- Email: [email protected]
Temperature and orientation effects on the deformation mechanisms of α-Fe micropillars
Accepted Manuscript Temperature and orientation effects on the deformation mechanisms of α-Fe micropillars
A.B. Hagen, B.D. Snartland, C. Thaulow PII:
S1359-6454(17)30185-4
DOI:
10.1016/j.actamat.2017.03.006
Reference:
AM 13612
To appear in:
Acta Materialia
Received Date:
20 December 2016
Revised Date:
01 March 2017
Accepted Date:
03 March 2017
Please cite this article as: A.B. Hagen, B.D. Snartland, C. Thaulow, Temperature and orientation effects on the deformation mechanisms of α-Fe micropillars, Acta Materialia (2017), doi: 10.1016/j. actamat.2017.03.006
This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
ACCEPTED MANUSCRIPT 1
Temperature and orientation effects on the deformation
2
mechanisms of α-Fe micropillars
3
A.B. Hagen1*, B. D. Snartland1, C. Thaulow1
4
1Department
5
and Technology (NTNU), NO-7491 Trondheim, Norway
6
*Corresponding author
7
E-mail: [email protected]
8
Abstract
9
In-situ uniaxial compression tests on [010] and [011] α-Fe pillars have been
10
conducted at room temperature and -75°C to study the mechanical response with
11
focus on temperature and orientation effect. All pillars exhibit larger yield stresses
12
and hardening at -75°C. We attribute this phenomenon to the non-planarity of screw
13
dislocations in bcc crystals and the larger contribution of screw dislocations in
14
governing the micro-scale plasticity at lower temperatures, similar to what is common
15
for many bcc metals. We employ molecular dynamics to simulate the compression
16
process to elucidate the underlying dislocation mechanisms. Nanopillars deformed on
17
the [011] orientation deform via twinning at both temperatures, while the plastic
18
deformation behavior for [010] pillars are governed by intense dislocation activity. In
19
addition, [011] nanopillars withstand higher stresses before yielding, in agreement
20
with the compression experimental results. TEM examinations are also reported and
21
reveal that temperature clearly influence the residual dislocation structure.
of Engineering Design and Materials, Norwegian University of Science
22 1
ACCEPTED MANUSCRIPT 23
Keywords: Temperature effect; Dislocations; Micro-scale plasticity; Bcc iron; Yield
24
stress
25
1. Introduction
26
The low-temperature embrittlement resulting in the Ductile-to-Brittle Transition
27
(DBT) is still of great concern for large steel structures in engineering applications.
28
Increase in yield and tensile strength at low temperature is widely observed metals
29
and alloys in general. However, fcc metals still retain much or all of their ductility at
30
low temperature in spite of the change in mechanical properties. In the case of bcc
31
metals (e.g. α–Fe, W), loss of ductility suddenly appear below a critical temperature
32
and brittle fracture may occur at subzero temperatures making the metals vulnerable
33
when operating in extreme environments. Thus, understanding of the mechanisms
34
controlling this abrupt transition is of great importance, but are however, still
35
insufficiently understood.
36
Small-scale mechanical testing techniques have attracted a lot of interest since it
37
allows for higher precision and selection of microstructural features for evaluation of
38
mechanical behavior. By doing this, fundamental details from deformation
39
mechanisms can be investigated in new ways that is not feasible using conventional
40
methods at larger scales. By using micro-scale sample manufacturing, such as focused
41
ion bean milling, a large range of nano and microscale compression, tension and
42
fracture geometries have become available. Plastic properties of both fcc and bcc
43
metals have been extensively studied by means of uniaxial micro-compression tests.
44
The extent of the studies has primarily been devoted to investigation of size
45
dependence, revealing a dramatically increase in yield strength with decreasing
46
sample size [1-8]. Another key observation is that fcc metals obtain a larger size
2
ACCEPTED MANUSCRIPT 47
effect that what observed in bcc metals [5-8]. The origin of the different plasticity
48
behavior of fcc and bcc metals can be traced down to the fundamental dislocation
49
mechanisms. The motion of screw dislocations generally governs deformation in bcc
50
crystal structures. Atomistic simulations have revealed that the non-planar screw
51
dislocation core structure leads to a high Peierls barrier, resulting in a lower mobility
52
of screw dislocations compared to edge dislocations [9-12]. At lower temperatures,
53
the motion of screw dislocations is thermally activated, leading to a strong
54
temperature and strain rate dependence of the yield and flow stresses in bcc metals
55
[13]. These processes where yield become dependent of temperature, occurs below
56
the so-called critical temperature. Above this temperature, the mobility of edge and
57
screw dislocations is equal, as in the case of fcc metals.
58
Reports of the plasticity behavior of small-scale bcc Fe samples at room temperature
59
[14-17] have revealed significant insights. Orientation dependent plasticity behavior
60
is observed [14] attributed to the non-planarity of screw dislocation cores and
61
twinning-antitwinning asymmetry typical of bcc metals [10, 12, 18, 19] and slip has
62
been found to occur on {110} planes [14, 15]. The hardening behavior observed in Fe
63
100 nm nanopillars have been attributed to increase in dislocation density due to
64
dislocation interactions and multiplication [16]. Dislocation Dynamics [6] and
65
molecular dynamics simulations [20] have suggested that such multiplication
66
mechanisms occur due to the longer residence time of screw dislocations in the
67
sample allowing it to multiply before exiting the pillar surface. The characteristics of
68
the compressive stress-strain curves observed in Fe samples consisting of strain bursts
69
have been attributed to the plastic flow along slip lines on the pillar surface [17]. In-
70
situ transmission electron microscopy (TEM) compression experiments of Fe
71
nanoblades, reported by Xie et al. [21], confirmed that the series of small strain burst
3
ACCEPTED MANUSCRIPT 72
were related to the collective movement of one or more dislocations and the more
73
extended strain burst were caused by slip formation nucleated from the free surface.
74
Very few investigations, however, have reported on the temperature dependence of
75
mechanical properties and dislocation behavior in small-scale bcc samples. This is
76
probably due to limited availability of micromechanical testing systems capable of
77
performing such precision testing at low temperature under stable conditions. To the
78
authors knowledge, only one low temperature study of Fe micropillars [22] have been
79
conducted. Mechanical properties and deformation morphology was reported to vary
80
widely as a function of temperature and crystallographic loading orientation.
81
A recent molecular dynamics simulation study of pre-notched Fe cantilevers [23] was
82
performed to investigate the effect of crystallographic orientations and its influence
83
on fracture mechanisms. Interestingly, two of the orientations tested, (101)[-101] and
84
(100)[0-11], display different fracture characteristics by means of ductile and brittle
85
behavior, respectively. The crack system (101)[-101] exhibits substantial ductility
86
with blunting on the crack tip. In contrast, the (100)[0-11] crack system indicates
87
brittle fracture with crack extension by cleavage, consistent with a previous atomistic
88
study of this crack system [24]. These studies reveal that orientation dependent
89
properties contribute to new features of the plastic behavior. Coupling the effects
90
between temperature and grain orientation on the plastic deformation and the
91
underlying dislocation mechanisms are thus of great interest.
92
For this purpose, the aim of this work is to increase the understanding of the plasticity
93
mechanisms at low temperature for these two crystallographic orientations. The
94
present work is dedicated to present new experimental data obtained from in-situ
95
SEM compression experiments on 1 μm diameter single crystal α- Fe micropillars,
4
ACCEPTED MANUSCRIPT 96
performed at room temperature and -75˚C. Our findings provide quantitative
97
information into plasticity relative to temperature at micro-scale. We perform MD
98
simulations and TEM investigations to obtain insight in the temperature dependent
99
dislocation behavior. The results are discussed in context with classical dislocation
100
theories in bcc metals while accounting for the influence of the size of microcrystal
101
samples, temperature and orientation.
102
2. Experimental procedures and methods
103
2.1. Sample preparation and micro-mechanical testing
104
A high purity (99.99%) α-Fe sample from Alfa Aesar GmbH & Co KG, with the
105
dimensions 1x1x0.1 cm was used in this investigation. The sample was heat treated in
106
a high vacuum furnace at 700 °C for 3 h in order to produce enlarged grains. The
107
sample surface was polished using 1 µm grit diamond and electrochemically polished
108
at 35 V for 20 seconds using an A2 electrolyte. After determination of
109
crystallographic orientations using EBSD mapping, micropillars in each grain with
110
orientation [010] and [011] were machined using focused ion beam (FIB) milling
111
(FEI Helios 600 DualBeam) with a 30 keV Ga+, Fig 1. A three-step milling procedure
112
with a final current of 48 pA was conducted in order to obtain surface refining with
113
minimal tapering angle and to reduce material redeposition. The resulting dimension
114
of the pillars, i.e. d=1 µm and a height of 3.5 µm, gave an aspect ratio (height/ top
115
diameter) of ∼3.5.
116
Mechanical compression tests were performed in a FEI Quanta Environmental SEM
117
(ESEM) using a PI-85 Picoindenter (Hysitron) with a cono spherical diamond
118
indenter with a diameter of 4 μm and a cone angle of 60°, produced by Synton-MDP.
119
The Fe pillars were tested in an open-loop control mode at 25 °C and -75 °C using a
5
ACCEPTED MANUSCRIPT 120
cooling system connected to the indenter device consisting of a rod made of copper
121
and with liquid nitrogen as the cooling source. The system has two independent
122
thermocouples to accurately control the temperature on the sample and indenter tip. A
123
detailed description of the system is found in [22]. The recorded load-displacements
124
data were converted into engineering stress-strain curves using the measured length
125
and top diameters of the pillars.
126 127
Figure 1: EBSD pattern quality map of Fe sample surface with [010] and [011] grains highlighted. The final
128
milled pillars within each grain are indicated by arrows.
129 130
2.2. TEM sample preparation
131
A FEI Helios 600 DualBeam FIB (Focused Ion Beam) was used to make thin,
132
electron transparent lamellas for ex-situ transmission electron microscopy (TEM)
133
characterization. The TEM lamellas were prepared in cross-section with the lamella
134
plane parallel to the loading direction. Prior to milling, protection layers of Pt and C
135
were deposited by electron beam and ion beam assisted depositions, respectively, on
136
top and on the sidewalls of the pillars to avoid ion beam implantation and damage in
137
the pillars. The coarse Ga+ ion beam thinning was done at 30 kV. Final thinning was
138
performed with 5 and 2 kV acceleration voltages. The thickness of the final lamellas
139
was typically in the range 50 – 100 nm. TEM characterization was performed with a
140
double Cs corrected coldFEG Jeol ARM200CF, operated at 200 kV. The TEM
141
lamellas were plasma cleaned for 2 min prior to TEM characterization to remove
142
possible hydrocarbon contamination on the surfaces of the lamellas.
143
2.3. Simulation methods
6
ACCEPTED MANUSCRIPT 144
Molecular dynamics (MD) simulations of [010] and [011] nanopillars were performed
145
to investigate the plasticity mechanisms at atomistic scale using Large scale
146
Atomic/Molecular Massively parallel Simulator (LAMMPS) [25] with a timestep of
147
0.0015 ps. Atom-atom interaction is described by the embedded atom method (EAM)
148
potential developed for Fe by Mendelev et al. [26]. Periodic boundary conditions are
149
defined in x– and y-direction, Fig. 2. Prior to loading, the nanopillars was relaxed for
150
75 ps using a NPT ensemble to obtain equilibrium configuration followed by NVT
151
ensemble for the main run, with a constant volume and temperature of 15 K and 300
152
K throughout the simulations. The low temperature of 15 K was chosen to elucidate
153
the temperature effect in the plasticity mechanisms. A strain rate of 𝜀 = 9 ∙ 109 s-1 was
154
used throughout the simulations. The results were visualized with the software
155
OVITO [27]. Dislocation defects in the pillars were detected and identified using the
156
dislocation extraction algorithm (DXA) [28, 29] allowing for dislocation density
157
measurements. Due to the large simulation model (∼51 million Fe atoms) and the
158
inherent timescale limitations with MD simulations, dislocation density calculations
159
were performed at predefined deformation steps.
160 161
Figure 2: Simulation model of the Fe nanopillar with diameter 50 nm, height 125 nm and a 3° taper angle.
162
4. Results
163
4.1. Compression test of micropillars
164
Fig. 3 shows representative SEM images of the pillars after compression. Irrespective
165
of orientation and test temperature, all Fe pillars exhibited localized slip bands with
166
significant shear offsets on the pillar surface, as recently reported elsewhere [14, 15,
167
22]. Multiple slip lines were mostly prevalent on the [010] pillar surfaces, Fig. 3a and
7
ACCEPTED MANUSCRIPT 168
3b, suggesting a larger number of activated slip systems than that observed for [011]
169
Fe pillars. The [011] pillars exhibit few slip lines at room temperature, Fig 3c, and
170
only one prevalent slip trace at low temperature, Fig. 3d.
171 172
Figure 3: Post-compression micrographs of [010] Fe pillars at a) 25 °C and b) -75 °C, and [011] Fe pillars at
173
c) 25 °C and d) -75 °C.
174 175
Fig. 4a and b show the engineering stress-strain curves for [010] and [011] pillars,
176
respectively. Representative engineering stress-strain curves are displayed in Fig. 5a,
177
accentuating the characteristics in the stress-strain behavior for each orientation and
178
test temperature. Low temperature stress-strain curves reveal multiple strain bursts
179
separated by elastic loading sequences and show a stronger hardening than that
180
observed in the room temperature curves, which consist of larger extended plastic
181
regimes with small amount of hardening.
182
Yield stresses, Fig. 5b, were determined at the level of stress where first sign of
183
plastic behavior occurred, indicated by a first small strain burst, illustrated in Fig. 5a.
184
Hence, the yield stress represents the stress level required for activation of the
185
weakest dislocation source [30]. Orientation and significant temperature dependence
186
of strength are found. The average yield stress of the low temperature [010] Fe pillars,
187
were estimated to 560 MPa, compared with 200 MPa for the room temperature pillars.
188
For the [011] pillars, a yield stress of 757 MPa was found at low temperature and 319
189
MPa at room temperature. Some scatter in strength are found and further discussed in
190
section “6.1. Effect of orientation”.
191 192
Figure 4: Engineering stress-strain curves for (a) [010] and (b) [011] Fe pillars at 25 °C and -75 °C.
193
8
ACCEPTED MANUSCRIPT 194
Figure 5: a) Representative stress-strain curves from each loading orientation and test temperature with
195
magnified view showing the yield stress point of determination indicated by arrows. b) Yield stresses versus
196
temperature for all [010] and [011] Fe pillars. The slope indicates the average increase in yield stress for
197
each orientation.
198 199
4.2. TEM characterization
200
Fig. 6 and Fig. 7 shows TEM bright field micrographs of [010] and [011] pillars,
201
respectively. The pillars compressed at room temperature (Fig. 6a-b and Fig. 7a-b)
202
clearly shows formation of complex dislocation networks consisting of loops,
203
junctions and entanglements at the top portion of the pillar, where deformation
204
predominantly occurs due to tapered geometry of the pillar [31]. The deformation is
205
characterized by large slip offsets across the pillar, e.g. Fig. 6a. A large number of
206
perfect dislocations are required to form such offsets emerging from the pillar surface,
207
suggesting that deformation is accommodated via several perfect dislocations rather
208
than partial dislocations [32]. This is also evident from the adjacent long straight
209
dislocations of <111> type, propagating into the pillar center, Fig 6a. The residual
210
dislocation structure consisting of both straight and smoothly curved dislocations for
211
both orientations, suggest contribution from both screw and mixed dislocations.
212 213
Bright field images of the pillars tested at -75 ˚C reveal the presence of long straight
214
screw segments (Fig. 6d and Fig 7d) consistent with those observed at room
215
temperature. However, the [010] pillar deformed at low temperature (Fig. 6d), shows
216
a less dense population of dislocations consisting of several small dislocation
217
segments homogeneously distributed within the pillar. These could also be a result of
218
FIB induced defects, further discussed in section “6.2. Effect of temperature “. The
219
[011] pillar deformed at -75 ˚C (Fig. 7d), contains several straight dislocation 9
ACCEPTED MANUSCRIPT 220
segments of <111> type, suggesting that perfect dislocations nucleate at the surface
221
and propagate towards the pillar center. Since no evidence of twin formation is
222
observed, the deformation at low temperature predominantly occurs by the motion of
223
screw segments.
224 225
Figure 6: Bright field TEM images of [010] Fe pillars with corresponding diffraction pattern compressed at
226
(a-b) 25 °C and (c-d) -75 °C. Magnified view showing b) dislocation loops and d) straight <111> dislocations.
227 228 229
Figure 7: Bright field TEM images of [011] Fe pillars with corresponding diffraction pattern compressed at
230
(a-b) 25 °C and (c-d) -75 °C. Magnified view showing b) dislocation loops and d) straight <111> dislocations.
231 232
4.3. Molecular dynamics (MD) simulation of Fe nanopillars
233
A series of MD simulations was performed to elucidate the dislocation behavior.
234
Compressive engineering stress-strain curves for simulated [010] and [011] Fe
235
nanopillars at 300 K and 15 K are shown in Fig. 8a. Overall, the deformation is
236
characterized by initial elastic deformation up to a maximum stress peak followed by
237
a decrease in stress. Considering that all pillars are initially dislocation-free, the
238
maximum stress peaks reflect the stress necessary for the full, or partial, dislocation
239
nucleation [33]. However, the stress-strain characteristics undergo some changes with
240
orientation and temperature. This is discernible particularly by means of decreasing
241
strength with increasing temperature and a much sharper abrupt stress drop after
242
yielding for the [011] pillars due to the appearance of twinning, while [010] pillars
243
displayed progressive plastic deformation with dislocation slip as the dominating
244
deformation mechanism. Fig. 8b shows the evolution of dislocation density,
245
calculated from the total length of all dislocation segments at each chosen timestep,
246
divided by nanopillar volume, using the DXA. The [010] pillars obtain higher 10
ACCEPTED MANUSCRIPT 247
dislocation density than [011] pillars, in the range of ∼1016 m-2 versus ∼1015 m-2,
248
respectively. At 15 K the density for the [010] pillar continues to increase throughout
249
the simulation, while the density evolution at 300 K levels out. For [011] pillars, a
250
nearly constant density is reached at both 15 K and 300 K.
251 252
Figure 8: a) Engineering stress-strain curves and b) dislocation density evolution for all [010] and [011] Fe
253
nanopillars at 15 K and 300 K.
254 255
Atomic snapshots at various strain levels show the evolution of the initial dislocation
256
nucleation for all the parallel tests, Fig 9. Typically 1/2 <111> dislocations form at the
257
pillar surface bottom moving upward on {112}<111> slip systems for all tests. The
258
yielding in [010] nanopillars occurs by dislocation nucleation in the four symmetrical
259
{112}<111> slip systems with a Schmid factor of 0.47, shown in Fig. 9a-h. For the
260
[011] pillars, there are two symmetrical {112}<111> slip systems activated also with
261
a Schmid factor of 0.47, Fig. 9i-p. The more easily available slip possibilities in the
262
[010] pillars are also reflected in the stress strain curves, by means of a lower yield
263
stress, Fig. 8a.
264
Overall, the dislocations nucleate as curved lines resembling dislocation of mixed
265
character. At 300 K, the dislocation loops easily expand in multiple directions.
266
Similar structure is initially observed at 15 K as well. However, as the dislocation
267
lines continue to grow, they develop into straight lines, typical of pure screw character
268
[34], Fig. 9e-h. For the [011] nanopillar, twinning nucleation is present at 15 K as
269
soon as the first dislocation is initiating, Fig. 9 m-p. The deformation mechanisms
270
observed for each orientation are summarized in Table 1.
271
11
ACCEPTED MANUSCRIPT 272
Figure 9: Initial dislocation configurations at various strains viewed along the loading direction. The [010]
273
nanopillars obtain dislocation nucleation from four symmetrical sites (a-d) subsequently colliding and
274
forming loops with increased strain at 300 K, while (e-h) initially curved dislocations propagates into
275
straight dislocation lines at 15 K. The [011] nanopillars nucleate dislocations from two opposite sites, (i-l)
276
forming dislocation loops with increased strain at 300 K and (m-p) twin configurations at 15 K.
277 278
Table 1: Deformation mechanisms for [010] and [011] Fe nanopillars at 300 and 15 K.
Loading direction
Temperature
Slip system
Schmid factor
Mechanism
[011]
300 K
(211)[111]
0.4714
Twinning
[011]
15 K
(211)[111]
0.4714
Twinning
[010]
300 K
(121)[111]
0.4714
Dislocation slip
[010]
15 K
(121)[111]
0.4714
Dislocation slip
279 280
Fig. 10 shows stress-strain curves for all the parallels, with insets of atomic snapshots
281
at strain levels before, at- and after the maximum stress peak. [010] pillars mainly
282
consists of massive dislocation generation and loop formation leading to dislocation
283
slip, Fig. 10a-b. Dislocations with ½<111> burgers vector start to nucleate at four
284
symmetrical sites, as shown in detail in Fig. 9a-h, moving upwards into the pillar
285
center on {121}<111> slip systems, and escaping the free surface. At 300 K,
286
dislocations tend to rearrange themselves, creating dislocation loops that easily
287
expand in multiple directions and leaving behind vacancies on their path, Fig. 10a
288
(inset 2 and 3a). At 15 K, the curved front of the dislocations escapes the free surface,
289
while most of the straight lines are remained in the pillar for a longer time, continuing
290
to operate with kink pair mechanisms and interact with new dislocations upon further
291
loading. Moreover, a small twin embryo starts to develop after yielding, quickly
292
growing into two small parallel planes, leaving behind a slip step on the pillar surface,
293
Fig. 10b (also see inset 3a and b). However, the deformation mainly consists of a
12
ACCEPTED MANUSCRIPT 294
continuous accumulation of dislocations during compression. The dislocation density
295
increases continuously with increasing strain throughout the simulation, Fig. 8b.
296
For [011] pillars, the twinning evolution is clearly reflected in the stress-strain curves
297
by a sharp stress drop at both 300 K and 15 K, Fig. 10c and 10d, respectively. At 300
298
K, the twin embryo propagates rapidly at the maximum stress level and gradually
299
evolves into two parallel twinning planes, Fig 10c inset 2-3. In the inset 2, another
300
twinning plane is initiated. However, this plane starts to disappear (completely
301
vanished at ∼10% strain) after the stress drop as the other two parallel twinning
302
planes increases in distance and dominates the deformation. Massive dislocation
303
interaction and vacancy formation are observed to occur between these planes. The
304
dislocation density, Fig. 8b, increases until point 2 in the stress-strain curve, Fig. 10c.
305
From this point, twinning starts to govern the deformation the density remains nearly
306
constant throughout the simulation with only small variations as new dislocations
307
nucleate and escape the free surface. For the [011] nanopillar at 15 K, Fig. 10d, twin
308
configuration appears as soon as the first dislocation starts to nucleate. As also
309
evident for the [011] pillar at 300 K, twinning occurs on the two symmetrical slip
310
systems {211}<111>. Only one of the twin planes “survive” and develop into two
311
parallel planes with increasing deformation, inset 2-3 in Fig. 10d. By studying the
312
dislocation density evolution, Fig. 8b, the trend is more and less similar as seen at 300
313
K for the [011] nanopillar. However, a higher density is observed at 15 K.
314 315
Figure 10: Engineering stress-strain curves of simulated (a-b) [010] and (c-d) [011] Fe nanopillars at 300 K
316
and 15 K, with insets of dislocation structure at various strains.
317 318
6. Discussion
13
ACCEPTED MANUSCRIPT 319
6.1. Effect of orientation
320
Fe pillars with [011] orientation withstand higher stresses before yielding than the
321
[010] pillars, independent of test temperature, Fig 5b. Some scatter in yield stress is
322
evident from Fig. 5b, suggested to occur due to the randomness of dislocation sources
323
(i.e. source length and dislocation source orientation) in the position where the
324
micropillar is milled out and the inherent initial realization of the dislocation
325
structure. Larger dislocation sources are weaker, resulting in lower activation stresses,
326
while smaller sources require higher stresses to control the onset of plasticity [35, 36].
327
Additionally, artifacts such as slight misalignment between the pillar and the loading
328
axis and roughness of the contacting surfaces could contribute to variations in yield
329
stresses. However, it is well within the scatter typically observed in these dimensions
330
[37].
331
The difference in strength with crystal orientation may partly be explained by the
332
available slip possibilities for each loading orientation [36]. [011] pillars have four
333
equivalent slip systems with the highest Schmid factor, while [010] has eight. Thus, a
334
larger number of well-oriented dislocation sources are expected to be present in the
335
[010] orientation, compared to the [011] pillars. Intuitively, the easily available slip
336
possibilities may facilitate dislocation-dislocation interactions [37], manifested
337
through the overall lower deformation stresses for [010] pillars, Fig. 5b. SEM
338
examinations of deformation morphologies (Fig. 3) also confirm that slip in [010]
339
pillars seems to be distributed on a much larger number of slip planes than in the case
340
of [011] pillars.
341
Additional evidences supporting these observations were provided from the MD
342
simulations. Typically, the [010] nanopillar demonstrates larger slip system activation
14
ACCEPTED MANUSCRIPT 343
by means of slip in four slip systems, while deformation on [011] pillars is distributed
344
on two slip systems. Moreover, the larger availability for dislocation nucleation
345
events in [010] pillars, is also confirmed by the larger dislocation density, Fig. 8b.
346
The lower dislocation density obtained for [011] could be a signature of the twinning
347
activity. A more detailed examination reveals that when perfect dislocations with ½
348
<111> burgers vector, decomposes into partial dislocation to form the low-energy
349
state of twinning, indeed, the dislocation density of perfect dislocations decreases.
350
Since twinning take over as the governing mechanism, dislocation nucleation and
351
dislocation pile-ups becomes less prominent compared to the [010] pillars. The
352
remaining dislocations after twin propagation tend to escape from the free surface as
353
new dislocations are nucleated. The dislocation density saturates as these two
354
processes are balanced. Such evolution of dislocation density corresponds to the
355
nearly constant density obtained after twinning is formed, Fig. 8b.
356
6.2. Effect of temperature
357
The compressive engineering stress-strain curves in Fig. 4a-b indicate a large
358
temperature effect by means of higher yield and flow stresses and significant increase
359
in strain hardening when the temperature is reduced. In bcc metals, the mobility of
360
screw dislocations decreases at temperatures below 340 K for α-Fe [38], due to
361
higher Peierls stress. As a consequence, a larger dislocation storage and increased
362
probability for dislocation interaction occur. These dislocations might serve as
363
obstacles and hinder further dislocation motion. Hence increased strength and strain
364
hardening are expected [6, 16, 20]. This coincides with the strong temperature
365
dependence and strain hardening observed in the present stress-strain curves, Fig. 4a-
366
b.
15
ACCEPTED MANUSCRIPT 367
Indeed, for increasing temperature, Peierls barrier do not considerably constrict
368
dislocation movement and screw dislocation mobility is not a limiting factor since it is
369
approaching similar mobility as edge dislocations. The temperature also influences
370
the shape of the stress-strain curves. Initially at room temperature tests, small strain
371
bursts occurs, arising from propagation of dislocation avalanches within the sample
372
from dislocation sources [39]. Subsequently, the appearance of extended plastic
373
regimes with absence of strain hardening occurs. These large strain bursts are
374
suggested to be associated to dislocation elimination at the pillar surface [40, 41]
375
when local shearing occurs [42, 43]. This was also evidenced during the present in-
376
situ observation, leaving clear shear bands on the pillar surface when larger strain
377
bursts occurred. Our observation agrees well with the dislocation behavior reported
378
by Xie et al. [21] from TEM in-situ compression tests of α-Fe nanoblades.
379
Generation of series of small strain bursts is more pronounced at the low temperature
380
Fig. 4a and b. A possible explanation to this could be due to the larger disparity in
381
dislocation mobility of pure edge and pure screw segments at lower temperatures,
382
affecting the dislocation behavior. As the edge dislocations move quicker away from
383
the dislocation source, long screw segment remains close to the source, leading to pile
384
up with continuing deformation. The screw dislocation pile ups can produce back
385
stresses on the source reducing its ability to continue to operate [44]. Back stresses or
386
dislocation exhaustion that further suppress plastic deformation, are suggested to be
387
reflected in stress strain curves by means smaller strain bursts with limited amount of
388
strain [42, 43].
389
The temperature dependence of dislocation behavior is observed in the current TEM
390
examinations. TEM examination of room temperature Fe pillars reveal that
16
ACCEPTED MANUSCRIPT 391
deformation is mediated by pinning, entanglement, dislocation loops as well as
392
straight dislocation segments distributed on different sites in the pillar. Moreover, a
393
high density of dislocations was found in heavily deformed zones, and only a few
394
dislocations were present in others areas. The large free surfaces contribute to
395
continuous nucleation of dislocations, causing dislocation interactions and a dense
396
dislocation structure. This is consistent with the residual dislocation structure found in
397
post-compression TEM observations of 1 µm Fe pillars, reported by Huang et al [38].
398
The appearance of long straight dislocations segments, of screw character, is more
399
distinct for pillars deformed at low temperature. These dislocations are parallel to
400
each other, indicating dislocation movement in parallel crystallographic planes. Kim
401
et al. [45] reported similar dislocation behavior from TEM examination of Nb
402
nanopillars. It was suggested that contribution of cross-slip did not occur since any
403
pinning points or dislocation interactions was observed. This behavior is different
404
from previous TEM observation of Mo nanopillars [46], consisting of an entangled
405
dislocation substructure with curved dislocation segments, junctions and loops.
406
Additionally, the dislocation multiplication mechanism reported in molecular
407
dynamics [20] and dislocation dynamics simulations [6], was suggested to mediate
408
the deformation in the Mo nanopillars [46].
409
We also observed shorter segments distributed throughout the pillar volume. Such
410
defects are previously observed in bcc pillars, suggested being clusters of small loops
411
or FIB induced damages due to TEM sample preparation [45-47]. Even though the
412
TEM sample thinning process was finalized with a very low accelerating voltage, the
413
ion-induced surface damage may still occur [47]. However, it is difficult to
414
distinguish between defects caused by the TEM thinning process or deformation.
17
ACCEPTED MANUSCRIPT 415
For any systematic conclusion to be drawn from these examinations, additional TEM
416
samples from similar orientations are needed. Nevertheless, Fig. 6 and Fig. 7 indicate
417
that, after deformation and examination, one consistently observe a larger appearance
418
of straight screw segments at low temperature, consistent with observations from the
419
present MD simulations (e.g. see Fig. 7e-h). Here, the straight dislocation segments,
420
remains in the pillars for a longer time than the curved front part of mixed character,
421
consistent with previous observations in MD simulations [20] and dislocation
422
dynamics simulations [6]. The larger mobility of mixed dislocations allows for an
423
easier escape at the free surface, leading to pile-up of the remaining screw dislocation
424
segments. The dislocation motion of the straight screw segments occurs through
425
double kink nucleation mechanisms, in agreement with previous simulation results of
426
bcc Fe [48, 49].
427
Simulation of Fe nanopillars at 300 K captures a different dislocation behavior, Fig.
428
9i-l, which may be due to sufficient thermal energy allowing for easier
429
rearrangements. Here, dislocations generate loops and expand in several directions,
430
also observed in TEM examinations, Fig 6b and 7b. Moreover, a large amount of
431
debris, in the form of lattice vacancies and clusters, are immediately emitted from
432
dislocations, Fig. 10. The amount of debris is more prominent and larger at 300 K in
433
agreement with previous Fe studies [48], suggested to be due to intrinsic behavior of
434
screw dislocations and regulated by applied stress, temperature and segment length.
435
There are of course quantitative discrepancies between MD simulations and
436
experimental results. Evidently, the time scale limitations in MD simulations raise the
437
need for using strain rates several orders of magnitude higher than in experiments,
438
reflected by the significantly higher peak stresses in simulated pillars than those
18
ACCEPTED MANUSCRIPT 439
obtained from experiments. Also, since MD simulations can only use small structures
440
containing up to tens of millions atoms, the simulated pillars are considerable smaller
441
than experimental pillars. Although the shortcomings of the MD approach cause
442
limitations, it is expected that the governing mechanisms of dislocation motion will
443
apply [50]. In the present MD investigation apparent correlation to experimental
444
results are present and the simulations provide insight into the underlying dislocation
445
mechanisms governing the deformation that cannot be provided from experiments.
446 447
7. Conclusions
448
Low and room temperature compression tests were performed on [010] and [011] Fe
449
micropillars. Experimental compression tests have been combined with TEM
450
examinations and MD simulations to reveal dislocation mechanisms. Temperature
451
dependent yield stress and strain hardening behavior was prominent for both
452
orientations. It was clearly found to decrease with increasing temperature, attributed
453
to easier activation of dislocation sources and increased dislocation mobility at higher
454
temperature. Post-compression TEM observation found a high density of residual
455
dislocations in deformed pillars, where straight screw segments were predominantly
456
distinct at low temperature and dislocations of mixed character were evident at room
457
temperature. [011] pillars obtain highest strength in both MD simulations and
458
experiments as a result of less available slip systems compared to the [010] pillars.
459
Plasticity for all pillars is mainly governed dislocation slip.
460 461
Acknowledgements
462
The authors wish to thank the Research Council of Norway for funding through the 19
ACCEPTED MANUSCRIPT 463
Petromaks 2 Programme, Contract No.228513/E30. The financial support from ENI,
464
Statoil, Lundin, Total, Scana Steel Stavanger, JFE Steel Corporation, Posco, Kobe
465
Steel, SSAB, Bredero Shaw, Borealis, Trelleborg, Nexans, Aker Solutions, Marine
466
Aluminium, FMC Kongsberg Subsea, Hydro and Sapa are also acknowledged. The
467
Research Council of Norway is acknowledged for the support to the Norwegian
468
Micro- and Nano-Fabrication Facility, NorFab.
469
[SIMILAR] were performed on resources provided by UNINETT Sigma2 - the
470
National Infrastructure for High Performance Computing and Data Storage in
471
Norway. The Authors would also like to thank Dr. Per Erik Vullum for TEM sample
472
preparation and imaging.
The computations/simulations/
473 474
References
475 476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496 497 498 499 500 501 502
[1] Uchic MD, Dimiduk DM, Florando JN, Nix WD,Sample Dimensions Influence Strength and Crystal Plasticity,Science 2004;305:986. [2] Dimiduk DM, Uchic MD, Parthasarathy TA,Size-affected single-slip behavior of pure nickel microcrystals,Acta Materialia 2005;53:4065. [3] Uchic MD, Dimiduk DM,A methodology to investigate size scale effects in crystalline plasticity using uniaxial compression testing,Materials Science and Engineering: A 2005;400–401:268. [4] Greer JR, Oliver WC, Nix WD,Size dependence of mechanical properties of gold at the micron scale in the absence of strain gradients,Acta Materialia 2005;53:1821. [5] Brinckmann S, Kim J-Y, Greer JR,Fundamental Differences in Mechanical Behavior between Two Types of Crystals at the Nanoscale,Physical Review Letters 2008;100:155502. [6] Greer JR, Weinberger CR, Cai W,Comparing the strength of f.c.c. and b.c.c. submicrometer pillars: Compression experiments and dislocation dynamics simulations,Materials Science and Engineering: A 2008;493:21. [7] Schneider AS, Clark BG, Frick CP, Gruber PA, Arzt E,Effect of orientation and loading rate on compression behavior of small-scale Mo pillars,Materials Science and Engineering: A 2009;508:241. [8] Schneider AS, Kaufmann D, Clark BG, Frick CP, Gruber PA, Mönig R, Kraft O, Arzt E,Correlation between Critical Temperature and Strength of Small-Scale bcc Pillars,Physical Review Letters 2009;103:105501. [9] Vitek † V,Core structure of screw dislocations in body-centred cubic metals: relation to symmetry and interatomic bonding,Philosophical Magazine 2004;84:415. [10] Ito K, Vitek V,Atomistic study of non-Schmid effects in the plastic yielding of bcc metals,Philosophical Magazine A 2001;81:1387. [11] Gröger R, Vitek V,Directional versus central-force bonding in studies of the structure and glide of 1/2⟨111⟩ screw dislocations in bcc transition metals,Philosophical Magazine 2009;89:3163.
20
ACCEPTED MANUSCRIPT 503 504 505 506 507 508 509 510 511 512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528 529 530 531 532 533 534 535 536 537 538 539 540 541 542 543 544 545 546 547 548 549 550 551 552 553 554
[12] Gröger R, Bailey AG, Vitek V,Multiscale modeling of plastic deformation of molybdenum and tungsten: I. Atomistic studies of the core structure and glide of 1/2〈1 1 1〉 screw dislocations at 0 K,Acta Materialia 2008;56:5401. [13] Christian JW,Some surprising features of the plastic deformation of body-centered cubic metals and alloys,MTA 1983;14:1237. [14] Rogne BRS, Thaulow C,Effect of crystal orientation on the strengthening of iron micro pillars,Materials Science and Engineering: A 2015;621:133. [15] Rogne BRS, Thaulow C,Strengthening mechanisms of iron micropillars,Philosophical Magazine 2014;95:1814. [16] Landau P, Guo Q, Hosemann P, Wang Y, Greer JR,Deformation of as-fabricated and helium implanted 100 nm-diameter iron nano-pillars,Materials Science and Engineering: A 2014;612:316. [17] Grieveson EM, Armstrong DEJ, Xu S, Roberts SG,Compression of self-ion implanted iron micropillars,Journal of Nuclear Materials 2012;430:119. [18] Argon AS,Strengthening Mechanisms in Crystal Plasticity, 2008:78. [19] Vítek V,Intrinsic stacking faults in body-centred cubic crystals,Philosophical Magazine 1968;18:773. [20] Weinberger CR, Cai W,Surface-controlled dislocation multiplication in metal micropillars,Proc Natl Acad Sci U S A 2008;105:14304. [21] Xie KY, Wang Y, Ni S, Liao X, Cairney JM, Ringer SP,Insight into the deformation mechanisms of α-Fe at the nanoscale,Scripta Materialia 2011;65:1037. [22] Hagen AB, Thaulow C,Low temperature in-situ micro-compression testing of iron pillars,Materials Science and Engineering: A 2016;678:355. [23] Skogsrud J, Thaulow C,Effect of crystallographic orientation on nanomechanical modelling of an iron single crystal cracked cantilever beam,Materials Science and Engineering: A 2016;In press. [24] Ringdalen Vatne I, Stukowski A, Thaulow C, Østby E, Marian J,Three-dimensional crack initiation mechanisms in bcc-Fe under loading modes I, II and III,Materials Science and Engineering: A 2013;560:306. [25] Plimpton S,Fast Parallel Algorithms for Short-Range Molecular Dynamics,Journal of Computational Physics 1995;117:1. [26] Mendelev MI, Han S, Srolovitz DJ, Ackland GJ, Sun DY, Asta M,Development of new interatomic potentials appropriate for crystalline and liquid iron,Philosophical Magazine 2003;83:3977. [27] Stukowski,Visualization and analysis of atomistic simulation data with OVITO–the Open Visualization Tool,Modelling and Simulation in Materials Science and Engineering 2010;18:015012. [28] Alexander S, Karsten A,Extracting dislocations and non-dislocation crystal defects from atomistic simulation data,Modelling and Simulation in Materials Science and Engineering 2010;18:085001. [29] Alexander S, Vasily VB, Athanasios A,Automated identification and indexing of dislocations in crystal interfaces,Modelling and Simulation in Materials Science and Engineering 2012;20:085007. [30] Lee S-W, Cheng Y, Ryu I, Greer J,Cold-temperature deformation of nano-sized tungsten and niobium as revealed by in-situ nano-mechanical experiments,Science China Technological Sciences 2014;57:652. [31] Lee S, Jeong J, Kim Y, Han SM, Kiener D, Oh SH,FIB-induced dislocations in Al submicron pillars: Annihilation by thermal annealing and effects on deformation behavior,Acta Materialia 2016;110:283. [32] Wheeler JM, Thilly L, Morel A, Taylor AA, Montagne A, Ghisleni R, Michler J,The plasticity of indium antimonide: Insights from variable temperature, strain rate jump micro-compression testing,Acta Materialia 2016;106:283.
21
ACCEPTED MANUSCRIPT 555 556 557 558 559 560 561 562 563 564 565 566 567 568 569 570 571 572 573 574 575 576 577 578 579 580 581 582 583 584 585 586 587 588 589 590 591 592 593 594 595 596 597
[33] Jang D, Li X, Gao H, Greer JR,Deformation mechanisms in nanotwinned metal nanopillars,Nat Nano 2012;7:594. [34] Healy CJ, Ackland GJ,Molecular dynamics simulations of compression–tension asymmetry in plasticity of Fe nanopillars,Acta Materialia 2014;70:105. [35] Kiener D, Hosemann P, Maloy SA, Minor AM,In situ nanocompression testing of irradiated copper,Nat Mater 2011;10:608. [36] Senger J, Weygand D, Motz C, Gumbsch P, Kraft O,Aspect ratio and stochastic effects in the plasticity of uniformly loaded micrometer-sized specimens,Acta Materialia 2011;59:2937. [37] Schreijäg S, Kaufmann D, Wenk M, Kraft O, Mönig R,Size and microstructural effects in the mechanical response of α-Fe and low alloyed steel,Acta Materialia 2015;97:94. [38] Huang R, Li Q-J, Wang Z-J, Huang L, Li J, Ma E, Shan Z-W,Flow Stress in Submicron BCC Iron Single Crystals: Sample-size-dependent Strain-rate Sensitivity and Ratedependent Size Strengthening,Materials Research Letters 2015;3:121. [39] Dimiduk DM, Woodward C, LeSar R, Uchic MD,Scale-Free Intermittent Flow in Crystal Plasticity,Science 2006;312:1188. [40] Rinaldi A, Peralta P, Friesen C, Sieradzki K,Sample-size effects in the yield behavior of nanocrystalline nickel,Acta Materialia 2008;56:511. [41] Mompiou F, Legros M, Sedlmayr A, Gianola DS, Caillard D, Kraft O,Source-based strengthening of sub-micrometer Al fibers,Acta Materialia 2012;60:977. [42] Choi WS, De Cooman BC, Sandlöbes S, Raabe D,Size and orientation effects in partial dislocation-mediated deformation of twinning-induced plasticity steel micro-pillars,Acta Materialia 2015;98:391. [43] Csikor FF, Motz C, Weygand D, Zaiser M, Zapperi S,Dislocation Avalanches, Strain Bursts, and the Problem of Plastic Forming at the Micrometer Scale,Science 2007;318:251. [44] Gröger R, Vitek V,Explanation of the discrepancy between the measured and atomistically calculated yield stresses in body-centred cubic metals,Philosophical Magazine Letters 2007;87:113. [45] Kim J-Y, Jang D, Greer JR,Insight into the deformation behavior of niobium single crystals under uniaxial compression and tension at the nanoscale,Scripta Materialia 2009;61:300. [46] Kim J-Y, Jang D, Greer JR,Tensile and compressive behavior of tungsten, molybdenum, tantalum and niobium at the nanoscale,Acta Materialia 2010;58:2355. [47] Kim JY, Greer JR,Tensile and compressive behavior of gold and molybdenum single crystals at the nano-scale,Acta Materialia 2009;57:5245. [48] Marian J, Cai W, Bulatov VV,Dynamic transitions from smooth to rough to twinning in dislocation motion,Nat Mater 2004;3:158. [49] Chaussidon J, Fivel M, Rodney D,The glide of screw dislocations in bcc Fe: Atomistic static and dynamic simulations,Acta Materialia 2006;54:3407. [50] Tang M, Marian J,Temperature and high strain rate dependence of tensile deformation behavior in single-crystal iron from dislocation dynamics simulations,Acta Materialia 2014;70:123.
598
22
A.B. Hagen, B.D. Snartland, C. Thaulow PII:
S1359-6454(17)30185-4
DOI:
10.1016/j.actamat.2017.03.006
Reference:
AM 13612
To appear in:
Acta Materialia
Received Date:
20 December 2016
Revised Date:
01 March 2017
Accepted Date:
03 March 2017
Please cite this article as: A.B. Hagen, B.D. Snartland, C. Thaulow, Temperature and orientation effects on the deformation mechanisms of α-Fe micropillars, Acta Materialia (2017), doi: 10.1016/j. actamat.2017.03.006
This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
ACCEPTED MANUSCRIPT 1
Temperature and orientation effects on the deformation
2
mechanisms of α-Fe micropillars
3
A.B. Hagen1*, B. D. Snartland1, C. Thaulow1
4
1Department
5
and Technology (NTNU), NO-7491 Trondheim, Norway
6
*Corresponding author
7
E-mail: [email protected]
8
Abstract
9
In-situ uniaxial compression tests on [010] and [011] α-Fe pillars have been
10
conducted at room temperature and -75°C to study the mechanical response with
11
focus on temperature and orientation effect. All pillars exhibit larger yield stresses
12
and hardening at -75°C. We attribute this phenomenon to the non-planarity of screw
13
dislocations in bcc crystals and the larger contribution of screw dislocations in
14
governing the micro-scale plasticity at lower temperatures, similar to what is common
15
for many bcc metals. We employ molecular dynamics to simulate the compression
16
process to elucidate the underlying dislocation mechanisms. Nanopillars deformed on
17
the [011] orientation deform via twinning at both temperatures, while the plastic
18
deformation behavior for [010] pillars are governed by intense dislocation activity. In
19
addition, [011] nanopillars withstand higher stresses before yielding, in agreement
20
with the compression experimental results. TEM examinations are also reported and
21
reveal that temperature clearly influence the residual dislocation structure.
of Engineering Design and Materials, Norwegian University of Science
22 1
ACCEPTED MANUSCRIPT 23
Keywords: Temperature effect; Dislocations; Micro-scale plasticity; Bcc iron; Yield
24
stress
25
1. Introduction
26
The low-temperature embrittlement resulting in the Ductile-to-Brittle Transition
27
(DBT) is still of great concern for large steel structures in engineering applications.
28
Increase in yield and tensile strength at low temperature is widely observed metals
29
and alloys in general. However, fcc metals still retain much or all of their ductility at
30
low temperature in spite of the change in mechanical properties. In the case of bcc
31
metals (e.g. α–Fe, W), loss of ductility suddenly appear below a critical temperature
32
and brittle fracture may occur at subzero temperatures making the metals vulnerable
33
when operating in extreme environments. Thus, understanding of the mechanisms
34
controlling this abrupt transition is of great importance, but are however, still
35
insufficiently understood.
36
Small-scale mechanical testing techniques have attracted a lot of interest since it
37
allows for higher precision and selection of microstructural features for evaluation of
38
mechanical behavior. By doing this, fundamental details from deformation
39
mechanisms can be investigated in new ways that is not feasible using conventional
40
methods at larger scales. By using micro-scale sample manufacturing, such as focused
41
ion bean milling, a large range of nano and microscale compression, tension and
42
fracture geometries have become available. Plastic properties of both fcc and bcc
43
metals have been extensively studied by means of uniaxial micro-compression tests.
44
The extent of the studies has primarily been devoted to investigation of size
45
dependence, revealing a dramatically increase in yield strength with decreasing
46
sample size [1-8]. Another key observation is that fcc metals obtain a larger size
2
ACCEPTED MANUSCRIPT 47
effect that what observed in bcc metals [5-8]. The origin of the different plasticity
48
behavior of fcc and bcc metals can be traced down to the fundamental dislocation
49
mechanisms. The motion of screw dislocations generally governs deformation in bcc
50
crystal structures. Atomistic simulations have revealed that the non-planar screw
51
dislocation core structure leads to a high Peierls barrier, resulting in a lower mobility
52
of screw dislocations compared to edge dislocations [9-12]. At lower temperatures,
53
the motion of screw dislocations is thermally activated, leading to a strong
54
temperature and strain rate dependence of the yield and flow stresses in bcc metals
55
[13]. These processes where yield become dependent of temperature, occurs below
56
the so-called critical temperature. Above this temperature, the mobility of edge and
57
screw dislocations is equal, as in the case of fcc metals.
58
Reports of the plasticity behavior of small-scale bcc Fe samples at room temperature
59
[14-17] have revealed significant insights. Orientation dependent plasticity behavior
60
is observed [14] attributed to the non-planarity of screw dislocation cores and
61
twinning-antitwinning asymmetry typical of bcc metals [10, 12, 18, 19] and slip has
62
been found to occur on {110} planes [14, 15]. The hardening behavior observed in Fe
63
100 nm nanopillars have been attributed to increase in dislocation density due to
64
dislocation interactions and multiplication [16]. Dislocation Dynamics [6] and
65
molecular dynamics simulations [20] have suggested that such multiplication
66
mechanisms occur due to the longer residence time of screw dislocations in the
67
sample allowing it to multiply before exiting the pillar surface. The characteristics of
68
the compressive stress-strain curves observed in Fe samples consisting of strain bursts
69
have been attributed to the plastic flow along slip lines on the pillar surface [17]. In-
70
situ transmission electron microscopy (TEM) compression experiments of Fe
71
nanoblades, reported by Xie et al. [21], confirmed that the series of small strain burst
3
ACCEPTED MANUSCRIPT 72
were related to the collective movement of one or more dislocations and the more
73
extended strain burst were caused by slip formation nucleated from the free surface.
74
Very few investigations, however, have reported on the temperature dependence of
75
mechanical properties and dislocation behavior in small-scale bcc samples. This is
76
probably due to limited availability of micromechanical testing systems capable of
77
performing such precision testing at low temperature under stable conditions. To the
78
authors knowledge, only one low temperature study of Fe micropillars [22] have been
79
conducted. Mechanical properties and deformation morphology was reported to vary
80
widely as a function of temperature and crystallographic loading orientation.
81
A recent molecular dynamics simulation study of pre-notched Fe cantilevers [23] was
82
performed to investigate the effect of crystallographic orientations and its influence
83
on fracture mechanisms. Interestingly, two of the orientations tested, (101)[-101] and
84
(100)[0-11], display different fracture characteristics by means of ductile and brittle
85
behavior, respectively. The crack system (101)[-101] exhibits substantial ductility
86
with blunting on the crack tip. In contrast, the (100)[0-11] crack system indicates
87
brittle fracture with crack extension by cleavage, consistent with a previous atomistic
88
study of this crack system [24]. These studies reveal that orientation dependent
89
properties contribute to new features of the plastic behavior. Coupling the effects
90
between temperature and grain orientation on the plastic deformation and the
91
underlying dislocation mechanisms are thus of great interest.
92
For this purpose, the aim of this work is to increase the understanding of the plasticity
93
mechanisms at low temperature for these two crystallographic orientations. The
94
present work is dedicated to present new experimental data obtained from in-situ
95
SEM compression experiments on 1 μm diameter single crystal α- Fe micropillars,
4
ACCEPTED MANUSCRIPT 96
performed at room temperature and -75˚C. Our findings provide quantitative
97
information into plasticity relative to temperature at micro-scale. We perform MD
98
simulations and TEM investigations to obtain insight in the temperature dependent
99
dislocation behavior. The results are discussed in context with classical dislocation
100
theories in bcc metals while accounting for the influence of the size of microcrystal
101
samples, temperature and orientation.
102
2. Experimental procedures and methods
103
2.1. Sample preparation and micro-mechanical testing
104
A high purity (99.99%) α-Fe sample from Alfa Aesar GmbH & Co KG, with the
105
dimensions 1x1x0.1 cm was used in this investigation. The sample was heat treated in
106
a high vacuum furnace at 700 °C for 3 h in order to produce enlarged grains. The
107
sample surface was polished using 1 µm grit diamond and electrochemically polished
108
at 35 V for 20 seconds using an A2 electrolyte. After determination of
109
crystallographic orientations using EBSD mapping, micropillars in each grain with
110
orientation [010] and [011] were machined using focused ion beam (FIB) milling
111
(FEI Helios 600 DualBeam) with a 30 keV Ga+, Fig 1. A three-step milling procedure
112
with a final current of 48 pA was conducted in order to obtain surface refining with
113
minimal tapering angle and to reduce material redeposition. The resulting dimension
114
of the pillars, i.e. d=1 µm and a height of 3.5 µm, gave an aspect ratio (height/ top
115
diameter) of ∼3.5.
116
Mechanical compression tests were performed in a FEI Quanta Environmental SEM
117
(ESEM) using a PI-85 Picoindenter (Hysitron) with a cono spherical diamond
118
indenter with a diameter of 4 μm and a cone angle of 60°, produced by Synton-MDP.
119
The Fe pillars were tested in an open-loop control mode at 25 °C and -75 °C using a
5
ACCEPTED MANUSCRIPT 120
cooling system connected to the indenter device consisting of a rod made of copper
121
and with liquid nitrogen as the cooling source. The system has two independent
122
thermocouples to accurately control the temperature on the sample and indenter tip. A
123
detailed description of the system is found in [22]. The recorded load-displacements
124
data were converted into engineering stress-strain curves using the measured length
125
and top diameters of the pillars.
126 127
Figure 1: EBSD pattern quality map of Fe sample surface with [010] and [011] grains highlighted. The final
128
milled pillars within each grain are indicated by arrows.
129 130
2.2. TEM sample preparation
131
A FEI Helios 600 DualBeam FIB (Focused Ion Beam) was used to make thin,
132
electron transparent lamellas for ex-situ transmission electron microscopy (TEM)
133
characterization. The TEM lamellas were prepared in cross-section with the lamella
134
plane parallel to the loading direction. Prior to milling, protection layers of Pt and C
135
were deposited by electron beam and ion beam assisted depositions, respectively, on
136
top and on the sidewalls of the pillars to avoid ion beam implantation and damage in
137
the pillars. The coarse Ga+ ion beam thinning was done at 30 kV. Final thinning was
138
performed with 5 and 2 kV acceleration voltages. The thickness of the final lamellas
139
was typically in the range 50 – 100 nm. TEM characterization was performed with a
140
double Cs corrected coldFEG Jeol ARM200CF, operated at 200 kV. The TEM
141
lamellas were plasma cleaned for 2 min prior to TEM characterization to remove
142
possible hydrocarbon contamination on the surfaces of the lamellas.
143
2.3. Simulation methods
6
ACCEPTED MANUSCRIPT 144
Molecular dynamics (MD) simulations of [010] and [011] nanopillars were performed
145
to investigate the plasticity mechanisms at atomistic scale using Large scale
146
Atomic/Molecular Massively parallel Simulator (LAMMPS) [25] with a timestep of
147
0.0015 ps. Atom-atom interaction is described by the embedded atom method (EAM)
148
potential developed for Fe by Mendelev et al. [26]. Periodic boundary conditions are
149
defined in x– and y-direction, Fig. 2. Prior to loading, the nanopillars was relaxed for
150
75 ps using a NPT ensemble to obtain equilibrium configuration followed by NVT
151
ensemble for the main run, with a constant volume and temperature of 15 K and 300
152
K throughout the simulations. The low temperature of 15 K was chosen to elucidate
153
the temperature effect in the plasticity mechanisms. A strain rate of 𝜀 = 9 ∙ 109 s-1 was
154
used throughout the simulations. The results were visualized with the software
155
OVITO [27]. Dislocation defects in the pillars were detected and identified using the
156
dislocation extraction algorithm (DXA) [28, 29] allowing for dislocation density
157
measurements. Due to the large simulation model (∼51 million Fe atoms) and the
158
inherent timescale limitations with MD simulations, dislocation density calculations
159
were performed at predefined deformation steps.
160 161
Figure 2: Simulation model of the Fe nanopillar with diameter 50 nm, height 125 nm and a 3° taper angle.
162
4. Results
163
4.1. Compression test of micropillars
164
Fig. 3 shows representative SEM images of the pillars after compression. Irrespective
165
of orientation and test temperature, all Fe pillars exhibited localized slip bands with
166
significant shear offsets on the pillar surface, as recently reported elsewhere [14, 15,
167
22]. Multiple slip lines were mostly prevalent on the [010] pillar surfaces, Fig. 3a and
7
ACCEPTED MANUSCRIPT 168
3b, suggesting a larger number of activated slip systems than that observed for [011]
169
Fe pillars. The [011] pillars exhibit few slip lines at room temperature, Fig 3c, and
170
only one prevalent slip trace at low temperature, Fig. 3d.
171 172
Figure 3: Post-compression micrographs of [010] Fe pillars at a) 25 °C and b) -75 °C, and [011] Fe pillars at
173
c) 25 °C and d) -75 °C.
174 175
Fig. 4a and b show the engineering stress-strain curves for [010] and [011] pillars,
176
respectively. Representative engineering stress-strain curves are displayed in Fig. 5a,
177
accentuating the characteristics in the stress-strain behavior for each orientation and
178
test temperature. Low temperature stress-strain curves reveal multiple strain bursts
179
separated by elastic loading sequences and show a stronger hardening than that
180
observed in the room temperature curves, which consist of larger extended plastic
181
regimes with small amount of hardening.
182
Yield stresses, Fig. 5b, were determined at the level of stress where first sign of
183
plastic behavior occurred, indicated by a first small strain burst, illustrated in Fig. 5a.
184
Hence, the yield stress represents the stress level required for activation of the
185
weakest dislocation source [30]. Orientation and significant temperature dependence
186
of strength are found. The average yield stress of the low temperature [010] Fe pillars,
187
were estimated to 560 MPa, compared with 200 MPa for the room temperature pillars.
188
For the [011] pillars, a yield stress of 757 MPa was found at low temperature and 319
189
MPa at room temperature. Some scatter in strength are found and further discussed in
190
section “6.1. Effect of orientation”.
191 192
Figure 4: Engineering stress-strain curves for (a) [010] and (b) [011] Fe pillars at 25 °C and -75 °C.
193
8
ACCEPTED MANUSCRIPT 194
Figure 5: a) Representative stress-strain curves from each loading orientation and test temperature with
195
magnified view showing the yield stress point of determination indicated by arrows. b) Yield stresses versus
196
temperature for all [010] and [011] Fe pillars. The slope indicates the average increase in yield stress for
197
each orientation.
198 199
4.2. TEM characterization
200
Fig. 6 and Fig. 7 shows TEM bright field micrographs of [010] and [011] pillars,
201
respectively. The pillars compressed at room temperature (Fig. 6a-b and Fig. 7a-b)
202
clearly shows formation of complex dislocation networks consisting of loops,
203
junctions and entanglements at the top portion of the pillar, where deformation
204
predominantly occurs due to tapered geometry of the pillar [31]. The deformation is
205
characterized by large slip offsets across the pillar, e.g. Fig. 6a. A large number of
206
perfect dislocations are required to form such offsets emerging from the pillar surface,
207
suggesting that deformation is accommodated via several perfect dislocations rather
208
than partial dislocations [32]. This is also evident from the adjacent long straight
209
dislocations of <111> type, propagating into the pillar center, Fig 6a. The residual
210
dislocation structure consisting of both straight and smoothly curved dislocations for
211
both orientations, suggest contribution from both screw and mixed dislocations.
212 213
Bright field images of the pillars tested at -75 ˚C reveal the presence of long straight
214
screw segments (Fig. 6d and Fig 7d) consistent with those observed at room
215
temperature. However, the [010] pillar deformed at low temperature (Fig. 6d), shows
216
a less dense population of dislocations consisting of several small dislocation
217
segments homogeneously distributed within the pillar. These could also be a result of
218
FIB induced defects, further discussed in section “6.2. Effect of temperature “. The
219
[011] pillar deformed at -75 ˚C (Fig. 7d), contains several straight dislocation 9
ACCEPTED MANUSCRIPT 220
segments of <111> type, suggesting that perfect dislocations nucleate at the surface
221
and propagate towards the pillar center. Since no evidence of twin formation is
222
observed, the deformation at low temperature predominantly occurs by the motion of
223
screw segments.
224 225
Figure 6: Bright field TEM images of [010] Fe pillars with corresponding diffraction pattern compressed at
226
(a-b) 25 °C and (c-d) -75 °C. Magnified view showing b) dislocation loops and d) straight <111> dislocations.
227 228 229
Figure 7: Bright field TEM images of [011] Fe pillars with corresponding diffraction pattern compressed at
230
(a-b) 25 °C and (c-d) -75 °C. Magnified view showing b) dislocation loops and d) straight <111> dislocations.
231 232
4.3. Molecular dynamics (MD) simulation of Fe nanopillars
233
A series of MD simulations was performed to elucidate the dislocation behavior.
234
Compressive engineering stress-strain curves for simulated [010] and [011] Fe
235
nanopillars at 300 K and 15 K are shown in Fig. 8a. Overall, the deformation is
236
characterized by initial elastic deformation up to a maximum stress peak followed by
237
a decrease in stress. Considering that all pillars are initially dislocation-free, the
238
maximum stress peaks reflect the stress necessary for the full, or partial, dislocation
239
nucleation [33]. However, the stress-strain characteristics undergo some changes with
240
orientation and temperature. This is discernible particularly by means of decreasing
241
strength with increasing temperature and a much sharper abrupt stress drop after
242
yielding for the [011] pillars due to the appearance of twinning, while [010] pillars
243
displayed progressive plastic deformation with dislocation slip as the dominating
244
deformation mechanism. Fig. 8b shows the evolution of dislocation density,
245
calculated from the total length of all dislocation segments at each chosen timestep,
246
divided by nanopillar volume, using the DXA. The [010] pillars obtain higher 10
ACCEPTED MANUSCRIPT 247
dislocation density than [011] pillars, in the range of ∼1016 m-2 versus ∼1015 m-2,
248
respectively. At 15 K the density for the [010] pillar continues to increase throughout
249
the simulation, while the density evolution at 300 K levels out. For [011] pillars, a
250
nearly constant density is reached at both 15 K and 300 K.
251 252
Figure 8: a) Engineering stress-strain curves and b) dislocation density evolution for all [010] and [011] Fe
253
nanopillars at 15 K and 300 K.
254 255
Atomic snapshots at various strain levels show the evolution of the initial dislocation
256
nucleation for all the parallel tests, Fig 9. Typically 1/2 <111> dislocations form at the
257
pillar surface bottom moving upward on {112}<111> slip systems for all tests. The
258
yielding in [010] nanopillars occurs by dislocation nucleation in the four symmetrical
259
{112}<111> slip systems with a Schmid factor of 0.47, shown in Fig. 9a-h. For the
260
[011] pillars, there are two symmetrical {112}<111> slip systems activated also with
261
a Schmid factor of 0.47, Fig. 9i-p. The more easily available slip possibilities in the
262
[010] pillars are also reflected in the stress strain curves, by means of a lower yield
263
stress, Fig. 8a.
264
Overall, the dislocations nucleate as curved lines resembling dislocation of mixed
265
character. At 300 K, the dislocation loops easily expand in multiple directions.
266
Similar structure is initially observed at 15 K as well. However, as the dislocation
267
lines continue to grow, they develop into straight lines, typical of pure screw character
268
[34], Fig. 9e-h. For the [011] nanopillar, twinning nucleation is present at 15 K as
269
soon as the first dislocation is initiating, Fig. 9 m-p. The deformation mechanisms
270
observed for each orientation are summarized in Table 1.
271
11
ACCEPTED MANUSCRIPT 272
Figure 9: Initial dislocation configurations at various strains viewed along the loading direction. The [010]
273
nanopillars obtain dislocation nucleation from four symmetrical sites (a-d) subsequently colliding and
274
forming loops with increased strain at 300 K, while (e-h) initially curved dislocations propagates into
275
straight dislocation lines at 15 K. The [011] nanopillars nucleate dislocations from two opposite sites, (i-l)
276
forming dislocation loops with increased strain at 300 K and (m-p) twin configurations at 15 K.
277 278
Table 1: Deformation mechanisms for [010] and [011] Fe nanopillars at 300 and 15 K.
Loading direction
Temperature
Slip system
Schmid factor
Mechanism
[011]
300 K
(211)[111]
0.4714
Twinning
[011]
15 K
(211)[111]
0.4714
Twinning
[010]
300 K
(121)[111]
0.4714
Dislocation slip
[010]
15 K
(121)[111]
0.4714
Dislocation slip
279 280
Fig. 10 shows stress-strain curves for all the parallels, with insets of atomic snapshots
281
at strain levels before, at- and after the maximum stress peak. [010] pillars mainly
282
consists of massive dislocation generation and loop formation leading to dislocation
283
slip, Fig. 10a-b. Dislocations with ½<111> burgers vector start to nucleate at four
284
symmetrical sites, as shown in detail in Fig. 9a-h, moving upwards into the pillar
285
center on {121}<111> slip systems, and escaping the free surface. At 300 K,
286
dislocations tend to rearrange themselves, creating dislocation loops that easily
287
expand in multiple directions and leaving behind vacancies on their path, Fig. 10a
288
(inset 2 and 3a). At 15 K, the curved front of the dislocations escapes the free surface,
289
while most of the straight lines are remained in the pillar for a longer time, continuing
290
to operate with kink pair mechanisms and interact with new dislocations upon further
291
loading. Moreover, a small twin embryo starts to develop after yielding, quickly
292
growing into two small parallel planes, leaving behind a slip step on the pillar surface,
293
Fig. 10b (also see inset 3a and b). However, the deformation mainly consists of a
12
ACCEPTED MANUSCRIPT 294
continuous accumulation of dislocations during compression. The dislocation density
295
increases continuously with increasing strain throughout the simulation, Fig. 8b.
296
For [011] pillars, the twinning evolution is clearly reflected in the stress-strain curves
297
by a sharp stress drop at both 300 K and 15 K, Fig. 10c and 10d, respectively. At 300
298
K, the twin embryo propagates rapidly at the maximum stress level and gradually
299
evolves into two parallel twinning planes, Fig 10c inset 2-3. In the inset 2, another
300
twinning plane is initiated. However, this plane starts to disappear (completely
301
vanished at ∼10% strain) after the stress drop as the other two parallel twinning
302
planes increases in distance and dominates the deformation. Massive dislocation
303
interaction and vacancy formation are observed to occur between these planes. The
304
dislocation density, Fig. 8b, increases until point 2 in the stress-strain curve, Fig. 10c.
305
From this point, twinning starts to govern the deformation the density remains nearly
306
constant throughout the simulation with only small variations as new dislocations
307
nucleate and escape the free surface. For the [011] nanopillar at 15 K, Fig. 10d, twin
308
configuration appears as soon as the first dislocation starts to nucleate. As also
309
evident for the [011] pillar at 300 K, twinning occurs on the two symmetrical slip
310
systems {211}<111>. Only one of the twin planes “survive” and develop into two
311
parallel planes with increasing deformation, inset 2-3 in Fig. 10d. By studying the
312
dislocation density evolution, Fig. 8b, the trend is more and less similar as seen at 300
313
K for the [011] nanopillar. However, a higher density is observed at 15 K.
314 315
Figure 10: Engineering stress-strain curves of simulated (a-b) [010] and (c-d) [011] Fe nanopillars at 300 K
316
and 15 K, with insets of dislocation structure at various strains.
317 318
6. Discussion
13
ACCEPTED MANUSCRIPT 319
6.1. Effect of orientation
320
Fe pillars with [011] orientation withstand higher stresses before yielding than the
321
[010] pillars, independent of test temperature, Fig 5b. Some scatter in yield stress is
322
evident from Fig. 5b, suggested to occur due to the randomness of dislocation sources
323
(i.e. source length and dislocation source orientation) in the position where the
324
micropillar is milled out and the inherent initial realization of the dislocation
325
structure. Larger dislocation sources are weaker, resulting in lower activation stresses,
326
while smaller sources require higher stresses to control the onset of plasticity [35, 36].
327
Additionally, artifacts such as slight misalignment between the pillar and the loading
328
axis and roughness of the contacting surfaces could contribute to variations in yield
329
stresses. However, it is well within the scatter typically observed in these dimensions
330
[37].
331
The difference in strength with crystal orientation may partly be explained by the
332
available slip possibilities for each loading orientation [36]. [011] pillars have four
333
equivalent slip systems with the highest Schmid factor, while [010] has eight. Thus, a
334
larger number of well-oriented dislocation sources are expected to be present in the
335
[010] orientation, compared to the [011] pillars. Intuitively, the easily available slip
336
possibilities may facilitate dislocation-dislocation interactions [37], manifested
337
through the overall lower deformation stresses for [010] pillars, Fig. 5b. SEM
338
examinations of deformation morphologies (Fig. 3) also confirm that slip in [010]
339
pillars seems to be distributed on a much larger number of slip planes than in the case
340
of [011] pillars.
341
Additional evidences supporting these observations were provided from the MD
342
simulations. Typically, the [010] nanopillar demonstrates larger slip system activation
14
ACCEPTED MANUSCRIPT 343
by means of slip in four slip systems, while deformation on [011] pillars is distributed
344
on two slip systems. Moreover, the larger availability for dislocation nucleation
345
events in [010] pillars, is also confirmed by the larger dislocation density, Fig. 8b.
346
The lower dislocation density obtained for [011] could be a signature of the twinning
347
activity. A more detailed examination reveals that when perfect dislocations with ½
348
<111> burgers vector, decomposes into partial dislocation to form the low-energy
349
state of twinning, indeed, the dislocation density of perfect dislocations decreases.
350
Since twinning take over as the governing mechanism, dislocation nucleation and
351
dislocation pile-ups becomes less prominent compared to the [010] pillars. The
352
remaining dislocations after twin propagation tend to escape from the free surface as
353
new dislocations are nucleated. The dislocation density saturates as these two
354
processes are balanced. Such evolution of dislocation density corresponds to the
355
nearly constant density obtained after twinning is formed, Fig. 8b.
356
6.2. Effect of temperature
357
The compressive engineering stress-strain curves in Fig. 4a-b indicate a large
358
temperature effect by means of higher yield and flow stresses and significant increase
359
in strain hardening when the temperature is reduced. In bcc metals, the mobility of
360
screw dislocations decreases at temperatures below 340 K for α-Fe [38], due to
361
higher Peierls stress. As a consequence, a larger dislocation storage and increased
362
probability for dislocation interaction occur. These dislocations might serve as
363
obstacles and hinder further dislocation motion. Hence increased strength and strain
364
hardening are expected [6, 16, 20]. This coincides with the strong temperature
365
dependence and strain hardening observed in the present stress-strain curves, Fig. 4a-
366
b.
15
ACCEPTED MANUSCRIPT 367
Indeed, for increasing temperature, Peierls barrier do not considerably constrict
368
dislocation movement and screw dislocation mobility is not a limiting factor since it is
369
approaching similar mobility as edge dislocations. The temperature also influences
370
the shape of the stress-strain curves. Initially at room temperature tests, small strain
371
bursts occurs, arising from propagation of dislocation avalanches within the sample
372
from dislocation sources [39]. Subsequently, the appearance of extended plastic
373
regimes with absence of strain hardening occurs. These large strain bursts are
374
suggested to be associated to dislocation elimination at the pillar surface [40, 41]
375
when local shearing occurs [42, 43]. This was also evidenced during the present in-
376
situ observation, leaving clear shear bands on the pillar surface when larger strain
377
bursts occurred. Our observation agrees well with the dislocation behavior reported
378
by Xie et al. [21] from TEM in-situ compression tests of α-Fe nanoblades.
379
Generation of series of small strain bursts is more pronounced at the low temperature
380
Fig. 4a and b. A possible explanation to this could be due to the larger disparity in
381
dislocation mobility of pure edge and pure screw segments at lower temperatures,
382
affecting the dislocation behavior. As the edge dislocations move quicker away from
383
the dislocation source, long screw segment remains close to the source, leading to pile
384
up with continuing deformation. The screw dislocation pile ups can produce back
385
stresses on the source reducing its ability to continue to operate [44]. Back stresses or
386
dislocation exhaustion that further suppress plastic deformation, are suggested to be
387
reflected in stress strain curves by means smaller strain bursts with limited amount of
388
strain [42, 43].
389
The temperature dependence of dislocation behavior is observed in the current TEM
390
examinations. TEM examination of room temperature Fe pillars reveal that
16
ACCEPTED MANUSCRIPT 391
deformation is mediated by pinning, entanglement, dislocation loops as well as
392
straight dislocation segments distributed on different sites in the pillar. Moreover, a
393
high density of dislocations was found in heavily deformed zones, and only a few
394
dislocations were present in others areas. The large free surfaces contribute to
395
continuous nucleation of dislocations, causing dislocation interactions and a dense
396
dislocation structure. This is consistent with the residual dislocation structure found in
397
post-compression TEM observations of 1 µm Fe pillars, reported by Huang et al [38].
398
The appearance of long straight dislocations segments, of screw character, is more
399
distinct for pillars deformed at low temperature. These dislocations are parallel to
400
each other, indicating dislocation movement in parallel crystallographic planes. Kim
401
et al. [45] reported similar dislocation behavior from TEM examination of Nb
402
nanopillars. It was suggested that contribution of cross-slip did not occur since any
403
pinning points or dislocation interactions was observed. This behavior is different
404
from previous TEM observation of Mo nanopillars [46], consisting of an entangled
405
dislocation substructure with curved dislocation segments, junctions and loops.
406
Additionally, the dislocation multiplication mechanism reported in molecular
407
dynamics [20] and dislocation dynamics simulations [6], was suggested to mediate
408
the deformation in the Mo nanopillars [46].
409
We also observed shorter segments distributed throughout the pillar volume. Such
410
defects are previously observed in bcc pillars, suggested being clusters of small loops
411
or FIB induced damages due to TEM sample preparation [45-47]. Even though the
412
TEM sample thinning process was finalized with a very low accelerating voltage, the
413
ion-induced surface damage may still occur [47]. However, it is difficult to
414
distinguish between defects caused by the TEM thinning process or deformation.
17
ACCEPTED MANUSCRIPT 415
For any systematic conclusion to be drawn from these examinations, additional TEM
416
samples from similar orientations are needed. Nevertheless, Fig. 6 and Fig. 7 indicate
417
that, after deformation and examination, one consistently observe a larger appearance
418
of straight screw segments at low temperature, consistent with observations from the
419
present MD simulations (e.g. see Fig. 7e-h). Here, the straight dislocation segments,
420
remains in the pillars for a longer time than the curved front part of mixed character,
421
consistent with previous observations in MD simulations [20] and dislocation
422
dynamics simulations [6]. The larger mobility of mixed dislocations allows for an
423
easier escape at the free surface, leading to pile-up of the remaining screw dislocation
424
segments. The dislocation motion of the straight screw segments occurs through
425
double kink nucleation mechanisms, in agreement with previous simulation results of
426
bcc Fe [48, 49].
427
Simulation of Fe nanopillars at 300 K captures a different dislocation behavior, Fig.
428
9i-l, which may be due to sufficient thermal energy allowing for easier
429
rearrangements. Here, dislocations generate loops and expand in several directions,
430
also observed in TEM examinations, Fig 6b and 7b. Moreover, a large amount of
431
debris, in the form of lattice vacancies and clusters, are immediately emitted from
432
dislocations, Fig. 10. The amount of debris is more prominent and larger at 300 K in
433
agreement with previous Fe studies [48], suggested to be due to intrinsic behavior of
434
screw dislocations and regulated by applied stress, temperature and segment length.
435
There are of course quantitative discrepancies between MD simulations and
436
experimental results. Evidently, the time scale limitations in MD simulations raise the
437
need for using strain rates several orders of magnitude higher than in experiments,
438
reflected by the significantly higher peak stresses in simulated pillars than those
18
ACCEPTED MANUSCRIPT 439
obtained from experiments. Also, since MD simulations can only use small structures
440
containing up to tens of millions atoms, the simulated pillars are considerable smaller
441
than experimental pillars. Although the shortcomings of the MD approach cause
442
limitations, it is expected that the governing mechanisms of dislocation motion will
443
apply [50]. In the present MD investigation apparent correlation to experimental
444
results are present and the simulations provide insight into the underlying dislocation
445
mechanisms governing the deformation that cannot be provided from experiments.
446 447
7. Conclusions
448
Low and room temperature compression tests were performed on [010] and [011] Fe
449
micropillars. Experimental compression tests have been combined with TEM
450
examinations and MD simulations to reveal dislocation mechanisms. Temperature
451
dependent yield stress and strain hardening behavior was prominent for both
452
orientations. It was clearly found to decrease with increasing temperature, attributed
453
to easier activation of dislocation sources and increased dislocation mobility at higher
454
temperature. Post-compression TEM observation found a high density of residual
455
dislocations in deformed pillars, where straight screw segments were predominantly
456
distinct at low temperature and dislocations of mixed character were evident at room
457
temperature. [011] pillars obtain highest strength in both MD simulations and
458
experiments as a result of less available slip systems compared to the [010] pillars.
459
Plasticity for all pillars is mainly governed dislocation slip.
460 461
Acknowledgements
462
The authors wish to thank the Research Council of Norway for funding through the 19
ACCEPTED MANUSCRIPT 463
Petromaks 2 Programme, Contract No.228513/E30. The financial support from ENI,
464
Statoil, Lundin, Total, Scana Steel Stavanger, JFE Steel Corporation, Posco, Kobe
465
Steel, SSAB, Bredero Shaw, Borealis, Trelleborg, Nexans, Aker Solutions, Marine
466
Aluminium, FMC Kongsberg Subsea, Hydro and Sapa are also acknowledged. The
467
Research Council of Norway is acknowledged for the support to the Norwegian
468
Micro- and Nano-Fabrication Facility, NorFab.
469
[SIMILAR] were performed on resources provided by UNINETT Sigma2 - the
470
National Infrastructure for High Performance Computing and Data Storage in
471
Norway. The Authors would also like to thank Dr. Per Erik Vullum for TEM sample
472
preparation and imaging.
The computations/simulations/
473 474
References
475 476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496 497 498 499 500 501 502
[1] Uchic MD, Dimiduk DM, Florando JN, Nix WD,Sample Dimensions Influence Strength and Crystal Plasticity,Science 2004;305:986. [2] Dimiduk DM, Uchic MD, Parthasarathy TA,Size-affected single-slip behavior of pure nickel microcrystals,Acta Materialia 2005;53:4065. [3] Uchic MD, Dimiduk DM,A methodology to investigate size scale effects in crystalline plasticity using uniaxial compression testing,Materials Science and Engineering: A 2005;400–401:268. [4] Greer JR, Oliver WC, Nix WD,Size dependence of mechanical properties of gold at the micron scale in the absence of strain gradients,Acta Materialia 2005;53:1821. [5] Brinckmann S, Kim J-Y, Greer JR,Fundamental Differences in Mechanical Behavior between Two Types of Crystals at the Nanoscale,Physical Review Letters 2008;100:155502. [6] Greer JR, Weinberger CR, Cai W,Comparing the strength of f.c.c. and b.c.c. submicrometer pillars: Compression experiments and dislocation dynamics simulations,Materials Science and Engineering: A 2008;493:21. [7] Schneider AS, Clark BG, Frick CP, Gruber PA, Arzt E,Effect of orientation and loading rate on compression behavior of small-scale Mo pillars,Materials Science and Engineering: A 2009;508:241. [8] Schneider AS, Kaufmann D, Clark BG, Frick CP, Gruber PA, Mönig R, Kraft O, Arzt E,Correlation between Critical Temperature and Strength of Small-Scale bcc Pillars,Physical Review Letters 2009;103:105501. [9] Vitek † V,Core structure of screw dislocations in body-centred cubic metals: relation to symmetry and interatomic bonding,Philosophical Magazine 2004;84:415. [10] Ito K, Vitek V,Atomistic study of non-Schmid effects in the plastic yielding of bcc metals,Philosophical Magazine A 2001;81:1387. [11] Gröger R, Vitek V,Directional versus central-force bonding in studies of the structure and glide of 1/2⟨111⟩ screw dislocations in bcc transition metals,Philosophical Magazine 2009;89:3163.
20
ACCEPTED MANUSCRIPT 503 504 505 506 507 508 509 510 511 512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528 529 530 531 532 533 534 535 536 537 538 539 540 541 542 543 544 545 546 547 548 549 550 551 552 553 554
[12] Gröger R, Bailey AG, Vitek V,Multiscale modeling of plastic deformation of molybdenum and tungsten: I. Atomistic studies of the core structure and glide of 1/2〈1 1 1〉 screw dislocations at 0 K,Acta Materialia 2008;56:5401. [13] Christian JW,Some surprising features of the plastic deformation of body-centered cubic metals and alloys,MTA 1983;14:1237. [14] Rogne BRS, Thaulow C,Effect of crystal orientation on the strengthening of iron micro pillars,Materials Science and Engineering: A 2015;621:133. [15] Rogne BRS, Thaulow C,Strengthening mechanisms of iron micropillars,Philosophical Magazine 2014;95:1814. [16] Landau P, Guo Q, Hosemann P, Wang Y, Greer JR,Deformation of as-fabricated and helium implanted 100 nm-diameter iron nano-pillars,Materials Science and Engineering: A 2014;612:316. [17] Grieveson EM, Armstrong DEJ, Xu S, Roberts SG,Compression of self-ion implanted iron micropillars,Journal of Nuclear Materials 2012;430:119. [18] Argon AS,Strengthening Mechanisms in Crystal Plasticity, 2008:78. [19] Vítek V,Intrinsic stacking faults in body-centred cubic crystals,Philosophical Magazine 1968;18:773. [20] Weinberger CR, Cai W,Surface-controlled dislocation multiplication in metal micropillars,Proc Natl Acad Sci U S A 2008;105:14304. [21] Xie KY, Wang Y, Ni S, Liao X, Cairney JM, Ringer SP,Insight into the deformation mechanisms of α-Fe at the nanoscale,Scripta Materialia 2011;65:1037. [22] Hagen AB, Thaulow C,Low temperature in-situ micro-compression testing of iron pillars,Materials Science and Engineering: A 2016;678:355. [23] Skogsrud J, Thaulow C,Effect of crystallographic orientation on nanomechanical modelling of an iron single crystal cracked cantilever beam,Materials Science and Engineering: A 2016;In press. [24] Ringdalen Vatne I, Stukowski A, Thaulow C, Østby E, Marian J,Three-dimensional crack initiation mechanisms in bcc-Fe under loading modes I, II and III,Materials Science and Engineering: A 2013;560:306. [25] Plimpton S,Fast Parallel Algorithms for Short-Range Molecular Dynamics,Journal of Computational Physics 1995;117:1. [26] Mendelev MI, Han S, Srolovitz DJ, Ackland GJ, Sun DY, Asta M,Development of new interatomic potentials appropriate for crystalline and liquid iron,Philosophical Magazine 2003;83:3977. [27] Stukowski,Visualization and analysis of atomistic simulation data with OVITO–the Open Visualization Tool,Modelling and Simulation in Materials Science and Engineering 2010;18:015012. [28] Alexander S, Karsten A,Extracting dislocations and non-dislocation crystal defects from atomistic simulation data,Modelling and Simulation in Materials Science and Engineering 2010;18:085001. [29] Alexander S, Vasily VB, Athanasios A,Automated identification and indexing of dislocations in crystal interfaces,Modelling and Simulation in Materials Science and Engineering 2012;20:085007. [30] Lee S-W, Cheng Y, Ryu I, Greer J,Cold-temperature deformation of nano-sized tungsten and niobium as revealed by in-situ nano-mechanical experiments,Science China Technological Sciences 2014;57:652. [31] Lee S, Jeong J, Kim Y, Han SM, Kiener D, Oh SH,FIB-induced dislocations in Al submicron pillars: Annihilation by thermal annealing and effects on deformation behavior,Acta Materialia 2016;110:283. [32] Wheeler JM, Thilly L, Morel A, Taylor AA, Montagne A, Ghisleni R, Michler J,The plasticity of indium antimonide: Insights from variable temperature, strain rate jump micro-compression testing,Acta Materialia 2016;106:283.
21
ACCEPTED MANUSCRIPT 555 556 557 558 559 560 561 562 563 564 565 566 567 568 569 570 571 572 573 574 575 576 577 578 579 580 581 582 583 584 585 586 587 588 589 590 591 592 593 594 595 596 597
[33] Jang D, Li X, Gao H, Greer JR,Deformation mechanisms in nanotwinned metal nanopillars,Nat Nano 2012;7:594. [34] Healy CJ, Ackland GJ,Molecular dynamics simulations of compression–tension asymmetry in plasticity of Fe nanopillars,Acta Materialia 2014;70:105. [35] Kiener D, Hosemann P, Maloy SA, Minor AM,In situ nanocompression testing of irradiated copper,Nat Mater 2011;10:608. [36] Senger J, Weygand D, Motz C, Gumbsch P, Kraft O,Aspect ratio and stochastic effects in the plasticity of uniformly loaded micrometer-sized specimens,Acta Materialia 2011;59:2937. [37] Schreijäg S, Kaufmann D, Wenk M, Kraft O, Mönig R,Size and microstructural effects in the mechanical response of α-Fe and low alloyed steel,Acta Materialia 2015;97:94. [38] Huang R, Li Q-J, Wang Z-J, Huang L, Li J, Ma E, Shan Z-W,Flow Stress in Submicron BCC Iron Single Crystals: Sample-size-dependent Strain-rate Sensitivity and Ratedependent Size Strengthening,Materials Research Letters 2015;3:121. [39] Dimiduk DM, Woodward C, LeSar R, Uchic MD,Scale-Free Intermittent Flow in Crystal Plasticity,Science 2006;312:1188. [40] Rinaldi A, Peralta P, Friesen C, Sieradzki K,Sample-size effects in the yield behavior of nanocrystalline nickel,Acta Materialia 2008;56:511. [41] Mompiou F, Legros M, Sedlmayr A, Gianola DS, Caillard D, Kraft O,Source-based strengthening of sub-micrometer Al fibers,Acta Materialia 2012;60:977. [42] Choi WS, De Cooman BC, Sandlöbes S, Raabe D,Size and orientation effects in partial dislocation-mediated deformation of twinning-induced plasticity steel micro-pillars,Acta Materialia 2015;98:391. [43] Csikor FF, Motz C, Weygand D, Zaiser M, Zapperi S,Dislocation Avalanches, Strain Bursts, and the Problem of Plastic Forming at the Micrometer Scale,Science 2007;318:251. [44] Gröger R, Vitek V,Explanation of the discrepancy between the measured and atomistically calculated yield stresses in body-centred cubic metals,Philosophical Magazine Letters 2007;87:113. [45] Kim J-Y, Jang D, Greer JR,Insight into the deformation behavior of niobium single crystals under uniaxial compression and tension at the nanoscale,Scripta Materialia 2009;61:300. [46] Kim J-Y, Jang D, Greer JR,Tensile and compressive behavior of tungsten, molybdenum, tantalum and niobium at the nanoscale,Acta Materialia 2010;58:2355. [47] Kim JY, Greer JR,Tensile and compressive behavior of gold and molybdenum single crystals at the nano-scale,Acta Materialia 2009;57:5245. [48] Marian J, Cai W, Bulatov VV,Dynamic transitions from smooth to rough to twinning in dislocation motion,Nat Mater 2004;3:158. [49] Chaussidon J, Fivel M, Rodney D,The glide of screw dislocations in bcc Fe: Atomistic static and dynamic simulations,Acta Materialia 2006;54:3407. [50] Tang M, Marian J,Temperature and high strain rate dependence of tensile deformation behavior in single-crystal iron from dislocation dynamics simulations,Acta Materialia 2014;70:123.
598
22