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Author’s Accepted Manuscript
Grain size effects in aluminum processed by severe
plastic deformation
Takayuki Koizumi, Mitsutoshi Kuroda
www.elsevier.com/locate/msea
PII:
DOI:
Reference:
S0921-5093(17)31402-8
https://doi.org/10.1016/j.msea.2017.10.077
MSA35680
To appear in: Materials Science & Engineering A
Received date: 9 May 2017
Revised date: 21 October 2017
Accepted date: 23 October 2017
Cite this article as: Takayuki Koizumi and Mitsutoshi Kuroda, Grain size effects
in aluminum processed by severe plastic deformation, Materials Science &
Engineering A, https://doi.org/10.1016/j.msea.2017.10.077
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Grain size effects in aluminum processed by severe plastic deformation
Takayuki Koizumi1,*, Mitsutoshi Kuroda2
1
Engineering department, Yamagata University, Jonan 4-3-16, Yonezawa, Yamagata 992-8510, Japan
2
Graduate School of Science and Engineering, Mechanical Engineering, Yamagata University, Jonan
4-3-16, Yonezawa, Yamagata 992-8510, Japan
*Corresponding author. koizumi@yz.yamagata-u.ac.jp.
Abstract
––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––
We investigated the effects of the grain size on the yield strength of aluminum using a
group of samples with grains successively refined by equal-channel angular pressing (ECAP)
and another group of samples produced by 8 ECAP passes and subsequently annealed step by
step to produce coarser grains. Tensile tests were performed on all the samples. Adopting a
linear addition model for different strengthening contributions, the observed yield strength
was resolved into dislocation-related and grain-size-related strengthening contributions. The
former was directly evaluated using the Taylor equation with dislocation densities determined
by the Williamson–Hall method, and the latter was quantified by subtracting the former and
the friction stress from the observed yield strength. It was found that for the
as-ECAP-processed samples, the degree of the grain size-related strengthening relative to the
observed yield strength was consistent with an extrapolation of the conventional Hall–Petch
relation, and marked extra strengthening, which was clearly related to the grain refinement,
appeared after annealing.
––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––
Keywords: Equal channel angular pressing (ECAP); Hall-Petch relation; Dislocations;
Strengthening; Annealing
––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––
1
1. Introduction
It is known that the yield strength of metals linearly increases with the minus square root
of the grain size, which is called Hall-Petch relation [1],[2]. By use of conventional materials
processing technologies such as rolling and extrusion with general heat treatments, it was
difficult to produce metals having grains whose sizes are smaller than 5 Pm. For the past few
decades, severe plastic deformation (SPD) method has been developed, by which bulk
submicron-grain sized (ultrafine-grained (UFG) or nanostructured) metals can easily be
produced. Typical SPD methods are equal channel angular pressing (ECAP) [3],[4]㸪high
pressure torsion (HPT) [5],[6], and accumulative roll bonding (ARB) [7],[8]. Studies on the
UFG metals using SPD methods have been actively carried out by many researchers,
expecting to find a new frontier of extraordinary high-strength and high-performance metals
[9][22].
Tsuji et al. [9] performed tensile tests on ARB-processed aluminum and interstitial-free
(IF) steel having grain sizes ranging from 10 Pm to 0.2 Pm, and found that such grain
refinement by SPD led to tensile strength 4 times greater than that of the initial materials.
Kamikawa et al. [21] investigated a relationship between the yield strength and the grain size
for pure aluminum produced by ARB and annealing, and provided a Hall–Petch-like plot. In
their experiments, samples were first processed by 6 ARB passes and subsequently annealed
step by step at various temperatures to coarsen the grains. They showed that variation of the
yield strength with respect to the grain size significantly deviated from the conventional Hall–
Petch relation in the range of the grain size smaller than 10 Pm. Gao et al. [22] conducted
similar experiments on IF steel, and showed that grain size smaller than 4 Pm brought
significantly high yield strength. In general, as-SPD-processed metals are expected to contain
some amount of dislocations as a consequence of undergoing plastic deformation, and their
total strength is expected to be contributed from both grain size-related strengthening and
2
dislocation-related strengthening. During the annealing process in the experiments of
Kamikawa et al. [21] and Gao et al. [22], an increase in the grain size and a decrease in the
dislocation density would have occurred simultaneously, as they discussed it using their own
strengthening model. Gubicza et al. [23] showed that the yield strength of as-ECAP-processed
(as-ECAPed) metals (Al, Al-Mg alloys, Cu and Ni) could be described solely by the
dislocation-related strengthening using the Taylor equation [24] without consideration of the
grain-size effect as a first approximation. Recently, Čížek et al. [25] investigated
strengthening mechanisms of as-HPT-processed (as-HPTed) IF steel. Values of yield strength
used for their data analysis were estimated from Vickers microhardness values. The estimated
yield strength was resolved into contributions from the dislocation-related and grain
size-related strengthening mechanisms. They found that the amount of the grain size-related
strengthening was well described by the classical Hall–Petch relation with a coefficient ‘k’
being in agreement with that for conventional ferritic steel. Krajňák et al. [26] studied
mechanical properties and strengthening mechanisms of as-ECAPed AX41 magnesium alloy.
Their experimental results and data analysis suggested that amounts of the dislocation-related
strengthening and the grain size-related strengthening were comparable after 8 ECAP passes.
Thus, for SPD-processed metals, the degree of the grain size-related strengthening relative
to the observed yield strength has not been fully understood. Furthermore, whether or not the
grain size effect in the refining process by SPD and that in the coarsening process by
annealing are equivalent is uncertain. No sufficient understanding has been reached on these
questions.
In the present study, we investigated systematically the effects of the grain size on the
yield strength of industrial pure aluminum using a group of samples with grains successively
refined using ECAP and another group of samples first produced by 8 ECAP passes and
subsequently annealed to coarsen the grains step by step. Tensile tests were performed on all
3
the samples. The observed yield strength was separated into the dislocation-related and
grain-size-related strengthening contributions. The former was directly evaluated using the
Taylor equation with the dislocation densities determined by the Williamson–Hall method,
and the latter was quantified by subtracting the former and the friction stress from the
observed yield strength. It was found that for the as-ECAPed samples, the degree of the
grain-size-related strengthening relative to the observed yield strength remained consistent
with an extrapolation of the conventional Hall–Petch relation, and marked extra strengthening
related to the grain size first appeared after annealing.
2. Experiments
2.1. Sample preparations
All the samples used in the present study were made of industrial pure aluminum (JIS
A1070-H) rods with a diameter of 9.95 mm and a length of 60 mm. Before the ECAP
deformation, all the rods were annealed at 425°C for 1 h. Each annealed rod was the starting
material for the ECAP process, and is hereinafter referred to as the sample with ‘0’ ECAP
passes. The ECAP process with the ‘route Bc’ was adopted, which is known to give
approximately equiaxial crystal grains [27]. The shape of the ECAP die and the definition of
the coordinate system used in our micrographs are given in Fig. 1. We prepared two groups of
samples. The first group consists of samples with grains successively refined by repeated
ECAP processes (henceforth referred to as samples subjected to the refining approach). The
second group consisted of samples processed by 8 ECAP passes and subsequently annealed
step by step at various temperatures to produce coarser grains (henceforth referred to as
samples subjected to the coarsening approach). For the refining approach, samples underwent
1 to 8 ECAP passes. For the coarsening approach, a sufficient number of samples with 8
ECAP passes were first produced, which were then annealed at different temperatures. The
4
annealing conditions and the names of the annealed samples are shown in Table 1. A two-step
annealing strategy was employed following Refs. [21],[28].
2.2. Grain sizes
EBSD measurements to determine average grain sizes (hereafter simply referred to as
‘grain sizes’), d, were carried out using an orientation imaging microscopy (OIM) system
(EDAX) attached to our scanning electron microscope (SEM) equipment (JEOL
JSM7600-FA) with an accelerating voltage of 15 V. The number of measurement areas and
the magnification for each sample are shown in Supplementary Table S1. To determine the
grain size using OIM, a tolerance angle for misorientations needs to be specified. An angle of
5˚ is often used, while an angle of 2˚ has also been used for as-ECAPed materials in the
literature [29],[30] In the present study, an angle of 2˚ was adopted for the refining approach,
while an angle of 5˚ was used for the coarsening approach to quantify the grain sizes. The
grain sizes were evaluated after eliminating the data with confidence index (CI) less than 0.1.
Examples of crystal orientation maps (IPF maps) obtained from EBSD measurements are
shown in Fig. 2. In the case of 1 ECAP pass (Fig. 2(b)), the grain size was evaluated as 44.4
Pm when the tolerance angle was set to be 2˚, while it was determined as 121.5 Pm when the
tolerance angle was 5˚. This indicates that the apparently coarse grains were generated due to
occurrence of dynamic recrystallization during 1 ECAP pass, and many subgrains were
formed inside the coarse grains. As will be stated later (in section 4), this fluctuation in the
apparent grain size, which is caused by the choice of the tolerance angle, does not affect the
conclusions of the present study.
2.3. Dislocation densities
The XRD line profiles were measured on a cross section along the rod axis using an
X-ray diffractometer (Rigaku Ultima IV with a scintillation counter), which was operated at
40 kV and 40 mA using CuKD radiation with a sampling interval of 0.01˚ and a scanning
5
speed of 1˚/min. The dislocation densities were evaluated using a Williamson–Hall plot
[31][33] based on the full width at half maximum (FWHM) of the reflection peaks for (111),
(200), (220), (222), (311), (331), (400), (420) and (422). The detailed procedure is shown in
Appendix A. The variation of the dislocation density with the successive grain refinement by
ECAP and with the gain coarsening by subsequent annealing is shown in Fig. 3. Error bars
indicate the maximum and minimum values for three measurements except for 8 passes-O3
and 8 passes-O4 samples, whose dislocation densities were measured only one time. In the
refining approach, the dislocation density reached its maximum at the first ECAP pass, then it
decreased with further grain refinement accomplished by the repeated ECAP processes, and
finally a steady state appeared to be reached with an almost constant dislocation density and
saturation of the grain size (at around 1.6 Pm). The dislocation density of the sample with 8
ECAP passes was half that of the sample with 1 ECAP pass. This variation and the values of
the dislocation density are in agreement with those reported in Ref. [34] for high-purity Al
(99.99% 4 N). In Ref. [23], the dislocation densities of the 4 N Al processed by ECAP were
also measured, but their absolute values were three to five times greater than those reported in
Ref. [34] and in the present study. The obtained dislocation density might depend on the
equipment used to measure the XRD diffraction line profiles and on the calculation method
adopted. Consequently, it may be difficult to discuss the values quantitatively. Nevertheless,
the tendency that the dislocation density reaches its peak after a small number of ECAP
passes and decreases towards a steady state upon the subsequent ECAP deformation was
common to these studies. It is known that the fraction of high-angle grain boundaries
(HAGBs) successively increases with repeated SPD processes [30],[35],[36]. It was pointed
out in Ref. [36] that HAGBs tend to absorb dislocations and a stable state, where the
generation of dislocations is balanced with the absorption of dislocations at HAGBs, is
eventually established. In the coarsening approach, the dislocation densities of the 8
6
passes-O1 and 8 passes-O2 samples were comparable to those of the samples with 6 to 8
ECAP passes, while the dislocation densities of 8 passes-O3 and 8 passes-O4 significantly
decreased to about 10% of these values. For 8 passes-O5 to -O8, reliable values of the
dislocation density could not be obtained from the Williamson–Hall method. It is considered
that the dislocation densities of these samples decreased to values comparable to that of a
fully annealed material.
2.4. Tensile behavior
For tensile tests, all the rod-shaped samples were machined into dumbbell-shaped
specimens. The specimen shape and dimensions with the positions at which wire-strain
gauges were pasted are given in Fig. 4. The specimens had threaded grips. The mechanical
tests were carried out using a universal testing machine (Shimadzu AG-IS 50 kN), in which a
special chucking device with thread-cut parts was installed to hold the specimen. The nominal
strain rate was quantified with the crosshead speed set to be 0.001 s-1. The data from the
wire-strain gauges were used to compute the true strain. A specimen with a similar shape and
slightly longer gauge (parallel part) length (10 mm) was used in Ref. [37]. Experimental
curves of true stress versus true strain up to a strain of 0.02 for the refining approach and the
coarsening approach are shown in Figs. 5(a) and 5(b), respectively. Corresponding nominal
stress–nominal strain curves up to a strain of 0.4 are given in Fig. B1 in Appendix B.
In the refining approach (Fig. 5(a)), the 0.2% proof stress ߪ଴Ǥଶ (indicated by ‘z’ in the
graph) of the sample with 1 ECAP pass became six times greater than that of the initial
sample with 0 ECAP passes, although the grain size remained almost the same (i.e. from 39.2
Pm to 44.4 Pm as indicated in the graph). In contrast, the ߪ଴Ǥଶ of the sample with 8 ECAP
passes was only 1.2 times greater than that of the sample with 1 ECAP pass. In the coarsening
approach (Fig. 5(b)), 8 passes-O1 to -O4 exhibited peculiar hardening/softening behavior. The
ߪ଴Ǥଶ of 8 passes-O1 and 8 passes-O2 exceeded that of the sample with 8 ECAP passes even
7
after annealing. These three samples had almost the same grain size (i.e., about 1.61.8 Pm).
This “hardening by annealing” phenomenon has previously been reported for industrial pure
aluminum (A1100) and interstitial-free (IF) steel with submicron-sized grains processed by
accumulated roll bonding (ARB) [38],[39]. The present experimental results show that the
same phenomenon occurs in industrial pure aluminum with micron-sized grains processed by
ECAP. In samples 8 passes-O5 to -O9, the grains were coarsened to greater than 10 Pm and
the ߪ଴Ǥଶ decreased markedly. These samples can be considered to have low dislocation
densities and to be in a fully annealed state. However, in 8 passes-O1 to -O4, moderate
amounts of dislocations remained, as quantified in Fig. 3, which should contribute to the
strengthening of the material. Thus, the material strength data shown here are considered to be
consequences of a combined effect of the dislocation-related strengthening and the
grain-size-related strengthening. The two strengthening effects must be split to investigate the
effect of only the grain size on the total strengthening.
3. Modeling of strengthening mechanisms
In order to resolve the experimentally observed ߪ଴Ǥଶ into the contributions from
dislocation-related strengthening and grain-size-related strengthening, we adopt the following
additive strengthening model for polycrystalline pure metals [40]:
ߪ଴Ǥଶ ൌ ߪ଴ ൅ ߪ୥ୱ ൅ ߪୢ୧ୱ୪୭ୡ ,
(1)
where ߪ଴ is the friction stress, i.e., the resistance stress for the material with sufficiently
large grains and low dislocation density, ߪ୥ୱ is the contribution from the grain-size-related
strengthening, and ߪୢ୧ୱ୪୭ୡ is the contribution from the dislocation-related strengthening. The
ߪ୥ୱ is often considered to be a grain-boundary-related strengthening term. In the present
formulation, ߪ୥ୱ includes the effects of both the grain boundaries and the grain size since
they cannot be separated in our experimental study and there is no established way to split
8
them theoretically. The ߪ଴ can be determined as the intercept of a conventional Hall–Petch
plot for coarse-grained samples subjected to appropriate annealing treatments. As our
experimental data are too crude for such a determination (there were only five data, i.e., for 8
passes-O5 to -O9), 17 Hall–Petch plots for aluminum with grain sizes greater than 10 Pm
were collected from Refs. [21],[41],[42] (see details in Supplementary Table S2). We
determined ߪ଴ to be 11.4 MPa by adopting the mean value of the collected data.
For the dislocation-related strengthening, the Taylor equation [24],[43] is adopted:
ߪୢ୧ୱ୪୭ୡ ൌ ‫ܾߤߙܯ‬ඥߩ,
(2)
where M, which is taken to be 3.06, is the Taylor factor neglecting the crystallographic texture
effects as the first approximation, P
(= 26 GPa for Al) is the shear elastic modulus, b (=
0.286 nm for Al) is the magnitude of the Burgers vector, U is the dislocation density, and Dis
a coefficient often taken to be 0.2 to 0.7. We identified D via the following procedure.
According to Figs. 2, 3 and 5, the grain size of the sample with 1 ECAP pass was rather large,
i.e. 44.4 Pm, and the dislocation density of this sample was the highest among the samples.
The strength of this sample is considered to be mostly governed by the dislocation-related
strengthening mechanism. In this range of grain size, we consider that the value of ߪ଴ ൅ ߪ୥ୱ
in Eq. (1) follows the conventional Hall–Petch relation (given in Supplementary Table S2).
Then, taking the mean value of the Hall–Petch coefficient (i.e., k = 43.5 MPa Pm1/2), we
assume that the following relation holds for the sample with 1 ECAP pass: ߪ଴Ǥଶ ൌ ߪ଴ ൅ ߪ୥ୱ ൅
ߪୢ୧ୱ୪୭ୡ 㸻ͳͳǤͶ ൅ Ͷ͵Ǥͷ݀ ିଵȀଶ ൅ ‫ܾߤߙܯ‬ඥߩ [MPa]. Using this relation, D is finally determined to
be 0.51 by adopting the average value for the calculations using the grain size (44.4 Pm), the
three ߪ଴Ǥଶ values for the three tensile tests1, and the three U values for the three XRD
1
We carried out two tensile tests for each condition in the refining approach. One additional data for each
condition was taken from our previous study [37].
9
measurements. This value of D will be used throughout our analysis of the experimental data.
For the dislocation density data reported in Ref. [23], we identified D to be 0.25 using the
same procedure (the grain sizes were substituted by our data since they were not reported in
Ref. [23]). Recently, it has been reported that the dislocation densities of differently annealed
SPD processed aluminum samples with grain sizes of 0.96 Pm and 0.26 Pm quickly increased
at the early stage of plastic deformation in tensile tests [44]. The dislocation density became
almost double the initial value at a plastic strain of 0.2% for both the samples [44]. If we
adopt an assumption that the ratio of the dislocation density at a plastic strain of 0.2% to that
before the deformation is approximately constant for different samples, this phenomenon only
appears as a change in the constant value of D. In the present study, we adopt this assumption
and use the constant value of D (= 0.51) determined above with no direct consideration of the
change in the dislocation density at the early stage of the deformation.
4. Results of experimental data analysis: effects of grain size on yield strength
Based on the model and data analysis procedure shown above, the grain-size-related
strengthening term, ߪ୥ୱ , is evaluated by ߪ୥ୱ ൌ ߪ଴Ǥଶ െ ߪ଴ െ ‫ܾߤߙܯ‬ඥߩ using the measured
ߪ଴Ǥଶ and U and the determined parameter values. For 8 passes-O5 to -O9, for which the
dislocation densities could not be measured due to their too low values, ߪ୥ୱ is simply
evaluated by ߪ୥ୱ ൌ ߪ଴Ǥଶ െ ߪ଴ .
Plots of the ߪ଴Ǥଶ , and its breakdown into ߪ଴ , ߪ୥ୱ , and ߪୢ୧ୱ୪୭ୡ , versus grain size are shown
in Figs. 6(a) and 6(b) for the refining approach and the coarsening approach, respectively. The
blue and red circles indicate the ߪ଴Ǥଶ of the samples in the refining and coarsening
approaches, respectively, with error bars showing the maximum and minimum values
obtained in the three tensile tests under the same conditions2. The blue squares exhibit the
2
See footnote 1.
10
values of ߪ଴ ൅ ߪ୥ୱ with error bars showing the maximum and minimum values determined
from the combinations of the three corresponding measured values for ߪ଴Ǥଶ and U. The Hall–
Petch relation with the mean values of ߪ଴ and k calculated from the data in the literature
[21],[41],[42] and the present study (see Supplementary Table S2) is shown by a gray solid
line. The area specified with the standard deviations of ߪ଴ and k is designated as the Hall–
Petch zone. The contribution of ߪୢ୧ୱ୪୭ୡ generally predominates. It is noteworthy that the
plots of ߪ଴ ൅ ߪ୥ୱ (indicated by blue squares) are close to the upper boundary of the Hall–
Petch zone. The green solid line indicates the regression line for the data for the ߪ଴Ǥଶ of the
well-annealed samples (indicated by red circles) and ߪ଴ ൅ ߪ୥ୱ for the samples processed by
ECAP (indicated by blue squares). This dataset is naturally represented by a single line, which
appears near the upper boundary of the Hall–Petch zone.
In Fig. 6(a), the values of ߪ଴Ǥଶ reported in Ref. [23] and their breakdowns into ߪ଴ , ߪ୥ୱ ,
and ߪୢ୧ୱ୪୭ୡ are also shown. The grain sizes were substituted by our data since they were not
given in Ref. [23]. We assume that the grain sizes in Ref. [23] and the present study were
nearly the same since the dimensions of the ECAP die and the aluminum rods used were the
same and also the route Bc was used in both the studies. The plots of ߪ଴ ൅ ߪ୥ୱ (indicated by
purple open squares) computed from the data given in Ref. [23] appear inside the Hall–Petch
zone and their regression line (purple dotted line) is close to the mean Hall–Petch line. Thus,
the effect of the grain refinement associated with the ECAP on the material strength remains
similar to that estimated by extrapolation of the conventional Hall–Petch relation. We did not
observe any peculiar grain-size-related strengthening beyond the Hall-Petch prediction in Fig.
6(a). The grain sizes used here were determined with a tolerance angle of 2˚ as mentioned
earlier. In Fig. C1 in Appendix C, a plot with a tolerance angle of 5˚ is depicted for
comparison. The value chosen for the tolerance angle does not fundamentally affect the
findings of this study.
11
In the coarsening approach (Fig. 6(b)), the ߪ଴Ǥଶ decreased markedly with the grain
coarsening associated with annealing. The values of the grain-size-related strengthening term,
ߪ୥ୱ , are clearly greater than those in the refining approach (Fig. 6(a)) for grain sizes below 5
Pm. The plots of ߪ଴ ൅ ߪ୥ୱ (indicated by red crosses) are far above the Hall–Petch zone. In
particular, the ratio of ߪ୥ୱ to ߪ଴Ǥଶ for 8 passes-O3 amounts to 70%. This observation
suggests that the excess of ߪ୥ୱ above the upper boundary of the Hall–Petch zone might result
from a change in the grain boundary character due to annealing. The zone labeled “Extra
strengthening” in Fig. 6(b) illustrates the corresponding amounts of excess strengthening. The
grain sizes used in the coarsening approach were determined with a tolerance angle of 5˚ as
mentioned earlier. We have confirmed that the difference between plots with tolerance angles
of 5˚ and 2˚ is not visible on the scale plotted.
5. Discussion
In Ref. [23], the yield strength of as-ECAPed pure Al (4N) was correlated solely to the
dislocation density using the Taylor equation without consideration of the grain-size effect as
a first order approximation. The data analysis done in the present study (Fig. 6(a)) showed
that the grain size-related strengthening had contributed to the observed yield strength. The
degree of the grain size-related contribution was comparable with the extrapolation of the
classical Hall–Petch relation. In the case of the pure Al in Ref. [23], the dislocation density
reached its maximum at 2 ECAP passes, and it was gradually reduced with the subsequent
ECAP passes. The corresponding reduction of the dislocation related-strengthening was
compensated by the increase in the grain size-related strengthening associated with the grain
refinement under the almost saturated yield strength, as illustrated in Fig. 6(a).
In Ref. [23], the experimental data of the yield strength and dislocation densities for
Al-Mg alloys (up to 8 ECAP passes) were also given. In the cases of the alloys, the reduction
of the dislocation density with repeated ECAP was not observed. These data suggest that the
12
grain size-related strengthening effect in alloys might be smaller than that in pure metals.
Since the grain sizes were not given in Ref. [23], here we do not further discuss their data.
The authors are now working on a replication study on alloys along with measurement of
grain sizes.
Čížek et al. [25] investigated strengthening mechanisms of as-HPTed IF steel in detail.
They assumed a linear addition rule for the different strengthening contributions, ߪ ൌ ߪ଴ ൅
‫ܾߤߙܯ‬ඥߩ ൅ ݇Ȁξ݀, which is basically equivalent to Eq. (1), and expressed the measured grain
size and dislocation density as functions of an equivalent strain. The yield strength ߪ was
estimated from Vickers microhardness values. In their data analysis, the Hall–Petch
coefficient k was chosen as a fitting parameter. They found that k obtained from the fitting
was in reasonable agreement with that for conventional ferritic steel [45]. Their finding is
fundamentally consistent with the finding in the present paper for the refining approach, even
though the target materials and the detailed experimental procedures were different.
As seen in Figs. 6(a) and 6(b), the degrees of the grain size-related strengthening relative
to the total yield strength much differed between the refining and coarsening approaches even
though the grain sizes were the same. These behaviors might also differ between different
materials. Therefore, experimental studies and corresponding data analysis like those
performed in the present paper should be accumulated for various materials in future work in
order to understand further the strengthening mechanisms in SPD-processed metals.
The physics behind the difference between the grain size-related strengthening behaviors
observed in the refining and coarsening approaches has not been clarified in the present study.
This difference might result from a change in the grain boundary character due to annealing.
In order to investigate directly the characteristics of the grain boundaries, micromechanical
test methods on small samples of the material including a grain boundary, which are extracted
from the bulk, e.g., bicrystalline micropillar tests [46],[47], will be efficient.
13
In Ref. [25], it was observed that even after increase in the dislocation density and
decrease in the grain size were saturated, the Vickers microhardness continued to increase
moderately with further HPT deformation. It was suggested that this additional strengthening
would be related to an increase in fraction of HAGBs, which augmented the Hall–Petch
coefficient. These observation and interpretation might suggest that the contribution from the
change in fraction of HAGBs to the total strengthening might be subordinate until the changes
in the dislocation density and the grain size were saturated.
The authors investigated the relationship between the grain size and the intensity of the
Bauschinger effect appearing in tension/compression and compression/tension reversed
loading tests on the same material (A1070) processed by ECAP [37]. A strong correlation
between the grain size and the intensity of the Bauschinger effect was not observed for the
as-ECAPed samples. Ref. [37] indicates that the effects of the grain size, the associated
increase in the grain boundary volume fraction, and the misorientations between the grains,
which increased upon severe plastic deformation on the overall mechanical behavior of the
material are not predominant compared with the dislocation-related strengthening effect. This
understanding is consistent with the present observation in Fig. 6(a).
6. Conclusions
In the present study, the effects of the grain size on the yield strength of industrial pure
aluminum were investigated using a group of samples with grains successively refined using
ECAP and another group of samples first produced by 8 ECAP passes and subsequently
annealed to coarsen the grains. It was found that for the as-ECAPed samples, the degree of the
grain-size-related strengthening relative to the observed yield strength, which was quantified
by subtracting the dislocation-related strengthening contribution from the yield strength, was
consistent with an extrapolation of the conventional Hall–Petch relation, and extra grain
size-related strengthening was observed after annealing in the range of the grain size below 10
14
Pm.
Acknowledgements: The authors gratefully acknowledge Professor Yuji Kume for his
helpful comments on SPD-processed materials. The authors also thank Mr. Noboru Imoto of
Yamagata University for support in the machining and Dr. Tadaaki Satake of Yamagata
University for support in the SEM-EBSD observations. Mr. Yuhei Nakata, Mr. Daisuke Miura,
Mr. Tomoya Shimada and Ms. Mako Saito are acknowledged for their help in the preparation
of the samples. This work was partly supported by a JSPS Grant-in-Aid for Scientific
Research (C), Grant number KAKENHI 16K05964.
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19
Appendix A: Details of calculation of the dislocation density according to XRD line
profiles
An example of the measured XRD line profiles was shown in Fig. A1. These raw data
were subjected to smoothing using X-ray diffraction software PDXL (Rigaku), and the
background and the KD2 lines were removed. Then, the diffraction angle 2T and FWHM
(߂ʹߠ) of the reflection peaks for (111), (200), (220), (222), (311), (331), (400), (420) and
(422) were calculated. The instrumental broadening would not have affected the accuracy of
the calculated results since the samples had significantly high dislocation densities due to
SPD.
For the lattice strain and the crystallite size, we adopted the Williamson–Hall equation [31],
•‹ߠ
߂ʹߠ…‘•ߠ ͲǤͻ
ൌ
൅ ʹߝ
ǡ
‫ܦ‬
ߣ
ߣ
(B1)
where O is the X-ray wave length (= 0.154 nm), D is an apparent crystallite size, and H is a
lattice strain. An example of Williamson-Hall plots is shown in Fig. A2. The dislocation
density ߩ [32] is computed as
ߩൌ
ʹξ͵ߝ
ǡ
‫ܾܦ‬
(B2)
where b is the magnitude of the Burgers vector, which is 0.286 nm for aluminum. All the
measured calculated values of FWHM, ʹߠ, ߝ, D and ߩ are listed in Supplementary Table S3.
Appendix B: Nominal stress–nominal strain curves
Curves of nominal stress versus nominal strain, which correspond to the true stress–true
strain curves shown in Fig. 5, are depicted in Fig. B1. A pair of extensometers (Tokyo Sokki
RA-5) was set at opposite positions across a diameter. The elongation of the specimen was
taken to be the average of the data recorded by the two extensometers. The ‘gauge length’ for
20
computing the nominal strain was taken to be the value giving a strain value identical to that
obtained with the wire-strain gauges in the elastic deformation range. After yielding, the
nominal strain determined by this method may not be a well-defined quantity due to the
plastic deformation that occurs in the round parts. However, we consider that such apparent
values of the nominal strain are useful for relative comparison of the ductility of the
specimens.
Appendix C: Effect of the tolerance angle for misorientations to specify the grain size
Fig. C1 shows a plot similar to Fig. 6(a), but with a tolerance angle of 5˚. In the case of
the as-ECAPed samples with a small number of ECAP passes, many subgrains with low
misorientation angles were generated inside the apparent coarse grains as can be seen in Fig.
2(b). For this situation, the evaluated grain size depends on values chosen for the tolerance
angle. A tolerance angle of 5˚ is often used for general materials with annealing treatments,
while an angle of 2˚ has been used for as-ECAPed materials in several studies [29,30]. The
comparison of Fig. 6(a) in the main text, which used 2˚, with the plot in Fig. C1, which used
5˚, confirms that the tolerance angle does not affect the findings in the present study.
21
Fig. 1. Schematic diagrams: (a) ECAP die; (b) material coordinates. The same die
was used in Ref. [37].
Fig. 2. Examples of EBSD crystal orientation maps. (a) 0 passes with a tolerance
angle of (TA) 5°, (b) 1 pass with TA 2° and (c) 8 passes with TA 2°.
Fig. 3. Relationship between dislocation density and grain size.
Fig. 4. Shape and dimensions of the specimen for uniaxial tensile tests with positions
at which wire-strain gauges were pasted.
Fig. 5. True stress–true strain curves obtained from uniaxial tensile tests with the grain
sizes: (a) refining approach, (b) coarsening approach. ‘TA’ stands for the tolerance
angle used to determine the grain size.
Fig. 6. Relationship between 0.2% proof stress V 0.2 , with its breakdown into V 0 , V gs
and V disloc , and grain size: (a) refining approach (with five additional data points
obtained from well-annealed samples), (b) coarsening approach.
Fig. A1. An example of measured XRD line profiles (raw data).
Fig. A2. An example of Williamson-Hall plots.
Fig. B1. Nominal stress–nominal strain curves obtained from the tensile tests for (a)
refining approach and (b) coarsening approach. ‘TA’ stands for the tolerance angle.
Fig. C1. Relationship between 0.2% proof stress and grain size in fining approach
when the tolerance angle was chosen to be 5°.
23
(a)
(b)
!"#$
Fig. 1. Schematic diagrams: (a) ECAP die; (b) material coordinates. The same die was used in
Ref. [37].
Fig. 2. Examples of EBSD crystal orientation maps. (a) 0 passes with a tolerance angle of
(TA) 5°, (b) 1 pass with TA 2° and (c) 8 passes with TA 2°.
1
d [m]
200 50
Dislocation density [1014m-2]
0.8
5
10
1
2
Refining approach
0.7
3 pass
passes
1 pass
0.6
4 ppasses
2 passes
0.5
7 passes
es
5 passes
0.4
0.3
8 ppasses
asses
6 passes
8 passes-O1
0.2
8 passes-O2
Coarsening approach
0.1
8 passes-O4
8 passes-O3
0
0
0.2
0.4
0.6
0.8
1
d-1/2 [m-1/2]
Fig. 3. Relationship between dislocation density and grain size.
!
Fig. 4. Shape and dimensions of the specimen for uniaxial tensile tests with positions at which
wire-strain gauges were pasted.
2
(a) 180 Refining
7 passes, 2.3 m (TA 2)
approach
160
8 passes, 1.6 m (TA 2)
True stress [MPa]
140
120
100
80
60
Young's modulus
40
0.2% proof stress
6 passes, 2.0 m (TA 2)
5 passes, 2.8 m (TA 2)
4 passes, 3.1 m (TA 2)
3 passes, 4.3 m (TA 2)
2 passes, 6.1 m (TA 2)
1 pass, 44.4 m (TA 2)
0 passes, 39.2 m (TA 5)
20
0
0
0.005
0.01
0.015
0.02
Logarithmic strain
(b) 180 Coarsening
approach
160
8 passes, 1.6 m (TA 2)
True stress [MPa]
140
8 passes-O1, 1.7 m (TA 5)
8 passes-O2, 1.8 m (TA 5)
120
8 passes-O3, 3.2 m (TA 5)
8 passes-O4, 4.7 m (TA 5)
100
80
8 passes-O5, 17.3 m (TA 5)
8 passes-O6, 15.8 m (TA 5)
8 passes-O7, 34.9 m (TA 5)
Young's modulus
60
0.2% proof stress
40
8 passes-O8, 137.0 m (TA 5)
8 passes-O9, 218.5 m (TA 5)
20
0
0
0.005
0.01
0.015
0.02
Logarithmic strain
Fig. 5. True stress–true strain curves obtained from uniaxial tensile tests with the grain sizes:
(a) refining approach, (b) coarsening approach. ‘TA’ stands for the tolerance angle used to
determine the grain size.
3
(a)
d [m]
200 50
160
6 passes
5 passes
3 passes 4 passes
2 passes
120
1 pass ߪ଴ଶ 1
2
Refining approach
140
0.2% proof stress [MPa]
5
10
ߪ଴ଶ ଵ
݀ ିଶ
8 passes
ଵ
݀ ିଶ
Ref. [23]
100
7 passes
80
disloc
8 passes-O9
8 passes-O8
8 passes-O7
60
8 passes-O5
40
ଵ
ߪ଴ଶ ݀ ିଶ
20
8 passes-O6
0
0
0.2
0.4
0.6
gs
0
0.8
1
d-1/2 [m-1/2]
(b)
d [m]
200 50
5
10
160
Coarsening approach
0.2% proof stress [MPa]
140
8 passes-O1
8 passes-O2
8 passes-O3
120
1
2
8 passes
"Hardening
by
annealing"
8 passes-O4
100
disloc
8 passes-O9
8 passes-O8
8 passes-O7
8 passes-O5
80
60
ଵ
40
ߪ଴ଶ ݀ ିଶ
20
gs
0
8 passes-O6
0
0
0.2
0.4
0.6
0.8
1
d-1/2 [m-1/2]
Fig. 6. Relationship between 0.2% proof stress , with its breakdown into , and
, and grain size: (a) refining approach (with five additional data points obtained from
well-annealed samples), (b) coarsening approach
4
Table 1. Annealing conditions in the coarsening approach.
Sample
Annealing conditions
8 passes
(As-ECAPed)
8 passes-O1
175°C 0.5 h
8 passes-O2
175°C 6 h
8 passes-O3
175°C 6 h + 225°C 0.5 h
8 passes-O4
175°C 6 h + 250°C 0.5 h
8 passes-O5
175°C 6 h + 300°C 0.5 h
8 passes-O6
175°C 6 h + 350°C 0.5 h
8 passes-O7
175°C 6 h + 400°C 0.5 h
8 passes-O8
175°C 6 h + 450°C 0.5 h
8 passes-O9
175°C 6 h + 550°C 10 min
1
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