Strain Rate Gradient Model with Couple Stress for Micro Scale Rigid-Viscosity-Plastic Deformation


Article Preview

In order to describe scale effects in rigid-viscosity-plastic deformation at micro scale, a strain rate gradient model with couple stress is proposed. In the constitutive equation, couple stress, strain rate gradient are introduced on the assumption that the potential energy depends upon the scalar invariants of the strain rate tensor and strain rate gradient tensor, at the same times, the influences of length scale of body, grain size and temperature are also considered. A FEM-based program based on this strain rate gradient model is used to simulate the process of high temperature gas pressure forming, and the value of length scale 2 l is evaluated by simulation pilot calculation. It is indicated that rigid-viscosity-plastic deformation can be more accurately simulated by the present strain gradient rate model as long as the material parameters in constitutive equation are selected suitably.



Materials Science Forum (Volumes 551-552)

Edited by:

K.F. Zhang




K. Lei and K. F. Zhang, "Strain Rate Gradient Model with Couple Stress for Micro Scale Rigid-Viscosity-Plastic Deformation", Materials Science Forum, Vols. 551-552, pp. 323-328, 2007

Online since:

July 2007




[1] M. Geiger, M. Kleiner, R. Eckstein, et al: Annals of the CIRP., Vol. 50 (2001), p.1.

[2] U. Engel, R. Eckstein: J. Mater. Process. Tech, Vol. 125-126(2002), p.35.

[3] L.V. Raulea, A.M. Goijaerts, L. E. Govaet, et al: J. Mater. Process. Tech, Vol. 115(2001), p.44.

[4] M. Geiger, F. Vollertsen, R. Kals: Annals of the CIRP, vol. 45(1996), p.277.

[5] De Guzman, M. S, G. Newbauer, P. Flinn, W.D. Nix: Mater. Res. Symposium Proceedings, Vol. 308(1993), p.613.

[7] W.J. Poole, M.F. Ashby, N.A. Fleck: Scripta Metall. Mater., Vol. 34(1996), p.559.

[8] Q. Ma, D.R. Clarke: J' Mater. Res, Vol. 10(1995), p.853.

[9] N.A. Fleck, G.M. Muller, M.F. Ashly et al: Acta Metall., Vol. 42(1994), p.475.

[10] N.A. Fleck, J.W. Hutchinson, in strain Gradient Plasticity: edited by Hutchinson, J.W., Wu, T. Y, Advances in Applied Mechanics, Vol. 33(1997), Academic Press, New York, p.295.


[11] H. Gao, Y. Huang, W.D. Nix, et al: J Mech. Phys. Solids. 1999b, Vol. 47 (1999), p.1239.

[12] Y. Huang, H. Gao, W.D. Nix, et al: J Mech. Phys. Solids, Vol. 48(2000): p.99.

[13] H. Gao, Y. Huang: Int. J. Solids. Struct., Vol. 38(2001) , p.2615.

[14] S.H. Chen, T.C. Wang:. Int. J. Plasticity, Vol. 18(2002), p.971.

[15] K.F. Zhang, W. Wu, Y.H. Song, K.B. Chen: NUMIFORM'98 p.753, Twente, Netherlands.