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A critical evaluation and extension of internal state variables consititutive models.pdf

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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