Kinetic Model of Thermoelastic Martensite Transformation in Niti and NiMn Based Shape Memory Alloys
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A new, quantitative model was developed to describe the martensite transformation kinetics of thermoelastic shape memory alloys (SMAs). In addition, a series of experiments were conducted to study the kinetics of thermoelastic martensite transformation in our SMA systems: NiTi, NiTi-15at%Hf, NiTi-20at%Zr and NiMn-7.5at%Ti alloys. Comparisons between data of the kinetic of martensite transformation with the present theoretic models show that the proposed model is in good agreement and concurs with the experimental data. Also, a comparison of data from the proposed model with data from existing kinetic models, such as Liang's and Magee's [1,7], indicates that the proposed model can better describe the experimental data, including the relationship between dý(T)/dT and 4, and dý(T)/dT and T. INTRODUCTION
Shape memory alloys are among the most exciting of the new, intelligent materials. The potential applications of shape memory alloys and similar composite materials continue to generate great interest, particularly in the area of adaptive structures and vibration sup ression [1-3]. In order to design and manufacture a sensor/actuator for these types of applications, the development of a constitutive model that can quantitatively describe the thermomechanical behavior of these materials is essential. One of the most important steps in developing the constitutive equation of SMAs is to accurately describe the kinetics of thermoelastic martensite transformation, i.e. the relationship between the product phase fraction ý(T) and temperature [6]. It is known that the phase fraction in SMAs depends on both temperature and applied stress, meaning that the ý is a function of temperature, T, and stress, C. Recently, several constitutive equations were proposed to describe the thermomechanical behavior of this particular material. However, few of the equations have been based on a vigorous kinetics consideration of the thermoelastic martensite transformation. At present, there are just two models available to describe the function, 4(T). Liang et al., [1] proposed a cosine relationship between martensite fraction, ý, and temperature. Liang's phenomenological equation has proved to be very simple, easy to apply and has been widely used. In his model the fraction of martensite during the phase transtormation can be described by the following equations: &=
[1+cos n ( T-M,. )
for A-M
(I a)
T-As
1
ýM:1 [l+cos x ( T
2
SAJ)]
A-A
for M-A
(Ib)
3
where A, and Af are the austenite start and finish temperatures, respectively, and M. and Mf are the martensite start and finish temperatures, respectively. Magee [7] also developed a kinetic equation for martensite transformation. In his model the fraction of martensite W(T) for heating and cooling is given by Eqs. 2(a) and 2(b):
M
where,ox and
aA
ý(T) = 1 - exp[fM (Ms - T)J, for A to M
(2a)
ý(T) = exp[aA (As - T)J,
(2b)
for M to A
are material constants. Eqs.(l a) and (I b) are phenomenological equations 537
Mat. Res. Soc. Symp. Proc. Vol. 398 ©1996 Materials Research Soc
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