UNCORRECTED PROOF 2 Microstructural based models for bcc and fcc metals 3 with temperature and strain rate dependency 4 George Z. Voyiadjis * , Farid H. Abed 5 Department of Civil and Environmental Engineering, Computational Solid Mechanics Laboratory, Louisiana State University, 6 CEBA 3508-B, Baton Rouge, LA 70803, USA Received 1 July 2003; received in revised form 1 December 2003 9 Abstract 10 Microstructural physical based constitutive models are developed in this work in order to characterize the deforma- 11 tion behavior of body centered cubic (bcc) and face centered cubic (fcc) metals under different strain rates and temper- 12 atures. The concept of thermal activation energy as well as the dislocations interaction mechanisms is used in the 13 derivation procedure taking into consideration the effect of the mobile dislocation density evolution on the flow stress 14 of the deformed material. The derivation of the Zerilli–Armstrong (Z–A) physical based model for both (bcc) and (fcc) 15 metals is investigated and a number of modifications are incorporated such as the evolution of mobile dislocation den- 16 sity.TheauthorsconcludethatinspiteofthephysicalbasisusedinthederivationoftheZ–Amodel,itsparameterscan 17 not be interpreted physically since the approximation ln(1+ x)  x isusedinthefinalstepofthederivation.Thisexpan- 18 sion, however, is valid only for values x  1.0 which is not the case at high strain rates and temperatures. New bcc and 19 fcc relations for the flow stress are therefore suggested and derived using the exact results of the expansion of ln(1+ x). 20 Several experimental data obtained by different authors for tantalum (Ta), niobium (Nb), molybdenum, (Mo), vana- 21 dium (V) (bcc metals) and Oxygen Free High Conductivity (OFHC) Copper (Cu) (an fcc metal) are used in evaluating 22 theproposedmodels.Agoodagreementbetweentheexperimentalresultsandtheproposedmodelsareobtained.More- 23 over, the predicted results show that the assumption of ignoring the generation of dislocation density during the plastic 24 deformation is not appropriate particularly in the case of high strain rates and temperatures. This causes the values of 25 thethermalstressestobeoverestimated.Numericalidentificationforthephysicalquantitiesusedinthedefinitionofthe 26 model parameters is also presented. 27 Ó 2004 Elsevier Ltd. All rights reserved. 28 Keywords: Constitutive modeling; Flow stress; Dislocation density; Strain rate and temperature effect; Activation energy; Plasticity 29 0167-6636/$ - see front matter Ó 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.mechmat.2004.02.003 * Corresponding author. Tel.: +1-225-578-8668; fax: +1-225-578-9176. E-mail address: voyiadjis@eng.lsu.edu (G.Z. Voyiadjis). Mechanics of Materials xxx (2004) xxx–xxx www.elsevier.com/locate/mechmat MECMAT 1321 No. of Pages 24, DTD = 5.0.1 1 July 2004; Disk Used ARTICLE IN PRESS