piotrowo 5, 61-138 Poznań

autor

Łodygowski T.

• Politechnika Poznańska, Instytut Konstrukcji Budowlanych, ul. Piotrowo 5, 61-138 Poznań

autor

Perzyna P.

• Polska Akademia Nauk, IPPT, ul. Świętokrzyska 21, 00-049 Warsaw, Poland

Bibliografia

• [1] M.A. Dowaikh, R.W. Ogden. Interfacial waves and deformations in pre-stressed elastic media. Proc. R. Soc. Land., A433: 313-328, 1991.
• [2] M.K. Duszek-Perzyna, P. Perzyna. Analysis of the influence of different effects on criteria for adiabatic shear band localization in inelastic solids. Material Instabilities: Theory and Applications, AMD-Vol. 183 / MD-Vol. 50, ASME, 59-85, 1994.
• [3] M.K. Duszek-Perzyna, P. Perzyna. Acceleration waves in analysis of adiabatic shear band localization. In: J.L. Wegner, F.R. Norwood, eds., Nonlinear Waves in Solids, Proc. IUTAM Symposium, August 15-20, 1993, Victoria, Canada, pp. 128-135. ASME, 1995.
• [4] M.K. Duszek-Perzyna, P. Perzyna. Analysis of anisotropy and plastic spin effects on localization phenomena. Archive of Applied Mechanics, 68: 352-374, 1998.
• [5] A. Glema, W. Kąkol, T.Łodygowski. Numerical modelling of adiabatic shear band formation in a twisting test. Engineering Transactions, 45(3-4): 419-431, 1997.
• [6] A. Glema, T. Łodygowski, P. Perzyna. Interaction of deformation waves and localization phenomena in inelastic solids. Int. Journ. Camp. Appl. Mech. Eng., 183: 123-140, 2000.
• [7] J. Hadamard. Lecons sur la Propagation des Ondes et les Equations de l'Hydrodynamique, Chap. 6. Paris, 1903.
• [8] R. Hill. Acceleration wave in solids. J. Mech. Phys. Solids 10: 1-16, 1962.
• [9] T. Łodygowski. On avoiding of spurious mesh sensitivity in numerical analysis of plastic strain localization. GAMES, 2: 231-248, 1995.
• [10] T. Łodygowski, M. Lengnick, P. Perzyna, E. Stein. Viscoplastic numerical analysis of dynamic plastic strain localization for a ductile material. Archives of Mechanics, 46: 1-25, 1994.
• [11] T. Łodygowski, P. Perzyna. Numerical modelling of localized fracture of inelastic solids in dynamic loading processes. Int. J. Num. Meth. Engng., 40: 4137-4158, 1997.
• [12] T. Łodygowski, P. Perzyna. Localized fracture in inelastic polycrystalline solids under dynamic loading processes. Int. J. Damage Mechanics, 6: 364-407, 1997.
• [13] J. Mandel. Conditions de stabilite et postulat de Drucker. In: J. Kravchenko, P.M. Sirieys, eds., Rheology and Soil Mechanics, pp. 58-68. Springer, New York, 1966.
• [14] A. Needleman. Material rate dependence and mesh sensitivity in localization problems. Computer Meths. Appl. Mechs. Eng., 67: 69-85, 1988.
• [15] A. Needleman. Dynamic shear band development in plane strain. J. Appl. Mech., 56: 1-9, 1989.
• [16] A. Needleman, M. Ortiz. Effects of boundaries and interfaces on shear-band localization. Int. J. Solids Structures, 28: 859-877, 1991.
• [17] J.A. Nemes, J. Eftis. Constitutive modelling on the dynamic fracture of smooth tensile bars. Int. J. Plasticity,
• 9: 243-270, 1993.
• [18] R.W. Ogden. Nonlinear effects associated with waves in pre-stressed elastic solids near bifurcation points. In: J.L. Wegner, F.R. Norwood, eds., Nonlinear Waves in Solids, Proc. IUTAM Symposium, August 15-20, 1993, Victoria, Canada, pp. 109-113. ASME, 1995.
• [19] N.S. Ottosen, K. Runesson. Acceleration waves in elasto-plasticity. Int. J. Solids Structures, 28: 135-159, 1991.
• [20] P. Perzyna. The constitutive equations for rate sensitive plastic materials. Quart. Appl. Math., 20: 321-332, 1963.
• [21] P. Perzyna. Thermodynamic theory of viscoplasticity. Advances in Applied Mechanics, 11: 313-354, 1971.
• [22] P. Perzyna. Adiabatic shear band localization fracture of solids in dynamic loading processes. In J. Harding, ed., Proc. of Int. Conference on Mechanical and Physical Behaviour of Materials under Dynamic Loading, Oxford, September 26-30, 1994, pp. 441-446. Les Editions de Physique Le Ulis 1994, 1994.
• [23] P. Perzyna. Instability phenomena and adiabatic shear band localization in thermoplastic flow processes. Acta Mechanica, 106: 173-205, 1994.
• [24] P. Perzyna. Interactions of elastic-viscoplastic waves and localization phenomena in solids. In: J.L. Wegner, F.R. Norwood, eds., Nonlinear Waves in Solids, Proc. IUTAM Symposium, August 15-20, 1993, Victoria, Canada, pp. 114-121. ASME, 1995.
• [25] P. Perzyna, M.K. Duszek-Perzyna. Phenomenological modelling of adiabatic shear band localization fracture of solids in dynamic loading processes. In: M.H. Aliabadi, A. Carpinteri, S. Kalisky, D.J. Cartwright, eds., Localized Damage III; Computer-Aided Assessment and Control, pp. 579-588. Computational Mechanics Publications, Southampton, 1994.
• [26] J.H. Prevost, B. Loret. Dynamic strain localization in elasto- (visco- )plastic solids, II. Plane strain examples. Computer Meths. Appl. Mechs. Eng., 83: 247-294, 1990.
• [27] J.R. Rice. The localization of plastic deformation. In: W.T. Koiter, ed., Theoretical and Applied Mechanics , pp. 207-220. North-Holland, 1976.
• [28] H.C. Simpson, S.J. Spector. On the positivity and the second variation in finite elasticity. Arch. Rat. Mech. Anal., 32: 369-399, 1989.
• [29] L.J. Sluys. Wave Propagation, Localization and Dispersion in Softening Solids, Doctoral Thesis. Delft University Press, Delft, 1992.
• [30] L.J. Sluys, J. Bolek, R. de Borst. Wave propagation and localization in viscoplastic media. In: D.R.J. Owen, E. Onate, E. Hinton, eds., Proc. Third Inter. Conference on Computational Plasticity, Fundamentals and Applications, Barcelona, April 6-10, 1992, pp. 539-550. Pineridge Press, Swansea 1992, 1992.
• [31] Z. Suo, M. Ortiz, A. Needleman. Stability of solids with interfaces. J. Mech. Phys. Solids, 40: 613-640, 1992.
• [32] S.A. Thau. Linear dispersive waves. In: S. Leibovich, A.R. Seebass, eds., Nonlinear Waves, pp. 44-81. Cornell University Press, Ithaca, 1974.
• [33] T.Y. Thomas. Plastic Flow and Fracture of Solids. Academic Press, New York, 1961.
• [34] C. Truesdell. General and exact theory of waves in finite elastic strain. Arch. Rat. Mech. Anal., 19: 263-296, 1965.
• [35] W.M. Wang. Stationary and Propagative Instabilities in Metals - A Computational Point of View, Doctoral Thesis. Delft University Press, Delft, 1997.
• [36] W.M. Wang, L.J . Sluys, R. de Borst. Interaction between material length scale and imperfection size for localization phenomena in viscoplastic media. European J. Mechanics, 15: 447-464, 1996.
• [37] G.B. Whitham. Linear and Nonlinear Waves. John Wiley, New York, 1974.