EXPERIMENTAL CHARACTERIZATION OF PHASE CHANGE
S. Valance, M. Coret, J. Réthoré and R. de Borst
LaMCoS, INSA-Lyon, CNRS UMR5259, F69621, France
ABSTRACT
This study focus on solid phase change in maraging steel on cooling and on heating, e.g. austenitic and martensitic
transformation. We present here the design and use of a device done for observation of front of phase change. This device is
constitute of a low vacuum box in which a test specimen could be submit to temperature and mechanic loading. While loading
the specimen in order to provoke phase change, the upper face of the specimen is observe with digital camera. We analyze
pictures issue from this observation we the help of digital image correlation. This finally enable us to find some indications on
phas front change position.
Introduction
While a phase transformation is happening, one of the most interesting phenomenon accompanying it is transformation
induced plasticity (TRIP). Consequences of this phenomenon are viewable at structural scale. It has been shown by Coret [1]
that TRIP simulation under complex load scenario is not achievable with actual analytic homogenization methods [2]. To
improve mechanical simulation of solid phase change in steels, it has been decide to study the real deformation happening in
such a phase change, with or without a mechanical load by simulating it at grain scale (mesoscopic scale).
The main problem in that simulation work is to get a real topology of phases throughout the transformation. At that time, this
kind of phase change as never been observed at mesoscopic scale. The only information consists then in heuristic hypothesis
[3]. To overcome this lake of information, we have design an experiment which enables the measurement of the displacement
field while a thermal phase change happens. To achieve that goal, we separate the work in two parts, the first one consists of
having images of the external surface of a sample while a transformation is happening. The second consist of interpreting
these images using Digital Image Correlation.
The paper will first present the experimentation device used to complete the observation of phase front and some images of
acquisition made during cooling while martensitic phase change happens. Then arise a discussion around the interpretation of
acquisitions using Digital Image Correlation method. We finally end by perspectives offered by using such a device.
Continuum mechanics in the phase change context
This paragraph deals with the description of a phase change in the context of continuum mechanics.
In continuum mechanics, the direct consequence of a phase change is a jump in density at the interface between the two
phases. We make here assumption that interface between the two phases is a surface, i.e. with null thickness. This hypothesis
is not realistic in a material point of view, where interface as a thickness of the same order than the lattice parameter, i.e., in
α
γ
pure metals, at 20 C, 0:286nm for Fe , and, at 916 C , 0:364nm for Fe , but is valid at an intermediate scale of observation.
Taking the precedent remarks into consideration, the mechanical problem associated to phase transformation could be
resume in the following set and on figure 1:
- Transformation between a phase γ (austenitic) and α (martensitic), without orientation (i.e. on cooling or heating)
- A continuous media Ω separated in two phase Ωα, density ρα and Ωγ, density ρα
- Normal velocity (W) of front Σt at time t between the two phases is perfectly known
Figure 1: model of continuous media submit to a phase change
The main interest of talking of continuum mechanics view on phase change is to emphasis the Hadamard jump condition.
Taking into account that we always deal with a continuous media, and that we have a strong discontinuity in the density field,
one can shows that it implies a weak discontinuity on the displacement field on the interface, i.e. the displacement field belong
0
to the function set C . Moreover, the derivative of the displacement field in time and space are discontinuous on the interface
of the phase change.
Main interest of emphasizing the Hadamard jump condition in the context of phase change study is to show a way for front
identification. If we are not able to measure the discontinuity in the density field, we are able to measure the displacement field
and what’s the more important, to identify the front on this displacement field.
Experimentation device
In order to explore the kinetic of phase transformation we build a device able to keep our test sample safe from oxidation and
authorize the observation of the upper face while heating and cooling in phase change temperature range. The
experimentation device is made of a box presented on figure 2. This box ensures tightness between the test atmosphere
which is under low vacuum (around .01mBar) and the room.
Figure 2: picture of the experimentation device showing the box, and the test sample
The thermal solicitation is applied using joule effect on the tested sample. The interest area of the sample test presented on
figure 3 is design to get a homogeneous temperature field. The cooling of the sample is ensured by liquid cooling of the whole
box. We could hence get a heating rate around 200°C /s and a cooling rate of 30°C/s. A temperature meas ure is done through
an encapsulated thermocouple applied on the surface of the test sample.
For the control of the tensile stress applied to the sample, we use a piezoelectric actuator. This piezo actuator is control in
force. It enables us to test the shape modification of the phase change controlling a really free dilatometry.
Figure 3: test sample design
To end the description of the experimentation, we present the optical system used for observation. A schematic view could be
found on figure 4. It is made of close up lenses in association with a bellows focusing. It gives a magnification of almost five
times while keeping a sufficient depth of field. A short edge filter, which suppress light wave of more than 565nm enable
observation at high temperature in spite of specimen radiation.
Figure 4: schema of the optical mount used for observation
Observations
In this section we present the use of the device for the observation of martensitic phase change.
For this paper we would only present one test campaign. Results are related to a phase transformation in a maraging steel on
cooling, i.e. a martensitic transformation. The chemical composition of the material we test is resume on figure 5. Maraging
steel is structural hardening material. There particularity is to transform into martensite even at low cooling rate.
C
< .01
Si
.06
Mn
.04
S
< .002
P
.005
Ni
9.01
Cr
12.20
Mo
2.
Al
.71
Figure 5: chemical composition of marval X12 maraging steel
Ti
.33
Fe
bal.
700
temperature (°C)
600
500
400
300
200
100
0
0
50
100
150
200
250
300
350
time (s)
Figure 6: temperature versus time for the considered test
The specimen is first warm at 600°C as shown on fig ure 6. At this temperature the austenitization of the sample begin. It is
kept at this temperature for enough long time in order to enable a complete transformation. Then, the specimen is cool down
to the room temperature. Observations shown in this paper come from the martensitic transformation. As shown on figure 7,
the temperature measure presents slow cooling rate part well revealed by polynomial interpolation of the measures. This slow
cooling rate part is due to exothermic transformation into martensite of the austenite.
400
temperature (°C)
350
temperature
300
Polynomial (temperature)
250
200
150
100
50
0
265
270
275
280
285
290
295
300
time (s)
Figure 7: temperature while martensitic phase change
Figure 8 (left) shows an acquisition of the upper face of the specimen on cooling at time 270s. This only observation is not
sufficient to observe the transformation front. We thus have to use Digital Image Correlation in order to retrieve the
displacement field on the upper face.
Interpretation
Here takes place the interpretation of acquisition done in the experiment presented above.
Digital image Correlation (DIC) is a way to retrieve the displacement field of a surface through the recognition of same pattern
in undeformed and deformed picture. Patterns use to correlate observations are made of scratch due to rough mechanical
etching.
Figure 8: surface of the specimen on cooling (left), different areas for strain integration (right)
In order to underline the variation of the displacement obtained after DIC, we use the norm presented below to plot it:
u=
were
ux
(u
x
− ux
) + (u
2
y
− uy
)
2
(1)
denotes the mean of displacement along the x axis on the whole specimen.
This norm presents two advantages. First one is to remove the rigid body motion of the correlated area due to the whole utility
area of the specimen. Second advantage is that with this norm, a free dilatation is plot by centered ellipse of iso-values.
Hence, in free dilatometry, if something else than dilatation is happening, it could be seen as through the lost ellipsoidal isovalues.
This phenomenon is shown on figure 9. Pictures presented issue from DIC of observation on cooling presented on figure 7.
The correlation area is visible on figure 8 (right). The reference picture takes for correlation corresponds to time 266s. These
pictures show the plot of the norm (equation (1)) rationalize by its maxima. It exergue the martensitic transformation
happening. First and last images show roughly ellipsis iso-values for the norm used. But central pictures show a break of those
ellipsoidal iso-values. These breaks correspond to phase transformation from austenite to martensite.
As this norm is not sufficient to retrieve the transformation front, we use a criterion on strain. From DIC, strains could be
retrieved using a mean on a local area. This processes imply a lost of information traduced by vanishing resolution on pictures.
The norm in strain use to represent strain is given by:
ε=
(ε
− ε yy ) + 4ε xy 2
2
xx
(2)
With the norm presented on equation (2), a free dilatometry is characterized by a constant value for any cooling rate. This is
represented on figure 10. We have plotted the mean of strain norm given by equation (2) on circle labeled 1 (figure 8 right).
The image reference for DIC used to obtain this graph is the last acquired, i.e. when the specimen is at room temperature.
This graph conforms to the macroscopic point of view of a phase change, i.e. global volume change. The phase change is
characterized by the passage from a constant value to zero. A discrepancy in time could be find by comparison to temperature
slow down. It could be explain by the fact that the temperature is not measure near circle but rather at the top of the correlated
area, as could be seen on figure 8.
Figure 9: iso-values of the mean of displacement field (equation (1)), from left to right, before the transformation,
while the transformation is happening, and after the transformation
400
0,0012
temperature
350
0,0010
c1
Polynomial (temperature)
0,0008
strain norm
temperature (°C)
300
250
0,0006
200
150
0,0004
100
0,0002
50
0
265
270
275
280
285
290
295
0,0000
300
time (s)
Figure 10: temperature and strain norm (equation (2)) in circle 1 versus time
We also investigate the variation of strain norm on littler areas (circles labeled 2 to 10 on figure 8 right). Graphs found are
collapse on figure 11. These graphs show a bit different point of view than the macro one presented on figure 10. Especially,
they show a maximum in the strain norm at different times. The variation of strain in local areas is due to transformation
happening in neighboring areas and to the crossing of the front in the considered area.
The first increase of strain should be due to the transformation happening in neighboring areas. The maxima should be related
to the crossing of the front. Indeed, as first explain by Greenwood [4], the maximal strain happening locally, concerns
principally the parent phase for such a transformation. We could then deduce that the decrease of deformation norm is related
to new phase. This criterion enable then us to identify the crossing of the phase change front in a local area.
c1
0,004
c2
0,003
c3
strain norm
0,003
c4
c5
0,002
c6
0,002
c7
0,001
c8
c9
0,001
0,000
265
c10
270
275
280
285
290
295
300
time (s)
Figure 11: strain norm (equation (2)) in different circles (c2-c10) while martensitic phase change
Conclusions
Due to evolution of numerical technique, we are now able to modelize behavior of material at finer scale for a structure design.
But this possibility comes with the necessity to get information at lower scale. The experiment shown here fill this objective.
The goal was to get information at mesoscopic scale on the position of the front of phase change.
Coarse understand of the mechanical consequences of a phase transformation associate to DIC enable us to find information
on the front position. Next step should lead to collapse all indications of the front position presented above in order to obtain an
explicit representation of the front position. We should then be able to observe consequences of a mechanical loading on the
front of phase change. Applications for different kind of metallic materials and solid phase change will also be affordable.
Acknowledgments
This research was sponsored by fédération Rhône-Alpes matériaux, conseil régional Rhône-Alpes, AREVA, EADS, EDF, ESI
software.
References
1.
2.
3.
4.
Coret, M., Calloch, S., and Combescure, A., “Experimental study of the phase transformation plasticity of 16MND5 low
carbon steel under multiaxial loading.” Eur. J. Mech. A/Solids, 823–842, 2004
Leblond, J.B., Mottet, G. and Devaux, J.C., “A theoretical and numerical approach to the plastic behavior of steels during
phase transformation i. derivation of general relations.” Jal. Mech. Phys. Solids, 34, 395-409, 1986
Magee, C.L., “Nucleation of martensite, phase transformations.” ASM, metal park, oh edition, 1970
Greenwood, G.W., and Johnson, R.H., “The deformation of metals under small stresses during phase transformations”
Proc. R. Soc., 283, 403-432, 1965