Compression of microspheres: Theory and application
Compression of microspheres: Theory and application
Compression of microspheres: Theory and application
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Hardness<br />
Abbott & Firestone:<br />
Contact area & 2<br />
Hardness / &<br />
& 2.8 0.1 <br />
• Simplification <strong>of</strong> contact mechanics<br />
• No volume conservation<br />
• Discontinuities at yield point<br />
• Fixed relation <strong>of</strong> yield strength <strong>and</strong> hardness<br />
• Conservative<br />
CEB:<br />
Contact area 2 <br />
Hardness / <br />
( 0.454 0.41)<br />
5.3 0.2 <br />
• Volume conservation<br />
• Small plastic deformation<br />
• Discontinuities at yield point<br />
• Fixed relation <strong>of</strong> yield strength <strong>and</strong> hardness<br />
in fully plastic regime<br />
Force [µN]<br />
J. Paul PiKo-Workshop Siegen 2012<br />
Count<br />
800<br />
600<br />
400<br />
200<br />
20<br />
16<br />
12<br />
0.00 0.21 0.42 0.63 0.84<br />
0<br />
0 100 200 300 400<br />
8<br />
4<br />
SiO 2<br />
(R = 250nm)<br />
yield point<br />
Rel. deformation<br />
Hertz<br />
A&F/CEB<br />
Deformation [nm]<br />
Abbott&Firestone<br />
SiO 2<br />
(R = 250nm)<br />
0<br />
2 3 4 5 6<br />
Hardness [GPa]<br />
CEB<br />
8
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