Summary
A perturbation analysis has been used to obtain a detailed and fundamental understanding of the high strain-rate material mechanisms associated with material instabilities and adiabatic shear-band formation in single body-centered cubic (b.c.c.) crystals. The interrelated effects of wave number, shear-band orientation, strain hardening, strain-rate sensitivity, and thermal and geometrical softening on material instability and shear-strain localization have been investigated in terms of the competition between the softening and hardening mechanisms for nominal strain-rates from 100/s to 5000/s. A perturbed system of equations has been obtained, accounting for arbitrary crystal orientations, and since no approximations have been made for the magnitude of the strain-rate sensitivity parameter, all the roots associated with the stability of the perturbed equations can be obtained for physically representative deformations. Hence, a comprehensive characterization of material instabilities can be obtained beyond the initial instability point, and the strength of material instabilities can be then monitored throughout the deformation history to distinguish between material instabilities and shear-strain localization.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Anand, L., Spitzig, W. A.: Initiation of localized shear bands in plane strain. J. Mech. Phys. Solids28, 113–128 (1980).
Anand, L., Kim, K. H., Shawki, T. G.: Onset of shear localization in viscoplastic solids. J. Mech. Phys. Solids35, 407–429 (1987).
Ansart, J. P., Dormeval, R.: Adiabatic shearing in martensitic steels. In: Impact loading and dynamic behavior of materials, vol. 2 (Chiem, C. Y., Kuntze, D.-D., Meyer, L. W., eds.), pp. 775–782, DGM Informationsgesellschaft, Germany 1988.
Asaro, R. J.: Geometrical effects in the inhomogeneous deformation of ductile single crystals. Acta Metal.27, 445–453 (1979).
Asaro, R. J., Rice, J. R.: Strain localization in ductile single crystals. J. Mech. Phys. Solids25, 309–338 (1977).
Bai, Y. L.: A criterion for thermo-plastic shear instability. J. Mech. Phys. Solids30, 195–207 (1981).
Baucom, J. N.: Master of science thesis, North Carolina State University 1996.
Clifton, R. J.: Adiabatic shear banding. In: Materials response to ultra-high-loading rates, NMAB-356, National Advisory Board (NRC), Washington, DC 1980.
Clifton, R. J., J. Duffy, Hartley, K. A., Shawki, T. G.: On critical conditions for shear band formation at high strain rates. Scripta Metal.18, 443–448 (1984).
Costin, L. S., Crisman, E. E., Hawley, R. H., Duffy, J.: On the localization of plastic flow in mild steel tubes under dynamic torsional loading. In: Mechanical properties at high rates of strain. Inst. Phys. Conf. Ser.47, 90 (1979).
Dève, H., Harren, S., McCullough, C., Asaro, R. J.: Micro and marcroscopic aspects of shear band formation in internally nitrided single crystals of Fe−Ti−Mn alloys. Acta Metal.36 (2), 343–365 (1987).
Dudzinski, D., Molinari, A.: Perturbation analysis of thermoviscoplastic instabilities in biaxial loading. Int. J. Solids Struct.27, 601–628 (1991).
Fressengeas, C., Molinari, A.: Inertia and thermal effects on the localization of plastic flow. Acta Metal.33, 387–396 (1985).
Fressengeas, C., Molinari, A.: Instability and localization in plastic flow in shear at high strain rates. J. Mech. Phys. Solids.35, 185–211 (1987).
Follansbee, P. S., Ragazzoni, G., Kocks, U. F.: The transition to drag-controlled deformation in copper at high strain-rates. In: Mechanical properties of materials at high rates of strain. Inst. Phys. Conf. Ser.70, 71 (1984).
Giovanola, J. H.: Adiabatic shear banding under pure shear loading, Part I: direct observation of strain localization and energy dissipation measurements. J. Mech. Mater.7, 59–71 (1988).
Hatherly, M., Malin, A. S.: Shear bands in deformed metals. Scripta Metal.18, 449–454 (1984).
Marchand, A., Duffy, J.: An experimental study of the formation process of adiabatic shear bands in a structural steel. J. Mech. Phys. Solids36, 251–283 (1988).
Molinari, A.: Shear band analysis. Solid State Phenomena3–4, 447–468 (1988).
Molinari, A., Clifton, R. J.: Localisation et la déformation viscoplastique en cisaillement simple: Résultats Exacts en Théorie non Linéaire. C. R. l'Acad. Sci., Ser. II,296, 1–4 (1983).
Molinari, A., Clifton, R. J.: Analytical characterization of shear localization in thermoviscoplastic solids. J. Appl. Mech.54, 806–812 (1988).
Pierce, D., Asaro, R. J., Needleman, A.: An analysis of nonuniform and localized deformation in ductile single crystals. Acta Metal.30, 1087–1119 (1982).
Pierce, D., Asaro, R. J., Needleman, A.: Material rate dependence and localized deformation in crystalline solids. Acta Metal.31, 1951–1976 (1983).
Rogers, H. C.: Adiabatic plastic deformation. Ann. Rev. Mater. Sci.9, 283 (1979).
Rogers, H. C.: Adiabatic shearing — general nature and material aspects in material behavior under high stress and ultrahigh loading rates. In: Sagamore Army Research Conference Proceedings 29 (Mescall, J., Weiss, V., eds.), pp. 101–118, New York: Plenum (1983).
Staker, M. R.: The relation between adiabatic shear instability strain and material properties. Acta Metal.29, 683–689 (1981).
Tresca, H.: On further application of the flow of solids. Proc. Inst. Mech. Eng.30, 301 (1878).
Wolfram, S.: Mathematica: A System for Doing Mathematics by Computer. Redwood City: Addison-Wesley 1991.
Wright, T. W.: Shear band susceptibility: Work Hardening Materials. Int. J. Plasticity8, 583–602 (1992).
Wright, T. W., Batra, R. C.: The initiation and growth of adiabatic shear bands. Int. J. Plasticity1, 205–212 (1985).
Wright, T. W., Walter, J. W.: On stress collapse in adiabatic shear bands. J. Mech. Phys. Solids35, 701–720 (1987).
Zhu, H., Zbib, H. M., Aifantis, E. C.: On the effect of anisotropy and inertia on shear banding: instability of biaxial stretching. Appl. Mech. Rev.45, 110–117 (1992).
Zikry, M. A.: An accurate and stable algorithm for high strain-rate finite strain plasticity. Computers and Structures50, 337–350 (1994).
Zikry, M. A.: Dynamic void collapse and material failure mechanisms in metallic crystals. Mechanics of Materials17, 273–288 (1994).
Zikry, M. A., Pothier, M.: High strain-rate shear strain localization in F. C. C. crystalline materials: A perturbation analysis (accepted for publication 1997).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Baucom, J.N., Zikry, M.A. Perturbation analysis of high strain-rate shear localization in B.C.C. crystalline materials. Acta Mechanica 137, 109–129 (1999). https://doi.org/10.1007/BF01313148
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01313148