HIGH STRAIN RATE BEHAVIOUR OF ALUMINIUM ALLOYS USING SPLIT
HOPKINSON BAR TESTING
G. I. Mylonas, G. N. Labeas, Sp. G. Pantelakis
Department of Mechanical Engineering and Aeronautics
University of Patras
Laboratory of Technology and Strength of Materials (LTSM)
Panepistimioupolis
Rion 26500
Greece
gmylonas@mech.upatras.gr, labeas@mech.upatras.gr, pantelak@mech.upatras.gr
ABSTRACT
In the present paper the mechanical properties of a 7000 series aluminium alloy at high strain rates (1000 sec-1 to 9500 sec-1),
o
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from room temperature up to elevated temperatures (80 C, 140 C, 200 C and 300 C) are presented. The mechanical
characterization is performed by means of an experimental Split Hopkinson Bar (SHB) facility. The material’s flow stress,
maximum stress and modulus of Elasticity have been evaluated under high strain rate compression testing. In the investigation
the effect of temperature has been also taken into account. The experimental results have shown a significant effect of both
temperature and strain rate on the investigated material properties.
Introduction
In certain engineering materials processes (e.g. machining, shot peening etc.) the material undergoes heating at high
temperature, while at the same time, mechanical deformation occurs over a very small period of time. In such cases the
material’s mechanical behaviour can differ significantly from the behaviour obtained by the usual quasi – static tension or
compression tests. Hence, experimental data is required that can describe the material’s behaviour under high strain rate (SR)
and high temperature conditions; In particular, for aluminium alloys of 7000 series there is limited data available (most
common is AA7075 and AA7108) compared to other materials, e.g. steel.
Conventional servo – hydraulic machines are commonly used for testing at quasi – static strain rates in the range of 1 sec-1 or
less. In order to investigate the material’s behaviour at high SR, several testing methods have been developed over the last
years. The most widely used technique for high SR testing is the Split Hopkinson pressure Bar test (SHB).
Background theory, LTSM/UP facility and experimental procedure of Split Hopkinson Bar testing
A compression SHB facility, consists of a striker bar, an input bar and an output bar, while the test specimen is placed between
the input and output bar. Strain gauges are attached on the input and output bars, in order to record strain histories, which are
send to a data acquisition system for data collection and further processing. The striker bar (impactor) is accelerated by a
sudden release of compressed air in the gas gun (pipe) and impact’s the input bar. By the impact, a compressive longitudinal
wave (incident wave) is developed in the input (or incident) bar, which travels along the bar towards the specimen; when this
compressive wave reaches the incident bar / specimen interface, a part of it is reflected back as a tensile wave, while the rest
travels through the specimen and towards the output bar as a compressive wave. For the material properties calculation only
the initial tensile reflected and the initial compressive transmitted waves are used and not the complete recorded pulse [1].
The segregated effective pulses, used as input in the Equations (1) to (3), shown hereafter, in order to derive the specimen’s
stress and strain histories, as well as, the strain rate during the experiment. The main SHB equations used are the following:
Specimen Stress:
σ s (t ) = Eo ⋅
A0
⋅ ε o (t )
As
(1)
where:
A0
As
Eo
εo(t)
σs(t)
Specimen Strain:
where:
=
=
=
=
=
ε s (t ) = −2 ⋅
Ci
Ls
ει(t)
εs(t)
=
=
=
=
Input and output bars cross sectional area
Specimen cross sectional area
Striker, input and output bars modulus of Elasticity
Strain at output bar
Specimen stress
t
Ci
⋅ ε i (t ) ⋅ dt
Ls ∫0
(2)
Wave velocity
Specimen length
Strain at input bar
Specimen strain
Strain Rate:
dε s (t )
C
= −2 ⋅ i ⋅ ε i (t )
dt
Ls
(3)
A classical Split Hopkinon bar facility is installed at the Laboratory of Technology and Strength of Materials of University of
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Patras (Figure 1), which can achieve SR of the order of 100 – 10000 sec .
Figure 1. SHB facility of LTSM/UP
Figure 2. SHB pressurization system
The pressurization system of the SHB, which is shown in Figure 2, enables the safe system pressurisation up to 12bar, which
is required in order to achieve strain rates of 10000 sec--1 or higher (depending on specimen size). A control box allows the
use of each pressure network branch with high accuracy, while fast activated pressure valves are installed to achieve high
velocity air flow in the air – gun. The experimental process is almost fully automated, with very limited human interaction during
the experiment execution. Typical electrical resistance strain gauges of 2mm gauge length are used. The input, output and
striker bars, of the SHB apparatus, are made of maraging steel, having ultimate tensile strength of 980 MPa and yield stress of
760 MPa. The geometries of the striker, input and output bars were in agreement with the American Society of Metals (ASM)
handbook guidelines [2] and the related literature for the experimental configuration of a SHB arrangement. The specimen type
used to conduct the experiments is cylindrical with a length to diameter ratio equal to one.
For the experiments that were performed at elevated temperatures a heating system was used; the system includes a special
furnace to heat – up the test specimen and a real time temperature recording device in order to monitor the temperature in the
furnace. Special attention was given in the preparation of the experiment in order to minimise heat loss from the specimen.
In order to record the strain pulses during the experiment, the LabView software has been employed. The LabView software
creates the necessary memory space to save the experimental data points. After the experiment, the recorded pulses are
inputted to MatLab software where the data points collected can be plotted and then the effective pulses can be identified. The
MatLab based evaluation software was developed to plot, identify the starting and ending points of the effective pulses and
isolate them out of the output files generated after the experiment. In Figure 3, typical effective pulses, isolated from the
complete strain pulse are presented.
Figure 3. Isolated effective pulses
Subsequently, the effective pulses are inserted in Equations (1), (2) and (3), from which the material’s stress, strain and the
strain rate during the experiment are computed. In Figure 4, a typical true stress – true strain curve of the AA7xxx at RT and
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strain rate of 5300 sec , is presented. Further strain data processing leads to the calculation of strain rate history during the
experiment evolution (Figure 5).
STRAIN RATE
True Stress - True Strain Curve
1000
1100
1000
0
0.0E+00
900
Starin rate (1/Sec)
800
Stress (MPa)
700
600
500
400
True Stress - True Strain
300
5.0E-05
1.0E-04
1.5E-04
2.0E-04
2.5E-04
3.5E-04
-2000
-3000
-4000
Stress - Strain
200
3.0E-04
-1000
STRAIN RATE (er)
-5000
100
0
0
0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09
0.1
0.11 0.12 0.13 0.14 0.15 0.16
-6000
Time (Sec)
Strain
Figure 4. Stress–Strain curves obtained from SHB
-
Figure 5 – Typical SR history (sec 1)
Using the true stress – true strain graphs generated for each experiment, the material flow stress (σ0.2), maximum stress and
an approximation of the Elasticity modulus at high strain rate conditions can be derived. It should be mentioned here, that the
modulus of Elasticity values as obtained from SHB tests, should be considered as rough approximations, as during high strain
rate SHB experiments, the specimen material volumes are not under static equilibrium, due to the dynamic effects taking
place. In fact the stress equilibrium occurs at approximately 1% plastic strain and so it is impossible to accurately measure the
compressive modulus of Elasticity of a material at such high strain rates [2]. Therefore, indicative modulus of Elasticity results
only for RT conditions, are presented hereafter.
Experimental results
In the present investigation the high strain rate compressive behaviour of the 7xxx aluminium alloy has been investigated at
temperatures of 20oC, 80oC, 140oC, 200oC and 300oC. The influence of the strain rate on the flow stress, maximum stress and
modulus of Elasticity (RT) is evaluated for each investigated temperature and is presented in Figures 6 to 16. It should be
mentioned that each point plotted in the figures represents the average value of six experiment repetitions conducted for the
nd
specific temperature and strain rate. The fitting curves in the flow stress and maximum stress figures, are a 2 order
polynomial approximation interpolating the experimental points while, the curve interpolating the experimental points for the
modulus of Elasticity is a 3rd order polynomial approximation.
a) Influence of strain rate at 20oC
850
1100
800
1000
Maximum Stress (MPa)
Flow Stress (MPa)
In total 120 experiments (20 testing conditions x 6 repetitions) have been conducted. The influence of the strain rate on the
flow stress and maximum stress for the temperature of 20oC is presented in Figure 6 and 7 respectively.
750
700
650
600
AA7xxx - 20 deg.C
900
800
700
600
AA7xxx - 20 deg.C
500
550
400
500
0
1000
2000
3000
4000
5000
6000
7000
8000
0
9000
1000
2000
3000
4000
5000
6000
7000
8000
9000
Strain Rate (1/Sec)
Strain Rate (1/Sec)
Figure 6. Flow stress (σ0,2) Vs SR (sec-1) at RT
Figure 7. Maximum stress (σmax) Vs SR (sec-1) at RT
Modulus of Elasticity (GPa)
The influence of the strain rate on the modulus of Elasticity is presented in Figure 8.
200
AA7xxx - 20 deg.C
150
100
50
0
0
1000
2000
3000
4000
5000
6000
7000
8000
9000
Strain Rate (1/Sec)
-1
Figure 8. Modulus of Elasticity Vs SR (sec ) at RT
b) Influence of strain rate at 80oC
In total 96 experiments have been conducted. The influence of the strain rate on the flow stress and maximum stress for the
o
temperature of 80 C is presented in Figure 9 and 10 respectively.
850
900
Maximum Stress (MPa)
Flow Stress (MPa)
800
750
700
650
600
550
850
800
750
700
650
AA7xxx - 80 deg.C
AA7xxx - 80deg.C
600
500
0
1000
2000
3000
4000
5000
6000
7000
8000
9000
Strain Rate (1/Sec)
Figure 9. Flow stress (σ0,2) Vs SR (sec-1) at 80oC
10000
0
1000
2000
3000
4000
5000
6000
7000
8000
9000
10000
Strain Rate (1/Sec)
Figure 10. Maximum stress (σmax) Vs SR (sec-1) at 80oC
c) Influence of strain rate at 140oC
800
900
750
850
700
650
600
550
500
AA7xxx - 140 deg.C
Maximum Stress (MPa)
Flow Stress (MPa)
In total 78 experiments have been conducted. The influence of the strain rate on the flow stress and maximum stress for the
temperature of 140oC is presented in Figure 11 and 12 respectively.
800
750
700
650
600
AA7xxx - 140 deg.C
550
450
500
400
0
1000
2000
3000
4000
5000
6000
7000
8000
9000
0
10000
2000
4000
6000
8000
10000
Strain Rate (1/Sec)
Strain Rate (1/Sec)
Figure 11. Flow stress (σ0,2) Vs SR (Sec-1) at 140oC
Figure 12. Maximum stress (σmax) Vs SR (sec-1) at 140oC
d) Influence of strain rate at 200oC
In total 90 experiments have been conducted. The influence of the strain rate on the flow stress and maximum stress for the
o
temperature of 200 C is presented in Figure 13 and 14 respectively.
700
550
450
400
350
300
250
200
AA7xxx - 200 deg.C
Maximum Stress (MPa)
Flow Stress (MPa)
500
150
600
500
400
300
AA7xxx - 200 deg.C
200
100
100
0
1000
2000
3000
4000
5000
6000
7000
8000
0
9000
1000
2000
3000
4000
5000
6000
7000
8000
9000
Strain Rate (1/Sec)
Strain Rate (1/Sec)
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o
Figure 13. Flow stress (σ0,2) Vs SR (sec ) at 200 C
Figure 14. Maximum stress (σmax) Vs SR (sec-1) at 200oC
e) Influence of strain rate at 300oC
In total 108 experiments have been conducted. The influence of the strain rate on the flow stress and maximum stress for the
o
temperature of 300 C is presented in Figure 15 and 16 respectively.
350
310
290
Maximum Stress (MPa)
Flow Stress (MPa)
500
AA7xxx - 300 deg.C
330
270
250
230
210
190
170
150
450
400
350
300
AA7xxx - 300 deg.C
0
1000 2000 3000 4000 5000 6000 7000 8000 9000 10000
250
0
Strain Rate (1/Sec)
Figure 15. Flow stress (σ0,2) Vs SR (sec-1) at 300oC
1000 2000 3000 4000
5000 6000 7000 8000 9000 10000
Strain Rate (1/Sec)
Figure 16. Maximum stress (σmax) Vs SR (sec-1) at 300oC
f) Experimental results overview
The influence of strain rate and temperature on the mechanical behaviour of the specific alloy is summarised in Figures 17 and
18.
900
800
700
Flow Stress (MPa)
600
AA7xxx - 20 deg.C
500
AA7xxx - 80 deg.C
AA7xxx - 140 deg.C
400
AA7xxx - 200 deg.C
300
AA7xxx - 300 deg.C
200
100
0
0
1000
2000
3000
4000
5000
6000
7000
8000
9000
10000
Strain Rate (1/Sec)
-1
Figure 17. Flow stress (σ0,2) Vs SR (sec ) at all Temperatures
1200
Maximum Stress (MPa)
1000
800
AA7xxx - 20 deg.C
AA7xxx - 80 deg.C
600
AA7xxx - 140 deg.C
AA7xxx - 200 deg.C
400
AA7xxx - 300 deg.C
200
0
0
1000
2000
3000
4000
5000
6000
7000
8000
9000
10000
Strain Rate (1/Sec)
Figure 18. Maximum stress (σmax) Vs SR (sec-1) at all Temperatures
Discussion of the experimental results
The experimental results presented in Figures 6 to 16 and summarised in Figures 17 and 18 indicate that there is a general
trend of flow stress increase with increasing strain rate. The increase in flow stress is observed for the majority of temperatures
investigated. In the case of 300oC, the flow stress is increasing with increasing strain rate up to the value of 5500 sec-1
(highest flow stress value) and after that is gradually decreasing with increasing strain rate up to the maximum value of 9000
sec-1. The mentioned behaviour observed at 300oC, where temperature effects on material microstructure are expected to be
more significant, is currently under investigation. It must be also mentioned that, at a number of temperatures (200oC and
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300 C) the increase is steeper compared to that of the temperatures of 20 C, 80 C and 140 C, where the increase is
smoother.
In Figures 17 and 18 the effect of temperature on the investigated material properties is also displayed. With increasing
o
temperature ranging from room temperature to 80 C no significant effect on the flow stress at small strain rate values is
observed. However, when the strain rate is increasing the effect of the temperature becomes more important and results to a
decrease of the flow stress; this observed trend of decreasing flow stress with increasing temperature may be noticed for the
majority of engineering materials [3]. The highest drop in flow stress values is observed at the temperature range between
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140 C and 200 C. At the temperature of 300 C, at strain rates of 1000 sec 1 to 5500 sec 1, flow stress values are very similar
o
to the flow stress obtained at 200 C, from strain rate higher than 5500 sec 1 the flow stress is gradually decreasing with
increasing strain rate.
In the case of the maximum stress (σmax) values, the obtained results are in accordance to the general trends observed for the
flow stress values. An increase of the maximum stress with increasing strain rate has been observed for all temperatures
investigated.
The modulus of Elasticity values obtained from SHB tests at different temperature (Figure 8) are as explained only an
approximation of the actual Elasticity modulus of the material at high strain rates. In particular for aluminium alloys, the form of
the linear part of the stress-strain curve is more difficult to be derived with accuracy compared to steel, due to the higher
damping of aluminium material. Hence the results presented in Figure 8 are used only for a qualitative evaluation of the
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modulus of Elasticity – strain rate dependence. Approximation errors are expected to be higher for high SR (5000 sec and
more) due to pronounced dynamic effects taking place.
Conclusions
In the present work the mechanical behaviour of an aluminium 7xxx series alloy at several high strain rates for room and
elevated temperatures is examined. The characterisation of the material is performed by initially deriving stress – strain curves
for strain rates between 1000 sec-1 and 9500 sec-1, and subsequently by determining the flow stress, the maximum stress and
modulus of Elasticity of the material at the strain rate values mentioned by taking into account the effect of temperature. The
obtained experimental results indicate a significant influence of the increased strain rate and temperature on the investigated
material properties. More specifically, a material’s flow stress and maximum stress increase with increasing strain rate has
been observed. Both properties have been found to decrease with increasing temperature at the strain rate values
investigated. The derived material data may be used for simulation of processes which force the material to undergo high
strain rates and elevated temperatures.
Acknowledgments
The authors wish to acknowledge the European Union for their financial support to this research. The results presented in this
paper are partially obtained in the frame of the European Union funded research program “COMPACT - A concurrent
approach to manufacturing induced part distortion in aerospace components”.
References
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2.
3.
Kaiser A. M., Advancements in the Split Hopkinson Bar Test, MSc Thesis, Blacksburg, Virginia, 1998
Kuhn, H., Medlin, D., ASM Handbook Volume 08: Mechanical Testing and Evaluation, ASM International, USA
Woei-Shyan Lee, Wu-Chung Sue, “The strain rate and temperature dependence of the dynamic impact properties of 7075
aluminium alloy”, Jounrnal of Materials Processing technology, 100, 116 – 122 (2000).