Abstract
A decrease in stiffness due to geometrical change and/or material softening caused by deformation is responsible for the occurrence of instability phenomena in engineering materials within the plastic range; i.e., beyond the yield point. Such phenomena manifest themselves in various ways; e.g., buckling, bulging, necking and shear banding. Once such instabilities are started, they tend to persist and the stiffness of the specific cross-sectional area of the specimen decreases; therefore deformation intensifies locally and eventually leads to final collapse and/or failure.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Bardet, P. (1990) Finite element analysis of plane strain bifurcation within compressible solids, Computers and Structures 36, 993–1007
Batra, R. C. and Liu De-Shin (1989) Adiabatic shear banding in plane strain problems, J. appl.Mech. 56, 527–34.
Batra, R. C. and Liu De-Shin (1990) Adiabatic shear banding in dynamic plane strain compression of a viscoplastic material, Int J. Plasticity 6, 231–46.
Batra, R. C. and Zhang, X. T. (1990) Shear band development in dynamic loading of a viscoplastic cylinder containing two voids, Acta Mech. 85, 221–34.
Batra, R. C. and Zhu, Z. G. (1991) Dynamic shear band development in a thermally softening bimetallic body containing two voids, Acta Mech. 86, 31–52.
Borst, R. de (1987) Integration of plasticity equation for singular yield functions, Computers and Structures 26, p. 823–29.
Borst, R. de (1989) Numerical methods for bifurcation analysis in geomechanics, Ing. Arch. 59, 160–74.
Boyce, M. C., Parks, D. M. and Argon, A. S. (1988) Large inelastic deformation of glassy polymers, Part I: Rate dependent constitutive model, Mech. Mat. 7, 15–33.
Boyce, M. C. and Arruda, M. (1990) An experimental and analytical investigation of the large strain compressive and tensile response of glassy polymers, Pol. Engng. Sci. 30, 1288–98.
Budiansky, B. (1959) Assessment of deformation theory, J. Appl. Mech. 26, 259–64.
Campbell, J.D., Eleiche, A.M. and Tsao, M.C.C. (1977) Fundamental Aspect of Structural Alloy Design, Plenum, New York, pp. 545.
Chater, E. and Hutchinson, J. W. (1984) On the propagation of bulges and buckles, J. appl. Mech. 51, 26977.
Christoffersen, J. and Hutchinson, J. W. (1979) A class of phenomenological corner theories of plasticity, J. Mech.Phys. Solids 27, 465–87.
Chu, C. C. (1979) Bifurcation of elastic-plastic circular cylindrical shells under internal pressure, J. Appl. Mech. 46, 889–94.
Chung, K. and Wagoner, R. (1986) Invariance of neck formation to material strength and strain rate for power-law -materials, Metall Trans. A17, 1632–3.
Dafalias, J.F. (1983) Co-rotational rates for kinematic hardening at large plastic of formations, J Appl. Mech. 50, 561–5.
Dafalias, J.F. and Aifantis, E.C. (1990) On the macroscopic origin of the plastic spin, Acta Mech. 82, 31–48.
Dubey, R. N. (1970) Variational method for non conservation problems, J. Appl. Mech. 37, 133–6.
Gotoh, M. (1985) A class of plastic constitutive equation with vertex effect–I, Int J. Solids and Structures 21, 1101–16.
Gurson, A.L. (1977) Continuum theory of ductile rupture by void nucleation and growth, Part 1–Yield criteria and flow rules for porous ductile media, J. Eng. Mat. Tech. 99, p. 2–15.
G’Sell, G. and Jonas, C. (1979) Determination of the plastic behaviour of solid polymers at constant true strain rate, J. Mater. Sci. 14, 583–91.
Hill, R (1958) A general theory of uniqueness and stability in elastic-plastic solids, J. Mech. Phys. Solids 8, 236–49.
Hill, R. (1962a) Acceleration waves in solids, J. Mech. Phys. Solids 10, 1–16.
Hill, R. (1962b) Uniqueness criteria and extremum principles in self-adjoin problems of continuum-mechanics, J. Mech. Phys. Solids 10, 185–94.
Hill, R and Hutchinson, J.W. (1975) Bifurcation phenomena in the plane tension test, J. Mech. Phys. Solids 23, 236–64.
Hughes, T. J. R. and Winget, J. (1980) Finite rotation effects in numerical integration of rate constitutive equations arising in large deformation analysis, Int. J. Num. Meth. Engng. 15, 1862–7.
Hutchinson, J.W. (1973a) Post bifurcation behaviour in the plastic range, J. Mech. Phys. Solids 21, 163–90.
Hutchinson, J.W. (1973b) Finite strain analysis of elasto-plastic solids and structures, in Numerical Solution of Nonlinear Structural Problems, Hartung, RF. ( Ed. ), ASME, pp. 17–29.
Hutchinson, J. W. and Neale, K.W. (1973) Sheet necking. II. Time independent behaviour, in Mechanics and Sheet Metal Forming, Koistinen, D.P. and Wang, N.M. ( Eds ), Plennum Press, pp. 127–53.
Hutchinson, J. W. and Neale, K. W. (1983) Neck propagation, J. Mech. Phys. Solids 31, 405–26.
Kim, K. H. and Anand, L. (1987) A note on adiabatic flow localization in visco-plastic solids, in: Computational Methods for Predicting Material Processing Defects, M. Predeanu (ed.), Elsevier, London, pp. 181–92.
Kitagawa, H. and Matsushita, H. (1987) Flow localization in elastic-plastic material developing from stress-free surface, Int. J. Solids Structures 23, 351–68.
Kitagawa, H., Seguchi, Y. and Tornita, Y. (1972) An incremental theory of large strain and large displacement problems and its finite element application, Ing. Arch. 41, 213–24.
Krieg, R D. and Krieg, D. B. (1977) Accuracies of numerical solution method for the elastic-perfectly plastic model, Trans ASME, J. Pressure Vessel Tech. 99, 510–15.
Lamson, M., Needleman, A., Tvergaard, V. and Storakers, B. (1982) Instability and failure of internally pressurized ductile metal cylinder, J. Mech. Phys. Solids 30, 121–54.
Lemonds, J. and Needleman, A. (1986a) Finite element analyses of shear localization in rate and temperature dependent solids, Mech. Materials 5 339–61.
Lemonds, J. and Needleman, A. (1986b) An analysis of shear band development incorporating heat conduction, Mech. Materials 5, 363–73.
Leroy, Y.M. and Ortiz, M. (1989) Finite element analyses of strain localization in frictional materials, Int. J. Num. Anal. Mech. Geomech. 13, 53–74
Leroy, Y.M. and Ortiz, M. (1990) Finite element analysis of transient strain localization phenomena in frictional solids, Int J. Num. Anal. Meth. Geomech. 13, 53–74.
Leroy, Y.M. and Chapuis, O. (1991) Localization in strain-rate-dependent solids, Comp. Meth. Appl. Mech. Engng. 90, 969–86.
Loret, B. (1983) On the effects of plastic rotation in finite deformation of anisotropic elastplastic materials, Mech. Materials 2, 287–304
Minura, K. and Tornita, Y. (1991) Constitutive relations of mold steel and alpha-titanium at high rates under multiaxial loading condition, Journal de Physique IV, DYMAT 91, Les editions de Physique, France, 813–20.
Nagtegaarl, J.C. and de Jong, J.E. (1981) Some computational aspects of elastic-plastic large strain analysis, Int J. Num Meth. Eng. 17, 15.
Neale, K.W. (1980) Phenomenotogical constitutive laws in finite plasticity, SM arch 6, 79–128.
Needleman, A. (1989) Dynamic shear band development in plane strain, J. appl. Mech. 56, 1–9.
Needleman, A. and Ortiz, M. (1991) Effects of boundaries and interfaces on shear band localization, Int. J. Solid Structures 28, 859–77.
Needleman, A. and Rice, J. R. (1978) Limits to ductility set by plastic flow localization, in: Mechanics of Sheet Metal Forming, Koistinen, D. P. and Wang, N -M. (Eds.), Plenum Press, New York, pp. 23767.
Needleman, A. and Tvergaard, V. (1977) Necking of biaxially stretched elastic plastic circular plates, J. Mech. Phys. Solids 25, 159.
Nemat-Nasser, S. (1988) Micromechanics of failure at high strain rate: Theory, experiments, and computations, Computer and Structures 30, 95–104.
Nemat-Nasser, S., Chung, D. T. and Taylor, L.M. (1989). Phenomonological modelling of rate-dependent plasticity for high strain rate problems, Mech. Materials 7, 319–44.
Nemat-Nasser, S. and Li, Y.F. (1992) A new explicit algorithm for finite-deformation elastoplasticity and elastoviscoplasticity: Performance evaluation, Computers and Structures 44, 937–63.
Ortiz, M. and Popov, E.P. (1985) Accuracy and stability of integration algorithms for elastoplastic constitutive relations, Int. J. Num. Mech. Eng. 21, pp. 1561–76.
Ortiz, M. and Simo, J. C. (1986) An analysis of a new class of integration algorithms for elasto plastic constitutive relation, Int. J. Numerical Meth Eng. 23, p. 353–66.
Peirce, D., Shih, C.F. and Needleman, A (1984) A tangent modulus method for rate dependent solids, Computers and Structures 18, 875.
Raniecki, B. (1979) Uniqueness criteria in solids with non-associated plastic flow laws at finite deformations, Bull. Acad. Pol. Ser. Sci. Tech. 27, 7219.
Raniecki, B. and Bnmhs, O. (1981) Bounds to bifurcation stresses in solids with non-associated plastic flow law at finite strain, J. Mech. Phys. Solids 29, 153–72.
Rashid, M.M. and Nemat-Nasser, S. (1992). A constitutive algorithm for rate dependent plasticity, Comp. Mech Appl. Mech. Eng. 94, 201–28.
Reddy, B. D. (1982) A deformation-theory analysis of the bifurcation of pressurized thick-walled cylinders, Q. J. Mech. Appl. Math. 35, 183–96.
Rice, J.R (1976) The localization of plastic deformation, Proc. 14` h IUTAM congress, Koiter, W. (ed.), North Holland, Amsterdam, 207–20.
Rice, J.R. and Tracey, D.M. (1973) Numerical and Computational Methods in Structural Mechanics,Academic press, pp. 585.
Rudnicki, J.W. and Rice, J.R. (1975) Conditions for the localization of deformation in pressure, sensitive dilutant materials, J. Mech. Phys. Solids 23, p. 371–94.
Runneson, K., Samuelsson, A. and Bemspang, L. (1986) Numerical Technique in plasticity including solution advancement control, Int. J. Num. Math. Engng 22, 769–88.
Runneson, K., Sture, S. and William, K. (1988) Integration in computational plasticity, Computers and Structures 30, 119–30.
Sewell, M.J. (1967) On configuration dependent loading, Arch. Rate Mech. Anal. 23, 327–51.
Simo, J.C., Kennedy, J.G. and Govindjee, S. (1988) Nonsmooth multi-surface plasticity and viscoplasticity. Loading /unloading conditions and numerical algorithms, Int. J. Num Mech. Eng. 26, 2161–85.
Simo, J.C. and Ortiz, M. (1985) A unified approach to finite deformation elastoplastic analysis based on the use of hyper elastic constitutive equations, Corn. Meth. Appl. Mech. Engng 49, pp. 221–45.
Simo, J.C. and Taylor, R.L. (1985) Consistant tangent operators for rate -independent elastoplasticity, Comp. Meth. Appl. Mech. Eng. 48, 101–18.
Stören, S. and Rice, J.R. (1975) Localized necking in thin sheets, J. Mech. Phys. Solids 23, 221–41.
Timoshenko, S. P. and Gere, J. M. (1961) Theory of Elastic Stability, 2“d Edition, McGraw-Hill, New York.
Taylor, G.I. and Quinney, H. (1934) The latent energy remaining in a metal after cold working, Proc. Roy Soc. London A 143, p. 307.
Tornita, Y. (1994) Simulations of plastic instabilities in solid mechanics, Appl. Mech. Rev. 47(6), Part 1, 171205.
Tornita, Y. and Hayashi, K. (1991) Deformation behaviour in elasto-viscoplastic polymeric bars under tension, Proc. Int. Symp. on Plasticity and its Current Applications, Grenoble, France, Boehler, J. P. and Khan, A.S. ( Eds ), Elsevier, pp. 524–27.
Tornita, Y. and Hayashi, K. (1993) Thermo-elasto-viscoplastic deformation of polymeric bars under tension, Int. J. Solids Structures 30 (2), 225–35.
Tornita, Y. and Higo, T. (1993) Plane-strain flow localization in tension and compression of thermo-elastoviscoplatic blocks under high rates of deformation, Int. J. Mech. Sci. 35, 985–94.
Tomita, Y. and Nakao, T. (1991) Flow localization of elasto-viscoplastic tension blocks, Proc. ICM6, Jono, M. and Inoue, T. (Eds.), Pergamon Press, New York, pp. 1997–2002.
Tomita, Y., Mimura, K. and Sasayama, T. (1993) Effects of intermediate process annealing on surface roughening and forming limit in polycrystalline thin sheet metal subjected to tension, MECAMAT’91, Large plastic deformations, Teodosiu, C., Raphanel, J. L. and Sidoroff, F. (Eds.), Balkema, Rotterdam, pp. 177–83.
Tornita, Y. and Nakao, T. (1992) Shear localization in thermo-elasto-viscoplastic plane strain block, Proc. IU TAM Symposium, Finite Inelastic Deformations, Theory and Application, Besdo, D. and Stein, E. ( Eds ), Springer-Verlag, 179–88.
Tornita, Y. and Shindo, A. (1982) On the bifurcation and post-bifurcation behaviour of thick circular tubes under lateral pressure, Comp. Meth. Appl. Mech. Engng. 35, 207–19.
Tornita, Y. and Shindo, A. (1985) Bifurcation behaviour of thin square elastic-plastic orthotropic plates subjected to diagonal tension, Proc. Considere Memorial Symposium, Salencon, J. ( ed. ), Ecole Nationale des Ponts et Chaussés, pp. 203–13.
Tornita, Y. and Shindo, A (1990) Wrinkling behaviour in thin-walled bodies during plastic forming, computational plasticity, Inoue, T., Kitagawa, H. and Shima, S. (Eds), CJMR7, Elsevier, pp. 165–78.
Tornita, Y., Shindo, A., Kim, Y. S. and Michiura, K. (1986). Deformation behaviour of elastic plastic tubes under external pressure and axial load, Int. J. Mech. Sci. 28, 263–74.
Tornita, Y., Shindo, A., and Kitagawa, H. (1981) Bifurcation and post bifurcation behaviour of internally pressurized elastic-plastic circular tubes under plane strain conditions, Int. J. Mech. Sci. 23, 723–32.
Tornita, Y., Shindo, A. and Nagai, M. (1984). Axisynunetric deformation of circular elastic-plastic tubes under axial tension and internal pressure, Int. J. Mech. Sci. 26, 437–44.
Tornita, Y., Shindo, A. and Sasayama, T. (1990) Plane strain tension of thermoelastic viscoplastic blocks, Int. J. Mech. Sci 32, 613–22.
Triantafyllidis, N. (1985) Puckering instability phenomena in the hemispherical cup test, J. Mech. Phys. Solids 33, 117–39.
Tugcu, P. and Neale, K. W. (1987) Analysis of plane-strain neck propagation in viscoelastic polymeric films, Int. J. Mech. Sci. 29, 793–805.
Tugcu, P. and Neale, K. W. (1988) Analysis of neck propagation in polymeric fibers including the effects of viscoplasticity, J. Engng. Mat. Tech. 110, 395–400.
Tugcu, P. and Neale, K. W. (1990) Cold drawing of polymers with rate and temperature dependent properties, Int. J. Mech. Sci. 32, 405–16.
Tugcu, P., Neale, K. W., Marques-Lucerno, A. (1991) Effect of deformation induced heating on the cold drawing of polymeric films, J. Engng. Mat. Tech. 113, 104–11.
Tvergaard, V. (1978) Effects of kinematic hardening on localization necking in biaxially stretched sheets, Int. J. Mech. Sci. 20, 651–58.
Tvergaard, V. (1981) Influence of voids on shear band instabilities under plane strain localization, Int. J. Fracture 171, p. 389–437.
Tvergaard, V. (1982) Influence of void nucleation on ductile shear fracture at a free surface, J. Mech. Phys. Solids 30, 399–425.
Tvergaard, V. (1987) Effect of yield surface curvature and void nucleation on plan flow localization, J. Mech. Phys. Solids 35, p. 43–60.
Wright, T. W. and Walter, J. W. (1987) On stress collapse in adiabatic shear bands, J. Mech. Phys. Solids 35, 701–20.
Yamada, Y., Yoshimura, N. and Sakurai, T. (1968) Plastic stress stain matrix and its application for the solution of elastic-plastic problems by finite element method, Int. J. Mech. Sci. 10, 343–54.
Zbib, H. M. and Jubran, J. S. (1992) Dynamic Shearbanding: A three-element analysis, Int. J. Platicity 8, 619–41.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2000 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
Haddad, Y.M. (2000). Plastic Instability and Localization Effects. In: Mechanical Behaviour of Engineering Materials. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-2231-5_3
Download citation
DOI: https://doi.org/10.1007/978-94-017-2231-5_3
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-5473-9
Online ISBN: 978-94-017-2231-5
eBook Packages: Springer Book Archive