Prediction of Thermodynamic Equilibrium Temperature of Cu-Based Shape-Memory Smart Materials
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INTRODUCTION
IN contrast to conventional materials, smart materials are known to be functional and intelligent. Shapememory alloys (SMAs) are interesting because of their ability to return to their previous cold-forged shape after plastic deformation by heat. The mechanism of this change depends on the displacive transformation called martensitic transition when cooling from high temperatures.[1] Some Cu-based alloys exhibit shape-memory effect (SME) within a certain range of composition, and this is important in some practical applications.[2] The free energies of the two phases (parent and product) are similar, and the prediction of their relative stability requires an appropriate experimental determination of the chemical entropy (DS) changes during the transformation.[3] The free energy which represents the maximum work a system can exert on its surroundings can be shown as DG ¼ DH TDS; MfiA
½1 AfiM
= 0 and also DG = and if T = T0 then DG 0, where DGMfiA = GA GM = DHMfiA TDSMfiA. MfiA = GA GM = DHMfiA TDSMfiA. From all the equations above, an alloy in which the Gibbs free energies (G) are equal for the austenite (A) and martensite (M) phases, T0 which is the main investigation subject of this study can be expressed as T0 ¼
DHM!A DSM!A
½2
and also, T0 can be calculated as
_ Assistant Professor, is with the Physics DepartMURAT ESKIL, ment, Faculty of Science and Literature, Aksaray University, 68100 Aksaray, Turkey. KEMAL ALDAS ¸ , Associate Professor, and _ ISKENDER O¨ZKUL, Ph.D. Candidate, are with the Mechanical Engineering Department, Engineering Faculty, Aksaray University. Contact e-mail: [email protected] Manuscript submitted February 7, 2014. METALLURGICAL AND MATERIALS TRANSACTIONS A
T0 ¼
Ms þ A f ; 2
½3
where Ms is the martensite start temperature and Af is the austenite finish temperature. The equilibrium condition of a two-phase system is obtained by equating the free energies of each phase if no external potential field is applied. There are two components for a system consisting of chemical energy and mechanical work. If the chemical energies of the two phases are equal at a certain temperature, then that temperature is designated T0 to make it clear that the equilibrium temperature T0 causes the change in entropy as shown in Eq. [2]. There are many physical phenomena and complex thermodynamic behaviors of Cu-based SMAs, and thus theoretical investigations must be undertaken with different models to determine these behaviors from various perspectives. Although other analyses have been carried out as reported in the literature, there is no report on the effect of alloying elements and thermal treatments on T0 temperature as a thermodynamic parameter of Cu-based SMAs using Genetic Programming (GP). Thus, this study focuses on the effect of the alloying elements and thermal treatments on T0 temperatures using GP. GP has been used in many applications such as symbolic regression. GP may generate an initial population of random compositions of the functions and terminals of the problem (c
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