# Thermal Arrest Memory Effect in Ni-Mn-Ga Alloys

Authors: A. Rudajevova
Journal: Advances in Materials Science and Engineering
 (2008)

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## Abstract

Dilatation characteristics were measured to investigate the thermal arrest memory effect inNi53.6Mn27.1Ga19.3 and Ni54.2Mn29.4Ga16.4 alloys. Interruption of the martensite-austenite phase transformation is connected with the reduction of the sample length after thermal cycle. If a total phase transformation took place in the complete thermal cycle following the interruption, then the sample length would return to its original length. Analysis of these results has shown that the thermal arrest memory effect is a consequence of a stress-focusing effect and shape memory effect. The stress-focusing effect occurs when the phase transformation propagates radially in a cylindrical sample from the surface, inward to the center. Evolution and release of the thermoelastic deformations in both alloys during heating and cooling are analyzed.


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## Body

## 1. Introduction

Johnson et al. [1] were the first to show the effect of interruption of phase
transformations on  transformations in subsequent cycles. They have shown that
after arresting the M-P transformation in Ni-Ti alloy during the first thermal
cycle, cooling causes the endothermic peak in the second thermal cycle to split
into two. The M-P transformation in the second cycle remembers the arrest in
the first thermal cycle. The authors of this study called this effect the
“thermal arrest memory effect” (TAME) [2].
The authors of the cited work assume
that the TAME is a consequence of the locked-in transformation strain energy in
the self-accommodation martensitic structure.  TAME effect has been the subject
of intense investigation [3–8]. In contrast
to Madangopal et al. [2], Airoldi et
al. (they called this effect stepwise
martensite to austenite reversible transformation (SMART)) suggest that the phenomenon
TAME is related to the hysteresis associated with the martensitic
transformation. Both hypotheses are based on DSC studies performed on Ti-Ni and
Cu-Zn-Al shape memory alloys.The
TAME effect is undoubtedly a very interesting phenomenon that, with further
investigation, can provide very important information about the behavior of
shape memory alloys. Dilatometry is a method that measures all deformations
occurring in a material. Dilatometry has not been used for the study of the
TAME effect. The aim of this work is the dilatation investigation of the TAME
effect inNi53.6Mn27.1Ga19.3 and Ni54.2Mn29.4Ga16.4 alloys in the temperature range of 20–380°C.


## 2. Experimental

The polycrystalline ingots of bothNi53.6Mn27.1Ga19.3 and Ni54.2Mn29.4Ga16.4 alloys were prepared by arc melting in an argon atmosphere. The samples
prepared from the ingots were annealed for 4 days at 850°C. The samples studied had structure with the
columnar grains. The results obtained by studying the dilatation
characteristics of Ni53.6Mn27.1Ga19.3 and
the microstructure are presented in [9]. The linear thermal expansion of
the samples was measured in a helium atmosphere using a Netzsch 402E
dilatometer from room temperature to 380°C with a heating/cooling
rate 2°C/min.
During the interruption experiments, the interruption temperature was reached
at a rate of 2°C/min followed by a 60-minute delay at the
interruption temperature. The temperature was then decreased at a rate of 2°C/min.
The samples were 6 mm in diameter and 25 mm in length. The accuracy of the
measuring apparatus was checked by measuring the coefficient of thermal
expansion (CTE) of pure Mg and comparing it with the data available from
literature. The agreement between the measured values and the values in
literature is in the range of ±1%. Before investigation, the Ni53.6Mn27.1Ga19.3 alloy was predeformed by compression up to 1% using an Instron
type deformation machine. The sample is placed in the center of the furnace,
with a thermocouple located 1 mm above the sample. The front part of the sample
is pushed on lock; the push rod is placed on the end part of the sample. We
measured deformation changes only along the longitudinal axis (LA direction) of
the sample. In this direction, the Ni53.6Mn27.1Ga19.3 alloy was predeformed in compression. The Ni54.2Mn29.4Ga16.4 alloy was studied in the as-prepared and annealed state.The
total thermal cycle-up to380°C was always made before and after the
thermal cycle in which the interruption was performed. The dilatation
characteristics were then compared. The dilatation characteristics of both
materials before interruption are presented in Figures 1 and 2. The
interruption temperatures are marked in these figures. Reproducibility of all
experiments was perfect.Temperature dependence of (a) the relative elongation and (b) the CTE forNi53.6Mn27.1Ga19.3 alloy in a complete cycle.
(a)(b)Temperature dependence of (a) the relative elongation and (b) the CTE forNi54.2Mn29.4Ga16.4 alloy in a complete cycle.
(a)(b)


## 3. Results

Figure3 reveals the temperature
dependence of the relative elongation for the Ni53.6Mn27.1Ga19.3 alloy in the experiment where the temperature was increased up to 177°C,
then stabilized for one hour, and cooled to room temperature. With this
temperature sequence, the phase transformation takes place only partially. It
can be seen that shortening of the sample occurs after this thermal cycle. The
sample length was reduced by about 20 μm. The results presented in Figure 4 show
the results after an additional total thermal cycle, after interruption. This
figure reveals that permanent elongation of the sample occurs after this
thermal cycle. Figure 5 displays the splitting of the peaks of the CTE during
the phase transformation M→A. If additional complete (without
interruption) thermal cycles were then made, the dilatation characteristics
would be the same as before interruption. The Ni54.2Mn29.4Ga16.4 alloy shows similar results; however, splitting of the CTE peaks is more
visible than in the first alloy. Figure 6 shows the temperature dependence of
the CTE after interruption when the interruption temperatures were 260°C,
261°C, and 265°C. The uninterrupted case is also shown in
this figure.Figure 3
Temperature
dependence of the relative elongation forNi53.6Mn27.1Ga19.3 alloy during the incomplete cycle with a stop at T=177°C.Figure 4
Temperature
dependence of the relative elongation forNi53.6Mn27.1Ga19.3 alloy after an incomplete cycle.Figure 5
Temperature
dependence of  CTE forNi53.6Mn27.1Ga19.3 alloy
after an incomplete cycle.Figure 6
Temperature
dependence of  CTE forNi54.2Mn29.4Ga16.4 alloy
after a single stop at T=260°C, 261°C, and 264°C.


## 4. Discussion

The
phase transformation starts to occur in the sample when its temperature reaches
the transformation temperatureTtr. When the surface sample
temperature reaches this temperature, the phase interface between
martensite-austenite propagates from the surface towards the core of the sample
during heating as well as cooling. The rate of the transient process (u)
depends on the thermal conductivity of the both phases (KM,KA),
the latent heat (H), density (ρ), heating rate, and time. For a given
time, u is given by following relation:
(1)u=1ρH(KM(∂T∂x)−KA(∂T∂x)). This relation
was modulated from a relation that was originally derived for the propagation
of a melting front in a conducting region [10]. In this relation, it was
assumed that the density of both phases is the same. The rate of propagation of
the phase interface, u, increases with an increasing/decreasing
temperature rate during heating/cooling. The phase transformation in the Ni53.6Mn27.1Ga19.3 alloy (Figure 1) takes about 10 minutes for the given heating rate of 2°C/min
(the time between the start and end of the phase transformation). This time is
reduced to 7 minutes for 5°C/min or 4 minutes for 7°C/min.
On the other hand, it increases to 40 minutes for a heating rate of 0.5°C/min.
It is necessary to note that the M-A transformation is an athermal phase
transformation that depends only on the temperature, and that it occurs
practically immediately [11] after reaching the transient temperature. The
relatively long duration of the phase transformation is a result of cooperation
of phase transformation (the latent heat) and thermal conductivity.It was mentioned in the experimental
section that our samples have a cylindrical shape. If a cylindrical sample is
suddenly subjected to an impact cooling or a phase transformation, thermal
stress waves occur at the surface of the sample. Stress waves in a cylinder
with a focusing point proceed radially inward to the center of the cylinder
sample. The waves may accumulate at the focusing point and give rise to very
large magnitude stresses. This phenomenon is known in the literature as the
stress-focusing effect [12, 13]. Theoretical analysis of the stress-focusing
effect induced by thermal expansion and phase transformation is presented in
the work of Hata and Sumi [14]. These authors have shown that when a cylindrical metal
sample is cooled instantaneously below the phase transformation temperature,
the stress-focusing effect occurs via expansion due to phase transformation and
thermal contraction.WhenTtr is reached at
the sample surface, the phase interface propagates into the sample and it
divides the sample into two ranges that have different structures and sizes. During the phase transformation M→A, the austenite layer occurs first on the
surface of the cylinder. As the austenite volume increases in the cylindrical
sample, the stress-focusing effect occurs at the center where the martensite
exists. This martensite then experiences compressive stress. If we interrupt
the phase transformation in a certain state, the sample will stay in this state
as long as the temperature does not change (Figure 3). Decreasing temperature
causes the austenite to transform to martensite (only the outside part of
sample). As the martensite in the center of the sample is deformed by
compression by the focusing effect, at the end of the interrupted thermal
cycle, the sample length is reduced (Figure 3). The sample returns to the
initial size when total thermal cycle including phase transformation is applied
(Figure 4). It can be seen that the influence of interruption on CTE is higher
in the nondeformed Ni53.6Mn27.1Ga19.3 alloy
than in the predeformed Ni53.6Mn27.1Ga19.3 alloy.
Figure 6 shows the influence of the interruption temperature on the splitting
of the CTE. The interruption temperatures were 260°C, 261°C,
and 265°C. Splitting of the transformation peak occurs only in the
case when the interruption was applied in the first cycle of transformation. It
can be seen from Figure 6 that the second peak shifts to higher temperature
with increasing interruption temperature. A higher interruption temperature
corresponds to a higher compression stress in the center of the sample.
Releasing of the compression deformation is a thermally activated process.
We
assume that the compression deformed center of the sample transforms at a
higher temperature than the nondeformed
center outside of the sample. The
difference of these temperatures is 2°C for an interruption
temperature of 260°C, and 2.5°C for an interruption
temperature of 261°C. This shift of the transient temperature
results in a splitting of the CTE transient peak. The splitting of the CTE does
not occur when the phase transformation is interrupted before its end (264°C)
because nearly the whole sample is transformed.Evolution of the
thermoelastic deformations during the phase transformation is schematically
shown in Figure7. In this schematic, we consider only heating because all
deformation changes occur during heating. The schematic of the phase
transformation M→A without interruption is shown in the first part of Figure 7.
In this schematic, we divide the duration of the phase transformation into two
parts. First, the transformation occurs in the external part of the cylinder.
This transformation is connected with the compression of the internal part of
the sample due to the focusing stress effect. In the second cycle of
transformation, the central part of the sample transforms and stresses what occurred in the
first cycle of transformation release. If we interrupt the M→A phase transformation, then the sample stays
deformed in compression (the second part of Figure 7). The sample is then
comprised of two parts: the center of the sample, which is the deformed
martensite, and the outside of the sample, which is the austenite. During the
following A→M transformation, only the austenite part of
the sample transforms and the martensite center of the sample stays unchanged.
After this thermal cycle, the sample stays macroscopically deformed in
compression at room temperature, resulting in a shortening of the sample. The
compression deformation is released only after the total M→A transformation, resulting in elongation of
the sample.Figure 7
Scheme
of evolution of the thermoelastic deformations in the sample during the phase
transformation.The results,
which are for both alloys, are summarized as follows.(1)
Part of the compression deformation is released during heating of the martensite below the transient temperature. The
second part of the deformation is released during the phase transformation.(2)
If the interruption is applied in the
first transformation cycle, then splitting of the CTE is found in the transformation
cycle when the sample center transforms.
During cooling,
no changes occur in the alloy.In our previous work [15], we have studied the dilatation characteristics
of a compression predeformed Ni53.6Mn27.1Ga19.3 alloy up to 1% with a maximum thermal cycle temperature of 380°C.
Relaxation of two sorts of strains took place in the thermal cycle after
predeformation. First, the memory strain could not be removed from the sample
because it is released during heating and occurs once more during cooling. Second,
the residual strain is released only during heating as a thermally activated
process. The residual strain is released in two temperature regions, during
heating of the martensite below the transformation temperature and during the
phase transformation. Release of compression deformation after interruption
takes place in a similar manner. A chief difference between both types of
relaxation is that in the first case, the entire sample was deformed and in the
second case only a part was
deformed. We assume that the deformed part of the sample (center) has a
higher transient temperature than the nondeformed part. This difference was
determined to be 2°C (from the temperature difference of the peak
maximum) for an interruption temperature of 260°C and 2.5°C
for an interruption temperature of 261°C. The first peak in the
temperature dependence of the CTE in Figure 6 belongs to the phase
transformation of the outside of the sample and the second lower peak in the
temperature dependence of the CTE is connected with the phase transformation of
the deformed sample center. This shift of the transient temperatures results in
splitting of the CTE transient peak. The same results are presented in the DSC
investigations. The transformation temperature of the second (third) peak is
shifted to higher temperatures (see, e.g., [4]).


## 5. Conclusion

The dilatation measurements and
their analyses show the evolution and release of thermoelastic deformations inNi53.6Mn27.1Ga19.3 and Ni54.2Mn29.4Ga16.4 shape memory alloys. If a cylindrical sample of the shape memory alloy is
heated or cooled from the outside, the martensitic phase transformation starts
on the surface and it propagates radially into the center of the sample. As a
consequence of this process, the stress-focusing effect occurs in the sample
center. During the M→A phase transformation, this effect causes a compression
deformation of the martensitic center of the sample. Interruption of the M→A
phase transformation results in a macroscopic compression deformation of the
sample. The shortening of the sample length is a consequence of this process.
Release of this compression deformation can be realized only with a total
thermal cycle where the phase transformation M→A is completed. The compression
deformation due to the focusing effect is released in two steps: during heating
of the martensite and during the phase transformation of the sample center.
These investigations show that TAME effect is a consequence of the stress-focusing
effect and the shape memory effect.



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*Source: 659145-2008-11-30.xml*