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A critical evaluation and extension of internal state variables consititutive models
Pergamon
International Journal of Plasticity, Vol. 11, No. 4, pp. 33 i-345, 1995
Copyright ? 1995 Elsevier Science Ltd
Printed in the USA. All rights reserved
0749-6419/95 $9.50 + .00
0749-6419(95)00002-X
A C R I T I C A L E V A L U A T I O N A N D E X T E N S I O N O F I N T E R N A L
STATE V A R I A B L E S C O N S T I T U T I V E M O D E L S
HuI LI,* SUNIL SAIGAL,* P. T. WAN~,I and H. R. PIEI-ILER*
*Carnegie Mellon University and tALCOA Technical Center
(Communicated by Michael G. Stout, Los Alamos National Laboratory)
Abstract-This study provides a critical comparison of the internal state variables constitutive
models proposed recently in the literature for metals at elevated temperatures and deformed over
a wide range of strain rates. As a result of the observations from this comparative evaluation,
a set of modified constitutive relations is also presented. The experimental data available in the
]literature for 1100 aluminum and a fully dense high purity aluminum were used along with a
Jaonlinear least squares fitting procedure to estimate the material constants. A nonlinear func-
r.ional dependence of the effective stress with respect to the internal state variable in the evolu-
~Lion relationship was determined to model more effectively, compared to previous models, the
case that a material may exhibit both hardening and softening behaviors, respectively, corre-
.sponding to different applied strain rates at the same temperature. The modified relations pre-
sented here propose a simple form of this nonlinear function, which accurately models the
:material response and which allows a more robust implementation in numerical simulations.
The deformation of an aluminum gradient specimen was studied for further comparison of the
three constitutive models considered and for a demonstration of the validity of this model.
1. INTRODUCTION
The deformation processing of metals commonly involves hot working operations to
fabricate th
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