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Mechanical behavior and deformation of nanotwinned metallic alloys

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Mechanical behavior and deformation of nanotwinned metallic alloys

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Mechanical Behavior and Deformation
of Nanotwinned Metallic Alloys
Nathan Heckman

Advisor: Dr. Andrea Hodge

A Dissertation Presented to the Faculty of the USC Graduate School in Partial Fulfillment of the
Requirements for the Degree Doctorate of Philosophy (Mechanical Engineering)

University of Southern California

August 2017

i

Acknowledgements
First and foremost, I would like to thank my advisor, Professor Andrea Hodge, for all her
guidance, support, and patience. Her advisement has helped me to become not only a better
scientist but also a better person throughout my years working with her.
I would like to thank the faculty at USC for their teachings and support. The classes I have taken
for both undergraduate and graduate studies at USC have given me a strong foundation for my
scientific career. In addition, I would like to thank Professor Michael Kassner, Professor Ivan
Bermejo-Moreno, and Dr. Lessa Grunenfelder for agreeing to serve on my dissertation
committee.
I am grateful to the staff at USC for their constant support. I always felt I was a top priority when
any staff at USC was attending to me, no matter how busy they were. In particular, Kim Klotz,
Sam Graves, Irice Castro, and Melissa Medeiros have been indispensable during my PhD career.
I am thankful for the Center for Electron Microscopy and Microanalysis for their help in training
and supporting me in materials characterization using their facilities. Both John Curulli and Matt
Mecklenburg proved invaluable.
I am appreciative of Professor Dr. Chris Eberl and the research staff at Fraunhofer IWM in
Freiburg, Germany who extended their facilities to me for research. I was never treated like an
outsider there, and working with everyone at Fraunhofer Institute was a highlight of my
collaborative work in Germany.
I would like to express gratitude to my funding sources, which includes both NSF (DMR-
0955338 and IRES-1460006) and DARPA (YFA-N66001-12-1-4243). This research would not
be possible without this funding, which helped to support not only my research but also myself.
ii

I would like to thank my colleagues, including everyone in the Hodge research group and Kamia
Smith, who have always supported me not only with technical guidance, but also with emotional
and moral support. You will all be family to me, always.
Finally, I would like to thank all my family, friends, and girlfriend BeiBei, who have always
been there to support me. I am extremely lucky to have each and every one of you in my life. I
only hope I can be as bright a light in your lives as you are in mine.

iii

Table of Contents
Acknowledgements .......................................................................................................................... i
List of Figures ................................................................................................................................ vi
List of Tables ............................................................................................................................... xiii
Abstract ......................................................................................................................................... xv
Chapter 1. Introduction ............................................................................................................... 1
Chapter 2. Background ............................................................................................................... 3
2.1 Coincident Site Lattice ..................................................................................................... 3
2.2 Twin boundaries ............................................................................................................... 4
2.2.1 Types and formation of twin boundaries in FCC metals .......................................... 6
2.2.2 Energies related to twin boundaries .......................................................................... 7
2.3 Nanotwinned Materials .................................................................................................... 9
2.3.1 Microstructures of nanotwinned metals .................................................................... 9
2.3.2 Synthesis of nanotwinned metals ............................................................................ 11
2.4 Mechanical Behavior of Nanotwinned Cu ..................................................................... 17
2.4.1 Deformation mechanisms ....................................................................................... 17
2.4.2 Influence of microstructure on tensile behavior ..................................................... 21
2.4.3 Influence of composition on mechanical behavior ................................................. 23
2.4.4 Activation Volumes of Nanotwinned Metals ......................................................... 25
2.5 Fatigue Behavior of Nanotwinned Metals ..................................................................... 26
2.5.1 Comparison to fatigue behavior of nanocrystalline metals..................................... 30
2.6 Summary ........................................................................................................................ 31
Chapter 3. Experimental Methods and Materials ..................................................................... 33
iv

3.1 As-Sputtered Sample Characterization .......................................................................... 34
3.1.1 Characterization of Overall Microstructure ............................................................ 34
3.1.2 Measurement of Microstructural Features .............................................................. 36
3.1.3 Grain Orientation and Grain Boundary Characterization ....................................... 37
3.2 Tensile Testing ............................................................................................................... 38
3.2.1 Microtensile Tester Design ..................................................................................... 38
3.2.2 Digital Image Correlation ....................................................................................... 39
3.2.3 Microtensile Tester and Tensile Sample Geometry Performance Verification ...... 41
3.3 Nanoindentation Measurements ..................................................................................... 44
3.4 Fatigue Testing ............................................................................................................... 45
3.5 Post-Mortem Sample Characterization .......................................................................... 47
Chapter 4. Tensile Behavior of Nanotwinned CuAl................................................................. 50
4.1 As-Sputtered Samples .................................................................................................... 50
4.2 Tensile Behavior and Localized Deformation Behavior ................................................ 53
4.3 Summary ........................................................................................................................ 58
Chapter 5. Tensile Behavior of Nanotwinned Alloys with Varying SFE ................................ 60
5.1 As-Sputtered Samples .................................................................................................... 60
5.2 Tensile Behavior ............................................................................................................ 65
5.3 Activation Volumes........................................................................................................ 67
5.4 Summary ........................................................................................................................ 69
Chapter 6. Fatigue Behavior of Nanotwinned Cu Alloys ......................................................... 72
6.1 Microstructural and Tensile Behavior ............................................................................ 72
6.2 Fatigue Strength in Uniaxial Tension-Tension Fatigue ................................................. 76
v

6.3 Crack Growth and Propagation Mechanisms ................................................................. 80
6.4 Fatigue Mechanisms Compared: NT, NC, and UFG Cu Alloys .................................... 85
6.5 Summary ........................................................................................................................ 87
Chapter 7. Conclusions and Future Work ................................................................................ 90
References ..................................................................................................................................... 95
Appendix A: Nanotwinned Inconel 600 ..................................................................................... 102
Appendix B: Digital Image Correlation Data Processing ........................................................... 107

vi

List of Figures
Figure 1. Diagram representing two grains (represented by yellow and red spots) with a Ʃ5
boundary, where the blue dots represent the coincident sites [22] ................................................. 3
Figure 2. Illustration of an FCC structure from the (110) zone axis displaying a perfect crystal (a)
and twin boundary (b) ..................................................................................................................... 5
Figure 3. Cross sectional TEM image of Cu-2wt%Al highlighting two CTB’s with red lines. ..... 5
Figure 4. General stacking fault energy curves (red) where the peak indicates the unstable
stacking fault energy. Blue curves indicate energy boundaries for twin formation [59] ................ 9
Figure 5. FIB cross section micrographs comparing equiaxed NT Cu (a) [61] and columnar NT
Cu (b) [62]..................................................................................................................................... 10
Figure 6. Schematic of magnetron sputtering technique. Argon atoms near a negatively charged
sputtering target are ionized which causes them to bombard the target, releasing atoms of the
target material which then coat the substrate ................................................................................ 12
Figure 7. Protean contour map showing twin thickness density as a function of both film
temperature and SFE in magnetron sputtered Cu alloys [14] ....................................................... 14
Figure 8. Schematic of Electrodeposition Technique. The negative potential on the left electrode
promotes reduction of metallic ions in the solution while the positive potential on the right
electrode promotes oxidation of metallic ions in the electrode .................................................... 15
Figure 9. Schematic of equal-channel angular pressing for a block sample [66] ......................... 16
Figure 10. Illustration of Hard Mode I, Hard Mode II, and Soft Mode slip systems. Blue
boundaries in this schematic represent twin boundaries. Adapted from [70] ............................... 18
vii

Figure 11. Four mechanisms for detwinning as proposed by Wang et al. [17] where the blue
section shows the twin, white section shows the matrix, red lines show CTB’s, and partial
dislocations are represented in orange. ......................................................................................... 20
Figure 12. Effect of twin thickness in equiaxed NT Cu with twin thicknesses ranging from 96-15
nm (A) and 15-4 nm (B) that shows there is a constant increase in ductility with decreasing twin
thickness, and transition from increasing strength to decreasing strength at 15 nm [15] ............. 21
Figure 13. Combined effect of both twin thickness and grain width on the yield stress of NT Cu
combining simulation and experimental data. Data tends to follow the trend of the Hall-Petch
relationship above the critical grain width and transition to decreasing strength below a critical
twin thickness that decreases with decreasing grain width [16] ................................................... 22
Figure 14. Tensile stress-strain curves for columnar NT Cu (a) with varying twin thicknesses, λ,
and grain widths, d, (b) which shows increasing strength and decreasing ductility for decreasing
twin thickness. Adapted from [18]................................................................................................ 23
Figure 15. S-N curves comparing fatigue behavior of nanotwinned (NT) Cu, ultrafine-grain
(UFG) Cu, and coarse-grained (CG) Cu, showing a 47% increase in fatigue limit for NT Cu
compared to CG Cu[93] ................................................................................................................ 27
Figure 16. Twin thickness distributions for columnar NT Cu before fatigue (a), after compression
(b), and after fatigue at 450MPa fatigue stress both away from the crack (c) and close to the
crack (d) showing that there was a shift in twin thickness due to detwinning under cyclic loading
[94] ................................................................................................................................................ 28
Figure 17. Cross-sectional SEM showing formation of ‘zigzag’ shear bands with very little
detwinning observed in columnar NT Cu exposed to fatigue at small cumulative strains (a-b),
viii

high cumulative strains (c), and observed ‘block structures’ intersecting twin boundaries (d) [93]
....................................................................................................................................................... 29
Figure 18. S-N curves for UFG and NC Cu, Cu-5at%Al, and Cu-11at%Al with grain sizes of
200, 100 and 70 nm respectively [97]. .......................................................................................... 31
Figure 19. Cross-Sectional FIB Image of Fully NT Ag, where the white arrow represents growth
direction [103]. Change in contrast between vertical grains represents columnar grain boundaries
while changing contrast within columnar grains represents the presence of twin boundaries,
hardly resolvable due to poor FIB resolution ............................................................................... 35
Figure 20. Representative TEM Images of fully NT Cu-2wt%Al including both bright field TEM
with an inset electron diffraction pattern (a) and a dark field image highlighting 2 columnar
grains, where the bright vertical columns are single columnar grains (b), and high resolution
TEM (c) ......................................................................................................................................... 36
Figure 21. Microtensile testing machine highlighting key components ....................................... 38
Figure 22. Representative DIC alumina speckle pattern on a tensile sample ............................... 41
Figure 23. Representative engineering stress-strain curves comparing tensile behavior for SS304
as determined by a calibrated Instron 5965 tensile tester (red) and custom built tensile tester
(black) and comparing calibration (black) and microtensile (blue) geometries on the microtensile
tester .............................................................................................................................................. 42
Figure 24. Drawing of tensile geometry used in testing of NT films. Tensile sample thickness
varies from 15 to 20 μm. All units are in mm ............................................................................... 43
Figure 25. Representative stress-strain curves for annealed Inconel 600 samples with gauge areas
of 0.8 by 3.6 mm comparing behavior for thicknesses of 25 microns (black) and 200 microns
(blue) ............................................................................................................................................. 44
ix

Figure 26. Setup utilized for fatigue testing of nanotwinned samples. Image modified from [112].
....................................................................................................................................................... 46
Figure 27. Raw data output received from fatigue testing program. Input parameters are shown in
top two rows (mean piezo and piezo amplitude input) and measured load cell parameters are
shown in bottom two rows (load cell amplitude and mean load outputs) .................................... 47
Figure 28. Schematic showing protected FIB liftout, where dogbone sample with fracture surface
(indicated in red) was coated in carbon layer (indicated in blue) and then FIB liftout was
performed ...................................................................................................................................... 48
Figure 29. Cross-sectional TEM images showing representative images for sample A of the
columnar microstructure (a) and twinned structure (b) and representative distributions for grain
width (c) and twin thickness (d).................................................................................................... 51
Figure 30. Representative engineering stress-strain curves for fully NT Cu-2wt%Al (a) and Cu-
6wt%Al (b). Note small grains are 80-110 nm, large grains are 170-180 nm, small twins are 5-6
nm, and large twins are 18 nm. Inset image displays the tensile sample geometry with gauge area
highlighted in red. ......................................................................................................................... 53
Figure 31. Strain maps of the gauge area immediately prior to failure (left) and average values of
strain as a function of normalized distance along the gauge section (right) comparing Cu-
2wt%Al and Cu-6wt%Al (a) and Cu-6wt%Al with varying twin thickness (b)........................... 56
Figure 32. Microstructural characterization images showing representative cross-sectional TEM
images and inset diffraction patterns where the white arrow indicates growth direction (a-c),
grain width distribution scaled proportional to average grain width (d-f), and top surface EBSD
grain orientation maps (g-i) of Cu-2wt%Al, Cu-6wt%Al, and Cu-10wt%Ni samples. The color in
the EBSD images corresponds to the orientation in the growth direction according to the legend
x

on the bottom. Black locations in EBSD indicate poorly indexed regimes where the average
grain confidence index is below 0.1. ............................................................................................ 62
Figure 33. Cross sectional TEM image (a) and t-EBSD orientation map (b) of Cu10Ni-A. Colors
in the orientation map correspond to the crystal orientation in the growth direction, analogous to
Fig. 1. The top-right inset image highlights the representative microstructure of non-111 oriented
regimes, where twin boundaries tilted to the growth direction are observed. The bottom-inset
represents a typical SAED pattern ................................................................................................ 64
Figure 34. Stress-strain curves comparing the impact of grain width on the mechanical behavior
for NT Cu-6wt%Al (a), Cu-2wt%Al (b), and Cu-10wt%Ni (c). Representative SEM micrographs
of fracture surfaces are shown for Cu6Al (d), Cu2Al (e), and Cu10Ni (f) samples. .................... 66
Figure 35. Hardness as a function of loading rate in nanoindentation with a peak load of 8 mN
for Cu2Al-A (a) and Cu10Ni-A (b), utilized to estimate the activation volume, which is shown
for each sample in (c) .................................................................................................................... 68
Figure 36. Microstructural and tensile data for nanotwinned alloys investigated in this study
including cross-sectional TEM images of the different alloys (a), stress-strain curves (b), and
twin thickness distributions (c). Note the white arrow in TEM images indicates the growth
direction. ....................................................................................................................................... 74
Figure 37. S-N curve comparing fatigue behavior of nanotwinned Cu alloys from this study
(squares) and NT Cu from other studies (circles). The inset graph displays a representative time-
stress plot obtained from the load cell for Cu2Al-LS at a stress amplitude of 210 MPa, where the
blue line indicates the mean stress and green lines indicate minimum and maximum stress. [93,
95] ................................................................................................................................................. 77
xi

Figure 38. S-N curves of copper alloys with NT microstructures (squares and circles), UFG and
NC microstructures (triangles) and coarse grained microstructures (diamonds) normalized by the
UTS. The inset image displays a similar plot for UFG and NC Ni [95, 97, 99, 135, 136]........... 79
Figure 39. SEM images showing representative fracture surface of Cu10Ni sample, as indicated
by schematic on the left, loaded at 370 MPa that fractured at 7.28*10
5
cycles. A low
magnification image of the fracture surface (a) shows vertical columnar features at the crack
initiation site (b), a transition to microvoid coalescence (c), and microvoid coalescence which is
observed for the rest of the fracture surface (d) ............................................................................ 81
Figure 40. Cross sectional bright field TEM image at the fracture surface (represented by dashed
red line), where both fully twinned (a) and detwinned (b) regimes are observed. Inset images
show SAED patterns of the encircled areas. ................................................................................. 82
Figure 41. Cross-sectional TEM image showing intergranular fracture observed near the fracture
edge where one side of the fracture shows a fully twinned microstructure and the other side
shows a fully de-twinned microstructure. This is further supported by SAED patterns of
encircled areas. .............................................................................................................................. 83
Figure 42. As sputtered microstructure of nanotwinned INCONEL 600 revealing fully twinned
structure with twin thickness of approximately 4 nm and grain width of approximately 100 nm
..................................................................................................................................................... 102
Figure 43. Schematic temperature vs time curve showing the heat treatment steps performed on
NT Inconel samples in vacuum................................................................................................... 103
Figure 44. Tensile behavior of as-sputtered, heat treated, and commercially purchased Inconel
600............................................................................................................................................... 105
xii

Figure 45. Top surface EBSD and cross-sectional FIB showing microstructural changes in
nanotwinned Inconel after sputtering and after being heat treated above 600°C ....................... 106
Figure 46. Tracked points on a NT Cu-6wt%Al tensile sample indicated by crossing blue lines.
The tracked points are spaced 10 pixels with a rectangular array. ............................................. 107
Figure 47. Displacement of tracked points in the loading direction vs position for the NT Cu-
6wt%Al film shown in Figure 46................................................................................................ 108
Figure 48. Motion of all tracked points for the raw data relative to their neighbors as a function
of image number in the loading (left) and transverse (right) direction for the NT Cu-6wt%Al film
shown in Figure 46...................................................................................................................... 109
Figure 49. Motion of all tracked points for the cleaned data relative to their neighbors as a
function of image number in the loading (left) and transverse (right) direction for the NT Cu-
6wt%Al film shown in Figure 46................................................................................................ 110
Figure 50. Examples of output data obtained from ‘displacement.m’. Displacement and strain
maps (a) are obtained from the ‘Full Strain Plots’ option while average true strain data (b) is
obtained from the ‘1D Average Strain Measurement’ option .................................................... 111

xiii

List of Tables
Table 1. Stacking fault energies for various common single element FCC metals and alloys
relevant to this study [53-58] .......................................................................................................... 8
Table 2. Summary of strain rate sensitivities and activation volumes for FCC metals with
different microstructures, adapted from [83]. Sources for activation volumes are [82, 84-91] ... 26
Table 3. Average microstructural properties and mechanical properties of fully NT columnar
CuAl samples ................................................................................................................................ 52
Table 4. Stacking fault energies, average microstructural parameters, mechanical properties, and
measured strain rate sensitivities (nanoindentation) of fully NT Cu6Al, Cu2Al, and Cu10Ni
samples .......................................................................................................................................... 61
Table 5. Microstructural properties and yield strengths of nanotwinned materials compared in
fatigue. .......................................................................................................................................... 75
Table 6. Summary of various fatigue studies on UFG, NC, or NT Cu or Cu alloy systems
comparing microstructural properties, observed microstructural changes, surface morphologies,
and fracture surface morphologies [95, 97, 99, 135] .................................................................... 86
Table 7. Vickers hardness of as-sputtered, heat treated, and commercially purchased Inconel 600
..................................................................................................................................................... 104

xiv

(blank page)
xv

Abstract
Nanotwinned metals have been of much research interest in recent times, largely due to their
potential for improved thermal stability, corrosion resistance, and ductility as compared to
nanocrystalline metals. Most studies investigating the mechanical behavior of nanotwinned
metals have focused on single element systems, specifically Cu and Ag. By introducing a
nanotwinned microstructure to metallic alloys, the potential engineering applications of these
materials can be expanded. In this study, the tensile and fatigue behavior of fully nanotwinned
alloys synthesized by magnetron sputtering are investigated to understand the influence of
microstructure and composition on their mechanical behavior. Furthermore, mechanical
properties and deformation behavior are evaluated to understand how the deformation
mechanisms correlate with the material strengths. Nanotwinned CuNi and CuAl alloys, with
stacking fault energies ranging from 6 to 60 mJ/m
2
, twin thicknesses ranging from 4 to 18 nm,
and grain widths ranging from 80 to 260 nm are evaluated.
Tensile behavior of these materials is assessed utilizing a custom designed and built microtensile
tester. The testing setup incorporates digital image correlation, which allows for the observation
of local macroscopic deformation behavior. The yield strength of these materials range from 0.8
to 1.5 GPa and exhibit limited ductility. Correlations between the materials’ strength and average
twin thickness/grain width reveal that separate alloys respond differently to microstructural
changes. From digital image correlation, all samples show localized deformation regimes prior to
fracture, with varying degrees of localized strains. The activation volume, which is correlated
with the rate-controlling deformation mechanism, is explored through variable loading rate
nanoindentation. The materials had values around 10b
3
, consistent with a rate-controlling
deformation mechanism of dislocation nucleation. This indicates that differences in tensile
xvi

properties of the alloys are not correlated with a change in the rate-controlling deformation
mechanism.
Fatigue behavior of the nanotwinned alloys in the high-cycle regime (10
3
to 10
7
cycles) are
assessed by performing uniaxial stress-controlled fatigue tests with stress amplitudes ranging
from 210 to 370 MPa. Nanotwinned alloys show improved fatigue strengths compared to
previously studied nanotwinned Cu. Fatigue strengths normalized by tensile strength reveal how
the tensile properties of nanotwinned Cu alloys influence the fatigue properties, where the
normalized fatigue strengths of the nanotwinned alloys falls below that of coarse grained,
ultrafine-grained, and nanocrystalline Cu alloys. The deformation behavior is explored through
post-mortem microstructural characterization. The nanotwinned Cu alloys reveal a newly
observed fatigue mechanism, where localized detwinning leads to intergranular fracture. The
correlation between fatigue strength and tensile strength depends on the fatigue mechanism
which varies with different microstructures. Overall, this study expands the comprehension of
the mechanical behavior of nanotwinned alloys through an understanding of how the nanoscale
deformation phenomena contribute to the material properties.

1

Chapter 1. Introduction
Nanocrystalline (nc) metals, where the grain size of the material is below 100 nm, can achieve
strengths more than ten times that of their coarse-grained counterparts [1]. However, there are
some established drawbacks to nc materials, as they tend to display relatively low ductility [1],
are susceptible to grain growth at relatively low temperatures, and can have low corrosion
resistance. One method to improve the properties of nc metals is grain boundary engineering
(GBE) [2]. In GBE, a high percentage of special grain boundaries are introduced into the
material, which results in improvements to the material properties [2]. Of specific interest are
nanotwinned (NT) metals, which are a type of GBE material that possess a high percentage of
low energy coherent twin boundaries. Compared to nc materials, NT metals offer potential
improvements in thermal stability, corrosion resistance, can achieve simultaneous strength and
ductility, and show improved electrical conductivity properties [3-6]. These properties make NT
Cu desirable for use as interconnects [7, 8], and nanotwinned alloys could have potential
applications as high strength coatings where high temperatures or corrosion limit nanocrystalline
metals.
Materials containing a nanotwinned microstructure have been synthesized by multiple
techniques, including magnetron sputtering, electrodeposition, and severe plastic deformation[6,
9-12]. An advantage of utilizing magnetron sputtering to study nanotwinned alloys is the ability
to synthesize materials that maintain the stoichiometry of the source material [13]. Moreover,
previous research has demonstrated the potential to synthesize fully nanotwinned Cu-based
alloys through magnetron sputtering [14], all of which are all solid-solution, face-centered cubic
(FCC) materials. By varying the synthesis parameters, it is possible to control the microstructural
2

features, allowing for analysis of the influence of microstructure on the mechanical behavior.
Accordingly, this study focuses on nanotwinned Cu alloys synthesized by magnetron sputtering.
Most of the research investigating the mechanical properties of nanotwinned metals has focused
primarily on how the microstructural parameters (twin thickness, grain width, twin orientation,
and percentage of the structure that contains nanotwins) influence the mechanical properties [15-
18]. In addition, a combination of simulation, post-fracture microstructural characterization, and
in-situ testing of nanotwinned metals has given some insight on the deformation mechanisms
that occur in these materials [16, 19]. These previous studies focus primarily on nanotwinned Cu,
however, and there is limited research exploring how alloying elements influence the mechanical
behavior of nanotwinned materials. While there is a strong understanding of how alloy
composition influences the mechanical properties in coarse grained materials (for example
through solid solution strengthening or SFE influencing slip mechanisms) [20], deformation
mechanisms are different at the nanoscale and so responses to alloy content may vary. This study
serves to bridge this gap, expanding the understanding of how alloy content influences materials
at the nanoscale by investigating tensile and fatigue behavior of nanotwinned alloys.

3

Chapter 2. Background
In this chapter, a background on nanotwinned metals is presented. This includes a discussion on
what nanotwinned metals are, how they are synthesized, and their mechanical properties. Note
that nanotwinned metals have only been demonstrated in face-centered cubic (FCC) materials, so
only metals with this structure are presented.
2.1 Coincident Site Lattice
Twin boundaries are a type of special boundary in FCC materials that have a coincident site
lattice (CSL), which describes the relative orientation of the two adjoining grains. CSL grain
boundaries are denoted ƩN, where the inverse of N represents the percentage of lattice sites that
are shared between the two grains [21]. For example, Figure 1 shows the overlap of two grains
that would have a Ʃ5 grain boundary.

Figure 1. Diagram representing two grains (represented by yellow and red spots) with a Ʃ5
boundary, where the blue dots represent the coincident sites [22]

4

The repeating unit cell in the overlapping regime in this diagram is used to determine the Ʃ
value, where the red and yellow spots represent non-coincident sites in the crystal structure while
blue spots represent coincident sites. Since the blue spots occupy a fifth of the unit cell volume
compared to either the yellow or red spots, this is considered a Ʃ5 boundary.
The Ʃ value of a grain boundary in a crystal can influence the properties of the grain boundary.
More specifically, CSL boundaries with Ʃ<29 have been reported to have unique mechanical and
chemical properties [2]. The Ʃ value does not fully describe the grain boundary, however, as it
only describes the orientation of the crystals relative to each other. The grain boundary plane is
also important in determining the grain boundary properties, as it can influence the energy of the
grain boundary [23, 24].
2.2 Twin boundaries
Twin boundaries are Ʃ3 CSL boundaries, which tend to show improved properties compared to
typical grain boundaries [25]. Twin boundaries can be categorized as either coherent or
incoherent; coherent twin boundaries (CTB’s) have a (111) grain boundary plane while
incoherent twin boundaries have any other grain boundary plane. This section discusses CTB’s,
which are the lowest energy twin boundaries [26] and the primary twin boundary observed in
nanotwinned metals. Atoms along CTB’s lie within the crystal structure of both adjoining grains,
leading to generally lower energies at these boundaries compared to typical grain boundaries. A
schematic showing a CTB can be seen in Figure 2, where Figure 2a represents a perfect FCC
crystal and Figure 2b represents an FCC crystal with a CTB.
5

Figure 2. Illustration of an FCC structure from the (110) zone axis displaying a perfect
crystal (a) and twin boundary (b)

In a perfect FCC crystal in the (111) direction, there is a specific atomic stacking sequence, with
the typical pattern ABCABC (each letter represents a (111) plane of atoms in a specific stacking
location). With a CTB, there is a reversal of this stacking sequence, where the stacking sequence
switches from ABCABC… to CBACBA… [27].
In microscopy, CTB’s can be identified from multiple features. Figure 3 shows a microstructural
TEM image where two CTB’s are highlighting with red lines.

Figure 3. Cross sectional TEM image of Cu-2wt%Al highlighting two CTB’s with red lines.

A
B
C
A
B
C
A
A
B
C
A
C
A
B
Twin
Boundary
(111) (111)
(a) (b)
6

CTB’s tend to appear as straight boundaries and if there are multiple twin boundaries in
succession in the same material plane (as is the case in Figure 3) the boundaries are parallel to
each other with consistently switching contrast between two shades (since the grains are
switching between two orientations). These features can be utilized to locate twin boundaries in a
material with varying imaging techniques, ranging from electron microscopy to optical
microscopy of etched samples.
2.2.1 Types and formation of twin boundaries in FCC metals
There are three typical ways in which CTB’s can form in FCC metals: deformation, annealing,
and growth. In the following sections, the formation of twins by each of these methods is
discussed in detail.
2.2.1.1 Deformation Twins
In FCC metals it is possible that CTB’s form through deformation. The stress required for twins
to form varies based on the material being deformed and the deformation mechanism being
applied [28]. The applied stresses at which deformation twinning begins to occur in Cu, for
example, tend to range from around 400 to 500 MPa [28]. Specific conditions can promote the
formation of twinning as a deformation mechanism in materials, including deforming at low
temperatures [29, 30], high applied stresses [31-33], or deformation of nanocrystalline (NC)
materials [34-37]. While there are several postulated mechanisms for how twin boundaries may
form by deformation in FCC metals [38-42], all of these mechanisms are similar in that they
require multiple active slip systems in order to generate a twin boundary.
2.2.1.2 Annealing Twins
When different materials experience recovery, recrystallization, and grain growth via annealing,
it has been observed in FCC metals that CTB’s can form, introducing “annealing twins” into the
7

material. During annealing, there are many mechanisms by which these twins can form, typically
from the migration of stacking faults or grain boundaries leading to the formation of twin
boundaries [43, 44]. Although the formation of annealing twins is not fully understood [25, 43-
46], the twin boundaries typically serve to lower the system energy compared to the initial high
energy state. Depending on the formation mechanism, these boundaries can appear at various
locations, with either single or multiple twin boundaries appearing, and twins occurring either
along grain boundaries or isolated within annealed grains [43].
2.2.1.3 Growth Twins
In FCC metals synthesized by ‘bottom-up’ techniques, whereby materials are ‘built’ a single
atomic layer at a time, there is a possibility to introduce twin boundaries into the material,
forming ‘growth twins’. Faults in the stacking sequence in the (111) plane can occur during
deposition [47] which cause the formation of a CTB. Note that twin boundaries are more likely
to form if there is little energy difference between the twinned and non-twinned states, which
will be discusses in Section 2.1.2. The introduction of high densities of growth twins into
materials has been achieved with various deposition techniques, including magnetron sputtering
[48, 49] and electrodeposition [4, 6, 15]. While the mechanisms that lead to growth twins are not
fully understood, studies investigating how synthesis parameters and material properties
influence the formation of growth twins in magnetron sputtering are discussed in more detail in
Section 2.3.2.1.
2.2.2 Energies related to twin boundaries
In metals, CTB’s are high angle boundaries with a relatively low energy. A twin boundary’s
energy is related to a material’s stacking fault energy (SFE), which is defined as the energy
difference per unit area introduced to a perfect lattice by introducing a stacking fault; note a twin
8

boundary’s energy per unit area is typically about half of the SFE [50]. In lower SFE FCC
materials there is a higher likelihood of developing a fully NT microstructure in physical vapor
deposition techniques [51, 52] as many growth twins can be introduced during film growth.
Table 1 shows a comparison of values of SFE for some common single element FCC metals and
some alloys of interest in this study.
Material SFE (mJ/m
2
)
Al 166
Ni 128
Cu-23wt%Ni 74
Cu 45
Cu-2wt%Al 37
Ag 17
Cu-6wt%Al 6
Table 1. Stacking fault energies for various common single element FCC metals and alloys
relevant to this study [53-58]

As seen in this table, the stacking fault energy of single element FCC systems can vary orders of
magnitude, as the SFE of Ag and Al are 17 and 166 mJ/m
2
, respectively. A material’s SFE may
be further modified by introducing different alloying elements, which typically decreases but can
also increase the SFE of the base material. An example of this is shown in Table 1 where
alloying Cu (SFE 45 mJ/m
2
) with Al decreases the SFE (6 mJ/m
2
for Cu-6wt%Al) while alloying
Cu with Ni increases the SFE (74 mJ/m
2
for Cu-23wt%Ni).
Another energy related to twin boundaries is a material’s unstable stacking fault energy (USFE).
The USFE is correlated to the energy barrier which must be overcome to generate a stacking
fault or twin in a material by deformation, and can influence the mechanical properties in metals
[59]. While it has not been possible to experimentally measure this value, the unstable stacking
9

fault energy has been calculated by simulation by generating general stacking fault energy
curves, or the required energy to achieve various lattice displacements during stacking fault
formation, displayed in Figure 4 for various materials [59].

Figure 4. General stacking fault energy curves (red) where the peak indicates the unstable
stacking fault energy. Blue curves indicate energy boundaries for twin formation [59]

The peak energy in these curves (vertical axis) is called the USFE, which is above but otherwise
unrelated to the SFE and can vary depending on the material, with values ranging from around
120 to 600 mJ/m
2
in the provided examples. The USFE can impact the required stress for
stacking fault formation, twinning behavior [59], or the stress concentration required for
dislocation nucleation from boundaries [59, 60], as is discussed in more detail in Section 4.2.
2.3 Nanotwinned Materials
2.3.1 Microstructures of nanotwinned metals
In nanotwinned metals, there are multiple length scales defining the microstructure. Twins are
typically the smallest feature, where the twin thickness for nanotwinned metals is less than 100
10

nm. In addition to twin boundaries, there are typically larger grains containing the twinned
grains; the boundaries of these larger grains are referred to as ‘grain boundaries’. In the case
where the NT material is ‘equiaxed’, these grains have similar length scales in each direction and
the twins within these grains do not have a strong orientation preference. In the case of
‘columnar’ nanotwinned metals, these grains have columnar shapes and the twins typically have
a preferred orientation within these columnar grains. Figure 5 compares microstructures for both
equiaxed and columnar microstructures.

Figure 5. FIB cross section micrographs comparing equiaxed NT Cu (a) [61] and columnar
NT Cu (b) [62]

The sizes of both the twins and grains as well as the volume percent of the material that contains
twins have an impact on the behaviors observed in NT metals [63]. ‘Twin thickness’ is defined
as the spacing between twin boundaries. In the case of fully twinned microstructures, this is
equal to the distance between twin boundaries, since the structure is composed entirely of twins.
‘Grain size’ is used to describe the average diameter of the grains in equiaxed NT materials
while ‘grain width’ describes the thickness of columns in columnar NT materials. Lastly, for NT
materials that contain non-twinned regimes, the percent of the material that is twinned is referred
(b) (a)
11

to as the ‘twin density’ and is represented as a percentage, where 100% twin density represents
fully twinned structures.
2.3.2 Synthesis of nanotwinned metals
Various methods have been utilized to synthesize nanotwinned metals, including magnetron
sputtering [48, 49], electrodeposition [4, 6, 15], and severe plastic deformation [12]. Each of
these techniques can be utilize to produce various types of nanotwinned microstructures with
varying twin densities, twin thicknesses, grain widths, and textures. Each technique is described
in more detail in the following sections.
2.3.2.1 Magnetron Sputtering
Magnetron sputtering is a physical vapor deposition technique in which a material is vaporized to
coat various surfaces [13]. This is performed by placing a large disc of the material that will
provide the coating, called a ‘target,’ in a gas (typically neutral) environment, and applying a
large negative potential to the target material; this causes the neutral gas to ionize and bombard
the target material, causing vaporization and subsequent coating. A magnetron, or strong
permanent magnet is placed behind the target to confine electrons to the target surface,
enhancing the ability to sputter. A substrate in line with the metal vapor path will become coated
with this target material a single atomic layer at a time, producing a film. A schematic for the
sputtering process is illustrated in Figure 6.

12

Figure 6. Schematic of magnetron sputtering technique. Argon atoms near a negatively
charged sputtering target are ionized which causes them to bombard the target, releasing
atoms of the target material which then coat the substrate

The introduction of twins into sputtered films has been explored in some detail by Zhang et al.
[9], who investigated the influence of sputtering rate on the formation of twins in epitaxially
grown Cu/SS330 multilayers. These samples had columnar NT structure with a strong (111)
texture in the growth direction, similar to what is typically seen in NT metals synthesized by
sputtering [10]. A model was generated in this study which explains a relationship between
sputtering parameters and likelihood of twin formation. In this model, it is assumed that a small
packet of atoms is deposited on the surface with either a perfect stacking (represented in Figure
3a) or a twinned stacking. A critical radius is found for both a perfect, r
*
perfect, and twinned
stacking, r
*
twin, for the deposited atoms where the deposited atoms are in an energetically steady
state, defined as:

13











s
perfect
P
mkT J kT
r


2
ln
*
(1)
h P
mkT J kT
r
twin
s
twin
 












2
ln
*
(2)
Where γ is surface energy, γtwin is the twin boundary energy, k is the Boltzmann constant, T is the
temperature, Ω is the atomic volume, J is the deposition flux, m is the atomic mass of the
interacting species, h is (111) interplanar spacing, and Ps is the vapor pressure above the solid. In
all cases, the radius at which a packet of atoms with a perfect stacking is smaller than for a
twinned nucleus. However, at higher sputtering rates the difference in radius becomes small.
Smaller difference in the critical radius between a twinned and non-twinned state indicates a
higher likelihood of obtaining a twin boundary during sputtering, and thus a smaller twin
thickness is expected with higher sputtering rates, with all other variables constant. The
microstructure of sputtered films has been shown to also vary depending on the target material
[52], where Velasco et al. have demonstrated the potential to sputter nanotwinned CuAl alloys
with varying twin thickness and grain width.
In addition to sputtering conditions’ influence on the critical radius, the material’s SFE and
temperatures achieved during sputtering can alter the microstructure of magnetron sputtered NT
metals. This is investigated in detail by Velasco et al. [14] where fully twinned Cu alloys (CuNi
and CuAl) with stacking fault energies ranging from 6 to 60 mJ-m
-2
were sputtered with film
temperatures between 50 and 350°C. From this study, a protean contour map was generated
showing twin thickness as a function of SFE and film temperature, shown in Figure 7.
14

Figure 7. Protean contour map showing twin thickness density as a function of both film
temperature and SFE in magnetron sputtered Cu alloys [14]

As seen in this map, temperature has a different impact on the twin thickness for different
stacking fault energy materials. For high SFE materials, higher temperatures correlate with larger
twin thicknesses (Zone II in Figure 7), which is explained by an increase in incoherent twin
boundary (ITB) mobility leading to detwinning and an overall reduction in the number of twins
in the materials. For the lower SFE materials (Cu-6wt%Al), high temperatures correlate with a
decrease in twin thickness; this trend is explained in that the alloy content is higher in these films
and therefore the effect of Zener drag force is larger [14].
2.3.2.2 Electrodeposition
Electrodeposition is a technique by which metal ions in solution are reduced and then deposited
to a surface. Two electrodes are placed into a solution containing metal ions (often an aqueous
15

solution with dissolved metallic salts), and then a potential is applied to the electrodes [64]; the
schematic in Figure 8 indicates how this procedure is performed.

Figure 8. Schematic of Electrodeposition Technique. The negative potential on the left
electrode promotes reduction of metallic ions in the solution while the positive potential on
the right electrode promotes oxidation of metallic ions in the electrode

An oxidation reaction occurs at the positively charged electrode (typically consisting of the metal
being plated), which causes the metal atoms in the metal to go into solution as ions, and a
reduction reaction occurs at the negatively charged electrode, which causes metallic ions in the
solution to become neutrally charged, coating the electrode. The total charge transfer in
electrodeposition is typically normalized by the current density, or total current per unit area on
the surface being plated. The microstructure of the deposited atoms can vary based on the
composition of the solution, waveform and magnitude of applied current densities, temperature
of the solution, and amount of solution agitation (i.e. mixing) that is taking place [65].
+ -
Net mass flow
Positively charged
electrode
Negatively charged
electrode
Ionic
Liquid
Electron flow
Solution with
Metal Ions
16

Lu et al. have demonstrated that it is possible to deposit nanotwinned Cu with an acidic aqueous
solution of CuSO4 [6]. This is done by utilizing pulsed electrodeposition, where very high
current densities are applied for short pulses and then deposition is stopped to allow for
replenishment of the ions near the electrode surface. With this technique, various groups have
been able to synthesize nanotwinned Cu with both equiaxed NT structure [15] and columnar NT
structures [18]. With this technique, mean twin thicknesses ranging from 4 to 100 nm have been
achieved with grain sizes or grain widths typically above 500 nm [15, 18], which are larger than
the grain widths typically achieved with magnetron sputtering.
2.3.2.3 Severe Plastic Deformation
Severe plastic deformation (SPD) is a technique by which a material is deformed with very high
equivalent strains (on the order of 1) [66], leading to very high internal stresses in the material.
The diagram in Figure 9 shows an example of equal-channel angular pressing (ECAP), a
common SPD technique in which a material is pushed through an angled section with an equal
cross section before and after the angle. Figure 9 shows a schematic for ECAP.

Figure 9. Schematic of equal-channel angular pressing for a block sample [66]
17

When the sample plug is passed through the angle, it must deform significantly in order to form
into the channel to the right of the angle. The total strains reached in a single pass depend on the
geometry of the die and angles and can reach strains up to around 1 with a single pass [67]. High
internal stresses are related with these high strains which can lead to microstructural changes.
By performing ECAP on low stacking fault energy materials, various studies have shown the
potential to synthesize NT metals [11, 12]. The NT structures form due to the formation of
deformation twins, whose emergence is promoted by the high stresses and high dislocations
densities achieved by SPD [11]. The NT materials produced by this method typically contain
many defects in the forms of either dislocations or kinks along grain boundaries, which can be
reduced by means of annealing [12].
2.4 Mechanical Behavior of Nanotwinned Cu
Nanotwinned metals have garnered much interest due to their unique mechanical behavior
compared to nanocrystalline metals. Higher strengths can be achieved in NT metals compared to
nanocrystalline metals due to twin boundaries being more mechanically stable than typical
nanocrystalline boundaries [68]. In addition they have shown the potential to improve in ductility
with decreasing twin thickness [15]; this is due to unique deformation mechanisms in NT metals,
which lead to mechanical behavior which are dependent on both twin thickness and grain width.
2.4.1 Deformation mechanisms
The deformation behavior in NT metals is largely due to the presence of a high percentage of
CTB’s and the multiple length scales existing in the material. The observed deformation
mechanisms in NT metals are discussed in this section.
18

2.4.1.1 Slip Systems in Nanotwinned Metals
Due to the microstructure of NT metals, there are various means by which dislocations can
propagate in the material, each of which behaves differently. Slip systems in NT metals have
typically been divided into three categories: Soft Mode slip involves the motion of dislocations
along twin boundaries, Hard Mode I slip indicates dislocation motion between twin boundaries,
and Hard Mode II slip refers to threading dislocations, which are confined between twin
boundaries and travel within twins[69-71], represented in Figure 10.

Figure 10. Illustration of Hard Mode I, Hard Mode II, and Soft Mode slip systems. Blue
boundaries in this schematic represent twin boundaries. Adapted from [70]

You et. al [72] have investigated how each of these 3 modes of dislocation motion contributes to
material strength through both experiments and simulations. In their studies, nanotwinned Cu
was loaded in compression with the twin boundary oriented 0°, 45°, and 90° to the loading
direction with various twin thicknesses. When the twin thickness was sufficiently large (ie
>100nm) dislocations were not confined within twin boundaries and dislocation-dislocation
19

interactions governed the mechanical behavior. Below a 100nm twin thickness, however, the
dominant deformation mechanism depended on the loading direction. The dominant slip system
was Hard Mode II for 0°, Soft Mode for 45°, and Hard Mode I for 90°. For the same twin
thickness, the yield stress in compression changed for each loading direction; 45° showed the
lowest yield stress around 200 MPa while 90° showed the highest yield stress around 600 MPa.
2.4.1.2 Detwinning
In addition to dislocation motion, detwinning has been observed as a potential deformation
mechanism in NT metals, which allows for the removal of twin boundaries, either modifying the
twin thickness, or transforming the microstructure to a non-twinned structure. Experimentally,
the transformation of a NT structure to a nanocrystalline has been observed for tensile tested
columnar NT Cu [73]; macroscopic shear bands correlated with the formation of these
transformation zones. Several mechanisms which would allow detwinning to occur in NT metals
are postulated by Wang et al. [17], shown in Figure 11.

20

Figure 11. Four mechanisms for detwinning as proposed by Wang et al. [17] where the blue
section shows the twin, white section shows the matrix, red lines show CTB’s, and partial
dislocations are represented in orange.

In all of these proposed methods for detwinning, the mechanism is governed by the motion of
partial dislocations from one twin boundary to another, resulting in either a change in twin
boundary spacing or the complete removal of a twin. Note that the forces acting on the partial
dislocations in these different mechanisms is influenced by the material’s SFE [17].
Due to the deformation mechanisms mentioned in this section (slip systems and detwinning), NT
metals show some unique mechanical behaviors that are not observed in nanocrystalline
materials. These behaviors depend on the microstructural parameters and material composition,
as discussed in the following sections.
21

2.4.2 Influence of microstructure on tensile behavior
The mechanical behavior of NT materials depends on both twin thickness and grain width (see
section 2.2.1). This was highlighted by Lu et al.[15], who had found that with decreasing twin
thickness in equiaxed NT Cu, there was a simultaneous increase in both strength and ductility
down to a critical twin thickness of 15 nm. Below this twin thickness, samples showed a
decrease in yield strength while showing increased ductility, illustrated in Figure 12, where the
number after “nt-” represents the twin thickness in nanometers.

Figure 12. Effect of twin thickness in equiaxed NT Cu with twin thicknesses ranging from
96-15 nm (A) and 15-4 nm (B) that shows there is a constant increase in ductility with
decreasing twin thickness, and transition from increasing strength to decreasing strength at
15 nm [15]
This decreasing yield strength with decreasing twin thickness is still not fully understood; the
apparent softening of the material has been attributed to an increase in mobile dislocation density
due to more sources for dislocation nucleation at very small twin thicknesses [16], an increase in
ease for detwinning to occur [17], or a shift in dislocation nucleation slip from mixed Soft and
Hard I Mode to only Soft Mode (see section 2.3.1.1) [19].
22

A comprehensive study on the combined effect of grain size and twin thickness on the
mechanical behavior of equiaxed NT Cu was performed by Xiaoyan et. al. The mechanical
behavior of NT Cu from various studies (experimental and simulated) were compared showing
that the transition twin thickness is decreased with smaller grain sizes [16]. This is illustrated in
Figure 13, where the transition twin thickness is shown for various grain sizes.

Figure 13. Combined effect of both twin thickness and grain width on the yield stress of NT
Cu combining simulation and experimental data. Data tends to follow the trend of the Hall-
Petch relationship above the critical grain width and transition to decreasing strength
below a critical twin thickness that decreases with decreasing grain width [16]

With decreasing grain size, NT metals achieve higher potential yield strengths. While higher
strengths can be achieved with smaller grain sizes, it has been demonstrated that decreasing the
grain size can decrease the ductility of NT metals [74].
The observed dependence on twin thickness in columnar NT Cu is different than that observed
previously in equiaxed NT Cu. Influence of twin thickness on the tensile behavior of columnar
NT Cu loaded orthogonal to the twin boundaries is investigated by Lu et al, shown in Figure 14
[18].
23

Figure 14. Tensile stress-strain curves for columnar NT Cu (a) with varying twin
thicknesses, λ, and grain widths, d, (b) which shows increasing strength and decreasing
ductility for decreasing twin thickness. Adapted from [18]

Samples C, B, and A in Figure 14 have decreasing twin thickness, respectively, correlated with
an increase in strength, but decrease in ductility. This is different than equiaxed NT Cu, where
decreasing twin thickness consistently led to increasing ductility. Note a dependence on grain
width is seen when comparing samples C and D, where decreasing grain width leads to an
increase in strength and decrease in ductility.
2.4.3 Influence of composition on mechanical behavior
The mechanical behavior of partially nanotwinned alloyed systems have been studied, including
stainless steel, NiCrMo, CuZn, and CuAl systems [49, 75-77]; however, those studies do not
isolate the effect of introducing alloying elements. For example, in a study by Zhang et al,
partially nanotwinned CuAl containing between 20 to 60% twinned grains was synthesized using
a single sputtering condition with varying Al content between 0 to 4.5 wt%, leading to varying
twin thicknesses, grain widths, and twinned percentages at four different compositions [75]. As
each of these factors contributes to the mechanical behavior, the direct effect of varying alloy
content is not extractable. While the effect of introducing alloying elements is not currently well
(b) (a)
24

understood, previous research on how alloy content can affect the mechanical behavior of
different materials gives some potential insight as to how introducing alloying elements might
affect the mechanical behavior in NT metals.
As discussed in Section 2.1.2, introducing alloying elements can increase or decrease the SFE of
a material which can in turn alter the deformation behavior. This is highlighted in a simulation
performed by Borovikov et al. [78] who performed tensile loading of NT Cu with various values
of SFE ranging from 15 to 186 mJ/m
2
; note all other critical material properties were maintained
in order to isolate the effect of SFE. It was found that at lower stacking fault energies there was
an increase in activity for partial dislocations instead of full dislocations, twin boundaries
became less mobile, and there was higher vacancy formation. In addition, it was found that
changing SFE did not significantly impact the material strength [78].
While the study by Borovikov did not see any change in material strength with varying SFE,
studies by Kulkarni have shown that there may be some dependence on the material strength in
certain circumstances for NT metals [79]. It was found that the simulated indentation strength of
NT metals loaded in compression tended to increase with an increasing critical stress
concentration for dislocation emission from a grain boundary, K
crit
:
(3)
where µ is shear modulus, γsf is SFE, and γus is USFE. With decreasing SFE, therefore, there may
be a potential increase in strength, especially in cases where the mechanical properties depend on
nucleation of dislocations or the interaction of dislocations with boundaries.
Another factor that may influence the strength of alloyed NT metals is an addition to solid
solution strengthening that occurs in nanocrystalline materials. As reported by Rupert et al.[80],
us sf us
crit
K    / 1  
25

grain boundaries in nanocrystalline materials can pin dislocation motion and due to this there is
an additional change in shear strength, Δτnc, compared to non-alloyed materials with the same
grain size, defined as







 


 
solvent solvent
solvent solvent
nc
b
b
G
G
d
b G

(4)
where G is the shear modulus, b is the length of the Burgers vector, d is the grain size, and ΔG
and Δb refer to the change in modulus and Burgers vector compared to the base material.
Because the twin thickness in nanotwinned metals can be on the order of nanometers, this term
may become significant with a large change in either the modulus or Burgers vector due to the
addition of an alloying element.
2.4.4 Activation Volumes of Nanotwinned Metals
The activation volume is defined as the volume of material associated with the rate controlling
deformation mechanism. Activation volume is related to the strain rate sensitivity of a material
as shown in Equation 5










 ) ln(
3 *

kT v
(5)
Where k is the Boltzmann constant, T is the ambient temperature, is the strain rate (assumed to
be equivalent with the loading rate [81]), σ is the flow stress (assumed to be 1/3 of the hardness),
and 3 is an assumed term. The activation volume changes with the rate controlling
deformation mechanism in a material [82]. In Table 2, some activation volumes for nanotwinned,
ultrafine grained, and microcrystalline FCC metals are shown [83]. Note that the units for
activation volume are commonly written in b
3
, where b is the burgers vector of the material.
 
26

Table 2. Summary of strain rate sensitivities and activation volumes for FCC metals with
different microstructures, adapted from [83]. Sources for activation volumes are [82, 84-91]

As seen in Table 2, activation volume typically decreases with decreasing grain size or twin
thickness. Activation volumes on the range of 100-1000b
3
are typically associated with
dislocation intersection, typically seen in coarse grained or ultrafine grained (UFG) material,
while for NC and NT metals, the activation volume decreases to 1-100b
3
, associated with grain
boundary nucleation or cross slip as deformation mechanisms [92].
2.5 Fatigue Behavior of Nanotwinned Metals
While the fatigue behavior in NT metals has not been as thoroughly investigated, some existing
research on fatigue in NT metals has given insight as to how NT structures contributes to
deformation under cyclic loading. Due to the improved mechanical stability of CTB’s,
nanotwinned metals have shown improved fatigue behavior compared to coarse grained
materials. Figure 15 shows S-N curves for coarse grained, ultrafine grained, and NT Cu [93].
27

Figure 15. S-N curves comparing fatigue behavior of nanotwinned (NT) Cu, ultrafine-grain
(UFG) Cu, and coarse-grained (CG) Cu, showing a 47% increase in fatigue limit for NT Cu
compared to CG Cu[93]

As seen in this chart, the fatigue limit (10
7
cycles) of NT Cu is roughly 47% higher in NT Cu
than in coarse grained Cu. The reason for this increase in fatigue limit is attributed to the high
percentage of twin boundaries which can provide barriers to dislocations and crack propagation
in cyclic loading, and are mechanically stable.
In different studies, varying damage mechanisms are seen when columnar NT metals are
exposed to cyclic loading. In a study by Shute et. al [94], detwinning is found to occur when
columnar NT Cu synthesized by magnetron sputtering was exposed to cyclic tension-tension
fatigue loading with the twin boundary normal orthogonal to the loading direction. Figure 16
illustrates the change in twin thickness distributions observed with varying loading conditions or
at different locations on the fatigued sample, where mean twin thickness tended to increase with
applied fatigue stress and closer to the crack.
28

Figure 16. Twin thickness distributions for columnar NT Cu before fatigue (a), after
compression (b), and after fatigue at 450MPa fatigue stress both away from the crack (c)
and close to the crack (d) showing that there was a shift in twin thickness due to detwinning
under cyclic loading [94]

Detwinning was also observed by Yoo et al., [95] where high throughput fatigue testing was
performed on magnetron sputtered columnar NT Cu by 'swinging' a weighted NT Cu rectangular
film at a sinusoidal displacement, allowing for different cyclic strain amplitudes at various
locations on the film. In this study, it was found that both detwinning and grain growth occurred
within the sample, with larger growth occurring at areas with higher strain amplitudes. The
samples showed some softening after fatigue, where the largest decreases in strength were
observed in locations where the most detwinning occurred.
The fatigue mechanism in NT Cu depends on the microstructural parameters, demonstrated by
Pan et al., who performed fatigue tests on columnar NT Cu synthesized by electrodeposition
29

[93]. It was observed that the primary deformation mechanism was threading dislocations, or
Hard Mode II slip as discussed in Section 2.3.1.1; detwinning was not observed in these
materials. This slip mechanism led to the formation of 'zig-zag' slip bands spanning columnar
grains and ‘block structures’, as shown in Figure 17.

Figure 17. Cross-sectional SEM showing formation of ‘zigzag’ shear bands with very little
detwinning observed in columnar NT Cu exposed to fatigue at small cumulative strains (a-
b), high cumulative strains (c), and observed ‘block structures’ intersecting twin
boundaries (d) [93]

Similar to what was seen in the tensile properties, the fatigue behavior and deformation
mechanisms are correlated with both twin thickness and grain width, as suggested by Pan [93].
Larger microstructural parameters (twin thickness 78 nm, grain width 6 µm) correlates with
shear band behavior [93] while smaller microstructural parameters (twin thickness 35 nm, grain
width ~500 nm) correlates with detwinning [94]. The effect of varying twin thickness has been
explored in fatigue crack propagation tests, where it was found that smaller twin thickness in
columnar NT Cu correlated with improved fatigue resistance [96].
30

2.5.1 Comparison to fatigue behavior of nanocrystalline metals
Since twin thickness influences the strength of NT metals similarly to how grain size influences
strength in NC metals (i.e. Hall-Petch strengthening), a comparison to nanocrystalline metals
may provide some insight into the role nanotwins play in fatigue. There is little research on
nanocrystalline materials’ behavior in fatigue, however, so this discussion is limited.
Several studies have investigated the fatigue behavior of UFG and NC Cu and CuAl alloys
ranging in grain size from 18 to 200 nm [97-99]. In these studies, the mechanisms for fatigue are
very similar, where both persistent slip bands (PSB’s) and grain growth dominate the
deformation (independent of grain size or alloy content) [97, 98]. There are not any transitions in
fatigue mechanisms observed in nanocrystalline metals, as opposed to NT metals where different
mechanisms have been observed with different microstructural parameters.
The fatigue strengths for NC metals have been explored as well. S-N curves comparing some
UFG and NC CuAl alloys are compared in Figure 18 [97].

31

Figure 18. S-N curves for UFG and NC Cu, Cu-5at%Al, and Cu-11at%Al with grain sizes
of 200, 100 and 70 nm respectively [97].

Increasing Al content is correlated with an increase in the fatigue strength, also correlated with
decreasing grain size and increasing tensile strength. It should be noted that, in general, fatigue
strength increases with increased tensile strength [100-102], consistent with what was observed
in these UFG and NC metals.
2.6 Summary
In this chapter, previous research investigating the synthesis and mechanical behavior of
nanotwinned metals is discussed. The synthesis of nanotwinned metals has been achieved with
various methods, including electrodeposition, severe plastic deformation, and magnetron
sputtering. Utilizing each of these methods, different types of nanotwinned microstructures can
be obtained, with potential to achieve either columnar or equiaxed structures, and different
percentage of twinned regimes, twin thicknesses, and grain sizes/widths.
32

The deformation of nanotwinned metals occurs by a combination of one of several slip systems
and detwinning, which leads to some unique mechanical behaviors in these materials. In tension,
for example, fully NT Cu has shown the potential to achieve simultaneous high strength and
ductility compared to nanocrystalline Cu. Factors such as twin thickness, grain width/size,
percentage of twinned grains, and twin boundary orientation can influence the mechanical
behavior, however.
The fatigue behavior of nanotwinned Cu has been investigated to some extent, where NT Cu has
been shown to perform better in fatigue than coarse grained Cu. Simulations on the fatigue
behavior of nanotwinned metals reveal their potential for improved fatigue behavior compared to
nanocrystalline metals, primarily due to their potential for crack closure. Different mechanisms
have been observed in nanotwinned Cu in fatigue, where either “zig-zag” PSB’s and block-like
structures, or detwinning was observed as a primary deformation mechanisms in NT Cu.

33

(blank page)

34

Chapter 3. Experimental Methods and Materials
3.1 As-Sputtered Sample Characterization
All of the NT samples investigated in this study were synthesized by magnetron sputtering: 76.2
mm diameter targets were used in order to sputter onto <100> Si substrates with either 25.4 mm
or 50.8 mm diameter from Virginia Semiconductors. A combination of continuous and
interrupted sputtering were performed with both heated and non-heated stages at varying powers
in order to change the sputtering rate and film temperature, allowing for microstructural control.
All films were peeled from substrates after sputtering, generating free-standing films. Utilizing
this technique, 15 to 20 micron thick alloyed columnar NT films with twin thicknesses ranging
from 4 to 33 nm have been sputtered with grain widths ranging from 80 to 260 nm.
Because of the small size of the microstructural features in the NT metals, high resolution
electron microscopy techniques must be used for material characterization. Various techniques
were utilized to characterize the microstructure of NT metals, including focused ion beam (FIB),
transmission electron microscopy (TEM), high resolution TEM (HRTEM), scanning electron
microscopy (SEM), electron backscatter diffraction (EBSD), and transmission EBSD (t-EBSD).
Each of these techniques allows for investigation of the microstructure either at different length
scales or extracting different information, allowing for the comparison of how differing
microstructures in these materials are correlated with mechanical behavior.
3.1.1 Characterization of Overall Microstructure
The overall microstructure of NT metals was imaged utilizing FIB, a technique that utilizes
focused ions to either geometrically modify or image a material. A common technique with FIB
allows for the imaging of a cross-section of a material, where a trench is milled into the material
35

utilizing Ga
+
ions and then the newly exposed face is imaged using ions. When imaging with
ions, different grains typically show different contrast, allowing for imaging of the grain
structure of materials. This technique allows for the investigation of generally large areas of the
material cross section (10µm x 10µm or larger), enabling the visualization of the overall
microstructure in NT metals. Figure 19 shows a typical TEM cross-section of a fully NT
columnar microstructure.

Figure 19. Cross-Sectional FIB Image of Fully NT Ag, where the white arrow represents
growth direction [103]. Change in contrast between vertical grains represents columnar
grain boundaries while changing contrast within columnar grains represents the presence
of twin boundaries, hardly resolvable due to poor FIB resolution

The vertically oriented elliptical shapes represent columnar grains and alternating contrast within
the columnar grains indicate the presence of twins, although twins cannot be well resolved due to
the resolution of the FIB used in this study (JEOL 4500), which has a resolution of
approximately 50 nm. Resolving any features smaller than this requires higher resolution
microscopy techniques.
36

3.1.2 Measurement of Microstructural Features
Very high resolutions, on the order of ≈0.1nm, can be resolved utilizing TEM, a technique where
electrons are transmitted through a thin section of a material, which allows for measurement of
twin thicknesses and grain widths in the NT metals in this study. A JEOL 2001F TEM is utilized
to image microstructural features in this study, which can typically reach resolutions around 0.3
nm in specific imaging conditions. In order to perform TEM, very thin samples (typically
<100nm) of the material have to be prepared. Multiple methods are utilized to prepare these
samples in different situations; each technique will be explained where it was used in this study.
Once a thinned sample has been prepared, various types of images can be generated with TEM;
different types of TEM images for the same fully NT Cu-2wt%Al samples are displayed in
Figure 20.

Figure 20. Representative TEM Images of fully NT Cu-2wt%Al including both bright field
TEM with an inset electron diffraction pattern (a) and a dark field image highlighting 2
columnar grains, where the bright vertical columns are single columnar grains (b), and
high resolution TEM (c)

Each of the images highlights different features of the microstructure. Bright field images
account for all electrons interacting with the sample and can be utilized to measure thickness of
twins and grains, electron diffraction patterns indicate repetition in the atomic structure and can
a b c
37

indicate the existence of twin boundaries when streaking is present, dark field images utilize only
some of the electrons interacting with the sample and can ‘single out’ different grains in the
material, and HRTEM images can show single stacks of electrons and can be used to observe
twin boundaries and defects on twin boundaries.
3.1.3 Grain Orientation and Grain Boundary Characterization
While FIB and TEM can provide size information about a material’s microstructure, it is difficult
to extract information about crystal orientations or grain boundary character in the material from
these techniques. This can potentially be very important, as the grain boundary types can have an
impact on a material's mechanical behavior [104]. To investigate this behavior, EBSD is utilized;
this is an SEM technique whereby electrons are reflected off of a material from a specific spot,
captured on a very large detector, and diffracted 'Kikuchi lines' are measured on this detector to
determine the crystal's rotation at the spot of the beam. This is done at many spots over a
rectangular area on the sample, allowing for a full crystal orientation map (2-dimensional
rotation data at every point) to be obtained from areas as small as 100 nm by 100 nm or as large
as 100 µm by 100 µm. From these data, information about the grain rotations and grain boundary
character can be extracted, allowing for the investigation of how these factors influence the
mechanical behavior. In general, the best spatial resolutions achievable by traditional EBSD are
approximately 30 nm [105], meaning that investigation of the twin boundaries smaller than this
is not possible with this technique. Improvements to EBSD resolution can be made by utilizing t-
EBSD, where instead of reflecting electrons off of a material's surface, electrons are transmitted
through thin pieces (<100 nm) of the material; resolutions better than 10 nm have been
achievable with t-EBSD [106].

38

3.2 Tensile Testing
To determine the mechanical behavior of the films in this study, a custom tensile testing machine
has been designed and built which incorporates digital image correlation (DIC) utilizing an
optical camera. This provides various benefits compared to buying a pre-existing tensile
machine, as the modular design allows for control of the testing technique, load application, and
data capture and analysis. The various design and testing methods for the machine are discussed
in the following sections.
3.2.1 Microtensile Tester Design
The microtensile tester is a modular device which allows for single axis displacement control of
various stages with the measurements of loads in the loading direction. Figure 21 shows the fully
built tensile tester set up for film tensile testing with all the key components highlighted.

Figure 21. Microtensile testing machine highlighting key components

Load
Cell
Sample
Stage
Piezoelectric
Actuator
Coarse
Actuator
Optical Camera/Lenses
5 cm
39

Actuation for the device is provided by two linear actuators, including a ThorLabs PAZ015
piezoelectric actuator for very fine motion (25 nm resolution) and a coarse ThorLabs DRV001
actuator for long range motions up to 8 mm. These actuators can apply a maximum load of
220N, limited by the coarse actuator. Installed in line with these devices is an Omega LC703-100
load cell, which can measure a peak load of 440N in tension or compression and has a typical
error below 0.5%. The left side of the device is mounted on a two-directional stage which allows
for alignment of the loading axes. Stages attach to the load cell and actuators by a 6-32 UNC
female thread, allowing for the connection of many types of stages. The stage for tensile tests
consists of a clamp with flat clamping surfaces and pins for sample alignment. A switching DC
power supply provides power to the load cell, where the output is read by DAQ. Above the
sample stage, an optical camera is mounted where it can be moved and fixed in all three spatial
dimensions. This camera is capable of capturing resolutions up to 2200x3000 pixels and with the
attached lenses can achieve pixel resolutions ranging from roughly 0.5 to 5 microns per pixel.
The device is controlled by a custom-written MATLAB code, which controls the motor
positions/velocities and reads and saves the measured loads. Image or video capture is performed
simultaneously with mechanical tests to correlate images to the motor displacements and
measured loads.
3.2.2 Digital Image Correlation
Digital image correlation (DIC) is a technique in which multiple points are tracked in a series of
images [107]. This technique is used in many scientific fields and can be utilized to track points
in two or three dimensions [107]. By correlating the position of the tracked particles with the
time of capture for each image, many points on the image can be tracked to determine relative
trajectories or strains. In addition, other data captured simultaneously can be compared to the
40

point trajectory to find the relationship between the points and other experimental data.
Advances in computer technology have allowed for the tracking of thousands of points by DIC
for thousands of images in a reasonable period of time, allowing for the understanding of how a
large array of points on a surface move relative to each other over time. Materials scientists have
implemented this technique to understand localized deformation behavior of materials when
subject to mechanical loads [108, 109] or thermal loads [110, 111] at various length scales,
ranging from the nm scale (utilizing DIC on SEM images) to the mm scale (utilizing optical
microscope images). In this study, a single optical camera is utilized to capture images, and two
dimensional DIC is performed on samples ranging in size from ~10µm to 1mm.
The tracking of points for DIC relies on a gradient of intensities on the surface, typically a
‘speckle’ pattern seen in optical images. In order to track surface changes, the tracked points for
an image are rearranged until the correlation coefficient is maximized for all sample areas for the
rearranged state and reference state (e.g. first image) [107]. Point tracking resolutions below 1
pixel can be achieved with this method. In practice, DIC tends to be limited by the speckle
pattern in the material, peak intensity of the image, and vibration in the test setup. With all of
these things taken into account, background noise (similar to a lower limit for the resolution)
fluctuations below 0.1 pixels can be achieved in DIC performed with optical images [109]. The
‘speckle pattern’ is generated by creating a mixture of alumina and isopropanol, applying this
mixture to the sample surface, and allowing the isopropanol to evaporate; this forms the random
pattern shown in Figure 22.
41

Figure 22. Representative DIC alumina speckle pattern on a tensile sample

Each spot is approximately 10 microns in diameter with a random distribution as shown in
Figure 22. Because the alumina is not chemically bonded to the surface, it is not expected to
have any effect on mechanical behavior of tested films.
The speckle pattern is applied to samples before a test in this study. During a tensile test, optical
images are taken of the sample at a rate of 6-10 Hz. DIC analysis is performed using a
rectangular grid with 10 pixel spacing. This method allows for both average and localized strain
measurements on tensile sample.
3.2.3 Microtensile Tester and Tensile Sample Geometry Performance Verification
Calibration and verification of the tensile tester was performed in order to verify that it provides
accurate results in tension. The load cell was calibrated using calibration weights and verified at
500 μm
20 μm
42

different ranges of weights. Following calibration, tensile tests were performed on different films
to determine overall machine performance.
Tensile tests for similar tensile samples were compared to a calibrated tensile tester to indicate
the performance of the machine. Tensile samples were produced by polishing samples down 25
micron thick full-hard stainless steel (SS) 304 to the desired dogbone geometry in a die with a
gauge area of 3 mm x 6 mm, considered ‘calibration samples’ in this section. Tensile tests were
performed on the microtensile tester and a calibrated Instron 5965 tensile tester. Note for the
microtensile tester loads from the load cell were utilized to find the engineering stress, σ, and
average strain values from DIC were utilized to find engineering strain, ε. Stress-strain curves for
these two machines are shown in Figure 23 where the red and black curves show representative
stress-strain curves obtained from the two machines.

Figure 23. Representative engineering stress-strain curves comparing tensile behavior for
SS304 as determined by a calibrated Instron 5965 tensile tester (red) and custom built
tensile tester (black) and comparing calibration (black) and microtensile (blue) geometries
on the microtensile tester
Instron 5965 – Calibration Sample
Microtensile Tester – Calibration Sample
Microtensile Tester – Microtensile Sample
Instron 5965 – Calibration Sample
Microtensile Tester – Calibration Sample
Microtensile Tester – Microtensile Sample
43

Overlapping curves show agreement between the two tensile testing machines, indicating that the
calibrated load cell on the microtensile tester provides reasonable values. Due to the small size of
sputtered films, tensile samples with the ‘calibration sample’ were not used; a smaller tensile
sample was used which is based on ASTM E345-93 Type A, scaled down to a reduced section of
0.8 by 3.6 mm, shown in Figure 24. Note this geometry is called ‘microtensile sample’ in this
section.

Figure 24. Drawing of tensile geometry used in testing of NT films. Tensile sample
thickness varies from 15 to 20 μm. All units are in mm

Tensile testing has been performed with this geometry using full-hard SS304, with stress-strain
curves for the ‘microtensile sample’ shown in the blue curve in Figure 23. The smaller size of the
tensile sample does not affect the measured material strength or modulus of the material, and so
the sample geometry appears to be sufficient for determining materials’ tensile properties.
The samples tested in this study all have thicknesses on the order of 10-20 microns; in order to
investigate whether there is any size effect from samples with this thickness, tensile tests were
44

performed utilizing the geometry in Figure 24 for films with a 25 micron thickness and 200
micron thickness. Annealed INCONEL 600 was chosen as this is a solid solution material and
each sample thickness should have the same properties since samples were in their annealed
states. Representative stress-strain curves comparing the thin (25 micron) and thick (200 micron)
samples are compared in Figure 25:

Figure 25. Representative stress-strain curves for annealed Inconel 600 samples with gauge
areas of 0.8 by 3.6 mm comparing behavior for thicknesses of 25 microns (black) and 200
microns (blue)

The samples show mostly similar stress-strain curves; the reduced sample thickness seems to
only impact the tensile behavior after the ultimate tensile strength has been reached.
3.3 Nanoindentation Measurements
As mentioned in Section 2.3.4, the activation volume for a material can be determined from the
strain rate sensitivity of the material. A method for determining the strain rate sensitivity of a
45

material by nanoindentation has been developed by Schwaiger et al. [85], where either varying
loading rate or varying strain rate can be utilized to determine strain rate sensitivity. Following
this method, Lu et al [81] determined the activation volumes of NT Cu with different
microstructural parameters by nanoindentation at different loading rates. Similarly,
nanoindentation at varying loading rates was performed on some nanotwinned samples in this
study to determine activation volumes.
Nanoindentation samples were prepared initially by punching a 3mm disc of the material from
the as-sputtered film. The tops of each film were etched with a Fischione 1050 ion mill with a 1
kV accelerating voltage in order to ensure uniform surfaces for the different films. The films
were attached to a stainless steel disc, and indented in a Hysitron Triboindenter. A total of 100
indents were performed on each sample using a Berkovich Tip with loading rates ranging from
0.1 to 40 mN/s with a peak load of 8 mN for each indent. Nanoindentation hardness as a function
of loading rate was found, and equation 5 was utilized to estimate the activation volume for the
tested materials.
3.4 Fatigue Testing
Fatigue tests were performed in Collaboration with Professor Dr. Chris Eberl at the Fraunhofer
IWM institute in Freiburg, Germany. Fatigue samples were prepared using the same preparation
methods explained in Section 3.2.3 producing similar sample geometries as shown in Figure 24
except with reduced sections of roughly 0.65x3.6mm. Fatigue tests were performed on a custom-
built fatigue tester, which is shown in Figure 26.
46

Figure 26. Setup utilized for fatigue testing of nanotwinned samples. Image modified from
[112].

The uniaxial fatigue tester consists of a mounting stage (where the sample is gripped during the
test), a coarse linear actuator (to position the sample before a test), a piezoelectric actuator
(which provides the sinusoidal displacement of the sample during the test) and load cell (to
measure loads on the sample). Note that verification of this fatigue tester had been carried out
previously by Fraunhofer IWM, where this and similar machines have been utilized in other
scientific or industrial applications.
Prior to performing the fatigue test, the sample was mounted to grips on the mounting stage,
using the optical microscope mounted above the sample to align the test sample; note optical
images were taken both after the sample was mounted and after the test in order to diagnose any
problems with the test. After mounting and aligning, the sample is loaded until the desired mean
load, and then a fatigue test is performed on the sample. For all the fatigue tests performed in this
study, a stress ratio, R (σmin/σmax) of 0.1 is used with a cycle frequency of 30 Hz. Note that the
set-up utilizes PID control to maintain load mean and amplitude during the test, demonstrated in
Figure 27.
47

Figure 27. Raw data output received from fatigue testing program. Input parameters are
shown in top two rows (mean piezo and piezo amplitude input) and measured load cell
parameters are shown in bottom two rows (load cell amplitude and mean load outputs)

The piezoelectric motor’s mean and amplitude are adjusted over the course of a test to keep the
amplitude and mean load at the desired values. For the experiments performed, the error in
desired load does not exceed 1% once the load values settled (less than 400 cycles in all tests).
Fatigue tests were carried out until either the sample fractured or 5x10
6
cycles were reached.
3.5 Post-Mortem Sample Characterization
For some tensile and fatigue specimens, sample microstructures or surface morphologies were
analyzed after the sample fractured. This was done either using an SEM or TEM, described in
detail in this section.
SEM analysis was performed on some samples to investigate the fracture surface morphologies.
In order to do this, fractured samples were mounted in a cross-sectional holder and aligned in the
SEM to image the fracture surface head-on. For each sample analyzed by this means, SEM
images were taken across the entire fracture surface at various magnifications so that any
transitions in fracture mechanism could be observed.
48

Microstructural analysis of fractured films was performed utilizing TEM. In order to prepare
TEM samples, FIB liftout was performed on the fracture surface in such a way that the
microstructure was preserved. This was done by applying a protective carbon layer to the
fracture surface prior to performing liftout, shown below in Figure 28.

Figure 28. Schematic showing protected FIB liftout, where dogbone sample with fracture
surface (indicated in red) was coated in carbon layer (indicated in blue) and then FIB
liftout was performed

After lifting out the section, FIB thinning to thinner than 100 nm was performed such that the
carbon layer remained. When performing TEM analysis, sections along the fracture surface
could be identified as those where the protective carbon layer remained.

Fractured Dogbone
TEM Sample with
Protective Carbon
49

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50

Chapter 4. Tensile Behavior of Nanotwinned CuAl
In this chapter, the mechanical properties of fully nanotwinned Cu-2wt%Al and Cu-6wt%Al are
evaluated by tension testing utilizing digital image correlation, allowing for the observation of
local macroscopic deformation. By individually varying twin thickness, grain size, and
composition, the isolated effect of each of these parameters on both strength and ductility is
observed. Increased strength correlated with decreasing grain size or increasing Al content. It
was observed that with decreasing twin thickness the ductility could be improved. Note that this
study is published in Advanced Engineering Materials [113].
4.1 As-Sputtered Samples
Fully NT columnar 15-20 micron thick films of Cu-2wt%Al (samples A-C) and Cu-6wt%Al
(samples D-F) with varying mean twin thicknesses (4-18 nm) and grain widths (80-180 nm) were
synthesized by magnetron sputtering following procedures similar to those outlined by Velasco
et al [52]. Aluminum was selected as the alloying element as small additions can significantly
reduce the SFE from 45 mJ m
-2
for pure Cu to 37 and 6 mJ m
-2
for Cu-2wt%Al and Cu-6wt%Al,
respectively [54, 55, 57]. In addition, coarse-grained CuAl has been shown to increase in both
strength and ductility with increasing Al content [114], thus making it an interesting choice for
studying mechanical behavior of fully NT alloys. Characterization of the films was performed
utilizing both TEM (JEOL JEM-2100F) and XRD (Rigaku Ultima IV). Figure 29 shows
representative TEM images displaying the overall columnar microstructure, twins within
columnar grains, and representative twin and grain size distributions for various samples which
are compared in this study.
51

Figure 29. Cross-sectional TEM images showing representative images for sample A of the
columnar microstructure (a) and twinned structure (b) and representative distributions for
grain width (c) and twin thickness (d)

Note cross-sectional TEM samples were generated by mounting a cross section of the film in
silicon, dimple grinding, and ion milling using a Fischione Model 1050 TEM Mill. Bright field,
dark field, and high resolution TEM images were obtained in order to measure at least 500 twins
and 200 grains for each film at various locations to find distributions. All samples showed a fully
twinned structure with the twin plane normal in the growth direction. In addition, in XRD
patterns for all samples, only the (111) and (222) peaks were observed, typical for a fully NT
columnar microstructure [49, 115].
As-sputtered films were cut into 12x3 mm strips and mounted in a stainless steel die with the
desired tensile geometry, based on ASTM E345-93 Type A, scaled down with a reduced section
of 0.8 by 3.6 mm. A suspension of alumina in isopropanol was applied to the surface and
52

allowed to evaporate, providing a speckle pattern for DIC point tracking. Tensile tests were
performed on 2-3 samples from each film at strain rates of 5x10
-5
s
-1
on a custom-built
microtensile tester based on a design by Balk et al. [116]. Actuation was provided by a linear
actuator installed in line with the sample stage and load cell. An optical camera was mounted
above the sample stage and focused on the sample's reduced section, capturing images at a rate
of 6-10 frames per second at resolutions of approximately 800x3000 pixels. DIC was performed
on each sample after the tensile test using software developed by Eberl et al., as described
elsewhere [108], using a 0.8x3.2 mm rectangular grid in the reduced section containing roughly
7000 points. Engineering stress values were calculated utilizing loads measured from the load
cell and engineering strain values were obtained by averaging the strain values calculated by
DIC. Yield strength for each sample was determined utilizing the 0.2% strain offset method and
strain to failure was found from the tensile sample that showed the highest strain to failure; both
values are shown in Table 3.

Table 3. Average microstructural properties and mechanical properties of fully NT
columnar CuAl samples
The effect of grain width, twin thickness, and composition on the mechanical behavior is
discussed from these samples.
Sample Aluminum
Content
[wt%]
Mean Twin
Thickness
[nm]
Mean Grain
Width
[nm]
Yield
Strength
[MPa]
Strain to
Failure
[%]
A 2 6 180 830±60 5.1
B 2 18 170 1020±80 2.6
C 2 5 110 1260±60 2.3
D 6 4 100 1410±70 2.1
E 6 6 80 1490±70 2.1
F 6 8 90 1340±70 2.3

53

4.2 Tensile Behavior and Localized Deformation Behavior
The stress strain curves for both Cu-2wt%Al and Cu-6wt%Al samples are compared in Figure
30.

Figure 30. Representative engineering stress-strain curves for fully NT Cu-2wt%Al (a) and
Cu-6wt%Al (b). Note small grains are 80-110 nm, large grains are 170-180 nm, small twins
are 5-6 nm, and large twins are 18 nm. Inset image displays the tensile sample geometry
with gauge area highlighted in red.

In Figure 30a, a comparison of stress-strain curves for Cu-2wt%Al samples is shown. The effect
of varying grain width is highlighted by comparing samples A and C (see Figure 29c) which
have similar "small" twin thicknesses of 6 and 5 nm and grain widths of 180 nm and 110 nm,
respectively. An increase in yield strength from 830 MPa to 1260 MPa and a decrease in
ductility (elongation to failure) seem to correlate with this decrease in grain width. Note that
while the ductility of samples in this study is considerably less than that reported for NT Cu,
[9]

definitive differences in elongation to failure are compared to discuss how different parameters
may influence the ductile behavior. It has been observed in NT Cu that a decrease in grain size
leads to a decrease in ductility and can lead to either an increase or no change in strength [74,
54

117]. For the range of grain widths and twin thicknesses in the Cu-2wt%Al samples, the increase
in strength is fairly substantial, indicating that the grain size in this regime is critical for
determining the mechanical behavior.
In addition, Figure 2a compares Cu-2wt%Al samples A and B (see Figure 29d) which have
similar "large" grain sizes of 180 and 170 nm and twin thicknesses of 6 and 18 nm respectively.
Here, a decrease in twin thickness shows a reduction in strength from 1020 to 830 MPa and an
increase in ductility (elongation to failure). This is in contrast to what has been observed in
columnar NT Cu, where it was reported that a decrease in twin thickness consistently led to an
increase in strength and decrease in ductility [10, 18]. In those studies, however, samples with
decreasing twin thickness (from 30 nm to 4.5 nm) also had a decreasing grain width (from 500
nm to 43 nm); therefore, the reported increase in strength and decrease in ductility could be due
to the decrease in grain width rather than the decreasing twin thickness. In comparison, in
equiaxed grained NT Cu presented by Lu et al., decreasing the twin thickness below 15 nm led to
an increase in ductility and decrease in strength [15]. This behavior was attributed to an increase
in activity for an 'easy mode' slip system whereby dislocations move along twin boundaries [71,
118]. In columnar NT materials, such as in this study, there is little shear stress on this ‘easy
mode’ slip system, so it does not likely dominate deformation behavior [71, 118]; instead,
deformation is typically accommodated for by 'hard mode' slip systems that requires high stress
for dislocation motion [51]. Due to this, it was not expected that a decrease in twin thickness
could enhance the ductily as observed in this study. Whether this is occurring despite a 'hard
mode' slip system being dominant or due to other mechanisms is currently unclear and requires
further investigation.
55

The effect of varying composition on the mechanical behavior can be observed by comparing
stress-strain curves of sample C (2wt%Al) in Figure 30a and E (6wt%Al) in Figure 30b, which
have similar mean twin thickness and grain width distributions. The increase in Al content shows
an overall increase in strength from 1260 to 1490 MPa and a negligible change in ductility as
both samples show similar small elongation to failure. In order to further understand any
differences in the deformation behavior between these samples, data obtained from DIC is
compared in Figure 31, showing both the strain map prior to fracture and the plotted average
strain as a function of the gauge length. Figure 3a compares samples C (2wt%Al) and E
(6wt%Al), where a clear localized high strain regime forms in sample C prior to fracture and
does not appear in sample E.

56

Figure 31. Strain maps of the gauge area immediately prior to failure (left) and average
values of strain as a function of normalized distance along the gauge section (right)
comparing Cu-2wt%Al and Cu-6wt%Al (a) and Cu-6wt%Al with varying twin thickness
(b)
The increased strength with increasing Al content may be due to a decreasing SFE between the
two compositions. In order to evaluate how SFE might affect the mechanical behavior of
nanocrystalline metals, Suresh and Asaro generated a model calculating the required stress
concentration to emit partial or full dislocations at a nanocrystalline grain boundary in different
materials [119]. This approach was then applied to simulations of NT metals deformed by both
shear and nanoindentation [79]. The NT model can be utilized as a qualitative predictor of
material strength; it was found that strength typically increases with an increasing critical stress
concentration for dislocation emission, K
crit
[79]:
(6)
us sf us
crit
K    / 1  
57

where µ is shear modulus, γsf is SFE, and γus is unstable stacking fault energy. Note that unstable
stacking fault energy is the energy barrier a system must overcome to generate a stacking fault
from a perfect lattice by deformation [60]. The unstable stacking fault energy for Cu-2wt%Al
and Cu-6wt%Al should not be significantly different, since for Cu-2.2wt%Al and Cu-3.7wt%Al
the reported unstable stacking fault energy values are 170 and 169 mJ m
-2
respectively [120].
The averaged shear modulus [121] has a slight change from 47.1 to 45.6 GPa [122]

and thus a
change in SFE from 37 to 6 mJ m
-2
is the only significant difference in the material properties in
Equation 6. This leads to an increase of ~9% in K
crit
from Cu-2wt%Al to Cu-6wt%Al, indicating
an expected increase in yield strength with increasing Al content, as was seen in this study.

Further insight into the combined effect of twin thickness, grain width, and composition can be
gained by comparing all of the Cu-6wt%Al samples (D-F) in Figure 30b. The effect of varying
twin thickness for these samples contrasts with what was observed for Cu-2wt%Al since the Cu-
6wt%Al samples all have similar strengths and ductility despite having differing mean twin
thicknesses (4-8 nm) and similar mean grain sizes (80-100 nm). It is worth noting that a change
in twin thickness from 4 to 8 nm was sufficient to have a significant impact on mechanical
properties in NT Cu.
[9]
The similar deformation behavior between the Cu-6wt%Al samples is
confirmed by the strain maps in Figure 31b, where the samples show a uniform strain prior to
failure. The tensile behavior of the Cu-6wt%Al samples (D-F) seems to be dominated by the
small grain width and increased Al content which, as this study has shown, contribute to the
observed high strength, low ductility, and uniform macroscopic deformation.
58

4.3 Summary
In summary, the mechanical properties of fully NT columnar CuAl depend significantly on the
interplay between grain size, twin thickness, and composition. In this study, the effect of
increasing Al content has been isolated to show that in fully NT CuAl alloys, by decreasing the
SFE, the material's strength increases and deformation becomes uniform with no significant
macroscopic strain localization. By controlling the microstructure of Cu-2wt%Al, it has been
demonstrated that decreasing twin thickness can lead to an increase in overall ductility with a
simultaneous decrease in strength; this behavior had not been previously observed for NT
materials with columnar grains. Grain width as well can significantly affect the tensile behavior,
as it was observed that reducing grain size can lead to increased strength and decreased ductility.
Overall, small grain size in combination with low SFE can potentially dominate the mechanical
behavior, thus minimizing the impact of the twin thickness. This preliminary study on alloyed
fully NT materials gives some insight as to how high strength and improved ductility could be
achieved for NT alloys and the potential of other alloyed NT systems for engineering
applications.
59

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60

Chapter 5. Tensile Behavior of Nanotwinned Alloys with Varying SFE
In this chapter a comparison of the tensile behavior of fully nanotwinned Cu-6wt%Al, Cu-
2wt%Al, and Cu-10wt%Ni with stacking fault energies of 6, 37 and 60 mJ m
-2,
respectively is
presented. The samples displayed yield strengths ranging from 830 to 1340 MPa, varying with
both alloy content and microstructural parameters. All samples showed low ductility, even
though there are tilted twin boundaries present in Cu-10wt%Ni. The influence of varying grain
width is presented for each alloy and related to both the activation volume and stacking fault
energy.
This study aims to understand how microstructural parameters, specifically varying grain width,
influence the mechanical behavior of fully NT alloys. The alloys used in this study include Cu-
6wt%Al, Cu-2wt%Al, and Cu-10wt%Ni, which will be referred to as Cu6Al, Cu2Al, and
Cu10Ni respectively. All alloys are solid solution FCC metals with stacking fault energies (SFE)
ranging an order of magnitude with values of 6, 37, and 60 mJ m
-2
[54, 56, 58]. Extensive
mechanical (tensile and nanoindentation) and microstructural characterization were performed
for all samples with the goal of educing the influence of nanotwins in the different alloy systems.
5.1 As-Sputtered Samples
The samples in this study were synthesized by magnetron sputtering; 15-20 micron thick fully
NT films were sputtered onto Si (100) substrates using Cu6Al, Cu2Al, and Cu10Ni targets,
following procedures outlined by Velasco et al [14]. The films were peeled from the substrate,
generating free-standing films. For each alloy, two films were sputtered with similar average
twin thicknesses, ranging from 5-11 nm, and varying average grain widths, ranging from 90 to
260 nm. Cross sectional TEM samples of free-standing films were prepared with a Fischione
1050 ion mill and observed in a JEOL 2100F TEM. Over 300 twins and 100 grains were
61

measured for each film in order to quantify the average twin thicknesses and grain widths, as
shown in Table 4.
Sample
SFE
[mJ m
-2
]
Twin Thickness
[nm]
Grain Width
[nm]
Yield Strength
[MPa]
Tensile/Yield
Strength
Strain Rate
Sensitivity
Cu6Al-A
6
9±1 220±20 1110±60 1.10±0.08 0.049±0.007
Cu6Al-B 8±1 90±10 1340±70 1.09±0.08 0.049±0.007
Cu2Al-A
37
6±1 180±20 830±60 1.4±0.1 0.043±0.007
Cu2Al-B 4.8±0.6 110±10 1260±60 1.11±0.09 0.054±0.008
Cu10Ni-A
60
12±1 260±30 1110±70 1.1±0.1 0.044±0.007
Cu10Ni-B 11±1 150±20 1120±70 1.1±0.1 0.039±0.006
Table 4. Stacking fault energies, average microstructural parameters, mechanical
properties, and measured strain rate sensitivities (nanoindentation) of fully NT Cu6Al,
Cu2Al, and Cu10Ni samples

In addition, top surface EBSD was performed to identify differences in material texture.
Figure 32 displays representative cross-sectional TEM images, grain width distributions, and top
surface EBSD orientation maps for the largest grained sample for each composition (as shown in
Table 4).

62

Figure 32. Microstructural characterization images showing representative cross-sectional
TEM images and inset diffraction patterns where the white arrow indicates growth
direction (a-c), grain width distribution scaled proportional to average grain width (d-f),
and top surface EBSD grain orientation maps (g-i) of Cu-2wt%Al, Cu-6wt%Al, and Cu-
10wt%Ni samples. The color in the EBSD images corresponds to the orientation in the
growth direction according to the legend on the bottom. Black locations in EBSD indicate
poorly indexed regimes where the average grain confidence index is below 0.1.

All measured grains in TEM images were utilized to determine grain width distributions for the
six films; figures 32d through 32f depict typical distributions. All samples showed similar trends
100 nm
100 nm
100 nm
100 nm
100 nm
1 μm
100 nm
1 μm
100 nm
1 μm
100 nm
50 nm
(a) (b)
(c)
(d) (e)
(f)
(g) (h)
(i)
Cu6Al-A Cu2Al-A Cu10Ni-A
Cross Sectional
TEM Image
Grain Width
Distributions
Top Surface EBSD
Orientation Map
111
110 100
63

in the distributions except for Cu2Al-A (Figure 32e), where a higher percentage of large grain
widths were observed; roughly 11% of the grains were larger than 200% of the average,
compared to less than 1% in the other samples. Comparing TEM and EBSD images, the Cu6Al
and Cu2Al samples in the study showed similar microstructures where samples contain all
horizontally aligned twins and vertical columnar grains, and most of the grains have an
orientation close to (111) in the growth direction. In contrast, 5-15% of the grains in the Cu10Ni
films do not show a (111) texture.
In order to better understand the microstructure of the non-(111) regimes in the Cu10Ni films,
FIB liftout was performed to extract a lamella from the Cu10Ni-A film. Both transmission EBSD
(t-EBSD) and TEM were performed on the same section of this sample to characterize the
microstructure, displayed in Figure 33.
64

Figure 33. Cross sectional TEM image (a) and t-EBSD orientation map (b) of Cu10Ni-A.
Colors in the orientation map correspond to the crystal orientation in the growth direction,
analogous to Fig. 1. The top-right inset image highlights the representative microstructure
of non-111 oriented regimes, where twin boundaries tilted to the growth direction are
observed. The bottom-inset represents a typical SAED pattern

65

The t-EBSD orientation map is shown in Figure 33a, where the colors indicate the orientation of
the grains in the growth direction, analogous to Figure 32. Note that the spatial resolution of t-
EBSD does not allow for twins to be resolved, which is compensated for by the TEM image in
Figure 33b where the nanotwinned microstructure can be observed. As can be seen in the t-
EBSD image in Figure 33a, there are multiple columnar grains which are not (111) oriented and
correlate to the top surface EBSD map of Cu10Ni-A in Figure 32. Higher magnification TEM
images, such as the inset in Figure 33b, indicate that there are twin boundaries which are tilted to
the growth direction in the regimes that are not (111) oriented. This highlights a clear difference
in the alloys investigated in this study, as tilted boundaries are only observed in the Cu10Ni
samples.
5.2 Tensile Behavior
Tensile tests were carried out using free standing films which were mechanically polished into
multiple dogbones with geometries based on ASTM E345-93 with reduced sections of roughly
0.8x3.2 mm. Three tests were carried out on each film following procedures outlined elsewhere
[113]. Representative stress-strain curves are shown for the Cu6Al (Figure 34a), Cu2Al (Figure
34b) and Cu10Ni (Figure 34c) films, where the behavior for large and small grain width is
compared for the various alloys.

66

Figure 34. Stress-strain curves comparing the impact of grain width on the mechanical
behavior for NT Cu-6wt%Al (a), Cu-2wt%Al (b), and Cu-10wt%Ni (c). Representative
SEM micrographs of fracture surfaces are shown for Cu6Al (d), Cu2Al (e), and Cu10Ni (f)
samples.

The average 0.2% offset yield strengths as well as ratios of tensile to yield strength can be found
in Table 4. Representative SEM images of the fracture surfaces for each alloy are shown in
Figure 34 (d-e), where all samples displayed microvoid coalescence as a fracture mechanism.
Note that DIC was performed on each film during the tensile tests, where all samples displayed
localized shear band like behavior similar to what was observed previously [113].
As observed in Figure 34 (a-c), all of the alloys display similar strengths and relatively low
ductility despite the presence of tilted twin boundaries in the Cu10Ni samples. Previous
simulations have found that when twin boundaries are tilted to the loading direction in NT Cu,
the dominance of an ‘easy mode’ slip system can allow for higher ductility and lower strength
compared to twin boundaries which are orthogonal or parallel to the loading direction [71, 72,
123]. However, in NT Cu it has been shown that the twin thickness should be below 6 nm for
67

‘easy mode’ slip to be dominant for grain sizes below 250 nm [16, 124, 125]. Therefore, the lack
of improvement in ductility in the Cu10Ni samples may be due to having average twin
thicknesses around 12 nm.
The stress-strain curves in Figure 34 also indicate a clear difference in the response to varying
grain width for all samples. In Figure 34a and b, a comparable decrease of around 100 nm in
grain width corresponds to an increase in yield strength of more than 200 MPa for both Cu6Al
and Cu2Al, and a decrease in ductility (strain to failure) for Cu2Al. Note that the higher ductility
observed in Cu2Al-A may be related to the higher percentage of large grain widths (Figure 32e).
In addition, Cu2Al-A shows the highest strain hardening capacity of the studied materials (as
indicated by the tensile to yield strength ratio in Table 4), correlated with increased ductility in
nanostructured metals [126]. In contrast, there is no measureable difference in the tensile
behavior in Cu10Ni, shown in Figure 34c. This suggests that the response in mechanical
behavior of nanotwinned alloys to microstructural changes may vary depending on alloy content
which in turn determines the SFE.
5.3 Activation Volumes
The SFE is an important parameter since it affects the deformation mechanisms and behavior of
both coarse grained and nanocrystalline FCC metals [54, 58-60, 127]. While direct observation
of the active deformation mechanism requires in-situ testing, some information can be obtained
by measuring the activation volume, which is influenced by the rate controlling deformation
mechanism in a material [119]. A method for experimentally quantifying activation volume via
nanoindentation at varying loading rates has been identified by Lu et al [81], where the activation
volume, v*, is calculated utilizing equation 5.
68

Nanoindentation tests were performed on each sample with a total of 100 indents at a peak load
of 8mN with loading rates varying from 0.1 to 20 mN s
-1
in order to determine the activation
volume of each film. Representative curves showing the hardness as a function of loading rate
are found in Figure 35a and 35b, and calculated activation volumes are shown in Figure 35c,
where it is observed that all samples have activation volumes with values of 5-10b
3
(where b is
the burgers vector).

Figure 35. Hardness as a function of loading rate in nanoindentation with a peak load of 8
mN for Cu2Al-A (a) and Cu10Ni-A (b), utilized to estimate the activation volume, which is
shown for each sample in (c)

The samples do not show a significant difference in activation volume despite an order of
magnitude change in the SFE. This indicates that an overall change in deformation mechanism is
not responsible for the different response to grain width observed in the Cu10Ni compared to the
Cu2Al and Cu6Al samples, further supported by the similar fracture mechanisms observed in
SEM where all samples show a plastic fracture mechanism of microvoid coalescence. The
calculated activation volumes are similar to those reported for nanocrystalline and NT Cu (3-
69

20b
3
), where dislocation nucleation is believed to play a primary role in the material deformation
[81, 128]. The films with the highest activation volumes are Cu10Ni-A and Cu2Al-A with values
around 10b
3
. Both of these samples also have the largest grain width for their compositions,
indicating that grain width can influence the activation volume, similar to grain size in
nanocrystalline metals [119, 127, 129].
The question still remains why there is a lack of response to grain width in the Cu10Ni samples
compared to Cu2Al and Cu6Al, despite there being no apparent difference in the deformation
mechanism. It is possible that the answer is related to a transition that occurs in nanotwinned
metals when the twin thickness reaches a critical value (around 6 nm in NT Cu), above which
grain width does not significantly influence the material’s strength [16, 124]. Basically, the
transition indicates where the dislocations generate from; simulations have shown that below the
critical twin thickness, dislocation nucleation from twin boundary to twin boundary is suppressed
and dislocations primarily nucleate from grain boundaries [16, 72, 124]. A similar size-related
transition has been reported in nanocrystalline metals, where a higher SFE typically correlates
with a smaller transition grain size [119, 127, 129]. Since Cu10Ni has the largest SFE in this
study, it could have the smallest critical twin thickness. In this case, the grain width would have a
less significant impact in the strength of Cu10Ni samples and agrees with the observed
stress/strain curves presented in Figure 34c [16, 124].
5.4 Summary
In this study, the mechanical behavior of magnetron sputtered fully NT Cu6Al, Cu2Al, and
Cu10Ni films is analyzed. Tilted twin boundaries present in the Cu10Ni samples do not seem to
significantly introduce any ductility into the material when compared to CuAl samples. The
impact of grain width on the different samples varies by alloy content, where NT Cu2Al and
70

Cu6Al alloys show increasing strength with decreasing grain width, and no change is observed in
NT Cu10Ni. This dissimilarity in response to grain width does not appear to be due to an overall
change in the deformation mechanism, as all the materials tested have similar activation volumes
ranging from 5-10b
3
. The results from this study indicate that alloy content, correlated to the
SFE, is an important factor to consider in the design of NT alloys, as it can affect how
microstructure impacts the mechanical properties of the materials.

71

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72

Chapter 6. Fatigue Behavior of Nanotwinned Cu Alloys
In this section, the fatigue behavior of nanotwinned CuAl and CuNi alloys synthesized by
magnetron sputtering is investigated. To the author’s knowledge, no existing studies investigate
the fatigue behavior of fully nanotwinned alloys. This chapter aims to establish our
understanding of fully nanotwinned alloys behavior under cyclic loading through coupling of the
uniaxial fatigue behavior and the mechanisms that lead to fracture in the high cycle fatigue
regime (10
3
to 10
7
cycles). A wide range of Cu alloys including Cu-6wt%Al, Cu-2wt%Al, and
Cu-10wt%Ni were tested at various conditions. The microstructural changes after fatigue were
investigated to understand how the deformation mechanisms contribute to the fatigue properties.
Furthermore, the results from this study are compared to previous works for both nanotwinned
and nanocrystalline materials in order to highlight the role nanotwins play in the fatigue behavior
of nanoscale metals.
6.1 Microstructural and Tensile Behavior
12-18 µm thick free standing films were sputtered following procedures outlined by Velasco et
al. [14]. A total of four films were sputtered: one Cu-10wt%Ni sample, two Cu-2wt%Al samples
with both higher and lower strength, and one Cu-6wt%Al sample. These films will be referred to
as Cu10Ni, Cu2Al-HS, Cu2Al-LS, and Cu6Al respectively within this manuscript. Stacking fault
energies for these alloys are 6, 37, and 60 mJ-m
-2
respectively, spanning an order of magnitude
[54, 56, 58]. Thorough microstructural characterization was performed on each sample by TEM.
Cross-sectional TEM samples were prepared by mounting the materials in silicon, preparing 3
mm discs, dimple grinding, and then ion milling with a FISCHIONE Model 1050 ion mill with a
finishing accelerating voltage of 1 kV. TEM was then performed on each of the discs with a
JEOL 2100F TEM, utilizing a combination of bright field and dark field TEM at an accelerating
73

voltage of 200 kV. A minimum of 300 twins and 100 grains were measured for each film in
order to determine the average twin thickness and grain width as well as distributions. Errors in
the measured microstructural parameters were calculated as a combination of standard error from
averaging and the maximum expected error in TEM measurements.
From each film, a minimum of one dog bone sample was prepared in order to perform tensile
tests. The tensile behavior of some of the films (Cu6Al and Cu2Al-LS) had already been
characterized and discussed in a previous study [113]. Thin strips were cut from the films and
then mechanically polished in a die with a geometry proportional to ASTM E345-93 Type A
with a reduced section of 0.8x3.6 mm. Sample geometries were measured utilizing a
combination of optical microscopy (for sample widths) and SEM (for sample thicknesses) and
tensile tests were performed utilizing a custom made tensile tester. In tensile tests, optical digital
image correlation was utilized for strain measurements while a LC703-100 load cell was utilized
for load measurements. Tensile tests were performed at strain rates of roughly 10
-4
/s until
fracture, following procedures described elsewhere [113]. Errors in material strengths were
calculated from a combination of uncertainty in sample dimensions and maximum observed
deviations found in thorough testing of calibration samples and nanotwinned samples on this
tensile tester.
Figure 36 shows the microstructure, twin size distribution and tensile behavior of all the samples
used in this study.
74

Figure 36. Microstructural and tensile data for nanotwinned alloys investigated in this
study including cross-sectional TEM images of the different alloys (a), stress-strain curves
(b), and twin thickness distributions (c). Note the white arrow in TEM images indicates the
growth direction.

Figure 36a displays representative TEM images for the Cu alloys which showed a fully
nanotwinned columnar microstructure. The distribution of twin thicknesses can be seen in Figure
36b, where all the curves show typical distributions. Note some twin boundaries in Cu10Ni (on
75

the order of 5-15%) appeared tilted to the growth direction, which was not observed in any other
samples. This is potentially impactful, as previous studies on Cu bicrystals have revealed that
twin boundaries tilted to the loading direction are more prone to intergranular fracture [130,
131]. The geometries of these bicrystals are on the order of millimeters, however, so it is
uncertain how this translates to NT metals.
The tensile behavior of the different alloys is compared in Figure 36b, where stress-strain curves
of the films are shown. Samples display yield strengths between 0.83 and 1.28 GPa, ultimate
tensile strengths (UTS) between 1.05 and 1.53 GPa and all samples show relatively low ductility,
with strains-to-failure between 2 and 5%,consistent with previous studies on magnetron sputtered
columnar NT Cu alloys [113]. A summary of the average microstructural parameters, tensile
strengths, and stacking fault energy of the alloys in this study as well as columnar NT Cu in
previous fatigue studies is shown in Table 5.
Sample
SFE
[mJ m
-2
]
Twin Thickness
[nm]
Grain Width
[nm]
Tensile Strength
[GPa]
Cu6Al 6 8±1 90±10 1.53±0.08
Cu2Al-LS 37 6.2±0.7 180±20 1.05±0.07
Cu2Al-HS 37 4.4±0.5 120±10 1.20±0.07
Cu10Ni 60 5.4±0.7 130±20 1.28±0.08
NT Cu – Shute 45 35 500 0.57
NT Cu – Pan 45 78 6000 0.25
Table 5. Microstructural properties and yield strengths of nanotwinned materials
compared in fatigue.

The influence of the difference in microstructural parameters between the NT Cu Alloys and NT
Cu is considered in the analysis of the fatigue behavior of the NT alloys. It should also be noted
76

from Table 5 that the higher tensile strengths observed in the alloys are mostly due to the
reduced grain widths, which typically lead to high strength NT metals [113, 117, 125].
6.2 Fatigue Strength in Uniaxial Tension-Tension Fatigue
Fatigue samples were formed utilizing a similar preparation method to the tensile dogbones,
albeit with reduced sections of roughly 0.65x3.6 mm. Fatigue tests were carried out utilizing a
custom built uniaxial fatigue test setup, which is described in Section 3.4. Stress cycling was
performed with a piezoelectric actuator and load measurements were made with a load cell. All
fatigue tests were performed utilizing a 30 Hz sinusoidal wave with an R ratio (minimum to
maximum stress) of 0.1 (tension-tension fatigue). Tests were stopped either when the sample
completely fractured or when 5*10
6
cycles was reached. Proportional control was used to reach
the desired stress amplitude and mean load; this required a settling period of less than 400 cycles,
and no overshoot during initial loading was observed. Only cycles beyond the settling period
were considered for the number of cycles to failure. Optical images of the top surface of each
sample were captured both before and after the fatigue test in order to identify any potential test
anomalies. A total of 4 stress amplitudes between 210 and 370 MPa were utilized for the Cu2Al-
HD sample, while 2 stress amplitudes of 210 and 370 MPa were used for the remaining samples.
At least two tests were performed for each alloy at each load with the exception of Cu10Ni at
210MPa, where only one test was performed. Errors in applied loads were calculated from the
uncertainty of sample dimensions.
S-N curves (showing fatigue life at different stress amplitudes) in Figure 37 compare the fatigue
behavior for the NT alloys in this study to previous studies on NT Cu in the high cycle fatigue
range (10
3
to 10
7
cycles).
77

Figure 37. S-N curve comparing fatigue behavior of nanotwinned Cu alloys from this study
(squares) and NT Cu from other studies (circles). The inset graph displays a representative
time-stress plot obtained from the load cell for Cu2Al-LS at a stress amplitude of 210 MPa,
where the blue line indicates the mean stress and green lines indicate minimum and
maximum stress. [93, 95]

Where possible, a line of best fit (log-log) has been included to indicate the general trend for
each film. The inset graph shows recorded stress vs. time data from a fatigue test where it is
observed that a consistent sinusoidal stress was applied to each sample; note the maximum error
in mean stress and stress amplitude did not exceed 1% once the test load settled. As observed in
the S-N curves, the nanotwinned Cu alloy curves all lie above the Cu samples, achieving similar
cycles to fracture at higher loads. The behavior of the NT alloys is consistent with previous
78

studies where reduced twin thickness is expected to improve the fatigue resistance due to higher
material strengths [132-134].
Among the alloys tested, samples with higher tensile strengths do not always show improved
fatigue behavior. For example, as seen in Figure 37, NT Cu10Ni has a higher fatigue life than
Cu6Al at a stress amplitude of 370 MPa even though it has a UTS of 1.28 GPa compared to
Cu6Al which has a UTS of 1.53 GPa. In addition, Cu2Al-HS fractures at a lower number of
cycles to failure than Cu2Al-LS at stress amplitudes of 210 MPa and 370 MPa even though both
of these materials have the same composition and Cu2Al-HS has a higher tensile strength. These
results indicate that although UTS plays an important role, other factors such as composition and
microstructural parameters may influence fatigue behavior.
In Figure 38, S-N curves normalized by UTS compare NT Cu alloys, NT Cu, and UFG or NC Cu
alloys.
79

Figure 38. S-N curves of copper alloys with NT microstructures (squares and circles), UFG
and NC microstructures (triangles) and coarse grained microstructures (diamonds)
normalized by the UTS. The inset image displays a similar plot for UFG and NC Ni [95, 97,
99, 135, 136]

This allows for a better understanding of how the NT microstructure influences the fatigue
behavior since it removes the influence of differing strengths in the materials [100-102]. The
inset image displays the same chart for UFG and NC Ni in order to expand this analysis to other
available studies on nanoscale metals. Note the Gerber stress amplitude is used for each material
in order to remove the effects from differing mean stresses in each study [101, 102]. The curves
for CG, UFG, and NC Cu alloys all fall nearly on top of each other, near what appears to be an
80

upper limit on the fatigue behavior of copper alloys in the range of 10
4
to 10
7
cycles which is
represented by the equation:
(7)
where S is the stress amplitude, UTS is the engineering ultimate tensile strength, and N is the
number of cycles to fracture. The NT alloys in this study fall either in the same regime or below
the CG, UFG, and NC Cu alloys. This seems to indicate that while NT metals can improve
fatigue resistance through increased strength, the high percentage of twin boundaries does not
offer additional improvements to fatigue behavior compared to non-twinned grain boundaries.
This is in contrast to previous studies which suggest that NT structures should improve fatigue
resistance due to improved crack tip closure through detwinning [134].

6.3 Crack Growth and Propagation Mechanisms
Post-mortem morphological and microstructural analyses were performed on various samples
utilizing a combination of SEM and TEM. Both a Zeiss and JEOL 7001F SEM were utilized to
image the fracture surface morphologies at an accelerating voltage of 15 keV, although only
images from the JEOL 7001F are presented in this manuscript. The entire fracture surface was
imaged for one sample from each film at stress amplitudes of both 210 and 370 MPa. TEM was
carried out on three select samples at the fracture surface in order to investigate any changes in
microstructure during cyclic loading. TEM samples were prepared by FIB liftout, utilizing a
JEOL 4500 FIB at an accelerating voltage of 30 keV, where the fracture surfaces were covered
with a protective carbon layer prior to performing liftout in order to preserve the surface. A
  52 . 0 log 15 . 0 log
10 10
  






N
UTS
S
81

combination of bright field TEM and SAED were performed along and near to the fracture
surface in order to understand any changes in microstructure along the fracture surface.
Fracture surfaces observed from SEM are shown in Figure 39.

Figure 39. SEM images showing representative fracture surface of Cu10Ni sample, as
indicated by schematic on the left, loaded at 370 MPa that fractured at 7.28*10
5
cycles. A
low magnification image of the fracture surface (a) shows vertical columnar features at the
crack initiation site (b), a transition to microvoid coalescence (c), and microvoid
coalescence which is observed for the rest of the fracture surface (d)

Note that all tested samples showed similar fracture surfaces, despite microstructural parameters,
alloy content, or stress amplitude. Each film has exactly one region (ranging from 10-100
microns in length) resembling Figure 39b, where the fracture surface was characterized by
vertical columns with occasional breaks. The width of these columns range from roughly 100-
300 nm. Samples show a shift from smoother columns with less breaks to rougher columns with
more breaks, as can be seen in Figure 39a, with the smooth columns appearing near what seems
to be the crack initiation location. At the edge of the columnar fracture regime, each sample
shows a transition to microvoid coalescence, (Figure 39c) which continues for the rest of the
fracture surface as presented in Figure 39d. No fatigue striations or slip ledges were observed
anywhere on or near to the fracture surface.
Crack
Initiation
5 µm
20 µm (a)
5 µm 5 µm
(b) (c) (d)
Crack Propagation
82

Cross-sectional TEM was performed on the regime where columnar fracture was observed in
order to investigate microstructural changes that could be correlated with crack growth or
propagation. TEM was performed on a total of three samples: Cu10Ni at a stress amplitude of
370 MPa and Cu2Al-LS at stress amplitudes of both 370 MPa and 210 MPa to determine
whether alloy content or stress amplitude had any influence on the microstructural changes; the
samples all showed the same microstructural features. Representative TEM images in Figure 40
depict the various microstructures observed along the fracture surface, where both fully twinned
and de-twinned regimes were observed.

Figure 40. Cross sectional bright field TEM image at the fracture surface (represented by
dashed red line), where both fully twinned (a) and detwinned (b) regimes are observed.
Inset images show SAED patterns of the encircled areas.

This is somewhat similar to de-twinning seen in previous research on NT Cu performed by Shute
et al.[137], although the de-twinning in this study is more localized, typically no more than two
or three columnar grains wide (consistent with the column widths observed in SEM). Note that
100 nm 100 nm
(a) (b)
83

de-twinned regimes were observed both at and away from the fracture surfaces, which seems to
indicate that detwinning occurs before the crack.
Figure 41 displays a crack occurring between a twinned and de-twinned regime indicating that
intergranular cracking between these types of grains is a possible crack propagation mechanism.

Figure 41. Cross-sectional TEM image showing intergranular fracture observed near the
fracture edge where one side of the fracture shows a fully twinned microstructure and the
other side shows a fully de-twinned microstructure. This is further supported by SAED
patterns of encircled areas.

The mechanism appears to be a means by which the primary crack grows since both de-twinned
and twinned grains are observed along the primary crack (Figure 40). Please note that the TEM
samples for Figures 40 and 41 were taken from a region within Figure 39b, which is the crack
initiation site. This indicates that the intergranular fracture, represented by the vertical columnar
morphology in SEM, are linked to the initial crack formation. Intergranular fracture has not been
100 nm
84

previously observed in NT metals [138] or nanoscale alloys [139]. However, there are
microstructural differences between the samples used in this study and previous studies as shown
in Table 5. For example, grain widths vary from 90 to 180 nm in this study, compared to 500 to
6000 nm in NT Cu studies, while twin thicknesses vary from 4.4 to 8 nm in this study, compared
to 23 to 85 nm in NT Cu studies.
In order to better understand the fracture behavior in the NT alloys, one can look at more
traditional materials such as high strength steels, where the mechanisms for intergranular fracture
are well understood. Intergranular fracture in steels is the result of grain boundary embrittlement
which can be caused by accumulation of persistent slip bands (PSB’s) along the grain boundary,
segregation of ‘tramp’ elements to grain boundaries, or high temperatures [140-142]. In the NT
alloys in this study, however, no PSB’s were observed, segregation is not expected, and all tests
were carried out at room temperature. However, it is possible that grain boundary embrittlement
occurs due to damage from the accumulation of dislocations at grain boundaries [143, 144]
which can occur both during [145] and after [144] detwinning. Furthermore, the transition from
brittle intergranular fracture to ductile microvoid coalescence in Figure 39c is similar to a
mechanism shift observed in high strength steels, where a change from intergranular fracture to
ductile fracture can occur once the stress concentration exceeds 10-20 MPa-m
1/2
[142]. As the
crack grows in the NT alloys, the stress concentration is expected to increase [101, 102] which
could lead to the observed transition from brittle intergranular fracture to the more ductile
microvoid coalescence.
Although the deformation mechanisms are similar for all the NT alloys in this study, there is
some variation in the fatigue behavior shown in the S-N curves in Figure 37, which could be
influenced by the different microstructural parameters and SFE’s of the alloys. Previous studies
85

on the tensile behavior of NT metals may provide some insight as to how these parameters can
influence the mechanical properties. The tensile strengths, ductility, and deformation
mechanisms of NT Cu have been shown to depend on both twin thickness and grain size, where
a transition twin thickness decreases with decreasing grain size [16, 117, 125]. In addition, some
simulated results on NT Cu indicate that as the SFE of the material decreases, there is a change
in preferential deformation mechanism from partial dislocation driven deformation with low twin
boundary mobility to full dislocation driven deformation with high twin boundary mobility
[146]. Furthermore, it has been found that in NT metals, forces acting on dislocations for
detwinning to occur are correlated to the SFE of the material [145]. To what extent these
parameters influence the fatigue behavior is currently unknown and further research is necessary
to quantify these effects.
6.4 Fatigue Mechanisms Compared: NT, NC, and UFG Cu Alloys
Due to the limited fatigue data available for nanoscale microstructures, a comparison of the
fatigue mechanisms observed in the NT Cu alloys to those of UFG, NC, and NT microstructures
could provide some new insights. Table 6 presents such a comparison with the goal of
understanding the role of the NT microstructure and its influence in the fatigue behavior.
86

Table 6. Summary of various fatigue studies on UFG, NC, or NT Cu or Cu alloy systems
comparing microstructural properties, observed microstructural changes, surface
morphologies, and fracture surface morphologies [95, 97, 99, 135]

Different types of microstructures as well as different twin thicknesses or grain sizes are
considered in this analysis. Note that in all of these studies uniaxial fatigue tests were performed
on the material(s) investigated.
By comparing the NT metals in Table 6, shifts in fatigue mechanisms are observed with varying
twin thickness. At the largest twin thickness of 78 nm in NT Cu (Pan et al), PSB’s were observed
to play a primary role in the cyclic deformation. As the twin thickness decreases to 35 nm in NT
Cu (Shute et al), detwinning becomes a dominant fatigue mechanism. At the smallest twin
thicknesses of 4-11 nm, (this study) more localized detwinning occurs and brittle, intergranular
crack initiation and propagation is the fracture mechanism. Based on these observations, there
MATERIAL
TWIN
THICKNESS
[nm]
GRAIN
WIDTH
[nm]
GRAIN
SIZE
[nm]
MICROSTRUCTURAL
CHANGES
SURFACE
MORPHOLOGIES
FRACTURE
SURFACE
NT Cu10Ni
NT Cu2Al-HS/LS
NT Cu6Al
4-11 90-180 -
• Some detwinned grains near
fracture surface
• No observed
extrusions or surface
shifts
• Intergranular fracture
at crack origin
• Transition to
microvoid coalescence
NT Cu [ref a] 35 500 -
• Twin growth
• Some detwinning
• Dislocation structures in
detwinned regimes
• Surface shifts at
detwinned regimes
-
NT Cu [ref b] 78 6000 -
• Formation of twin ‘blocks’
inside of columnar grains
• Dislocation arrays within
twins
• ‘Zig-zag’ PSB-like
extrusions along surface
• ‘Zig-zag’ slip
morphologies across
columnar grains
UFG Cu [ref c] - - 200
• Grain growth
• Formation of dislocation cells
• PSB-like extrusions -
NC Cu-5at%Al [ref
c]
- - 100
• Grain growth
• Formation of dislocation cells
• PSB-like extrusions -
NC Cu-11at%Al
[ref c]
- - 70
• No observable changes in
microstructure
• PSB-like extrusions -
NC Cu [ref d] - - 18-23 • Grain growth • PSB-like extrusions -

87

are at least two transitions in mechanisms in NT metals in fatigue. One transition occurs in the
range of 80 to 30 nm twin thickness, where there is a shift from PSB controlled deformation to
detwinning controlled deformation. Another transition occurs in the range of 30 to 10 nm twin
thickness where the fracture initiation mechanism shifts to intergranular fracture. Note that each
of these transitions could also depend on the grain width, since smaller grain widths tends to
correspond to smaller twin thickness.
In order to better elucidate the role of grain size and understand the effect that twin boundaries
have on the fatigue behavior, NT metals (5-78 nm twin thickness) are compared to both UFG
and NC metals (20 to 270 nm grain size). Both Figure 38 and Table 6 are considered for this
analysis. Overall, the S-N curves (Fig 3) seemed to indicate that the fatigue strengths are
dependent on the fatigue mechanism. For example, for the UFG Cu alloys, NC Cu alloys, and
NT Cu with 78 nm twins [135] all the curves fall close to the apparent upper limit on Cu alloys,
and all of these materials showed PSB controlled fatigue (Table 6). In contrast, NT Cu with 35
nm twin thickness [137] and the NT alloys in this study tend to fall below this upper limit; these
materials displayed detwinning as a primary deformation mechanism. Grain size and twin
thickness appear to have different influence on the fatigue strength’s dependence on tensile
strength. Unlike grain size in NC metals which is not correlated with any shift in fatigue
mechanism, decreasing twin thickness in NT metals leads to a transition in fracture mechanism.
6.5 Summary
Sputtered fully nanotwinned Cu-6wt%Al, Cu-2wt%Al, and Cu-10wt%Ni films in this study
show improved fatigue behavior in the high cycle regime (10
3
to 10
7
cycles) compared to
previous studies on NT Cu. Intergranular fracture caused by localized detwinning was observed
as a means for crack initiation and propagation in the nanotwinned alloys which differs from
88

previously observed mechanisms in nanotwinned copper or nanocrystalline materials. A
comparison to previous fatigue studies on nanotwinned metals reveals multiple transitions that
occur with decreasing twin thickness: between 30 and 80 nm there is a transition from persistent
slip band controlled deformation to detwinning controlled deformation, and between 30 and 10
nm there is a transition to intergranular fracture.
Comparing nanotwinned copper alloys to ultrafine-grained and nanocrystalline materials reveals
that the fatigue strength’s dependence on tensile strength in these different materials appears to
be correlated with the active fatigue mechanisms. S-N curves normalized by tensile strength for
different microstructures revealed that there were two regimes. In the upper regime, PSB
controlled deformation plays a dominant role, while nanotwinned metals where detwinning is the
fatigue mechanism tend to fall below this. The results presented highlight changes in the fatigue
mechanism due to the influence of nanotwins which provides a better understanding of fatigue at
the nanoscale and can be used as a guide for future materials design.

89

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90

Chapter 7. Conclusions and Future Work
In summary, the tensile and fatigue behavior of fully nanotwinned metallic alloys has been
explored. Bulk properties of these materials were investigated through mechanical testing of 15-
25 micron thick films, with sample geometries on the order of millimeters. By independently
varying the twin thickness, grain width, and alloy content, the contribution from each of these
parameters to the mechanical behavior is understood. In addition, exploration of the deformation
behavior allowed for a deeper understanding of how different mechanisms contribute to material
properties.
Tensile tests were performed on fully nanotwinned CuAl and CuNi films with varying twin
microstructure and alloy content. Samples were compared by systematically varying a single
material parameter in order to understand the influence of each parameter. With varying twin
thickness, different behaviors were observed depending on alloy content and microstructure. In
Cu-2wt%Al, with larger grain widths (170-180nm), decreasing twin thickness was correlated
with decreased strength and increased ductility. In Cu-6wt%Al, with smaller grain widths (80-
100 nm), twin thickness did not influence the tensile properties.
The influence of alloy content was investigated by comparing Cu-2wt%Al and Cu-6wt%Al
samples with similar microstructures. As the Al content increased, an increase in strength was
observed. This increase in strength was higher than was expected just considering solid solution
strengthening. It is believed that this is correlated to a decreasing stacking fault energy in the
materials, leading to an increase in the energy barrier for dislocation nucleation (typically
observed to be the deformation mechanism in nanotwinned metals at these twin thicknesses).
91

The influence of grain width on tensile properties was compared for Cu-6wt%Al, Cu-2wt%Al,
and Cu-10wt%Ni samples. Different impacts on strength were observed for these different
materials. In both Cu-6wt%Al and Cu-2wt%Al, decreasing grain width was correlated with
increasing strength. However, no change in tensile behavior was observed in Cu-10wt%Ni.
Activation volumes of the materials were determined via nanoindentation at varying loading
rates to identify any differences in the rate-controlling deformation mechanism. However, all
samples showed similar activation volumes (with values consistent with dislocation nucleation),
indicating a similarity in the deformation mechanism in each material. It is possible, however,
that there are differences in where dislocations nucleate from which could influence the effect
grain width has on the tensile behavior in the different alloys; direct observation of the
deformation mechanism (for example by in-situ deformation in TEM) is required to validate this.
In addition to Cu alloys, some ongoing research is being performed to investigate the tensile
behavior of nanotwinned INCONEL 600, a Ni based superalloy; this work is summarized in
Appendix 1. The as-sputtered microstructure is fully twinned with an average twin thickness of 4
nm and average grain width of 100 nm. As with the Cu alloys with similar microstructures, the
as-sputtered structure shows high strengths (2.5 GPa tensile strength) and limited ductility. Heat
treatments up to 800°C were performed to tune the material microstructure and mechanical
properties. At temperatures at and above 600°C, an evolution to a partially twinned structure as
well as texture change (from (111) randomly oriented) was correlated with decrease strength and
increase ductility. Further research is being performed to characterize the microstructures at each
heat treatment temperature in order to understand how the microstructures correlates with tensile
behavior.
92

The fatigue behavior of nanotwinned CuNi and CuAl alloys in the high cycle regime (10
3
to 10
7

cycles) was investigated by uniaxial stress-controlled fatigue. The nanotwinned alloys displayed
higher fatigue strengths than previously studied nanotwinned Cu. However, it should be noted
that the alloys also had higher tensile strengths, which tends to correlate with increase fatigue
strengths. In order to remove the influence of tensile strength, fatigue strengths were normalized
by tensile strengths. Comparisons were also made to coarse grained, ultrafine grained, and
nanocrystalline Cu alloys to understand the influence that tensile strength has on the properties.
In general, it was observed that the nanotwinned alloys showed lower normalized fatigue
strengths compared to the materials without nanotwinned microstructures. Fatigue mechanisms
were analyzed to determine how the alloys’ deformation behavior might contribute to the fatigue
strengths.
Post-mortem analysis of the fatigued nanotwinned alloys revealed a deformation mechanism that
has not been previously observed. Specifically, localized detwinning was observed which led to
intergranular cracking between fully detwinned and fully twinned columnar grains. Comparing
normalized fatigue strengths to fatigue mechanism in nc, NT, and UFG CU alloys, it was
observed that materials displaying slip-band like behavior tended to have higher relative fatigue
strengths than materials that displayed detwinning as a mechanism. Detwinning, therefore,
appears to offer a relatively easier means for fatigue deformation to occur. This mechanism
appears to be microstructure-dependent, however, as previous studies on NT Cu with larger
microstructural parameters (78 nm twin thickness, 6 µm grain width) display slip-band like
behavior while the alloys in this study (4-11 nm twin thickness, 90-180 grain width) and
previous studies on NT Cu with smaller microstructural parameters (35 nm twin thickness, 500
nm grain width) display detwinning-controlled mechanisms. The influence that microstructure
93

and SFE have on the detwinning behavior is not well understood, however, and a better
understanding of this could provide further insight as to how microstructure influences the
deformation mechanism and why different alloys in this study displayed different fatigue
behavior compared to each other.
Several questions remain in this study, primarily as to why different responses to microstructure
and alloy composition are observed in tensile and fatigue behavior. Direct observation of the
deformation mechanisms would provide further insight. Specifically, techniques such as in-situ
indentation or tensile testing could indicate whether dislocation nucleation is indeed the
deformation mechanism and where the dislocation nucleation site is in the different materials. As
suggested by previous simulations on nanotwinned Cu, this could influence how the tensile
behavior changes with microstructure which could provide an explanation as to why different
nanotwinned alloys respond differently to microstructural changes, as was observed in this study.
A deeper understanding of the mechanism for detwinning in fatigue may provide clearer insight
as to the fatigue strengths in nanotwinned alloys. Specifically, generating a model to understand
how twin thickness, grain width, and stacking fault energy influence detwinning would provide a
deeper understanding of the observed fatigue properties. While the detwinning behavior in
nanotwinned metals has been modeled to an extent, these models are limited in that the slip
systems cannot occur in the case of columnar nanotwinned metals (due to there being no shear
stress acting on the active slip systems). Therefore, models would need to address both how the
detwinning occurs, and how a cyclic load affects this behavior. By doing this, it could be
understood when detwinning is preferred to slip-band like deformation in fatigue, and give
insight as to how microstructural parameters and alloy content in nanotwinned metals influence
the fatigue properties.
94

This study has enhanced the understanding of the tensile and fatigue properties of nanotwinned
alloys. An analysis of the nanoscale deformation mechanism in the materials lends to a deeper
understanding of why the nanotwinned alloys have some of the mechanical properties observed.
In general, nanotwinned alloys are potential alternatives to nanocrystalline alloys, with improved
thermal stability and corrosion resistance (while maintaining the high strength offered by metals
with nanoscale microstructural features). The results from this study as well as continuing
research investigating the mechanical behavior of nanotwinned alloys will allow scientists and
engineers to develop and tune the properties of these materials for advanced engineering
applications.

95

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102

Appendix A: Nanotwinned Inconel 600
NT Inconel 600 films were sputtered with parameters similar to that of the NT CuNi and CuAl
alloys in Chapters 4-6. Samples with thicknesses of approximately 25 µm were sputtered
utilizing an Inconel 600 target onto 25 mm glass substrates, with the same sputtering parameters
for all films. In order to produce free standing films, the substrates containing films were
submerged in an HF solution for approximately 2 minutes, where the HF solution completely
dissolved the glass substrate. Films were removed from the HF solution, cleaned, and inspected
in an optical microscope; no pitting, discoloration, or corrosion damage was observed on the
films.
TEM samples of the free-standing films were produced and then TEM images were acquired
using the method described in Section 3.1.2. In Figure 42, cross-sectional TEM images of the
Inconel 600 films are shown.

Figure 42. As sputtered microstructure of nanotwinned INCONEL 600 revealing fully
twinned structure with twin thickness of approximately 4 nm and grain width of
approximately 100 nm

Growth Direction
20 nm 200 nm
103

TEM images revealed a fully twinned structure with an average twin thickness of roughly 4 nm
and an average grain width of approximately 100 nm.
As-sputtered films were prepared into 3 x 12 mm strips. Heat treatments were then performed on
the different strips inside of a Vacuum furnace. For each heat treatment, the sample was heated at
a rate of 10°C/min. until the desired heat treatment temperature, left at that temperature for an
hour, and then allowed to naturally cool inside of the oven, as displayed below in Figure 43

Figure 43. Schematic temperature vs time curve showing the heat treatment steps
performed on NT Inconel samples in vacuum.

In this section, the samples are labeled as follows: the as-sputtered film is called ‘As Sputtered
NT Inconel 600’ while the heat treated films are called ‘NT Inconel – XX’ where XX represents
the heat treatment temperature of the film. The mechanical behavior of these films was also
compared to standard Inconel films purchased from Goodfellow Corporation, both of which have
sample thicknesses of 25 µm. Both an annealed (part number NI020202) and hard (part number
NI020201) sample were compared for Inconel .
Room
Temperature
Heating rate
10 C/min
Heat Treatment
Temperature
1 Hour
Natural
cooling
Time
Temperature
104

Vickers hardness tests were performed on the as-sputtered, heat treated, and Goodfellow films. A
load of 25g was used for the indents, with a dwell time of 10 seconds. Images of indents were
captured with an optical camera, and measurements of the indents were performed using these
images. The calculated hardness of the different samples is shown in Table 7

Table 7. Vickers hardness of as-sputtered, heat treated, and commercially purchased
Inconel 600

Tensile tests were performed on films using the custom-built microtensile tester described in
Section 3.2. Films were polished into the sample geometry shown in Figure 24, and then tensile
tests were carried out with strain rates of 10
-4
s
-1
. Engineering stress-strain curves for the films
are displayed in Figure 44.
Sample Hardness
As Sputtered NT Inconel 600 7.6 GPa
NT Inconel - 200°C 7.5 GPa
NT Inconel - 400°C 6.7 GPa
NT Inconel - 600°C 4.9 GPa
NT Inconel - 800°C 3.2 GPa
Hardened Inconel (Goodfellow) 3.1 GPa
Annealed Inconel (Goodfellow) 1.3 GPa
105

Figure 44. Tensile behavior of as-sputtered, heat treated, and commercially purchased
Inconel 600

In order to identify the microstructural changes in the material at elevated temperatures, both
EBSD and FIB were utilized. EBSD was performed on the top surface of the film, which was
polished with a Fischione 1050 ion mill with a 1 kV accelerating voltage for 2 minutes to
produce uniform and flat surfaces. EBSD was performed with a JEOL 7001F SEM at an
accelerating voltage of 15 kV, as described in Section 3.1.3.
Cross-sectional FIB imaging was performed with a JEOL JIB 4500 FIB, as described in Section
3.1.1. EBSD and FIB of the as-sputtered sample, and samples heat treated at 600°C and 800°C
are shown in Figure 45.
0
500
1000
1500
2000
2500
3000
0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 0.22 0.24
σ (MPa)
ε (mm/mm)
As Sputtered NT Inconel
NT Inconel - 200 C
NT Inconel - 400 C
NT Inconel - 600 C
NT Inconel - 800 C
Hardened Inconel (Goodfellow)
Annealed Inconel (Goodfellow)
0
500
1000
1500
2000
2500
3000
0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 0.22 0.24
σ (MPa)
ε (mm/mm)
As Sputtered NT Inconel
NT Inconel - 200 C
NT Inconel - 400 C
NT Inconel - 600 C
NT Inconel - 800 C
Hardened Inconel (Goodfellow)
Annealed Inconel (Goodfellow)
106

Figure 45. Top surface EBSD and cross-sectional FIB showing microstructural changes in
nanotwinned Inconel after sputtering and after being heat treated above 600°C

Note that the scale bars in the EBSD images change with increasing temperature, as the grain
sizes were observed to increase at higher temperatures. The colors in the EBSD images represent
the grain orientation in the growth direction, where the as-sputtered films and sample heat treated
at 600°C showed a (111) texture, and a more random texture was observed for the sample heat
treated at 800°C. In the FIB images, a change in the percentage of twinned grains was observed
as a function of temperature, where the as-sputtered sample displayed a fully twinned structure
and films at 600°C and 800°C displayed a partially twinned structure.

As-Sputtered 600 C 1 hr 800 C 1 hr
1 µm 1 µm 1 µm
500 nm 1 µm 4 µm
111
110 100
107

Appendix B: Digital Image Correlation Data Processing
After a tensile test was completed, localized deformation analysis was performed using DIC
software on MATLAB developed by Chris Eberl (available for download at
https://www.mathworks.com/matlabcentral/fileexchange/12413-digital-image-correlation-and-
tracking). This software maximizes the correlation coefficient of sub-regimes of images taken at
different times during the tensile test to track how different points on the sample surface move
throughout the test. This appendix describes how the digital image correlation data was obtained
and how poorly tracked points were removed from analysis.
Digital image correlation was performed on a gauge section of roughly 0.8 x 3.2 mm using the
‘jobskript.m’ script. A rectangular array was used with a 10 pixel spacing between the tracked
points, indicated by where the blue lines cross in Figure 46.

Figure 46. Tracked points on a NT Cu-6wt%Al tensile sample indicated by crossing blue
lines. The tracked points are spaced 10 pixels with a rectangular array.

The software determines how these points (roughly 5000 for each sample) move for each image;
the data obtained from this will be referred to as ‘raw data’. DIC tracking was performed on each
sample up to one image prior to sample fracture.
1 mm
108

Analysis of the raw data was performed utilizing the ‘displacement.m’ script. This software
allows for analysis and removal of points that don’t track well as well as data output. Initial
analysis of poorly tracked points was made using the ‘Delete markers from displacement vs.
position plot’ option, displaying the displacement of each point in the loading direction (for the
final image prior to fracture) as shown in Figure 47.

Figure 47. Displacement of tracked points in the loading direction vs position for the NT
Cu-6wt%Al film shown in Figure 46

In all of the samples analyzed in this study, the plots looked similar to Figure 47, where all of the
points fall roughly within this smooth curve. However, this check is critical to perform, as any
points that stop tracking during a test will fall below this regime, and should be removed from
DIC analysis by selecting these points during this step.
The next step in removing poorly tracked points is to remove points that ‘jump’ during analysis,
where the points constantly shift between potential locations. These points are identified and
109

removed utilizing the ‘Delete points moving relative to their neighbors’ option in
‘Displacement.m’; this finds the motion of every point relative to its neighbor (both in loading
and transverse direction) which is shown in Figure 48. Note that shifting between the loading and
transverse direction is achieved with the ‘Rotate Orientation (exchange x and y)’ option.

Figure 48. Motion of all tracked points for the raw data relative to their neighbors as a
function of image number in the loading (left) and transverse (right) direction for the NT
Cu-6wt%Al film shown in Figure 46

Points that move more than 0.1 pixels are removed. Data after this point is referred to as ‘cleaned
data’. The relative motion of points for the ‘cleaned data’ is shown in Figure 49.
110

Figure 49. Motion of all tracked points for the cleaned data relative to their neighbors as a
function of image number in the loading (left) and transverse (right) direction for the NT
Cu-6wt%Al film shown in Figure 46

At this point, points with poor tracking have been removed, and localized and average strain data
can be extracted from the DIC data. In the ‘displacement.m’ script, localized strain data is
obtained from the ‘Full Strain Plots’ option, which displays displacement and strain maps.
Average strain data is obtained from the ‘1D Average Strain Measurement’ option, which
displays (and can output) true strain data. Example outputs are shown in Figure 50.
111

Figure 50. Examples of output data obtained from ‘displacement.m’. Displacement and
strain maps (a) are obtained from the ‘Full Strain Plots’ option while average true strain
data (b) is obtained from the ‘1D Average Strain Measurement’ option

Data analysis for both the localized strain behavior and strain component of the stress-strain
curves (converted to engineering strain) are obtained from these outputs.

a) b)

Abstract (if available)

Abstract Nanotwinned metals have been of much research interest in recent times, largely due to their potential for improved thermal stability, corrosion resistance, and ductility as compared to nanocrystalline metals. Most studies investigating the mechanical behavior of nanotwinned metals have focused on single element systems, specifically Cu and Ag. By introducing a nanotwinned microstructure to metallic alloys, the potential engineering applications of these materials can be expanded. In this study, the tensile and fatigue behavior of fully nanotwinned alloys synthesized by magnetron sputtering are investigated to understand the influence of microstructure and composition on their mechanical behavior. Furthermore, mechanical properties and deformation behavior are evaluated to understand how the deformation mechanisms correlate with the material strengths. Nanotwinned CuNi and CuAl alloys, with stacking fault energies ranging from 6 to 60 mJ/m2, twin thicknesses ranging from 4 to 18 nm, and grain widths ranging from 80 to 260 nm are evaluated. ❧ Tensile behavior of these materials is assessed utilizing a custom designed and built microtensile tester. The testing setup incorporates digital image correlation, which allows for the observation of local macroscopic deformation behavior. The yield strength of these materials range from 0.8 to 1.5 GPa and exhibit limited ductility. Correlations between the materials’ strength and average twin thickness/grain width reveal that separate alloys respond differently to microstructural changes. From digital image correlation, all samples show localized deformation regimes prior to fracture, with varying degrees of localized strains. The activation volume, which is correlated with the rate-controlling deformation mechanism, is explored through variable loading rate nanoindentation. The materials had values around 10b3, consistent with a rate-controlling deformation mechanism of dislocation nucleation. This indicates that differences in tensile properties of the alloys are not correlated with a change in the rate-controlling deformation mechanism. ❧ Fatigue behavior of the nanotwinned alloys in the high-cycle regime (103 to 107 cycles) are assessed by performing uniaxial stress-controlled fatigue tests with stress amplitudes ranging from 210 to 370 MPa. Nanotwinned alloys show improved fatigue strengths compared to previously studied nanotwinned Cu. Fatigue strengths normalized by tensile strength reveal how the tensile properties of nanotwinned Cu alloys influence the fatigue properties, where the normalized fatigue strengths of the nanotwinned alloys falls below that of coarse grained, ultrafine-grained, and nanocrystalline Cu alloys. The deformation behavior is explored through post-mortem microstructural characterization. The nanotwinned Cu alloys reveal a newly observed fatigue mechanism, where localized detwinning leads to intergranular fracture. The correlation between fatigue strength and tensile strength depends on the fatigue mechanism which varies with different microstructures. Overall, this study expands the comprehension of the mechanical behavior of nanotwinned alloys through an understanding of how the nanoscale deformation phenomena contribute to the material properties.

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Creator Heckman, Nathan Michael (author)

Core Title Mechanical behavior and deformation of nanotwinned metallic alloys

School Viterbi School of Engineering

Degree Doctor of Philosophy

Degree Program Mechanical Engineering

Publication Date 07/07/2017

Defense Date 05/16/2017

Publisher University of Southern California (original), University of Southern California. Libraries (digital)

Tag alloys,fatigue,mechanical properties,Metals,nanotwin,OAI-PMH Harvest

Language English

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Advisor Hodge, Andrea (committee chair), Bermejo-Moreno, Ivan (committee member), Grunenfelder, Lessa (committee member), Kassner, Michael (committee member)

Creator Email heckman.nathan@gmail.com,nheckman@usc.edu

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