A uni®ed constitutive model for strain-rate and temperature dependent behavior of molybdenum Jingyi Cheng 1 , Sia Nemat-Nasser * , Weiguo Guo 2 Department of Mechanical and Aerospace Engineering, Center of Excellence for Advanced Materials, University of California, San Diego, 4207 Engineering Bldg, Unit 1, 9500 Gilman Drive, La Jolla, CA 92093-0416, USA Received 17 March 1999; received in revised form 30 July 2001 Abstract In this paper, a constitutive model proposed by Cheng and Nemat-Nasser [Acta Mater. 48 2000) 3131] is ex- tended to describe both the dynamic and quasi-static stress±strain response of a commercially pure molybdenum over the temperature range 300±1100 K. Experimental results of Nemat-Nasser et al. [Acta Mater. 47 1999) 3705; Scripta Mater. 40 1999) 859] suggest that molybdenum behaves plastically dierently at high and low strain rates. Within the framework of the classical theory of thermally activated dislocation motion, dierent models and model parameters must be used for high and low strain-rate deformations, indicating that dierent rate-controlling de- formation mechanisms may be involved. In the present paper, a uni®ed constitutive description of the mechanical behavior of molybdenum is developed. The activation energy and the maximum strength of the local barriers to the dislocation motion, change gradually with the changing strain-rate and temperature, due to the increased solute mobility with increasing temperature. Therefore, no change in the deformation mechanism is actually included. Only the con®guration of the local obstacles is assumed to change because of the change in the solute mobility. The model predictions are in good agreement with the experimental results. Ó 2001 Elsevier Science Ltd. All rights reserved. 1. Introduction Mostmetals'plasticresponseisstrain-rate-and temperature-dependent. At a given strain-rate, the temperature dependence of the ¯ow stress of crystalline solids has several distinctive character- istics. At low temperatures, the ¯ow stress de- creasesrapidlywithincreasingtemperature,untila plateauisreachedatatemperature,say, T L .Above T L ,thereisaplateauwithinwhichthe¯owstressis almost independent of the temperature, the de- pendence being no greater than the temperature dependence of the shear modulus. To a certain extent, raising the strain-rate is equivalent to lowering the temperature for the plastic ¯ow of metals. For almost all metals containing solute atoms both interstitial and substitutional), the phenomenonofdynamicstrain-agingiscommonly observed at high temperatures and low strain rates. Within the regime of strain rates and Mechanics of Materials 33 2001) 603±616 www.elsevier.com/locate/mechmat * Corresponding author. Tel.: +1-858-534-5930; fax: +1-858- 534-2727. E-mail address: sia@shiba.ucsd.edu S. Nemat-Nasser). 1 We report with sadness the sudden death of our coauthor, ProfessorJingyiChengattheyoungageof37,onFebruary14, 2000, in Hefei, China. 2 Present address: Department of Aircraft Engineering, Northwestern Polytechnical University, Xian, Shaanx 710072, People's Republic of China. 0167-6636/01/$ - see front matter Ó 2001 Elsevier Science Ltd. All rights reserved. PII:S0167-663601)00076-X