Instability analysis and shear band spacing in gradient-dependent thermoviscoplastic materials with finite speeds of thermal waves

• Autorzy: Batra R. C. , Chen L.
• Języki publikacji: EN

Abstrakty

EN

We analyze the stability of a homogeneous solution of coupled nonlinear equations governing simple shearing deformations of a strain-rate gradient-dependent thermoviscoplastic body in which thermal disturbances propagate at a finite speed. The homogeneous solution is perturbed by an infinitesimal amount and equations linear in the perturbation variables are derived. Conditions for these perturbations to grow are deduced. The shear band spacing, ... , is defined as ... where ... is the wave number of the perturbation introduced at time ... that has the maximum growth rate at time .... It is found that the thermal relaxation time (i.e. the ratio of the coefficient of the second time-derivative of the temperature in the heat equation to that of the first time-derivative) significantly affects the shear band spacing and the value of ... for which ... is maximum.

Słowa kluczowe

EN

material characteristic length; strain-rate gradient; thermal relaxation time; dominant growth rate

PL

wymiar charakterystyczny materiału; gradient prędkości odkształcenia; czas relaksacji; dominująca prędkość wzrostu

• Wydawca: Instytut Podstawowych Problemów Techniki PAN
• Czasopismo: Archives of Mechanics
• Rocznik: 2001
• Tom: Vol. 53, nr 2
• Strony: 167--192
• Opis fizyczny: Bibliogr. 30 poz., rys.

Twórcy

autor

Batra R. C.

• Department of Engineering Science and Mechanics (MC 0219), Virginia Polytechnic Institute and State University, Blacksburg, VA 24061, USA

autor

Chen L.

• Department of Engineering Science and Mechanics (MC 0219), Virginia Polytechnic Institute and State University, Blacksburg, VA 24061, USA

Bibliografia

• 1. R. ARMSTRONG, R. C. BATRA, M. A. MEYERS, T. W. WRIGHT [Eds.], Shear instabilities and viscoplasticity theories, Special issue of Mech. Mater., 17, 83-328, 1994.
• 2. Y. J. BAI, Thermo-plastic instability in simple shear, J. Mech. Physics of Solids, 30, 195-207, 1982.
• 3. Y. L. BAI, B. DODD, Adiabatic shear localization: occurrence, theories and applications, Pergamon, Oxford 1992.
• 4. R. C. BATRA, On heat conduction and wave propagation in non-simple rigid solids, Letters in Appl. and Engng. Sci., 3, 997-107, 1975.
• 5. R. C. BATRA, C. H. KIM, Effect of material characteristic length on the initiation, growth and band width of adiabatic shear bands in dipolar materials, J. Physique, 49, C3, 41-46. 1988.
• 6. R. C. BATRA, C. H. KIM, Analysis of shear bands in twelve materials, Int. J. Plasticity, 8, 425-452, 1992.
• 7. R. C. BATRA, Numerical solution of initial-boundary-value problems with shear strain localization, [In:] Localization and fracture phenomenon in inelastic solids, P. PERZYNA [Ed.], 301-389, Springer, Wien, New York 1998.
• 8. R. C. BATRA, L. CHEN, Shear band spacing in gradient-dependent thermoviscoplastic materials, Computational Mech., 23, 8-19, 1999.
• 9. R. C. BATRA, Y. D. S. RAJAPAKSE, A. ROSAKIS, [Eds.], Failure mode transitions under dynamic loading, special issue of Int. J. Fracture, 101, 1-180, 2000.
• 10. T. J. BURNS, Approximate linear stability analysis of a model of adiabatic shear band formation, Q. Appl. Math., 43, 65, 1985.
• 11. C. CATTANEO, A form of heat equation which eliminates the paradox of instantaneous propagation, CR Acad. Sci., 247, 431-433, 1958.
• 12. D. S. CHANDRASEKHARAIH, Thermoelasticity with second sound: A review, Appl. Mech. Rev., 39, 355-376, 1986.
• 13. L. CHEN, R. C. BATRA, Effect of material parameters on shear band spacing in work-hardening gradient-dependent thermoviscoplastic materials, Int. J. Plasticity, 15, 551-574, 1999.
• 14. M. CHESTER, Second sound in solids, Phys. Rev., 131, 2013-2015, 1963.
• 15. R. J. CLIFTON, Adiabatic shear in material response to ultrahigh loading rates, Report No. NMAB-356, National Materials Advisory Board Committee, Chapter 8,129-142, 1980.
• 16. P. H. FRANCIS, Thermomechanical effects in elastic wave propagation; A survey, J. Sound Vib., 21, 181-192, 1972.
• 17. D. E. GRADY, M. E. KIPP, The growth of unstable thermoplastic shear and application to steady-wave shock compression in solids, J. Mech. Phys. Solids, 35, 95, 1987.
• 18. A. E. GREEN, B. C. McINNIS, P. M. NAGHDI, Elastic-plastic continua with simple force dipole, Int. J. Engng. Sci., 6, 373, 1968.
• 19. A. MARCHAD, J. DUFFY, An experimental study of the formation process of adiabatic shear bands in a structural steel, J. Mech. Phys. Solids, 36, 251-283, 1988.
• 20. A. MOLINARI, Collective behavior and spacing of adiabatic shear bands, J. Mech. Phys. Solids, 45, 1551-1575, 1997.
• 21. V. F. NESTERENKO, M. A. MEYERS, T. W. WRIGHT, Self-organization in the initiation of adiabatic shear bands, Acta Mater., 46, 327-340, 1995.
• 22. P. PERZYNA, Constitutive modeling of dissipative solids for localization and fracture [In:] Localization and fracture phenomenon in inelastic solids, P. PERZYNA [Ed.], 99-242, Springer, Berlin 1998.
• 23. M. H. SAAD, C. Y. CHA, Axisymmetric non-Fourier temperature in cylindrically bounded domains, Int. J. Nonlinear Mechanics, 17, 129-136, 1982.
• 24. Y. TOMITA, Simulations of plastic instabilities in solid mechanics, Appl. Mech. Rev., 47, 171-205,1994.
• 25. H. TRESCA, On further application of the flow of solids, Proc. Int. Mech. Engng., 30, 301-345, 1878.
• 26. P. VERNOTTE, The true heat equation, CR Acad. Sci., 247, 2103, 1958.
• 27. T. W. WRIGHT, R. C. BATRA, Adiabatic shear bands in simple and dipolar plastic materials, K. KAWATA and J. SHIORI [Eds.], Macro- and micro-mechanics of high velocity deformation and fractute, 189-201, IUTAM Symp. on MMMHVDF, Tokyo, Japan, Springer-Verlag, Berlin, Heidelberg 1987.
• 28. T. W. WRIGHT, H. OCKENDON, A scaling law for the effect of inertia on the formation of adiabatic shear bands, Int. J. Plasticity, 12, 927-934, 1996.
• 29. H. M. ZBIB, T. SHAWKI, R. C. BATRA, [Eds.], Material instabilities, special issue of Appl. Mech. Rev., 45, 1-173, 1992.
• 30. C. ZENER, J. H. HOLLOMON, Effect of strain rate upon plastic flow of steel, J. Appl. Phys., 14, 22-32, 1944.