EXPERIMENTAL INVESTIGATIONS OF THE DYNAMICS
OF PLC BANDS IN AL-MG ALLOYS
Leobaldo Casarotto, Rainer Tutsch, Hanno Dierke and Hartmut Neuhäuser
Institut für Produktionsmesstechnik, Technische Universität Braunschweig
Schleinitzstrasse 20, 38106, Braunschweig, Germany
Institut für Physik der Kondensierten Materien, Technische Universität Braunschweig
Mendelsohnstrasse 3, 38106, Braunschweig, Germany
[email protected]
ABSTRACT
An experimental approach for the investigation of the PLC effect is here presented. It permits a complete characterization of
the PLC bands, regions of concentrated strain, thanks to the coupling of a global and a detailed observation scale. A deeper
insight into the dynamics of band emergence is also possible because the camera for the detailed observation is a high-speed
camera that can capture several phases of these fast events. Some experimental results are then provided to illustrate the
benefits of this approach.
Introduction
The Portevin-Le Châtelier (PLC) effect is a well known kind of plastic instability that, during the deformation of many metal
alloys, can be encountered in certain ranges of temperature and strain rate [1]. Manifestations of this effect are also influenced
by the previous history of the material. Aluminium alloys are particularly subject to this phenomenon and most investigations
are thus focused on this material class [2], nevertheless the PLC may affect any ductile alloy because it just originates from the
interaction between dislocations and solute atoms. The phenomenon is undesired because it induces a repetitive loss of
uniformity of the plastic deformation and the appearing of the effect in the industrial production is usually avoided by working in
confidence ranges where it is known not to occur. However, a more complete theoretical comprehension of the phenomenon
would be of great interest in order to develop working processes and reinforcement mechanisms that act on the origins of the
effect and are able to suppress its manifestations. Furthermore, the phenomenon is also paradigmatic for a large class of non
linear systems that exhibit intermittent bursts [3]. The results obtained with the investigations of the PLC effect could be thus
extended to the study of other phenomena.
th
The PLC effect is the object of many research works since its first observations in the 19 century and several experimental
methods have been employed for these studies [4]. However, some aspects of the effect are not well understood and the
dynamics of the strain localization is still under investigation. The methodical observation of the region of concentrated strain,
referred to as PLC bands, is in fact a relatively recent task of the investigations [5], but is of prominent importance since these
bands embody the connection between the macroscopical manifestations of the effect and its origins in a microscopical level.
In this work we present an approach for a complete observation of the PLC bands. Tensile tests on an Al-Mg alloy are assisted
by a two camera system for a global and a detailed observation of the material behaviour. The global observation is
continuous and thanks to a real-time analysis of the data it permits an immediate identification of the bands so that, if any is
found emerging in the area framed by the second camera, a trigger signal is released. For the detailed observation an highspeed camera is employed in order to capture band emergence with a good temporal and spatial resolution. Sequences from
this camera are processed after the test with a image correlation algorithm in order to determine the evolution of the strain
distribution associated to a band.
Phenomenology of the PLC effect
Manifestations of the PLC effect can be immediately seen in the stress-strain curve of a material as a series of discontinuities
in the plastic region. These discontinuities correspond to states of non uniform deformation of the material, i.e. to the
appearing of PLC bands, and carry therewith a first level of information about the effect. A typical curve is showed in Fig. 1
where the discontinuities have a saw-teeth shape. They are more numerous and less pronounced at the beginning than at the
end of the test, where the frequency falls below 1Hz and the stress drops grow over 10 MPa. Each discontinuity is associated
to a single band and can be explained in terms of reduction of the stress consequent to a small elongation of the specimen.
Figure 1. PLC discontinuities in the stress-strain curve from a tensile test on Al3Mg
Traditionally, it is distinguished among three kinds of band behaviour: type A, which is a strain profile that propagates
continuously and regularly along the specimen; type B, individual static bands that emerge one beside the other, giving rise to
an apparent propagation; and type C, individual bands regularly spaced in time, but with no correlation about their positions.
As a rule of thumb, the first type can be encountered at low temperatures and high strain rates, while type B and following type
C become probable with the increasing of the temperature and the decreasing of the velocity. The band behaviour is also
influenced by the deformation state of the material and, during a tensile test, a sequence A→B→C can be expected. However,
this order is not the only one possible and sequences C→B are experimentally encountered. Usually, the band type can be
associated to a specific pattern of discontinuities in the stress-strain curve, but this association is not always reliable and the
band type can be properly identified only by considering the position of the bands [6].
The appearing of bands is due to a negative strain rate sensitivity of the material that facilitates the concentration of strain in a
sort of necking [7]. This concentration, however, is counterbalanced by a local strain hardening that prevents the material
failure. A band corresponds therefore to a specimen thinning of few micrometers over an extension of a couple of millimetres.
After the emergence of some bands the material surface appear undulating, but at the end of the test is completely rough [8].
Under certain conditions, single bands can even be seen with bare eyes, but a direct observation of the phenomenon is often
not successful. Nonetheless, bands can be visualized by subtracting the values of two images, as suggested in Fig. 2, or after
calculating the strain distribution.
Figure 2. Pictures of the specimen a) before and b) after the band emergence. Band becomes visible after subtraction of the
two intensity fields (contrast and brightness are enhanced).
It is evident that, in the case of industrial production, these manifestations can not be accepted because they lead to a bad
superficial finiture or to a not uniform embrittlement of the material [9]. The most troublesome processes are of course the
ones based on the plastic deformation, as the deep drawing of sheets or the wire drawing [10], but also cutting can results in a
irregular chipping of the surface.
The investigation of the PLC effect is concerned with the measurements of these phenomenological aspects both at a
macroscopical and a microscopical scale. Aim of the macroscopical measurements, the only one that can be done during the
material tests, is to obtain data about the PLC bands in order to compare these values to the ones predicted by theoretical
models. These data are the position and, in case, the propagation velocity, the width, the displacement and strain distributions
inside bands. Information about band dynamics are also very important in order to ascertain the ruling factors.
Experimental
Tensile tests were performed at different strain rates by means of an Instron 1185 machine that was equipped with a 10 kN
load cell. The employed material was an Al-3wt.%Mg alloy, which belongs to the AA5754 class, i.e. it has good formability and
is typically used for the deep drawing of panels. Specimens were prepared in a dog-bone shape in order to be geometrically
engaged in the machine; they were cut from sheets rolled to a thickness of 0.5, 1 or 1.5 mm, have a gauge length of 54 mm
and are 4 mm width. Before testing, material was annealed for 5 h. at 400°C.
A two camera system is appended to the machine so that both sides of the specimen can be observed. A schema of the setup
is given Fig. 3 where the specimen is illustrated between a line-scan camera, that frames the whole gauge length, and a highspeed camera, for the imaging of the bands with high temporal and spatial resolution. The digital line-scan camera is a
Schäfter & Kirchhoff 1024DDE, it acquires lines with 1024 pixels at frequencies up to 10kH. The high-speed camera is a
Vosskühler HCC1000 with a 1024 × 1024 pixels sensor and a full-frame capability of 500 fps; in our applications, a sensor
window of 512 × 1024 pixels with resulting 1000 fps is used. The front side of the specimen is coated with a stripe pattern that
divides the whole length into small zones. The position and the width of these zones can be easily followed with the line-scan
camera, which permits the identification of emerging bands. Depending on the machine strain rate, the camera is operated
between 450 and 2500 fps so that a continuous survey of the zones is performed. Pictures are processed immediately after
their capture and the position of the zones are calculated with a subpixel accuracy. Given the camera resolution of 65 µm/pixel
and the high frame rate, the zone movements image by image are in fact well below the pixel. The history of the positions that
a zone occupies in the time is low-pass filtered with an exponential smoothing, an iterative calculation based only on the
current raw value and the previous filtered result. The chosen algorithms are simple in order to keep the processing time very
short, but are effective, as the curves in Fig. 4 clearly display.
Figure 3. The experimental setup
In Fig 4. the trajectories of two neighbouring zones in a time interval of 40 s can be seen (the image number in x-axis is
proportional to the elapsing time). As one can notice, the overall displacement of zones in the sequence is around one pixel,
but the trajectories are clearly discontinuous because of vertical “springs” that are caused by PLC occurrences. The arrows
indicate a band that emerges between the two zones and move them in opposite directions. The identification of bands, more
exactly of their position and time of appearance, is based on the recognition of similar patterns when all zones are taken into
consideration. This analysis is performed directly after the acquisition of a picture so that a trigger signal can be sent to the
second camera whenever a band is found to emerge in the area that it frames.
Figure 4. Positions of two neighbouring zones in a short time interval. Arrows indicate the instant in which a band emerges
between the two zones and move them in opposite directions.
The high-speed camera frames a region of 8 × 4 mm² in the middle of the specimen with a resolution of 8 µm/pixel. The onboard memory of the camera is organized with a system of 14 ring-buffers, each with slots for 70 pictures. Pictures are
continuously taken and temporary stored in the active ring-buffer; after reception of the trigger signal, some further pictures are
taken and then the current ring-buffer, that now contains images of the band emergence, is deactivated and the system is
switched to the next one. When the memory is completely occupied, the images are transferred to the hard disc of a PC unit,
where they will be processed with a digital image correlation method after the test. A programme was developed to load an
entire sequence and to calculate at first the complete band, by using an image before and one after the event, and then the
phases of its growth, where each phase is given by two successive pictures.
Results
An overview of the material behaviour can be obtained by means of the so called correlation diagrams, an example of which is
given in Fig. 5. These charts are based on the measurements of the line-scan camera and display the PLC events as a
function of the position and of the time of their appearing. From the disposition of the points on the chart it is possible to
identify the band types. Initially, the points in the example of Fig. 5 are randomly distributed, which characterizes bands as type
C, but after about ten minutes they begin to be piecewise aligned in short type B propagations. These propagations become
more regular but slower as the test proceeds; at the end, bands appear only in the region where the necking eventually occurs.
The propagation velocity can be calculated as the slope of the aligned points and in the case of this test it remains between 2
and 0.5 mm/s.
-4
Figure 5. The correlation diagram from a tensile test at 1.13 × 10 on an 1 mm thick specimen.
From the curves of the zone position, as the ones in Fig. 4, it is found that the development of a band (the almost vertical
discontinuity) has a duration of few milliseconds, while it induces a local elongation of about 5µm. This kind of information,
however, can be more comfortably gathered from the distribution of displacements and strains calculated with the images from
the high-speed camera.
In Fig. 6 an entire band is represented by means of the distribution of the first principal strain and appears as a narrow region
of about 2 mm width and tilted by 56° to the horizontal, the loading direction. The band is of type C, i.e. it is an isolated event.
One can notice that for a short time interval (20 ms in this case) the strain is practically concentrated only inside the band.
From the associated displacement filed, which is schematically illustrated in Fig. 7, it is clear that the band is oriented along the
direction of the maximal shear strain.
Figure 6. Distribution of the first principal strain (in horizontal direction) for an entire type C band.
Figure 7. Schematical representation of the displacement distribution associated to a PLC band.
From these distributions it is possible to measure the width of the bands and the level of strain inside them. Fig. 8 shows a
comparison among three specimens with different thickness in order to display the direct proportionality between this
geometrical factor and the width of the PLC bands. In Fig. 9 the trend of the average strain inside bands during tensile tests on
specimens with different thickness is given.
Figure 8. Band width for specimen having thickness of 0.5, 1 and 1.5 mm, respectively.
-4
Figure 9. The average strain inside bands during tensile tests at 1.13 × 10 on a) 0.5, b) 1, c) 1.5 mm thick specimens
(lines are guides for the eyes).
The observation of the phases of the band growth is useful to display the dynamics of the process. In Fig. 10 a sequence of six
phases for a type C band can be seen. The overall duration of the band growth is over 20 ms, but most of the deformation
occurs in the displayed sequence of 5 ms. The band starts from one border of the specimen and proceeds to the other one in
the direction of the highest strain.
Figure 10. The phases of formation of a type C band. The time between two following frames is 1 ms.
In case of type A propagation, longer picture sequences were recorded in order to investigate the movement of the band front.
In Fig. 11 one of these propagations is shown by means of the displacement distribution calculated on intervals with 50
frames. The band front seems to advance regularly and with the constant velocity of 18 mm/s. However, reducing the time
between two phases to 10 ms, the real advancing mechanism can be grasped. Fig. 12 shows phases from the same
propagation for a shorter interval and now the angle of the band front is seen to switch between two orientations. A possible
interpretation for this behaviour is that the propagation is not regular and continuous as it is always described, but rather
consisting of a fine succession of narrower bands that, one by one, enter from one border and move transversally to the axis,
similarly to the type C dynamics in Fig. 10. A schema for this interpretative model is given in Fig. 12.
Figure 11. Some phases from a type A propagation. The time interval between two following phases is 50 ms.
Figure 12. Some phases from the same propagation in Fig. 11, but now with an interval of 10 ms.
Figure 12. An interpretative model for the type A propagation
Conclusions
An approach for the complete characterization of the Portevin-Le Châtelier has been here proposed. The aim is to increase the
amount of information that can be obtained from a single test on the material and the key elements of the developed system
are the coupling of a global and of a detailed observation and the use of high-speed cameras. The high frame rate of the linescan camera used for the global observation permits the real-time identification of the PLC band and thus the triggering of the
second camera. The high frame rate of the second camera allows us to get a new insight in the dynamics of band emergence.
Several tensile tests have been assisted with this multiscale system and some of the results have been presented as example
of its potentialities.
An interesting development for these investigations is the calculation of the strain rate distribution from the image sequences
of the high-speed camera. A proposal for this approach is given in [11].
Acknowledgments
This work was possible thanks to the funding of the Deutsche Forschungsgemeinschaft (DFG).
References
1.
Zaiser, M. and Hähner, P., “Oscillatory modes of plastic deformation: theoretical concepts,” Phys. Stat. Sol. B, 199, 267330 (1997)
2. Klose, F., “Experimental and numerical studies on the Portevin-Le Châtelier effect in Cu-Al and Cu-Mg in strain and stress
controlled tensile tests,” Phd Thesis, Technische Universität Braunschweig (2004)
3. D’Anna, G. and Nori, F., “Critical dynamics of burst instabilities in the Portevin-Le Châtelier effect,” Phys. Rev. Let., 85, 19,
4096-4099 (2000)
4. Hähner, P., Ziegenbein, A., Rizzi, E. and Neuhäuser, H., “Spatiotemporal analysis of the Portevin-Le Châtelier
deformation bands: theory, simulations and experiment,” Phys. Rev. B, 65, 134109 (2001)
5. Chihab, K., “Etude des instabilities de la deformation plastique associees a l’effet Portevin-Le Châtelier dans alliage
aluminium- magnesium,” PhD thesis, Universitè de Poitiers (1986)
6. Ziegenbein, A., “Laserextensometrische Untersuchungen des Portevin-Le Châtelier Effektes an einer CuAl-Legierung,”
PhD thesis, Technische Universität Braunschweig (2000)
7. Hähner, P., “On the Physics of the Portevin-Le Châtelier Effect part1: the statistics of dynamic strain ageing,” Mat. Sci.
Eng., A 207, 208-215 (1996).
8. Webernig, W.M., Pink, E. and Krol, J., “Stretcher strain markings and the fracture of thin sheets of Al-Mg alloys. Part I:
experimental evidence,” Zeit. Für Metallkunde, 77, 3, 188-192 (1986)
9. Abbadi, M., Hähner, P. and Zeghloul, A., “On the characteristics of Portevin-Le Châtelier bands in aluminium alloy 5182
under stress-controlled tensile testing,” Mat. Sci. Eng. A, 337, 194-201 (2002)
10 Karim Taheri, A., Maccagno, T.M. and Jonas, J.J., “Dinamic strain ageing and the wire drawing of low carbon steel rods,”
ISIJ Int., 35, 12, 1532-1540 (1995)
11. Broggiato, G.B., Casarotto, L. and Del Prete, Z., “Full-field strain rate measurement by white light speckle image
correlation,” this book.