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Compression of microspheres: Theory and application

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Unloading<br />

Young’s modulus:<br />

Fully elastic unloading process<br />

Unknown particle shape<br />

Unknown correlation to ∗<br />

Residual stresses<br />

L.-Y. Li et al. (2002):<br />

4 3 ∗ /<br />

<br />

4 3<br />

∗<br />

<br />

/<br />

Uniform pressure distribution:<br />

̅<br />

16<br />

3 ∗ 16<br />

3² ∗<br />

Average true stress/strain:<br />

<br />

̅ <br />

<br />

<br />

<br />

<br />

/<br />

Red. E-Modul (GPa)<br />

70<br />

60<br />

50<br />

40<br />

30<br />

20<br />

Sphere Cap Cylinder<br />

10<br />

0.0 0.1 0.2 0.3 0.4<br />

Rel. deformation<br />

Hertz<br />

Cyl-fit (uniform pressure) Cap-fit (uniform pressur<br />

Cyl-fit (true stress/strain) Li-fit<br />

J. Paul PiKo-Workshop Siegen 2012<br />

9

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