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Elimination or Significant Reduction of the Effects of Stress Concentrators by Nanosizing

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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, Univ. of Arizona

C. 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

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 pigment

applications.

Courtesy: Sigma Tech. Intl., Inc.

10,000 layers of alternating metal/polymer.

Each layer is 20-30nm thick.

Courtesy: Sigma Tech. Intl., Inc.

Future Technologies

One Potential Important Future application:

Hydrogen storage by adsorption, where intentional surfaces, pores …

(STRESS CONCENTRATORS) increase the surface area.

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.

Size Effects – Since Galileo Galilei and Leonardo da Vinci

Note on Hall-Petch effects

Considering for a brittle material:

g=1J/m2, E=100GPa, sth=E/30] and a=p1/2

we obtain hcr = 30nm

Size Effects: Well Studied

Yield strengthof electroplated Cu thin films as a function

of film thickness t. In the plot of these nanoindentation

experimental results, sizing to ~200nm, the yield stress

was assumed as the 1/3 of the hardness.

Courtesy of Volinsky and Gerberich, 2003, Microel.

Engr. Journal.

Insensitivity to NSCs has not been speculated,

Plus difficulties in studying (experimental and simulation)

Koehler, 1970: a structure comprised of alternating layers

of two suitable metals exhibits a resistance to plastic deformation

that would be greater than that expected from a homogenous alloy

of the two.

Below Certain Nanoscales: More than Size Effects

Expected Behavior – Insensitivity to Defects

For NSC diameter = ½ thickness hcr

3D

views

Side views

stress (Pa)

strain

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

3D

views

side views

Stress (Pa)

strain

MD Simulations (EAM) – Cu Crystal w/o NSC Pulled in (001)

(111) slip planes form

Over 2,000,000 atoms

Two slip planes

High strain rate

Non Periodic BC

small system

with NSC

large system,

no NSC

(b)

(a)

stress (Pa)

large system with same NSC

stress (Pa)

small system, no NSC

strain

strain

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

N

with NSC

without NSC

strain

Why the Insensitivity ?

If, on average, the energy required for

forming each atomistic defect is constant,

this explains insensitivity of the material to NSCs

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

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

Without NSC

External surfaces start dominating as atomistic defect initiation sites

Surfaces, small system, high strain rate, periodic BC

With NSC, side views

Without NSC, side views

Loaded surfaces start dominating as atomistic defect initiation sites

for two large (infinite) lateral dimensions (periodic BC). NSCs

stimulate the clustering of atomistic defects.

Slower Strain Rates – Non Periodic BC

With NSC

N

N

Without NSC

With NSC

Without NSC

Strain

Strain

Large System

Small System

Number of Atomistic Defects Versus Strain,

(one realization, even though process is statistical)

Slower Strain Rates – Non Periodic BC

Stress (Pa)

Strain

Slow strain rate, large system, no NSC and 2 NSC sizes (3 curves)

Stress (Pa)

Strain

Slow strain rate, small system, no NSC and 1 large NSC

Surprise: Slower Strain Rates – Periodic BC

Without NSC

Without NSC

N

N

With NSC

With NSC

Strain

Strain

Large System

Small System

Number of Atomistic Defects Versus Strain.

NSCs stimulate the clustering of atomistic defects.

Slower Strain Rates – Periodic BC

Without NSC

Stress (Pa)

With NSC 1

With NSC 2

Strain

Slow strain rate, large system, no NSC and 2 NSC sizes (3 curves)

Without NSC

Stress (Pa)

With NSC

Strain

Slow strain rate, small system, no NSC and 1 NSC

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 work

The 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.

(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.

Experiments

(b)

(a)

Deflection (load)

Probe’s Vertical Position (displacement)

(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

Membrane tests

Smooth Probe

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!