Materials Transactions, Vol. 49, No. 1 (2008) pp. 20 to 23
Special Issue on Severe Plastic Deformation for Production of Ultrafine Structures and Unusual Mechanical Properties:
Investigating Role of High-Density Lattice Defects
#2008 The Japan Institute of Metals
Assessment of Strain Energy by Measuring Dislocation Density
in Copper and Aluminium Prepared by ECAP and ARB
Yoshinori Murata, Ippei Nakaya* and Masahiko Morinaga
Department of Physics, Materials and Energy Engineering, Graduate School of Engineering,
Nagoya University, Nagoya 464-8603, Japan
In order to estimate the strain energies of pure Cu and pure Al prepared by ECAP and ARB processes, dislocation densities remaining in
these metals after each process were analyzed by the Warren-Abervach method based on the Williamson-Hall plot from a series of data taken by
conventional X-ray diffractometry. The measured dislocation density was higher by several times in pure Cu than in pure Al regardless of ECAP
and ARB, resulting in the higher strain energy stored in pure Cu than in pure Al. Also, the dislocation density was found to be lower in the f.c.c.
phase in pure Cu than that in the lath martensite phase in high Cr ferritic steels. Furthermore, it was observed that the amount of stored strain
energy in pure Al depended considerably on its purity. [doi:10.2320/matertrans.ME200707]
(Received July 2, 2007; Accepted October 17, 2007; Published December 25, 2007)
Keywords: equal channel angular pressing (ECAP), accumulative roll bonding (ARB), giant strain, strain energy, dislocation, copper,
aluminium
1.
Introduction
For structural metallic materials, it is very important to
produce a unique property by microstructural control. One of
the ultimate controlling methods is the severely plastic
deformation, which produces ultra-fine grains and characteristic phenomena such as deformation softening,1) high corrosion resistance, etc. Although these phenomena have not
been clarified yet, the unique mechanism is probably
associated with the ultra-giant strain introduced by the
severely plastic deformation, so that the amount of the strain
in metals should be estimated quantitatively.
However, the stored strain energy in materials can not be
measured directly by conventional experimental methods.
Recently, the strain energy stored in the martensite phase has
been obtained successfully by measuring the dislocation
density, since the strain energy can be calculated using the
elastic modulus and the Burgers vector of the material.2)
Here, the microstructure formed by the martensite transformation in low carbon steels is composed of the lathmartensite phase containing high dislocation density without
twin. The large strain originated from the adiabatic transformation from the austenite phase to the martensite phase is
considered to be stored in the steels as dislocations, and
hence the strain energy in the metallic material can be
obtained experimentally by measuring the dislocation density
in it.
We applied this concept to the estimation of the strain
energy in metals undergone the severely plastic deformation.
The purpose of this study is to measure the dislocation
density as well as the strain energy introduced to pure Al and
pure Cu by severely plastic deformation in the ECAP or the
ARB process.
2.
Experimental Procedures
Materials used in this study were pure Cu of 4N and 3N
*Graduate
Student, Nagoya University
and pure Al of 2N and 4N. These metals were deformed in the
ECAP (Equal Channel Angular Pressing) process into rod
shape or in the ARB (Accumulative Roll Bonding) process
into plate shape. The number of passes was 14 for both the
processes. The equivalent strain after N passes, "N , in the
ECAP process was calculated by the following equation,3)
N
þ
þ cos ec
þ
: ð1Þ
"N ¼ pffiffiffi 2 cot
2 2
2 2
3
Here, and are the channel inner angle and outer angle,
respectively, and both of them were =2 in this study. In the
ARB process, the equivalent strain was set to be 0.8 times N
(the number of rolling).
Each specimen after the deformation was cut into a proper
size suitable for a conventional X-ray diffraction method, and
then it was polished mechanically with emery papers down to
#2000 followed by the buff polishing with Al2 O3 powders
down to 0.3 mm. After the mechanical polishing, specimens
were polished electrolytically in a 10%perchloric-acetic acid
solution for aluminium and in a 10%phosphoric acid-aqueous
solution for copper.
Dislocation density in each specimen was estimated by the
Warren-Averbach method based on the Williamson-Hall plot
using the conventional X-ray diffraction data of (111), (200),
(220), (311), (222) and (400) reflections. The detailed
explanation is given elsewhere.2) The estimated dislocation
density was converted into the stored strain energy in metals
using the following equation,4)
Edis b2 Re
ln ;
4
r
ð2Þ
where, is the shear modulus; ¼ 4:6 1010 N/m2 for
Cu5) and ¼ 2:6 1010 N/m2 for Al.6) b is the magnitude of
the Burgers vector, i.e., b ¼ 0:286 nm for Al and b ¼
0:256 nm for Cu. Re is the outer cut off radius for calculating
the strain energy around a dislocation, and is the dislocation
density. r is the radius of dislocation core to be set at 5b
in this study. Both Re and can be determined using
experimental data.
Assessment of Strain Energy by Measuring Dislocation Density in Copper and Aluminium Prepared by ECAP and ARB
Fig. 1 Dislocation density in pure Cu severely deformed in ECAP (3N-Cu)
and ARB (4N-Cu) processes.
21
Fig. 3 Dislocation density in Al severely deformed by ECAP (4N-Al) and
ARB (2N-Al) processes.
being in contrast to the less directional state in the ARB
process.
Fig. 2 Apparent grain size of Cu severely deformed by ECAP (3N-Cu) and
ARB (4N-Cu) processes.
3.
Experimental Results
3.1 Copper
Figure 1 shows the changes in the dislocation density with
the equivalent strain in pure Cu prepared by the ECAP and
ARB processes. In both the processes, the density increased
abruptly with increasing strain, and then it was saturated at
about 1:8 1014 m2 when the strain reached about 2. Here,
the purity of Cu specimen used was 3N for ECAP and 4N for
ARB, so that the change in the dislocation density was
independent of the purity of Cu.
The apparent grain size of Cu obtained from the WarrenAverbach method was plotted against the equivalent strain,
and the results are shown in Fig. 2. The size decreased
monotonously with the equivalent strain, irrespective of the
process, but the grain size was smaller in the specimen
prepared by ECAP than by ARB. This difference probably
arises from two reasons, one is the purity difference and the
other is the process difference, namely the stress state in the
specimen prepared by the ECAP process is three directional,
3.2 Aluminium
Figure 3 shows the changes in the dislocation density with
the equivalent strain in pure Al prepared by the ECAP and
ARB processes. Here, the purity of the specimen was 4N for
the ECAP process and 2N for the ARB process. Irrespective
of the process, the dislocation density increased abruptly with
increasing strain, and then it exhibited a maximum value of
about 5 1013 m2 for the ECAP process around the strain
value of 1.5 and of about 4 1013 m2 for the ARB process
around the strain value of 2.5, followed by a sudden decrease
in the strain range over their values. The maximum density
was much smaller in pure Al than in pure Cu (1:8 1014 m2 ).
The apparent grain size of Al prepared by both the
processes was plotted against the equivalent strain, and the
results are shown in Fig. 4. By the ECAP process, the grain
size of 4N Al decreased abruptly. It was as small as about
90 nm around the equivalent strain value of 2, and then it
tended to increase up to the strain of 4, followed by decrease
again in the strain range over 4. On the other hand, in the
ARB process, the grain size of 2N Al decreased gradually
with increasing equivalent strain. It is likely that this
difference was caused by the purity difference between the
Al specimens.
For both the 4N and 2N Al specimens, TEM microstructures observed after the ARB process are shown in
Fig. 5, which was taken by Prof. Tsuji in Osaka University. It
was found from these micrographs that the grain size of
2N Al decreased with increasing number of rolling cycles,
whereas that of 4N Al first decreased but increased after 3
cycles. This result is consistent with the change in the
apparent grain size with the equivalent strain as shown in
Fig. 4, although the values of grain size are different between
them.
3.3 Stored strain energy
The strain energy stored in the deformed Cu and Al are
22
Y. Murata, I. Nakaya and M. Morinaga
Table 1 Elastic energy estimated from dislocation density in Cu and Al
metals severely deformed by ECAP and ARB processes.
Strain energy
Equivalent strain
Cu (J/mol)
Fig. 4 Apparent grain size of Al severely deformed by ECAP (4N-Al) and
ARB (2N-Al) processes.
summarized in Table 1. These values were calculated from
the dislocation density by using eq. (2). It was found that the
maximum strain energy stored as dislocations was about
1.6 J/mol (226 kJ/m3 ) in Cu and about 0.4 J/mol (40 kJ/
m3 ) in Al. This difference implies that the stored energy is
dependent on the melting temperature of the metal, as Cu
metal has a higher melting temperature than Al metal.
4.
Discussion
The dislocation density became a constant in Cu when the
equivalent strain exceeded 2, whereas it showed a maximum
value in Al at the strain of about 2. Furthermore, the
maximum value of Al was much smaller than the constant
value of Cu, indicating that the dislocation density in the
metal undergone severely deformation depends considerably
on the character of metal itself such as melting temperature.
The melting temperature is related directly to the formation
energy of lattice defects, because the energy is originated
from the strength of chemical bond between atoms. It is
considered that the stored energy becomes larger in those
metals which have higher melting temperatures. For example, the dislocation density is smaller in the deformed Cu than
in the lath martensite formed in an as-quenched state, e.g.,
5:4 1014 m2 in an Fe-Cr-C ternary steel2) and 9:3 1014 m2 in a high Cr heat resistant steel,7) both of which
have higher melting temperatures than Cu.
In the severely deformed Cu and Al, a part of the energy
introduced by ECAP or ARB processes may be dissipated as
the thermal energy. In fact, grain growth occurred in the
4N Al specimen over the equivalent strain 3 as shown in
Fig. 4. A number of lattice defects introduced by severe
deformation should enhance the atomic diffusion, as if the
metal is kept at high temperatures. Since impurity of metals
plays an important role in the pinning site for grain growth as
well as the atomic diffusion, 2N aluminium exhibited no
grain growth even over the equivalent strain 3 (see Fig. 5).
In the future work, it is necessary to estimate the stored
energy as the interfacial energy such as grain boundary
energy, because a portion of the interfacial energy increases
Al (J/mol)
ECAP 0
0.09
0.20
ECAP 0.9
1.24
0.29
ECAP 1.8
1.62
0.36
ECAP 3.6
ECAP 7.2
1.32
1.35
0.37
0.16
ARB 0
0.27
—
ARB 0.8
ARB 2.4
1.48
1.11
0.24
0.32
ARB 4.8
1.43
0.19
as the grain size decreases. Furthermore, the grain boundary
formed by deformation should be a high angle boundary and
hence its interfacial energy is much higher than the lath
boundary energy and the block boundary energy in the
martensite phase, being comparable to the coherent interface
energy and the low angle grain boundary energy, respectively.
5.
Summary
In order to estimate the strain energy of pure Cu and pure
Al stored in the ECAP or ARB process, dislocation densities
of both metals were measured by the Warren-Averbach
method based on the modified Williamson-Hall plot using the
X-ray diffraction data. The results are summarized as
follows;
(1) The maximum dislocation density was about 1:8 1014 m2 in Cu and 4:5 1013 m2 in Al, and these values
were obtained around the equivalent strain of 2 in both the
ECAP and the ARB processes. Over this equivalent strain,
the dislocation density did not change in Cu but decreased in
Al.
(2) The apparent grain size obtained from the WarrenAverbach analysis decreased monotonously with increasing
equivalent strain in Cu and 2N Al, but it decreased at first and
then increased over the strain of 3 in 4N Al.
(3) In both Cu and Al, the dislocation densities introduced by
the two processes were much smaller than those in the lath
martensite phase in the as-quenched high chromium ferritic
steels.
Acknowledgements
The authors would like to thank Professors of Z. Horita of
Kyusyu University and N. Tsuji of Osaka University for
providing us the experimental specimens prepared by ECAP
and ARB. Also, we are grateful to Professor N. Tsuji for
supplying a figure on TEM microstructure (Fig. 5) and to Dr.
M. Sugamuma in the Aichi Industrial Technology Institute
for his kind support to use the X-ray instrument. This work
was supported by the Grant-in-Aid (Nos. 18062003 &
17360337) for Scientific Research of the Japan Society for
the Promotion of Science (JSPS).
Assessment of Strain Energy by Measuring Dislocation Density in Copper and Aluminium Prepared by ECAP and ARB
Fig. 5
23
TEM microstructures showing the grain size of 2N- and 4N-Al severely deformed by ARB process.
REFERENCES
1) X. Huang, N. Hansen and N. Tsuji: Science 312 (2006) 249–251.
2) T. Kunieda, M. Nakai, Y. Murata, T. Koyama and M. Morinaga: ISIJ
International, 45 (2005) 1909–1914.
3) Y. Iwashita, J. Wang, Z. Horita, M. Nemoto and T. G. Langdon: Scripta
Mater. 35 (1996) 143–146.
4) H. Suzuki: Teniron Nyumon, 4th ed., (AGNE, Tokyo, 1971) pp. 69.
5) Kinzoku Data Book: Ed. Japan Institute of Metals, 2nd ed., (Maruzen,
Tokyo, 1984) p. 35.
6) Butsuri Jyosu Hyo: Ed. by S. Iida et al., (Asakura-syoten, Tokyo, 1984)
p. 25.
7) J. Pesicka, R. Kuzel, A. Dronhofer and G. Eggeler: Acta Mater. 51
(2003) 4847–4862.