マイクロピラー圧縮試験による鉄鋼材料の局所力学特性評価法の確立
Micro-scale Mechanical Response of Ferrous Materials Measured by Micropillar
Compression Test
Naoki Takata
Associate professor, Dept. Materials and Sciences, Nagoya University
1．Introduction
Much previous research has been performed to assess the mechanical response of avariety of crystalline metals and alloys using micrometer and submicrometer-size
pillars milled using a focurs ion beam (FIB) 1). An attractive aspect of the micropillar
compression test2)

is that this approach provides an opportunity to obtainfundamental single-crystal mechanical properties that are much difficult to determine
for individual phases in multiphase materials. The extensive effort has been made to
identify the scaling law for the strength of micrometer and submicrometer-sized
specimens 1-13). In aspects of the constitute phases in steels, microscale deformation
behavior of ferrite (-Fe) phase has been examined 1) as well as different bcc metals
and alloys 1,14). However, it is unclear whether the scaling law can valid for solid
solution fcc phases corresponding to an austenite (-Fe) phase, since most of previous
results have identified the scaling low for pure fcc metals (Au, Ni, Cu, Al) 2-13).
In process to prepare cylindrical micropillars on the sample surface, the incident FIB
milling makes it inevitable to form micropillars with a trapezoidal cylinder shape 1),
whereas the effect of shape parameters of micropillars on the measured strength has
not been revealed. Such data are invaluable to understand the tolerance level of theirshape parameters for measuring the reliable mechanical data of cylindricalmicropillars.
In this study, the compression response of the -Fe (solid solution fcc) single-crystal
micropillars with various sizes and shape parameters was examined using a-Fe
single-phase steel, in comparison with the mechanical properties of millimeter-size
specimens previously measured. These results were then utilized in conjunction withprevious results on the scaling low for metals to understand the strength level of -Fe
single-crystal cylindrical micropillars associated with their diameter and shape fordetermining the appropriate dimension of micropillars to measure the reliablemechanical data.

－ 87 －

2．Experimental procedure
The nominal compositions (at.%) of the studied alloy
was Fe–20Cr–30Ni. The alloy ingot was prepared by
vacuum induction melting and were hot-forged at 1553
K into rods with a diameter of 12 mm. They wereannealed at 1173K for 1 h. The observed sample
surfaces were mechanically polished followed byelectro-polishing in a solution of phosphoric acid withsupersaturated Cr at 353 K, 1.8 A/cm2 for 4 s. Their
microstructures and fracture surfaces were observed by
optical microscope and scanning electron microscopy(SEM: JEOL JSM-7000F) operated at 15 kV.
Cylindricalmicropillars

withvariousdiameters(approximately 1~10 m) and shape parameters were

Fig.1 Schematics of thedimensional parameters ofcylindricalmicropillars
prepared by focused ion
beam in the present study.

fabricated on the sample surface by FIB milling (JEOL JIB-4601F) operated at 30 kV.
The dimensional parameters of micropillars studied were schematically shown in Fig.
1. The top and bottom diameters of prepared micropillars with a trapezoidal cylinder
shape were designated as D1 and D2, respectively. The specimen diameter (D) was usedas the average value of D1 and D2 in present study. D1, D2 and height of micropillars (h)were measured using SEM images. These micropillars were compressed using a
SHIMAZU DUH-211 dynamic ultra-micro tester equipped with a flat punch with adiameter of 20 μm in the load-control mode resulting in an initial strain rate of ~10-3 /s.
In order to identify the compression direction, the crystallographic orientation of the
-Fe phase was analyzed by electron-backscatter diffraction (EBSD) using the OIM
Data Collection and OIM Data Analysis (TSL Solutions) software. The deformed
micropillars were subsequently observed by SEM.
3．Results
3. 1 Single-crystal micropillars with different sizes
Fig. 2 illustrates -Fe single-crystal micropillars fabricated on the annealed sample of
the Fe–20Cr–30Ni alloy. The observed SEM image (Fig. 2(a)) and correspondingorientation color map (Fig. 2(b)) obtained from EBSD analysis determine thecrystallographic normal direction of the -Fe grains corresponding the compression
direction of -Fe single-crystal micropillars fabricated on the sample surface. The
following FIB milling on the particular grain can provide a number of cylindrical
single-crystal micropillars with an identified compression direction (Fig. 2 (c,d)).

－ 88 －

Fig. 2 (a) secondary electron image (SEI) showing microstructure and (b) correspondingorientation color map of the sample annealed at 1173 K for 1 h, (c, d) representative SEIs
showing -Fe single crystal micropillars prepared on the sample.

Fig. 3 shows the representative nominal stress–strain curves of -Fe single-crystal
micropillars with different diameters (D) ranging from 1.3 m to 10.4 m at room
temperature. The compression direction indicated in an unit triangle of the inverse
pole figure is close to [123]direction. There are distinct
changes in the stress–strain
curvesofmicropillars

withsmaller size. The micropillar
with D = 1.3 m exhibits anincrementally rising flow curvewith rapid strain bursts thatproceeds to a magnitude of a few
percent at several stress levels.
A similar flow response wasobserved for micropillars withsmaller

sizes

than

2

m.

Fig. 3 Nominal stress-strain curves of -Fe single
crystal micropillars with various diameters (D) atroom temperature. The compression direction is closeto [123] direction.

－ 89 －

However, there are the more scarcely rapid strain bursts for the larger-sized
micropillars. The flow curve of the micropillar with D = 3.5 m exhibits a continuous
yielding of approximately 190 MPa, followed by a large strain excursion at 230 MPathat would corresponds to the typical single-slip. The following slight strain-hardening
was observed at higher strain regime. The continuous flow curves were observed forthe larger-size micropillars. There was not a detectable systematic variation in the flow
stress level depending on the mean diameter of micropillars, although the higher
strength of smaller-size specimen is generally understood 1). Note that the lower slopeof the elastic portion was found in larger-size micropillars, which might be attributed
to the compliance associated with the stiffness of -Fe phase underneath themicropillars compressed 3).
Fig. 4 presents secondary electron images (SEIs) showing the single-crystal
micropillars before and after the compression test. Obvious differences were observedin the appearance of the micropillar with D = 1.3 m after testing. The compressed
micropillar exhibits a couple of distinct shear surfaces (Fig. 4(b)), indicating large
single-slip-plane displacements under compression loading, which is represented by
rapid strain bursts in the flow curve (Fig. 3). Fine discrete slip bands were observed
along the gauge portion of the cylindrical micropillar with D = 3.5 m (Fig. 4(d)),
whereas the localization of the slip surface was scarcely observed. In micropillars withlarger D (Fig. 4 (f,h)), slip traces on a single plane was observed on the whole surface ofthe micropillars. Note that secondary-slip traces were locally observed on the surface of
all micropillars, which is indicative of the strain-hardening at high strain regime (Fig.
3).
Fig. 5 presents SEIs showing a representative micropillar compressed, together with
111 and 110 pole figures indicating the activate slip plane and direction, respectively.
The measured angle between compression axis and slip trace lines (Fig. 5(a)) is close to
one between compression axis and a (111) plane determined by the 111 pole figure (Fig.
5(c)) obtained from the prior EBSD analysis. The top view of the compressed
micropillar represents the shear direction due to a primary single-slip (Fig. 5(b)). The
direction corresponds well to a [-101] direction indicating on the stereographic
projection (Fig. 5(d)). These comparisons determine an activated primary slip system of(111)[-101] in the single-crystal micropillars under the compression loading, which is amost favorable slip system for the activation in terms of Schmid factor.

－ 90 －

Fig. 4 SEIs showing the -Fe single crystal cylindrical micropillars with various diameters (D)before (a, c, e, g) and (b, d, f, h) after the compression test: (a, b) D = 1.2 m, (c, d) D = 3.5 m,(e, f) D = 5.9 m, (g, h) D = 10.4 m.

Fig. 6 shows changes of the 0.2 % proof stress (0.2%) and the stress at a strain of 5%(5%) determined from the stress–strain curves (as shown in Fig. 3) as a function ofmean diameter (D) of cylindrical micropillars. The clear size dependences of 0.2% and5% were not found in the mean diameters approximately ranging from 1 m to 10 m.
0.2% and 5% were nearly constant of around 160 MPa and 270 MPa respectively,
independent of D, whereas a trend of relatively scattered 0.2% values at smaller D than
2 m was also found.

－ 91 －

Fig. 5 (a, b) SEI showing the compressed micropillar and (c, d) corresponding 111 and 011 poles
indicated on the stereographic projection. (The angles between observation and thecompression directions in (a) and (b) are 53degrees and 0 degrees, respectively.)Fig. 6 Change in 0.2% and 0.5 % proof stresses as a function of average diameter of thecylindrical -Fe single crystal micropillar (D).

－ 92 －

3. 2 Single-crystal micropillars with different shapes
Fig. 7 shows the representative nominal stress–strain curves of -Fe single-crystal
micropillars with different trapezoidal-cylinder shape parameters designated as D1/D2
at room temperature. The compression direction is close to [123] direction as well. In
this figure, the mean diameter (D) was used to prepare the stress–strain curves fromthe load–displacement curves measured in the present study. Note that the mean
diameters of these micropillars were around 3 m (ranges from 2.9 to 3.5 m). The
micropillar with D1/D2 = 0.75 exhibits a continuous yielding of approximately 190 MPa,
followed by a large displacement due to the activation of single-slip system. In the
micropillar with D1/D2 =0.54, the flow curve shows arapid strain burst at a lower
stress of about 120 MPa.
The

strainbursts

were

found

at

higherstrainregime as well. In the
micropillar

withsmaller

D1/D2,

strainburst

theoccurs at much lower stressfollowed by the increase in
the stress under loading.
Fig.

8presents

SEIs

showing the micropillars
with different values ofFig. 7 Nominal stress-strain curves of -Fe single crystal
micropillars with different dimensional parameters at room
temperature (average diameter of these micropillars areapproximately 3 m).

D1/D2 before and after the compression test. The clear slip traces on a single plane
corresponding to the activation of the primary slip were observed on the whole surfaceof the micropillar with D1/D2 = 0.54, whereas local slip traces on the different plane
corresponding to the secondary slip system appears around the top surface of the
micropillar (Fig. 8(b)). The obvious shear surface was localized around the tip (topportion) of a distinctive trapezoidal-cylinder-shaped micropillar with D1/D2 = 0.22
(Fig. 8(d)). The shear surface morphology is similar to that observed on the surface of
micropillars with smaller diameter than 2 m (Fig. 4(b)). The slip traces appears only
on the specimen surface of top portion as well.

－ 93 －

Fig. 8 SEIs showing the -Fe single crystal micropillars with various dimensional parameter(D1/D2) before (a, c) and (b, d) after the compression test: (a, b) D1 = 2.2 m and D2 = 3.7m, (c,d) D1 = 0.9 m and D2 = 4.1 m.

Fig. 9 shows a variation in the 0.2 % proof stress (0.2%) of micropillars with mean
diameters ranging from 2.5 to 5.9 m as a function of D1/D2. The value of 0.2% is almost
constant of approximately 170 MPa at higher D1/D2 than 0.6, whereas it becomessignificantly lower at lower D1/D2 than 0.6. This result clearly indicates the critical
D1/D2 value for measuring the accurate stress level of cylindrical micropillars withseveral micrometer-sizes.

Fig. 9 Change in 0.2 % proof stress (yield stress) as a function of the ratio of top diameter
divided by bottom diameter of micropillars (D1/D2).

－ 94 －

4．Discussion
The present study investigated the strength level of -Fe single-crystal cylindricalmicropillars depending on their diameter and shape in comparison with themillimeter-size polycrystalline specimens. One of interesting findings in this study is anearly constant strength level of -Fe single-crystal micropillars independent of theirmean diameter (specimen size) approximately ranging from 1 m to 10 m (Fig. 6),
which is different from a general trend on the size dependence for the strength of fcc
metals 1,10). However, the compressed micropillars with a smaller diameter than 2 mappears the significant shear-surfaces on a (111) plane (Fig. 4 (b)) corresponding to theoccurrence of rapid strain-bursts, which is a typical deformation behavior of thesubmicron or nanometer-size specimens 1,2). The measured strength level of the -Fe
single-crystal micropillars is discussed in terms of the scaling low for fcc metals
previously proposed 1, 10) as follows.
Previous systematic studies have summarized the compressive strength forsingle-crystal pure fcc metals (Au, Al, Ni, and Cu) with sub-micron size and proposed auniversal scaling law for the strength of fcc metals 10) as follows:res /  = A (D/b)m(1)

where  is the shear modulus, res is the resolved shear stress on {111} slip planes to<110> directions, D is the pillar diameter, and b is the magnitude of the Burgers vector.
On the basis of the experimental data, the A and m were measured to be 0.71 and -0.66,
respectively. It was found that the scaling law is satisfied at lower D/b thanapproximately 3 × 104 10), corresponding to the pillar diameter smaller thanapproximately 8 m. In order to compare the scaling law for the strength with themeasured strength level of -Fe single-crystal micropillars, the resolved shear stressesof micropillars calculated using their 0.2% (Fig. 6) and Schmid factor (Fig. 5) wereplotted as a function of the mean micropillar diameter (D), together with the estimatedshear strength level of millimeter-size specimens. This result is shown in Fig. 10. In
this figure, the 0 value of 122 MPa in the 0.2% proof stress previously measured isindicated as well. In the mean diameter smaller than 3 m, the experimentallymeasured resolved shear stress is much lower than the strength level calculated basedon the proposed scaling law (equation (1)), whereas the measured shear stress islocated on the trend line following the scaling law in a pillar diameter range from 3 m
to 6 m. In case of larger diameter than 10m, it might be difficult to compare themeasured data with the scaling law, because of the size limitation (smaller thanapproximately 8 m) for satisfying the scaling law 10). Note that the measured resolved
shear stress is approximately twice higher than the estimated shear stress of－ 95 －

millimeter-size specimens. These results indicate that the strength would besignificantly reduced in the -Fe single-crystal micropillars with smaller sizes below
m, which is deviated from the scaling law for the strength of fcc metals reported in
the literature 1,10). One of possible contributors to reduce the strength is FIB damage
accumulated in the surface layer of -Fe micropillars fabricated 15, 16), whereas thedetailed mechanism is still in question. The minute observation of lattice defects in
TEM thin film samples prepared by different processes of FIB milling andelectro-polishing would be required to identify whether any damage are introduced
into the fcc solid solution of -Fe phase by FIB milling. This would await the future
work to understand the unique scaling law for the strength of -Fe phase.

Fig. 10 Change in resolved shear stress of -Fe single crystal micropillars as afunction of average specimen diameter.

Acknowledgments
The support of JFE 21st Century Foundation is gratefully acknowledged.
References
1) Julia R. Greer, Jeff Th.M. De Hosson, Plasticity in small-sized metallic systems:
Intrinsic versus extrinsic size effect, Prog. Mater. Sci., 56 (2011), 654-724.
2) Michael D. Uchic, Dennis M. Dimiduk, Jeffrey N. Florando, William D. Nix,
Sample Dimensions Influence Strength and Crystal Plasticity, Science, 305 (2004),
986-989.
3) Julia R. Greer, Warren C. Oliver, William D. Nix, Size dependence of mechanical－ 96 －

properties of gold at the micron scale in the absence of strain gradients, Acta Mater.,
53 (2005) 1821–1830.
4) D.M. Dimiduk, M.D. Uchic, T.A. Parthasarathy, Size-affected single-slip behaviorof pure nickel microcrystals, Acta Mater. 53 (2005) 4065–4077.
5) Julia R. Greer, William D. Nix, Nanoscale gold pillars strengthened throughdislocation starvation, PHYSICAL REVIEW B 73 (2006) 245410.
6) Triplicane A. Parthasarathy, Satish I. Rao, Dennis M. Dimiduk, Michael D. Uchic
and Dallas R. Trinkle, Contribution to size effect of yield strength from thestochastics of dislocation source lengths in finite samples, Scripta Mater. 56 (2007)
313–316.
7) S.I. Rao, D.M. Dimiduk, T.A. Parthasarathy, M.D. Uchic, M. Tang, C. Woodward,
Athermalmechanisms

ofsize-dependent

crystalflow

gleanedfromthree-dimensional discrete dislocation simulations, Acta Mater. 56 (2008)
3245–3259.
8) D.M. Norfleet, D.M. Dimiduk, S.J. Polasik, M.D. Uchic, M.J. Mills, Dislocation
structures and their relationship to strength in deformed nickel microcrystals, Acta
Mater. 56 (2008) 2988–3001.
9) C.P. Frick, B.G. Clark, S. Orso, A.S. Schneider, E. Arzt, Size effect on strength andstrain hardening of small-scale [1 1 1] nickel compression pillars, Mater. Sci. Eng. A
489 (2008) 319–329.
10) R. Dou, B. Derby, A universal scaling law for the strength of metal micropillars andnanowires, Scripta Mater. 61 (2009) 524–527.
11) Andrew T. Jennings, Michael J. Burek, Julia R. Greer, Microstructure versus Size:
Mechanical Properties of Electroplated Single Crystalline Cu Nanopillars,
PHYSICAL REVIEW LETTERS, 104 (2010), 135503.
12) William D. Nix, Seok-Woo Lee, Micro-pillar plasticity controlled by dislocation
nucleation at surfaces, Phil. Mag. 91 (2011), 1084–1096.
13) Qiaoyan Sun, Qiang Guo, Xi Yao, Lin Xiao, Julia R. Greer, Jun Sun, Size effects instrength and plasticity of single-crystalline titanium micropillars with prismatic
slip orientation, Scripta Mater. 65 (2011), 473-476.
14) A.S. Schneider, C.P. Frick, B.G. Clark, P.A. Gruber, E. Arzt, Influence of orientationon the size effect in bcc pillars with different critical temperatures, Mater. Sci. Eng.
A 528 (2011), 1540-1570.
15) S. Shim, H. Bei, M.K. Miller, G.M. Pharr, E.P. George, Effects of focused ion beam
milling on the compressive behavior of directionally solidified micropillars and thenanoindentation response of an electropolished surface, Acta Mater. 57 (2009)－ 97 －

503–510.
16) J. Zimmermann, S. Van Petegem, H. Bei, D. Grolimund, E.P. George, H. Van
Swygenhoven, Effects of focused ion beam milling and pre-straining on the
microstructure of directionally solidified molybdenum pillars: A Laue diffraction
analysis, Scripta Mater. 62 (2010) 746–749.

－ 98 －