HAL Id: hal-01007328
https://hal.archives-ouvertes.fr/hal-01007328
Submitted on 8 Mar 2017
HAL is a multi-disciplinary open access
archive for the deposit and dissemination of sci-
entic research documents, whether they are pub-
lished or not. The documents may come from
teaching and research institutions in France or
abroad, or from public or private research centers.
L’archive ouverte pluridisciplinaire HAL, est
destinée au dépôt et à la diusion de documents
scientiques de niveau recherche, publiés ou non,
émanant des établissements d’enseignement et de
recherche français ou étrangers, des laboratoires
publics ou privés.
Distributed under a Creative Commons Attribution| 4.0 International License
Strength eects in micropillars of a dispersion
strengthened superalloy
Baptiste Girault, Andreas Schneider, Carl Frick, Eduard Arzt
To cite this version:
Baptiste Girault, Andreas Schneider, Carl Frick, Eduard Arzt. Strength eects in micropillars of a
dispersion strengthened superalloy. Advanced Engineering Materials, Wiley-VCH Verlag, 2010, 12
(5), pp.385-388. �10.1002/adem.201000089�. �hal-01007328�
Strength Effects in Micropillars of a Dispersion Strengthened
Superalloy**
By Baptiste Girault
*
, Andreas S. Schneider, Carl P. Frick and Eduard Arzt
In order to realize the full potential of emerging micro-
and nanotechnologies, investigations have been carried out
to understand the mechanical behavior of materials as
their internal microstructural constraints or their external
size is reduced to sub-micron dimensions.
[1,2]
Focused ion
beam (FIB) manufactured pillar compression techniques
have been used to investigate size-dependent mechanical
properties at this scale on a variety of samples, includ-
ing single-crystalline,
[3–10]
nanocrystalline,
[11]
precipitate-
strengthened,
[12,13]
and nanoporous
[14,15]
metals. Tests
revealed that single-crystal metals exhibit strong size effects
in plastic deformation, suggesting that the mechanical
strength of the metal is related to the smallest dimension of
the tested sample. Among the various explanations that have
been pointed out to account for such a mechanical behavior,
one prevailing theory developed by Greer and Nix
[6]
invokes
‘‘dislocation starvation.’’ It assumes that dislocations leave the
pillar via the surface before dislocation multiplication occurs.
To accommodate the induced deformation new dislocations
have to be nucleated, which requires high stresses.
[6,16]
This
theory has been partially substantiated by direct in situ
transmission electron microscope (TEM) observations of FIB
manufactured pillars which demonstrate a clear decrease in
mobile dislocations with increasing deformation, a result
ascribed to a progressive exhaustion of dislocation sources.
[17]
Another origin of size-dependent strengthening may lie in the
constraints on active dislocation sources exerted by the
external surface, i.e., source-controlled mechanisms.
[18–20]
A
clear understanding of the mechanisms responsible for the
size effects in plastic deformation is still missing and other
origins of strength modification with size remains somewhat
controversial.
[17]
Unlike pure metals, pillars with an internal size parameter
smaller than the pillar diameter would be expected to exhibit no
size effect, reflecting the behavior of bulk material. This was
demonstrated for nanocrystalline
[11]
and nanoporous Au.
[14,15]
Nickel–titanium pillars with semi-coherent precipitates approxi-
mately 10 nm in size and spacing also exhibited no size
dependence, although results are difficult to interpret due to the
concurrent martensitic phase transformation.
[13]
Conversely,
precipitate strengthened superalloy pillars were reported to
show size-dependent behavior, a result left largely unex-
plained.
[12,21]
Therefore, a strong need exists to further explore
the influence of internal size parameters on the mechanical
properties of small-scale single crystals, to better understand the
associated mechanisms responsible for the size effect.
[*] Dr. B. Girault, Dr. A. S. Schneider, Prof. E. Arzt
INM – Leibniz Institute for New Materials, Functional
Surfaces Group, and Saarland University
Campus D2 2, 66123 Saarbruecken, Germany
E-mail: baptiste.girault@inm-gmbh.de
Dr. A. S. Schneider
Max Planck Institute for Metals Research Heisenbergstr. 3,
70569 Stuttgart, Germany
Dr. C. P. Frick
Department of Mechanical Engineering, University of
Wyoming Department 3295 1000 E. University Ave.,
Laramie, WY 82071, USA
[**] The authors would like to acknowledge J. Schmauch, Saarland
University for EBSD measurements, discussions with K.-P.
Schmitt, INM, and the assistance of Christof Schwenk, Max
Planck Institute for Metals Research, Stuttgart, and Birgit
Heiland, INM for SEM sample surface preparation.
The present paper investigates the uniaxial compression behavior of highly alloyed, focused ion beam
(FIB) manufactured micropillars, ranging from 200 up to 4000 nm in diameter. The material used was
the Ni-based oxide-dispersion strengthened (ODS) alloy Inconel MA6000. Stress–strain curves show a
change in slip behavior comparable to those observed in pure fcc metals. Contrary to pure Ni pillar
experiments, high critical resolved shear stress (CRSS) values were found independent of pillar
diameter. This suggests that the deformation behavior is primarily controlled by the internal obstacle
spacing, overwhelming any pillar-size-dependent mechanisms such as dislocation source action or
starvation.
1
The research presented here investigates the mechanical
behavior of single-crystalline micropillars made of a dispersion
strengthened metal with a small internal size scale: the
oxide-dispersion strengthened (ODS) Inconel MA6000,
1
which
isahighlystrengthenedNi-basedsuperalloyproducedby
means of mechanical alloying. This high-energy ball milling
process produces a uniform dispersion of refractory particles
(Y
2
O
3
) in a complex alloy matrix, and is followed by
thermo-mechanical and heat treatments (hot-extrusion and
hot-rolling) to obtain a large grained microstructure (in the
millimeter range). MA6000 has a nominal composition of
Ni-15Cr-4.5A1-2.5Ti-2Mo-4W-2Ta-0.15Zr-0.01B-0.05C-1.1Y
2
O
3
,
in wt%. Previous studies carried out on bulk MA6000 showed
that its strength is due to the oxide dispersoids and to coherent
precipitates of globular-shaped g
0
-(Ni
3
Al/Ti) particles, which
are formed during the heat treatment. Depending on the
studies, the average sizes in these two-particle populations are
about 20–30 and 275–300 nm, respectively.
[22–25]
TEM investigations of our sample revealed a dense
distribution of oxide particles with diameter and spacing
well below 100 nm; however, no indications of g
0
-precipitates
were found (Fig. 1(a)). Thus, in contrast to a recent study on
nanocrystalline pillars,
[11]
the tested specimens have no
internal grain boundaries, which would impede the disloca-
tions from leaving the sample, but have a characteristic length
scale smaller than the pillar diameter.
Experimental
Bulk MA6000 was mechanically and che-
mically polished. The polishing process and
testing were carried out in a plane allowing
access to elongated grains of several milli-
meters in size. Pillar manufacturing, testing,
and analysis were similar to the study by
Frick et al.
[26]
. Micro- and nanopillars with
diameters ranging from 200 to 4000 nm and a
diameter to length aspect ratio of approxi-
mately 3:1 were machined with a FIB FEI
Nova 600 NanoLab DualBeam
TM
. All pillars
were FIB manufactured within the same
grain (Fig. 1(b)) in order to avoid any
crystallographic orientation changes that
could activate different slip systems. To
minimize any FIB-related damage, a decreas-
ing ionic current intensity from 0.3 nA down
to 10 pA was used as appropriate with
decreasing pillar diameters
[27]
. The pillars
were subsequently compressed in load-
control mode by an MTS XP nanoindenter
system equipped with a conical diamond
indenter with a flat 10 mm diameter tip under
ambient conditions. Loading rates varied
between 1 and 250 mN s
1
depending on
pillar diameter in order to obtain equal stress rates of
20 MPa s
1
.
The pillar diameter, measured at the top of the column, was
used to calculate the engineering stress. It is important to
mention that the pillars had a slight taper of approximately
2.78 on average, with a standard deviation of 0.58. Hence,
stress as defined in this study represents an upper bound to
the stress experienced by the sample during testing.
Figure 1(c) and (d) shows representative post-compression
scanning electron microscope (SEM) micrographs of 304 and
1970 nm diameter pillars. Pillars with diameters above 1000 nm
retained their cylindrical shape and showed multiple slip steps
along their length; in some cases, barreling was observed.
Samples below this approximate size tended to show localized
deformation at the top with fewer, concentrated slip steps,
which have been observed in previous studies, e.g., see
Ref. [28]. Independent of pillar size, multiple slip was observed.
High-magnification pictures of the sidewalls showed fewer slip
steps in the vicinity of particles, emphasizing that particles act
as efficient dislocation obstacles.
Electron backscattered diffraction (EBSD) measurements
showed that the pillars were cut in a grain with the h110i
crystallographic orientation aligned normal to the sample
surface. Among the 12 different possible slip systems in fcc
crystals, only four present a non-zero Schmid factor equal to
0.41. The slip bands were oriented at approximately 348 with
regard to the pillar axis, nearly matching the expected 35.38
angle of the {111} h110i slip system for a h110i oriented fcc
crystal.
1
Inconel MA6000 is a trademark of the Inco Alloys International, Inc.,
Huntington, WV.
Fig. 1. TEM plane view of MA6000 microstructure (a) and SEM images of (b) location of pillar series (white
circles) with regards to grains boundaries (white dotted lines); (c) and (d) show deformed pillars with diameter of
304 and 1970 nm, respectively. Pictures were taken at a 528 tilt angle relative to the surface normal.
2
Results and Discussion
Typical engineering stress–strain curves are shown in
Figure 2. The features of the stress–strain curves changed with
decreasing pillar diameter. Larger pillars displayed a stress–
strain curve with strain hardening similar to bulk material.
Below approximately 2000 nm, staircase-like stress–strain
curves with plastic strain bursts separated by elastic loading
segments were observed. This has been demonstrated in
previous single-crystalline micropillar studies, where strain
bursts were related to dislocation avalanches.
[10,26]
For pillars
even smaller than 1000 nm in diameter, the staircase-like
shape under 4% strain is followed by large bursts over several
percent strain, which gave the appearance of strain softening.
The large bursts are consistent with SEM observations
showing highly localized deformation on a few glide planes
for pillars with diameters below 1000 nm. This behavior
suggests that, for small pillar diameters, the dispersoid
particles no longer promote homogeneous deformation, as
they do in bulk alloys. The pillars hence exhibit a size effect in
the slip behavior.
By contrast, the flow stresses are comparable for all pillar
diameters and do not exhibit a size effect (Fig. 2). This is
highlighted in Figure 3, where the flow stress measured at 3%
strain is plotted as a function of pillar diameter, and compared
with previous results on pure Ni micropillar.
[4,26]
Whereas the
pure Ni exhibits the frequently reported size effect, our data
are independent of pillar diameter and lie close to the bulk
value (critical resolved shear stress (CRSS) of about 500
MPa
[23]
). Best power-law fits gave a relationship between flow
stress s and diameter d of s a d
0.65
and d
0.62
for [111] and
[269] Ni, respectively; for MA6000, the exponent is
0.04 0.02, a value close to zero.
In contrast to the study on a superalloy containing only
coherent precipitates,
[12]
this study clearly shows that
incoherent particles can give rise to an internal size parameter,
which is dominant over any pillar-size effect in the entire size
range. The oxide particle spacing in our study is below
100 nm, which is much smaller than the pillar diameters.
[22–25]
It is notable that the extrapolated MA6000 strength values and
the pure Ni data in Figure 3 intersect at a pillar diameter of
about 150 nm, close to the oxide particle spacing. The smallest
pillars still contain about 10, the largest about 40 000 oxide
particles. In the latter case, continuous stress–strain curves as
in bulk are expected due to averaging effects; in the smaller
pillars, stochastic effects would explain the staircase-like
behavior.
The absence of the size effect in single-crystalline MA6000
implies that neither the starvation theory nor source-
controlled mechanisms may be applicable. The high density
of internal obstacles will be likely to prevent dislocations from
exiting excessively through the surface; and the small obstacle
spacing, compared to the pillar diameter, will make
source-operation insensitive to surface effects. As a result,
the flow stress will be determined by the interactions of
dislocations and obstacles, as in bulk alloys. Size effects might,
however, be expected for pillar diameters below the oxide
particle spacing, i.e., 100 nm, but are beyond the scope of the
present study.
Conclusions
In summary, compression tests were carried out on
single-crystal pillars of an ODS-Ni superalloy (MA6000).
The following conclusions were drawn:
i) As in pure fcc metals, the superalloy pillars undergo a
change in slip behavior. Pillars thinner than 2000 nm
showed staircase-like stress–strain curves. The localized
strain bursts suggest that the non-shearable particles no
longer manage to homogenize slip as in bulk alloys.
ii) Contrary to single-crystal studies on pure metals, no
dependence of yield stress on sample size was measured.
A high constant strength was found, which is comparable
Fig. 2. Representative compressive stress–strain behavior for MA6000 pillars of various
diameters ranging from approximately 200 to 4000 nm.
Fig. 3. Logarithmic plot of the critical resolved shear stress (CRSS) at 3% strain for all
[111] MA6000 pillars tested. The error bars correspond to the standard deviation of six
tests on different pillars presenting similar diameters. For comparison, 0.2% offset
compressive stresses are shown for pure [269] Ni
[5]
and 3% offset values for [111] Ni.
[23]
The solid lines represent best power-law fits.
3
to the highest flow stress value published for pure Ni
pillars (with a diameter of 150 nm).
iii) These results suggest that size-dependent mechanisms
such as dislocation starvation or source exhaustion are
not operative in a dispersion strengthened alloy. Instead,
the strong internal hardening dominates over any speci-
men size effect.
[1] E. Arzt, Acta Mater. 1998, 46, 5611.
[2] T. Volpp, E. Go
¨
hring, W.-M. Kuschke, E. Arzt, Nanos-
truct. Mater. 1998, 7, 855.
[3] M. D. Uchic, D. M. Dimiduk, J. N. Florando, W. D. Nix,
Science 2004, 305, 986.
[4] D. M. Dimiduk, M. D. Uchic, T. A. Parthasarathy, Acta
Mater. 2005, 53, 4065.
[5] M. D. Uchic, D. M. Dimiduk, R. Wheeler, P. A. Shade, H.
L. Fraser, Scr. Mater. 2006, 54, 759.
[6] J. R. Greer, W. D. Nix, Phys. Rev. B. 2006, 73, 245410.
[7] C. A. Volkert, E. T. Lilleodden, Philos. Mag. 2006, 86,
5567.
[8] D. Kiener, C. Motz, T. Scho
¨
berl, M. Jenko, G. Dehm, Adv.
Eng. Mater. 2006, 8, 1119.
[9] W. D. Nix, J. R. Greer, G. Feng, E. T. Lilleodden, Thin
Solid Films 2007, 515, 3152.
[10] R. Maaß, S. Van Petegem, H. Van Swygenhoven, P. M.
Derlet, C. A. Volkert, D. Grolimund, Phys. Rev. Lett. 2007,
99, 145505.
[11] B. E. Schuster, Q. Wei, H. Zhang, K. T. Ramesh, Appl.
Phys. Lett. 2006, 88, 103112.
[12] D. M. Dimiduk, M. D. Uchic, S. I. Rao, C. Woodward,
T. A. Parthasarathy, Modell. Simul. Mater. Sci. Eng. 2007,
15, 135.
[13] C. P. Frick, S. Orso, E. Arzt, Acta Mater. 2007, 55, 3845.
[14] J. Biener, A. M. Hodge, J. R. Hayes, C. A. Volkert, L. A.
Zepeda-Ruiz, A. V. Hamza, F. F. Abraham, Nano Lett.
2006, 6, 2379.
[15] C. A. Volkert, E. T. Lilleodden, D. Kramer, J.
Weissmuller, Appl. Phys. Lett. 2006, 89, 061920.
[16] J. R. Greer, W. C. Oliver, W. D. Nix, Acta Mater. 2005, 53,
1821.
[17] Z. W. Shan, R. K. Mishra, S. A. Syed Asif, O. L. Warren,
A. M. Minor, Nat. Mater. 2008, 7, 115.
[18] B. von Blanckenhagen, P. Gumbsch, E. Arzt, Modell.
Simul. Mater. Sci. Eng. 2001, 9, 157.
[19] B. von Blanckenhagen, P. Gumbsch, E. Arzt, Philos. Mag.
Lett. 2003, 83,1.
[20] B. von Blanckenhagen, E. Arzt, P. Gumbsch, Acta Mater.
2004, 52, 773.
[21] M. D. Uchic, D. M. Dimiduk, Mater. Sci. Eng. A 2005, 400,
268.
[22] J. H. Schro
¨
der, E. Arzt, Scr. Metall. 1985, 19, 1129.
[23] R. F. Singer, E. Arzt, in High Temperature Alloys for Gas
Turbines and Other Applications (Eds: W. Betz, R.
Brunetaud, D. Coutsouradis, H. Fischmeister, I.
Kvernes, Y. Lindblom, J. B. Marriott, D. B.
Meadowcroft), D. Reidel Publishing Company, 1986,
p. 97.
[24] B. Reppich, W. Listl, T. Meyer, in High Temperature Alloys
for Gas Turbines and Other Applications (Eds: W. Betz, R.
Brunetaud, D. Coutsouradis, H. Fischmeister, I.
Kvernes, Y. Lindblom, J. B. Marriott, D. B.
Meadowcroft), D. Reidel Publishing Company, 1986,
p. 1023.
[25] M. Heilmaier, B. Reppich, Metall. Mater. Trans. A 1996,
27, 3862.
[26] C. P. Frick, B. G. Clark, S. Orso, A. S. Schneider, E. Arzt,
Mater. Sci. Eng. A 2008, 489, 319.
[27] S. Shim, H. Bei, M. K. Miller, G. M. Pharr, E. P. George,
Acta Mater. 2009, 57, 503.
[28] Z. W. Shan, R. K. Mishra, S. A. S. Asif, O. L. Warren, A.
M. Minor, Nat. Mater. 2008, 7, 115.
4
![Fig. 3. Logarithmic plot of the critical resolved shear stress (CRSS) at 3% strain for all [111] MA6000 pillars tested. The error bars correspond to the standard deviation of six tests on different pillars presenting similar diameters. For comparison, 0.2% offset compressive stresses are shown for pure [269] Ni[5] and 3% offset values for [111] Ni.[23] The solid lines represent best power-law fits.](/figures/fig-3-logarithmic-plot-of-the-critical-resolved-shear-stress-1crrduak.webp)
