Elimination or Significant Reduction of the Effects of Stress Concentrators by Nanosizing Collaborators: P. Deymier, MSE, Univ. of Arizona E. Enikov, AME, Univ. of Arizona C. Haynie, CEEM, Univ. of Arizona tral Theme: When spatial dimensions are below a material specific one, which most likely is in the nanometer r stress concentrators become insignificant. ecular Dynamics results and design of experiments
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Elimination or Significant Reduction of the Effects of Stress Concentrators by Nanosizing Collaborators: P. Deymier, MSE, Univ. of Arizona E. Enikov, AME,
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Elimination or Significant Reduction of the Effects of StressConcentrators by Nanosizing
Collaborators:P. Deymier, MSE, Univ. of ArizonaE. Enikov, AME, Univ. of ArizonaC. Haynie, CEEM, Univ. of Arizona
Central Theme: When spatial dimensions are below a material specific one, which most likely is in the nanometer range, stress concentrators become insignificant.
Molecular Dynamics results and design of experiments
10,000 layers of alternating metal/polymer.Each layer is 20-30nm thick. Courtesy: Sigma Tech. Intl., Inc.
Components with Nanodimensional Structure
Technologies presently exist, and are becoming more efficient, in producing components of nanodimenions (nanolaminates, nanoflakes, nanofibers, comb, etc.)
Nano-composite for energetic pigmentapplications. Courtesy: Sigma Tech. Intl., Inc.
One Potential Important Future application: Hydrogen storage by adsorption, where intentional surfaces, pores …(STRESS CONCENTRATORS) increase the surface area.
Future Technologies
The mechanical integrity is paramount, and insensitivity to defects is a reliability design dream come true – stress concentrators are ubiquitous
Nature Knows
Courtesy: Gao et al, 2003, Proc.Nat. Acad. Sci.
The basic building components in many biological materials remarkable for their properties are at the nanoscale (mineral/organic).
Why the Nanoscale ??
Stress Concentrators
Nano stress concentrators (NSCs) here indicate defects such as impurities, inclusions, cracks, pores;
defects other than NSCs, e.g. dislocations, are also addressed yet they are considered part of the “bulk” material
Examples: from roughness of substrate, impurities, pores, inclusions
In biological materials NSCs are trapped proteins within mineral crystals during biomineralization. Consistency in these materials is remarkable.
σ
σ h
1.0
h
/f th
Griffith criterion for a cracked crystal
Theoretical strength for a perfect crystal
(a) (b)
Crack
hcr
Size Effects – Since Galileo Galilei and Leonardo da Vinci
/f a E h
Considering for a brittle material:1J/m2, E=100GPa, th=E/30] and
we obtain hcr = 30nm
Note on Hall-Petch effects
Yield strength of electroplated Cu thin films as a functionof film thickness t. In the plot of these nanoindentationexperimental results, sizing to ~200nm, the yield stresswas assumed as the 1/3 of the hardness. Courtesy of Volinsky and Gerberich, 2003, Microel. Engr. Journal.
Size Effects: Well Studied
Insensitivity to NSCs has not been speculated,Plus difficulties in studying (experimental and simulation)
Koehler, 1970: a structure comprised of alternating layersof two suitable metals exhibits a resistance to plastic deformationthat would be greater than that expected from a homogenous alloyof the two.
Below Certain Nanoscales: More than Size Effects
Strength
Thickness
NSC
dia
met
er
Strength
Thickness
NSC
dia
met
er
Expected Behavior – Insensitivity to Defects
For NSC diameter = ½ thickness hcr
Side views
strain
stre
ss (
Pa)
0.025 0.05 0.075 0.1 0.125 0.15
1109
2109
3109
4109
5109
3D views
MD Simulations (EAM) – Cu Crystal with a NSC Pulled in (001)
Over 2,000,000 atoms
Many slip planes
High strain rate
Non periodic BC
side views
0.025 0.05 0.075 0.1 0.125 0.15
-1109
1109
2109
3109
4109
5109
strain
Stre
ss (
Pa)
3Dviews
MD Simulations (EAM) – Cu Crystal w/o NSC Pulled in (001)
Over 2,000,000 atoms
Two slip planes
High strain rate
Non Periodic BC
(111) slip planes form
0.025 0.05 0.075 0.1 0.125 0.15-1109
1109
2109
3109
4109
5109
0.025 0.05 0.075 0.1 0.125 0.15
-1109
1109
2109
3109
4109
5109
strainstrain
stre
ss (
Pa)
stre
ss (
Pa)
(a) (b)small systemwith NSC
large system with same NSC
large system,no NSC
small system, no NSC
Insensitivity to the NSCs
Large system: 28.88x28.88x28.88 nm3 (over 2,000,000 atoms) 3.0x3.0x0.4 nm3 NSC
Small system: 18.05x18.05x18.05 nm3 (~ 500,000 atoms) 3.0x3.0x0.4 nm3 NSC
0.06 0.08 0.1 0.12 0.14 0.16
2500
5000
7500
10000
12500
15000
strain
N
without NSC
with NSC
Why the Insensitivity ?
Total number of atomistic defects, N, versus strain for the small Cu(001) system with and without NSC. Plot was obtained from atom positions at five strain levels during deformation.Role of Surfaces: ratio surface/volume ~ 1/a important for small a
If, on average, the energy required for
forming each atomistic defect is constant,
this explains insensitivity of the material to NSCs
With NSC
Without NSC
External surfaces start dominating as atomistic defect initiation sites
Surfaces – large system, high strain rate, non periodic BC
With NSC
Without NSC
External surfaces start dominating as atomistic defect initiation sites
Surfaces, small system, high strain rate, non periodic BC
With NSC, side views
Loaded surfaces start dominating as atomistic defect initiation sitesfor two large (infinite) lateral dimensions (periodic BC). NSCsstimulate the clustering of atomistic defects.
Surfaces, small system, high strain rate, periodic BC
Without NSC, side views
Slower Strain Rates – Non Periodic BC
Large System Small System
Number of Atomistic Defects Versus Strain,(one realization, even though process is statistical)
0.06 0.08 0.1 0.12 0.14
5000
10000
15000
20000
25000
0.04 0.06 0.08 0.1 0.12
5000
10000
15000
20000
25000
30000
Strain Strain
N N
With NSC
Without NSC
Without NSC
With NSC
Slow strain rate, large system, no NSC and 2 NSC sizes (3 curves)
Slow strain rate, small system, no NSC and 1 large NSC
0.025 0.05 0.075 0.1 0.125 0.15
-2109
-1109
1109
2109
3109
0.025 0.05 0.075 0.1 0.125 0.15
-2109
-1109
1109
2109
3109
4109
Slower Strain Rates – Non Periodic BC
Strain
Strain
Str
ess
(Pa)
Str
ess
(Pa)
Surprise: Slower Strain Rates – Periodic BC
Large System Small System
Number of Atomistic Defects Versus Strain.NSCs stimulate the clustering of atomistic defects.
0.06 0.08 0.1 0.12 0.14 0.16 0.18
5000
10000
15000
20000
25000
30000
35000
0.04 0.06 0.08 0.1 0.12
20000
40000
60000
80000
100000
Strain Strain
N
N
Without NSC
With NSC With NSC
Without NSC
0.025 0.05 0.075 0.1 0.125 0.15-1109
1109
2109
3109
4109
5109
6109
Slow strain rate, large system, no NSC and 2 NSC sizes (3 curves)
0.025 0.05 0.075 0.1 0.125 0.15
-2109
2109
4109
6109
Slow strain rate, small system, no NSC and 1 NSC
Slower Strain Rates – Periodic BC
Strain
Strain
Str
ess
(Pa)
Str
ess
(Pa)
Without NSC
Without NSC
With NSC
With NSC 1
With NSC 2
Slower strain rate, non periodic BC
Large system with NSC
Large system, no NSC
Slower strain rate, non periodic BC – side views
Large system with NSC
Large system, no NSC
Slower strain rate, periodic BC
Large system with NSC
Large system, no NSC
Atomistic defects cluster at the loading surfaces
Slower strain rate, periodic BC – side views
Large system with NSC
Large system, no NSC
Atomistic Defects cluster at the loading surfaces
Experiments
Nanoindentation: not appropriate for this workThe very local indenter, which introduces a NSC, interacts strongly with pre-existing NSCs; two samples(films of different thickness) are unlikely to have the same NSCs positioned near the indenter in a similar fashion.
Experiments
(Left) SPM 2.5x2.5 μm2 image of metal nanotubes, (right) higher magnification SPM image. The diameter of the metal tubes is about 40nm and the thickness about 10nm.
2.5 m
Def
lect
ion
(load
)
Probe’s Vertical Position (displacement)
(a) (b)
(c)
The SPM probe is pushed on the metal tubes lying on a flat wafer. Height image using contact mode (low resolution) after load is imposed by Force Volume SPM. (a) 1x1μm, (b) 500x500nm; the marked area (red ellipse) was damaged during the Force Volume SPM. (c) Typical force displacement curve. Limitations …. force volume SPM.
Experiments
SPM Probe
Membrane
WaferSpin-on Glass, Etched after Film Deposition
TOP VIEW (Partial): ARRAY OFCYLINDRICAL HOLES IN WAFER
SIDE VIEW: ONE HOLE AND MEMBRANE
SPM Probe
Membrane
WaferSpin-on Glass, Etched after Film Deposition
TOP VIEW (Partial): ARRAY OFCYLINDRICAL HOLES IN WAFER
SIDE VIEW: ONE HOLE AND MEMBRANE
Membrane tests
Smooth Probe
Wafer Wafer
Au/Al film
9 MD cells
Force
SPM probe FEM domain
SIDE VIEW
TOP VIEW (not to scale)
Cr bonding
Schematic of the membrane problem. Nine MD cells are coupled to FEs discretizing the rest of the film. The handshake region coupling the MD and FE regions is wavelet-based, filtering high frequencies that create unrealistic reflections at the interface.
Simulation of Experiments
Simulation Issues
-The MD-FE interface (not resolved – dispersion issues) use a wavelet-based absorbing interphase
- Propagation of atomistic defects in the FE domain use kMC (kinetic Monte Carlo) as intermediate technique to avoid artificial dislocation pileup Has been tested (Frantziskonis & Deymier, 2000)
Conclusions
For Cu subjected to tensile strain, the critical dimensions for the effects of NSCs are larger than the examined (up to) 28.8nm. Multiscale simulations are necessary to identify critical dimensions and also examine slower strain rates.
The spatial pattern of atomistic defects that develops during straining is different for a system with NSCs than one without NSCs. Yet, the number of atomistic defects (number of atoms with modified coordination number) seems to be independent of the NSCs. Samples larger than critical tend to cluster atomistic defects.
Surfaces are instrumental in initiating atomistic defects. Surface Effects, also instrumental at macro-scales, are beneficial at nano-scales, i.e. they eliminate the effects of stress concentrators.
Strain rate (1 order of magnitude difference) does not alter the conclusions
Computer power and experimental difficulties of the past did not allow one to even speculate that such a (materials processing and reliability) dream may be true!