Experimental study on the thermoelastic martensitic transformation in shape memory alloy polycrystal induced by combined
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I.
INTRODUCTION
THE thermally or stress-induced thermoelastic martensitic transformation (MT) in shape memory alloys now seems to be well understood, at least for the most simple single crystal, single interface conditions, for which the vast number of basic experimental and theoretical works have been performedS~]The progress of the transformation is controlled by the so-called thermoelastic criterion--balance of chemical and mechanical forces driving or opposing the motion of martensite variant interfaces that can be physically well formulated on the atomic level just at the moving martensite variant interfacesY~ When the external stress or temperature is varied in a proper range, characteristic for each thermoelastic shape memory alloy (SMA), the alloy responds by the nucleation and growth (forward MT) or shrinking (reverse MT) of martensite variant particles. This brings about a macroscopic strain change only if external stress is applied, due to the self-accommodation of crystallographic strains of growing martensite variant particles in stress-free, thermally induced MT. The stresses and strains considered in thermodynamical theory[2~ are typically scalars, suitable for experimental single crystal data. The effect of general external stress on the stress-induced, first-order solid state transformations has been discussed in the frame of thermodynamics by Kato and Pak. t3] On the other hand, the engineering applications of SMA require a simple but reliable estimation of the general mac-
PETR SITTNER, Research Associate, formerly with the Faculty of Engineering, Mie University, is with the Institute of Physics, Academy of Sciences of the Czech Republic, Prague, Czech Republic. YASUHIRO HARA, Graduate Student, and MASATAKA TOKUDA, Professor, are with the Faculty of Engineering, Mie University, Tsu, Mie 514, Japan. Manuscript submitted June 13, 1994. METALLURGICAL AND MATERIALS TRANSACTIONS A
roscopic thermomechanical behaviors of complex polycrystalline SMA for which the single crystal results and models are not directly applicable. For this reason, the transformation behavior of SMA polycrystals is now being widely studied micromechanically on the mesoscopic level. The formulation of the problem through an energetic balance by employing the thermodynamical potential in the form of complementary free energy 9 associated with the MT in a unit constitutive element is the most powerful and standard current approach.t4,5,6] As an example, Patoor et aL[r] introduced the complementary free energy 9 in the form of Eq. [1 ], where f represents the volume fraction of transformed Im martensite phase,f = -~, and serves as an internal variable; E~ is the external stress; M,~ktis the elastic compliance tensor; T is temperature; B and To are the material constants; and ~'~ is the part of local stress tensor due to the incompatibilities of transformation strain field, g~(r). (Zij, T , f ) = f - ~1 Z ,j f " eijtr (r) dV - B (T-To) f
1 1 + ] ZijMqk ,Zk, + 2-V Jr o',j'. . . .(r) e,: (r)dV
[1]
While the first two terms repr
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