CAVITATION, INDENTATION AND PENETRATION
CAVITATION, INDENTATION AND PENETRATION
CAVITATION, INDENTATION AND PENETRATION
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<strong>CAVITATION</strong>, <strong>INDENTATION</strong> <strong>AND</strong> <strong>PENETRATION</strong> 363<br />
Figure 1: Conical indentation. Included angle is 2α, imprint radius – a,<br />
hypothetical radial displacement – w. Inner core is bounded by r = a.<br />
Baruch [3], is<br />
Pc =<br />
∞<br />
0<br />
exp( 3<br />
2<br />
Σ (dǫ + βdΣ)<br />
β<br />
ǫ − 2Σ) − 1 + 2βΣ<br />
and for quasi-static, plain strain, cylindrical cavitation of compressible Mises<br />
and Tresca solids we have the general results, Masri and Durban [12], respec-<br />
tively<br />
and<br />
Pc =<br />
∞<br />
0<br />
Σ dǫ + 1−2κ<br />
3 βdΣ<br />
√3ǫ <br />
β<br />
exp − √3Σ − 1 + 2(1−κ)<br />
√ βΣ<br />
3<br />
∞<br />
<br />
Σ dǫ −<br />
<br />
2<br />
1−β<br />
2 dΣ<br />
(6)<br />
with κ = −0.4725, (7)<br />
Pc =<br />
0 exp(2ǫ − 1+β 3−β<br />
2 Σ) − 1 + 2 βΣ.<br />
(8)<br />
Here the total strain ǫ is a known function of the effective Mises stress Σ (nondimensionalized<br />
with respect to E) and β = 1 − 2ν is a compressibility measure.<br />
Formulae (6-8) generalize approximations (1-3) to include strain hardening. In<br />
the absence of elastic compressibility (β = 0) it is possible, Masri and Durban<br />
[13], to derive for power hardening materials the close approximations<br />
Pc = 2<br />
3 Σy<br />
n 2<br />
1 + F(n) −<br />
3Σy<br />
1<br />
<br />
, (9)<br />
n
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