Development and Application of Biaxial Compression Test Device
for Metallic Materials
Ichiro Shimizu
Associate Professor, Graduate School of Natural Science and Technology
Okayama University
3-1-1, Tsushima-naka, Okayama 700-8530, Japan
shimizu@mech.okayama-u.ac.jp
ABSTRACT
In order to investigate plastic deformation behavior of metallic materials to a large strain state, a biaxial compression test
device was newly developed. The device employs a specimen of rectangular block shape and is possible to attain an arbitrary
strain path. As the first application of this device to metallic materials, two types of biaxial compression tests with an abrupt
strain path change without unloading were performed on industrial pure aluminum and titanium. Attentions were paid to the
equivalent stress-equivalent plastic strain relation, especially after the strain path change. The transient abnormal behavior of
the stress-strain relation was found just after the strain path change for both materials. Thus the influences of a pre-strain
amplitude and a angular relation of the sequential strain paths on the transient behavior were shown and discussed.
Introduction
Biaxial testing methods of metallic materials have been developed to investigate various physical characteristics, such as yield
criterion, hardening phenomenon and forming limit. The popular testing methods employed in previous studies are stretching,
torsion combined with internal pressure or axial tension, biaxial tension and biaxial compression. The stretching test has been
used to impose biaxial tensile conditions primarily in forming limit studies of sheet or tube type specimen, e.g. by Azrin and
Backofen [1]. It can be performed using a bulge and deep drawing machines, and the different strain paths are achieved by
changing the shape of specimen or punch tool. Although this method has contributed much to the progress of materials
especially for press forming and deep drawing, it is impossible to measure stress component in each direction therefore
inadequate to evaluate stress-strain relation of the material. The torsion test combined with internal pressure (e.g. by Hecker
[2] and Stout et al. [3]) or axial tension (e.g. by Moon [4] and Khan et al. [5]) is the most common method in studies of
constitutive relations. This test method naturally uses the thin-walled circular tube specimen, which is relatively difficult to
prepare. The method is possible to attain biaxial strain paths to a large strain range, however, the strain gradients in the
thickness direction and the variation of principal strain direction of the tubular specimen are unavoidable because of the
torsional deformation. For the sheet metals, biaxial tensile test is the most appropriate method to obtain the stress-strain
relation during biaxial deformation. The recent developments of the biaxial tensile apparatuses by Makinde et al. [6], Green et
al. [7] and Kuwabara et al. [8,9] made it possible to apply arbitrary proportional and non-proportional strain paths to the central
part of cruciform sheet specimens. However, the strain is generally limited to small value, because of the localized
deformation and increasing stress non-uniformity. Compared to those test methods, the biaxial compression is the only
method that is applicable to bulk materials therefore effective for the simulation of compressive bulk metal forming processes
such as forging and extrusion. Another advantage of the biaxial compression is that the uniform stress condition can be
achieved to a large strain state. In the early studies of biaxial compression by Bridgman [10], the block type specimen was
subjected to the simultaneous compression in two directions at right angles by four hard blocks, so that the strain in one
direction had to be positive. Tozawa [11] developed the original biaxial compression apparatus, which made possible the
biaxial compression with negative strain in two perpendicular directions, by replacing tools at every strain increment. The
other biaxial compression method used the channel die, e.g. by Franciosi et al. [12] and Khan et al. [13, 14], by which the
possible condition was limited to plane strain. Although valuable results have been obtained by those biaxial compression
methods, they are still not very versatile and there are limitations on the applicable strain paths, compared to the strain
histories of workpieces in practical metal forming processes.
Based on these facts, a biaxial compression test device is newly developed in the present study. This device is designed to
have two flat dies facing each other in one compression axis, and each die can slide in the direction perpendicular to the
compressive direction. The similar idea was also found by a device developed by Papka and Kyriakides [15] for crushing of
cellular materials. The device developed in this study is to apply arbitrary biaxial compressive strain paths to bulk metal
specimens without replacing tools and unloading.
As the first application of the newly developed device, biaxial compression tests with a strain path change were performed to
investigate the mechanical behavior, especially the specific stress-strain relation that often appear with the strain path change
in the plastic deformation range. As a pioneer work, Basinski and Jackson [16] performed torsion followed by uniaxial tension
of copper single crystal and they showed a transient increase in flow stress, namely latent hardening, in the beginning of the
tensile test. This phenomenon was later investigated also by Franciosi, et al. [17]. The similar behavior induced by the strain
path change was later reported also for polycrystalline metals by several researchers, e.g. Stout et al. [18], Raphanel et al. [19],
Vieira et al. [20], Corrêa et al. [21] and Schmitt et al. [22]. In those experiments, however, the strain path change was
performed after unloading that possibly varies the mechanical response. Furthermore, the investigation of the mechanical
behavior during compressive stress conditions is important not only for the development of plastic theory but also for quality
control of products in bulk metal forming processes. In the present study, two types of biaxial compression tests with an
abrupt strain path change without unloading were conducted on industrial pure aluminum and pure titanium. Thus, the
influences of pre-strain amplitude and angular relation of the sequential strain paths on the stress-strain relations were
discussed.
Biaxial Compression Test Device
The new biaxial compression test device is developed for a bulk metal specimen of rectangular block shape, thus it permits
easy preparation of the specimen. The mechanism of biaxial compression is illustrated in Figure 1. The four compression
dies are contacting with flat surfaces of the rectangular block specimen, respectively. The pair of two dies (Die 1 and Die 3,
Die 2 and Die 4) are facing each other along the loading axis. Each die is attached to a linear slide unit (THK LM Guide,
HSR30 model), which enables the movement of the die in the direction perpendicular to the loading axis with very small force
even during the compression. The coil spring is also attached to the die to force the die contacting with the neighboring one.
In Figure 1, the compression of the specimen in the x direction is performed with Die 2 and Die 4. At the same time Die 1 and
Die 3 move in the x direction, so that they do not disturb the x compression. The y compression is performed with Die 1 and
Die 3 in the similar way. These compressions can be performed independently and simultaneously, therefore the arbitrary
strain path is enabled. The maximum compression load in each axis is designed as 50kN.
Figure 1 Mechanism of biaxial compression enabling an arbitrary strain path.
The biaxial compression test device is mainly comprised of a loading system and two hydraulic control systems. Figure 2
shows the configuration of the loading system. The biaxial compression mechanism shown in Figure 1 is placed in the center
of the loading system. The compression load in each axis is applied by two hydraulic actuators (Taiyo, S100-1 model), which
has capacity of 80kN and stroke of 15mm, to keep the specimen close to the intersection of two compressive axes. For the
measurement of the compression load, a load cell (Kyowa, LC-10TV model) is attached to the guide plate and placed between
the hydraulic actuator and the linear slide unit. To ensure the linear motion along the loading axis, the guide plate has linear
bushings that slide on the guide shafts. The frame is made of a structure steel plate of 25mm thick, thus the rigidity is assured
even with large compression load. Strain measurement of the specimen is a problem in biaxial compression tests, because
the specimen is surrounded by the compression dies, so the attachment of displacement sensor directly to the specimen is
almost impossible. In the present device, strain-gage type displacement transducers (Kyowa, DTH-A model) are attached on
the compression dies and the tip of the transducer is contacted with the surface of the slide unit in the opposite side. Since the
measured displacement data include the deformation of not only the specimen but also the dies, the strain of the specimen is
evaluated by the displacement obtained by subtracting the elastic deformation of the die from the measured value. In Figure 2
the transducer for horizontal axis is displayed, while that for vertical axis is placed on backside.
The cross section of the specimen gradually grows during the compression, so the necessary load increases even without
work hardening. By this fact the initial dimension of the rectangular block specimen should be small enough to achieve the
Figure 2 Schematic and photograph of the loading system for biaxial compression test.
compression to a large strain state within the maximum output load of the loading system. Because of the small size
specimen, very precise control of the applied load is required for the investigation of stress-strain relation. For that purpose, a
hydraulic control system is also developed as shown in Figure 3. The hydraulic actuator (Taiyo, 70Z-1 model) with the capable
hydraulic pressure of 10MPa and stroke of 400mm is actuated by linear motion of a feed screw mechanism with a trapezoidal
screw. The linear motion of the feed screw mechanism is ensured by means of a linear slide unit. The rotation force
generated by a speed controllable motor (Oriental motor, FBL5120AW-200 model) is transmitted to the trapezoidal screw via
pulleys. The hydraulic lines from the control system are connected to two actuators in one compression axis of the loading
system. Consequently, large displacement with small force of the hydraulic actuator in the control system is transformed into
small displacement with large force of the actuator in the loading system.
The whole device is illustrated in Figure 4. The signals of load and displacement are transmitted to a sensor interface unit
(Kyowa, PCD-300A model) and then recorded simultaneously on a personal computer. Meanwhile, the hydraulic control
systems are connected to a motor control unit, which controls the load in both compressive axes simultaneously.
Figure 3 The hydraulic control system for biaxial compression test.
Figure 4 A schematic of whole view of the biaxial compression test device.
Experimental Procedure
As the first application of the newly developed device to the study of mechanical behavior of metallic materials, two types of
biaxial compression tests with abrupt strain path change were performed. Materials used were industrial pure aluminum
(Al99.84wt%, fcc structure) and pure titanium (Ti99.91wt%, hcp structure). The aluminum specimens were cut to a rectangular
block of 7mmx7mmx6mm (in x, y and z direction) from a swaged round rod. The side of 6mm was taken to be across the
length of the rod material. After mechanical polishing of all surfaces, the specimens were annealed at 673K for one hour to
eliminate residual stress. The titanium specimens were cut to 6mmx6mmx5mm (in x, y and z) from a hot-rolled plate. The
specimens were also mechanically polished and then annealed at 973K for one hour in vacuum. The side of 5mm was taken
to be parallel to the rolling direction.
Two types of biaxial compression tests with strain path change shown in Figure 5 were performed. In test A, the plane strain
compression in x direction was performed until the preset strain εx0 as pre-straining, with no deformation in y direction. The
compressive direction was then promptly changed to y direction without unloading under plane strain condition, namely with no
strain increment in x direction. In test B, the biaxial compression with arbitrary strain ratio was performed as the first path, until
the equivalent plastic strain became 0.25 and 0.2 for the aluminum and titanium specimens, respectively. The compressive
direction was then changed and the plane strain compression in y direction was continued. The strain ratio in the first path
was selected as the angle between the sequential strain paths became the preset value α. In the biaxial compression, a
lubricant of silicone grease mixed with boron nitride powder was supplied between the specimen and the die to reduce friction.
-4 -1
All tests were performed at an ambient temperature with slow strain rate of ~5X10 s . For direct comparison of the results by
various biaxial compressions, von Mises equivalent stress and equivalent strain were employed.
Figure 5 Strain paths in two types of biaxial compression tests.
Results and Discussions
Before the biaxial compression tests, the uniaxial compression tests in x and y directions were performed by the newly
developed device, to obtain the reference stress-strain curves. The true stress-true strain relations shown in Figure 6 indicate
the existence of small anisotropy in both aluminum and titanium specimens. Additionally, it could be confirmed that the newly
developed device is applicable to the mechanical testing of metallic materials.
The equivalent stress-equivalent plastic strain relations of aluminum and titanium in test A are shown in Figure 7. The
transient abnormal behavior after the strain path change is observed on all the results. For the aluminum specimen, the stress
slightly decreases and rapidly increases just after the strain path change. The stress then turns to be constant (for small prestrain |εx0|<0.1 in this case) or gradually decreases (for 0.1<|εx0| ) and after a while, the hardening rate approaches to that of
the monotonic deformation. Meanwhile, the stress considerably decreases and then gradually increases just after the strain
path change for the titanium specimen. The local minimum stress just after the strain path change is found to be
approximately on the back extrapolated curve of the stress-strain relation enough far from the point of strain path change.
Figure 6 True stress-true strain curves of aluminum and titanium specimens by unaxial compression tests.
Figure 7 Equivalent stress-equivalent plastic strain curves of aluminum and titanium specimens in test A.
These transient variations of the equivalent stress-equivalent strain relations are similar to those shown by Stout et al. [18] in
rolling followed by plane strain compression of aluminum, by Raphael et al. [19] in rolling followed by uniaxial tension of low
carbon steel and by Schmitt et al. [22] in sequential uniaxial tensions of copper. However, the detailed feature of the transient
variations in their results and the present results are different each other. For instance, the gradual decrease in the stress
after the transient increase is clearly seen for large pre-strain in the results by Stout et al. [18] and in the present results, while
not in the results by Schmitt et al. [22]. The conceivable causes of those differences are the different deformation patterns, the
different materials and loading/unloading at the strain path change. It should be noted that the abrupt strain path change
without unloading is effective for the study of the transient stress-strain relations, because the unloading causes dimensional
change of the specimen by elastic recovery and thus influences on the mechanical behavior in the successive deformation. It
is also obvious that the transient decrease in the stress just after the strain path change can be observed only when the strain
path change is performed without unloading.
If the material continues to obey the isotropic von Mises yield criterion even with a strain path change, the transient abnormal
behavior would not appear on the equivalent stress-equivalent plastic strain relation. For explaining the transient stress
variation, some sort of causes by the first plane strain compression should be considered. One conceivable cause is the
evolution of plastic anisotropy that influences on the yield locus thus on the stress-strain relation. Another conceivable cause
is "latent hardening" effect, which is originally defined for single crystalline metals as the resistance of dislocation structures
formed by the primary slip systems in pre-straining to the newly activated slip systems in the successive deformation [16,17].
Although it is for single crystalline, such microstructural effect must also occur in grains of polycrystalline metal. In order to
evaluate these causes independently, two parameters are introduced as be defined in Figure 8. One is the magnitude of the
transient decrease of equivalent stress Δσ a , which indicates the effect of anisotropy evolution during the pre-straining. The
effect of anisotropy influences on the wide range of stress-strain relation after the strain path change. Another one is the
Figure 8 Definition of parameters for evaluation of transient abnormal stress-strain behavior caused by strain path change.
Figure 9 Changes in magnitudes of transient decrease Δσ a and transient increase Δσ l of equivalent stress
with pre-strain amplitude in test A.
magnitude of the transient increase of equivalent stress Δσ l , which indicates the influence of microstructural effects on the
narrow range of stress-strain relation. Figure 9 shows the variations of Δσ a and Δσ l with the pre-strain amplitude. The
magnitude of the transient decrease Δσ a is found to lessen with increase in the pre-strain amplitude for titanium, while it
scarcely varies regardless of the pre-strain amplitude for aluminum. These results show that the initial anisotropy of titanium
gradually changes with the pre-straining, probably because the number of slip systems is smaller than that of aluminum and
thus the variation of anisotropy is easier to occur. Meanwhile, the magnitude of transient increase Δσ l gradually grows with
the pre-strain for both materials. This result implies that the microstructural effect, such as latent hardening, develops during
pre-straining in both aluminum and titanium regardless of the difference in crystal structure.
Figure 10 shows the equivalent stress-equivalent plastic strain relations of aluminum and titanium in test B. The stress-strain
curves for titanium were rather unstable, because of the difficulty on controlling the strain path during the biaxial compressions
with relatively heavy load. This problem may be caused by the sensitivity of the motor control for hydraulic loading system,
and the feed back of the displacement signal to the motor control unit will possible to solve it. For the small angle α≤30º
between the sequential strain paths, the transient abnormal behavior is scarcely observed. The transient increase in the
stress begin to be clearly observed for the angle α of 45º and its magnitude rapidly increases with the angle for both materials.
Figure 11 shows the changes in the magnitude of the transient increase of equivalent stress Δσ l with the angle α. The
increase in the microstructural effect with the angle α is clearly seen for both materials. However, this variation tendency with
the angle is different from those of the results by sequential uniaxial tensions of polycrystalline copper by Schmitt et al. [22], in
which the reloading stress reaches its maximum for the angle between the tensile axes of 45º~60º and then slightly drops with
increase in the angle. In the constrained biaxial compression followed by the plane strain compression in test B, the direction
of the material flow is very limited compared to the sequential uniaxial tensions. As a result of the limitation of the material flow,
the microstructural effect is possible to be facilitated because of the restricted direction of the dislocation movement. In order
to investigate the influence of those restriction of material flow on the transient behavior, the investigations covering wide
range of compressive strain paths will be the subjects in the future study by using the newly developed device.
Conclusions
The new device for biaxial compression with an arbitrary strain path was developed for mechanical testing of metallic materials.
As the first application of the newly developed device, two types of biaxial compression tests were performed on pure
aluminum and pure titanium. The new device was successfully applied to the biaxial compression tests of metallic materials
and it could be confirmed that the device was capable of supplying stress-strain relations in the deformation patterns closer to
Figure 10 Equivalent stress-equivalent plastic strain curves of aluminum and titanium specimens in test B.
Figure 11 Changes in magnitude of transient increase Δσ l of equivalent stress with angle
between sequential strain paths in test B.
the practical metal forming processes than conventional test methods, with less efforts for specimen preparation. In the
sequential plane strain compression tests, the transient decrease and increase of the equivalent stress were observed just
after the strain path change for both aluminum and titanium. However, the transient decrease of the stress for titanium was
more conspicuous than that for alunimum and varied with the pre-strain amplitude, probably due to the variation of plastic
anisotropy. Meanwhile, the transient increase of the stress due to microstructural effects was found to grow with the pre-strain
amplitude. In the biaxial compression followed by the plane strain compression, the transient stress increase scarcely appears
for the small angle between the sequential strain paths. Then, the transient stress increase begin to be observed and rapidly
grows with increase in the angle. Comparison of the results in the present study with those by Schmitt et al. [22] indicates the
importance role of deformation patterns upon the transient stress variation with the strain path change.
Acknowledgments
This research was partially supported by the Japan Ministry of Education, Science, Sports and Culture, Grant-in-Aid for Young
Scientists (B), No.15760063, 2003-2005. The author is indebted to Professor T. Abe of Tsuyama National College of
Technology and Professor N. Tada of Okayama University, for the valuable advices and encouragement on constructing the
biaxial compression device.
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