Compression of microspheres: Theory and application
Compression of microspheres: Theory and application
Compression of microspheres: Theory and application
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Yield strength<br />
Yield criteria:<br />
max , , <br />
1/2 ² ² ²<br />
stress/ρ 0<br />
1.0<br />
0.8<br />
0.6<br />
0.4<br />
ν = 0.17<br />
σ z /ρ 0<br />
σ r/θ /ρ 0<br />
τ/ρ 0<br />
τ max<br />
( : principal stress; : maximum shear stress)<br />
0.2<br />
| / | <br />
Hertzian theory:<br />
• Calculation <strong>of</strong> principle stresses <br />
• Hertzian pressure: ∗ /<br />
Example: Stöber silica (R = 250nm)<br />
2∙0.34 3.9 <br />
J. Paul PiKo-Workshop Siegen 2012<br />
Force [µN]<br />
0.0<br />
0.0 0.5 1.0 1.5 2.0 2.5 3.0<br />
800<br />
600<br />
400<br />
200<br />
z/a<br />
Rel. deformation<br />
0.00 0.21 0.42 0.63 0.84<br />
SiO 2<br />
(R = 250nm)<br />
yield point<br />
Hertz<br />
0<br />
0 100 200 300 400<br />
Deformation [nm]<br />
7
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