Available online at www.sciencedirect.com
ScienceDirect Materials Today: Proceedings 2S (2015) S909 – S912
International Conference on Martensitic Transformations, ICOMAT-2014
Features of the internal friction in the temperature range of martensitic transformation in TiNi G.V. Markovaa, A.V. Shuytceva,*, D.M. Levina, A.V. Kasimtceva,b a
Tula State University, Tula, 300600, Russia b “Metsintez” LTD, Tula, 300041, Russia
Abstract The influence of the external parameters (deformation amplitude and oscillation frequency) on the components of the internal friction peak during a thermoelastic martensitic transformation in TiNi has been considered. Models describing the behavior of the transition components of the IF peak have been analyzed. On the basis of the best model experimental dependence of the transformed volume fraction on temperature has been established. © 2014 The TheAuthors. Authors.Published Published Elsevier © 2015 byby Elsevier Ltd.Ltd. This is an open access article under the CC BY-NC-ND license Selection and Peer-review under responsibility of the chairs of the International Conference on Martensitic Transformations (http://creativecommons.org/licenses/by-nc-nd/4.0/). 2014. This is Peer-review an open access article under theofCC license (http://creativecommons.org/licenses/by-nc-nd/3.0/). Selection and under responsibility the BY-NC-ND chairs of the International Conference on Martensitic Transformations 2014. Keywords: TiNi; Internal Friction; Martensitic Transformation; Gremaud model
1. Introduction The martensitic transformation (MT) can be examined in various ways, but one of the most informative methods is the internal friction (IF). It is known that the IF peak during termoelastic martensitic transformation (TEMT) can be decomposed into three contributions [1-3]: • The intrinsic contribution . This component corresponds to the additive energy dissipation in the austenitic and martensitic phases taking into account their volume ratio. • The phase transition contribution . Its contribution is detected during isothermal or high-frequency
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2214-7853 © 2015 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Selection and Peer-review under responsibility of the chairs of the International Conference on Martensitic Transformations 2014. doi:10.1016/j.matpr.2015.07.429
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measurements. The nature of this component is associated with the reversible movement of the interphase boundaries in the field of applied stresses. • The transient contribution . It exists only during cooling or heating and depends on external parameters like temperature rate, resonance frequency and oscillation amplitude. The mechanism of energy dissipation of the component is caused by the movement of the interphase and internal martensite twin boundaries over long distances, i.e. is actually a response to changes in the volume of martensite phase under the influence of external factors. The transient term provides the maximum contribution to the energy dissipation in the hertz frequency range. There are a lot of phenomenological models describing the transient component (table 1). These models have been summarized in [2-5] and have been tested with respect to copper-based alloys. Table 1. List of phenomenological models describing the IF peak during TEMT [2, 3]. IFTr (T)
Models 1
Belko (1969)
2
Delorme (1971)
3
Dejonghe (1976)
4
Xiao (1993)
5
Wang (1990)
6
Zhang (1987)
7
Gremaud (1987)
μ – shear modulus; V – volume associated to a critical germ; - transformation strain. μ – shear modulus; K – constant; – oscillation stress-amplitude. A – coefficient; - the quantity of material that transforms per stress-unit. A – constant. A(T) – temperature dependent coefficient; 0 < r < 1 – materials with elastic softening; r = 0 – materials without elastic softening. A(T) – temperature dependent function; 0 < m, q < 1. – oscillation stress-amplitude; α – stress induced change of critical temperature; J – elastic compliance; - stress-free transformation shear strain.
All the above mentioned models assume a direct dependence of the transient component Q-1Tr from the transformed phase volume , the temperature change rate and a inversely dependence from the frequency . However, only Delorme, Dejonghe and Gremaud models includes the effect of deformation amplitude in explicit form. Belko and Wang models takes into account this effect through the shear modulus μ and the exponent r. Delorme and Gremaud models implies inversely proportional dependence of the Q-1Tr from the , at the same time, the Dejonghe model - directly proportional. Gremaud model assumes the decreasing of the Q-1Tr with the increasing of the . There is a large number of experimental data [6, 7], which shows that the total IF in intermetallic TiNi based alloys is characterized by a strongly pronounced amplitude dependence increasing from the very small deformation amplitudes. At the same time, according to the models, taking into account the effect of deformation amplitude, the level of transient component of the IF should decrease with increasing deformation amplitude. In a previous paper [8] the effect of external parameters (temperature rate, oscillation frequency, deformation amplitude) for the entire peak of the IF during the TEMT has been studied. The aim of this work is to study the influence of the external parameters to the transient component of the IF, is to choose the most adequate model for the description of transient component of the IF in TiNi and is to get the temperature dependence of the transformed phase based on this model. 2. Materials and Methods The object of this research is an alloy with composition Ti50Ni50. Heat treatment consists of heating up to 800 °С in vacuum, holding for 1 hour, and then cooling with the furnace up to 600 °С, holding for 1 hour and cooling
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with the furnace.Internal Friction has been measured on an inverted torsion pendulum RCM-TPI in a temperature range from 20 to 100 °C, with different frequencies f = 1,25…3 Hz and deformation amplitudes γ = 5·10-5…2·10-4. The isothermal aging for 30 minutes has been carried out in the temperature range of MT for a detection phase component. Intrinsic component was determined by the addition the background of internal friction in the austenite (at 100 °C) and martensite (at 20 °C) taking into account their volume fraction. Peak area was selected as a measure of transient and phase components. 3. Results and Discussion The influence of temperature rate on the internal friction peak during a thermoelastic martensitic transformation in TiNi was described in many articles [8-10]: internal friction linearly increases with the increasing of the heating rate. It should be noted that in this case, separation of the phase component was not possible. Nevertheless, these results agree with all of the models above. The influence of the oscillation frequency on the IF peak components is shown in Fig. 1. Analysis of experimental data showed that the IF background level in the martensite and austenite remains constant and does not depend from the applied oscillation frequency. In the investigated range of frequency the value of the phase component decreases with increasing oscillation frequency, as well as the transient component. Equation view obtained from the experimental data corresponds to all the equations above. -1
Q
-1
M, A
0,005 0,10 0,004 - QM
- Qtr
0,08
- QPT
-1
-1
25
- QPT
0,04
-1
- QA
0,002
100
0,001 1,5
2,0 2,5 3,0 Oscillation Frequency f, Hz
Fig. 1. Influence of oscillation frequency to the components of the IF peak at = 0,5 °C/min; = 5·10-5.
0,0060 25
-1
- QA
0,06
0,0045
100
0,0030
0,05 0,0015
0,04 -5
5,0x10
M, A
-1
- QM
-1
0,06
0,003
tr, PT
-1
-1
Q
tr, PT
-1
- Qtr
0,07
0,08
Q
Q
-1
0,09
-4
1,0x10
-4
-4
1,5x10 2,0x10 Deformation amplitude
Fig. 2. Influence of deformation amplitude to the components of the IF peak at = 0,5 °C/min; = 1,9 Hz.
The influence of the deformation amplitude on the IF martensite peak components is shown in Fig. 2, which shows that with increasing deformation amplitude Q-1Tr decreases to some constant value. The background level in austenite remains unchanged ( ) and in martensite increases ( ) with increasing the deformation amplitude. The value the phase component is also increased ( ). At the same time, increase the deformation amplitude leads to a decrease of the transient component of the IF martensitic peak ( ). The character of the change curve in Fig. 2 does not contradict the Gremaud model. Thus, the total amplitude dependence of IF related to the growth of internal friction in the martensite and the increase in the contribution to the energy dissipation of the phase components. The total contribution of these two components is greater than the observed decline of the Q-1Tr component contribution. The decrease of the transient component from the amplitude corresponds to Delorme and Gremaud models, but Gremaud model seems the most adequate, because it assumes a reduction of the internal friction to a constant level, while the Delorme model predicts a decrease of the Q-1Tr to zero. The Gremaud equation takes into account the influence of the volume of transformed phases depending on the temperature. Differentiating Gremaud equation, the following relationship has been obtained: integrating that, we find the volume of transformed phases depending from the temperature:
.
,
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Fig. 3 shows the obtained dependences n(T) at different deformation amplitudes. General view of dependence corresponds to the classical representations to a volume phase changes during thermoelastic martensitic transformation [6]. 100
-5
60 40
γ = 6,1* 10 -5 γ = 7,3* 10 -5 γ = 9,7* 10 -5 γ = 14,6* 10 -5 γ = 19,5* 10
Af
35
60
% n Phase
80
20 As 0
30
40 45 50 55 о Temperature, С
Fig. 3. The dependence of the volume of transformed phase n from the temperature T.
As it can be seen from the Fig. 3, the character of n(T) dependence is the same for all amplitudes. A regular trend in curves obtained with different deformation amplitudes were not observed. It means that deformation amplitude influences the general level of internal friction and to the Q-1Tr component, but does not affect to the volume of transformed phase. 4. Conclusions So, studies have shown the following: • The influence of external factors on the transient component in TiNi corresponds to the Gremaud model. Increasing the amplitude dependence of the total internal friction in TiNi alloys with thermoelastic martensitic transformation is associated with an increase in the internal friction in the martensite and an increase in phase components. • The quantity of transformed phase during the temperature changes does not depend on deformation amplitude. • The character of the transformed phase volume changes with the temperature changing does not depend on the deformation amplitude in the investigated range (γ = 5·10-5…2·10-4). Acknowledgements This work has been carried out with the financial support of the RFBR (grant 13-03-97503 r_center_а and grant 12-03-00273-а). References [1] K. Otsuka, C.M. Wayman (Eds.), Shape Memory Materials, Cambridge University Press, 1998. [2] R.B. Perez-Saez, V. Recarte, M.L. No, J. San Juan, Phys. Rev. B 57 (1998) 5684–5692. [3] J. San Juan, R.B. Perez-Saez, M.L. No. Bulletin of TSU, Mater. Sci. 3 (2002) 154–167. [4] R.B. Perez-Saez, V. Recarte, M.L. No, J. San Juan. J. Alloys and Comp. 310 (2000) 334–338. [5] J. San Juan, R-B. Perez-Saez. Mater. Sci. Forum 366 (2001) 416–436. [6] V.A. Lihachev (Eds.), Materials with shape memory effect. In 3 v. V.1. StP: StPSU Press, 1998. [7] F. Chen, Y.X. Tong, X.L. Lu. Mater. Lett. 65 (2011) 1073–1075. [8] S.K. Wu, H.C. Lin. J. Alloy. Comp. 355 (2003) 72–78. [9] S.H. Chang, S.K. Wu. J. Alloy. Comp. 437 (2007) 120–126. [10] G.V. Markova, A.V. Shuytcev, A.V. Kasimtcev. Materials Science Forum V. 738-739 (2013) 377–382. [11] G. Gremaud, J.E. Bidaux, W. Benoit, Helv. Phys. Acta. 60 (1987), 947–958.
