Abstract
The stress collapse in the formation of shear bands in elasto-thermo-viscoplatic materials is systematically studied within the framework of one-dimensional formulation via analytical and numerical methods. The elastic energy released in a domain is found to play an important role in the collapse behavior of shear localization. A non-dimensional parameter named the stability indicator is introduced to characterize the collapse behavior, with approximate forms of the incremental governing equations. The stability indicator offers useful information regarding the degree of severity of an abrupt change of deformations during the stress collapse. Numerical experiments are carried out to verify the stability indicator by varying material properties.
Similar content being viewed by others
References
Batra, R. C. and Chen, L., 2001, “Effect of Viscoplastic Relations on the Instability Strain, Shear Band Initiation Strain, the Strain Corresponding to the Minimum Shear Band Spacing, and the Band Width in a Thermoviscoplastic Material,”International Journal of Plasticity, Vol. 17, pp. 1465–1489.
Batra, R. C. and Kim, C. H., 1990, “Effect of Integration Methods on the Solution of an Adiabatic Shear Banding Problem,”International Journal for Numerical Methods in Engineering, Vol. 29, pp. 1639–1652.
DiLellio, J. A. and Olmstead, W. E., 1997, “Temporal Evolution of Shear Band Thickness,”Journal of the Mechanics and Physics of Solids, Vol. 45, pp. 345–359.
DiLellio, J. A. and Olmstead, W. E., 2003, “Numerical Solution of Shear Localization in Johnson-Cook Materials,”Mechanics of Materials, Vol. 35, pp. 571–580.
Fressengeas, C., 1989, “Adiabatic Shear Morphology at Very High Strain Rates,”International Journal of Impact Engineering, Vol. 8, pp. 141–157.
Glimm, J. G., Plohr, B. J. and Sharp, D. H., 1996, “Tracking of Shear Bands I. The One-dimensional Case,”Mechanics of Materials, Vol. 24, pp. 31–41.
Kim, H. G. and Im, S., 1999, “Approximate Analysis of a Shear Band in a Thermoviscoplastic Material,”ASME Journal of Applied Mechanics, Vol. 66, pp. 687–694.
Litonski, J., 1977, “Plastic Flow of a Tube under Adiabatic Torsion,”Bulletin Acad. Polymer Sciences, Vol. 25, pp. 7–14.
Lush, A. M., Weber, G. and Anand, L., 1989, “An Implicit Time-integration Procedure for a Set of Internal Variable Constitutive Equations for Isotropic Elasto-viscoplasticity,”International Journal of Plasticity, Vol. 5, pp. 521–549.
Machand, A. and Duffy, J. W., 1988, “An Experimental Study of the Formation Process of Adiabatic Shear Bands in a Structural Steel,”Journal of the Mechanics and Physics of Solids, Vol. 35, pp. 251–283.
Merzer, A. M., 1982, “Modelling of Adiabatic Shear Band Development from Small Imperfections,”Journal of the Mechanics and Physics of Solids, Vol. 30, pp. 323–338.
Needleman, A., 1988, “Material Rate Dependence and Mesh Sensitivity in Localization Problems,”Computer Methods in Applied Mechanics and Engineering, Vol. 67, pp. 69–85.
Wright, T. W. and Walter, J. W., 1987, “On Stress Collapse in Adiabatic Shear Bands,”Journal of the Mechanics and Physics of Solids, Vol. 35, pp. 701–720.
Wright, T. W., 1987, “Steady Shearing in a Viscoplastic Solid,”Journal of the Mechanics and Physics of Solids, Vol. 35, pp. 269–282.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Kim, HG., Im, S. An investigation on collapse behavior of shear localization in elasto-thermo-viscoplastic materials. J Mech Sci Technol 20, 2178–2188 (2006). https://doi.org/10.1007/BF02916334
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02916334