CAVITATION, INDENTATION AND PENETRATION

CAVITATION, INDENTATION AND PENETRATION 365
P c
0.14
0.12
0.1
0.08
0.06
0.04
Titanium
Stainless steel
Steel
Aluminum
0.02
0 0.05 0.1 0.15 0.2 0.25 0.3
m
Figure 2: Variation of cavitation pressure Pc with expansion velocity m
for four metals. The different markers represent the power expansion
solution (16) with Σ∗ y instead of Σy.
solution, valid for the practical range m 2 ≪ 1, and the dynamic cavitation
pressure follows, to the third order, as
Pc = P0 + P1m + P2m 2 + P3m 3 , (16)
where coefficient P0 is the quasi-static cavitation pressure (1) normalized by E,
P1 = 0 (no linear term) and
2
3
P3 = − 2
β
9
P2 = 3
2 −
2
3 (7 + 5
3 β)
(1 + β) 5
3
βΣ 1
3
y , (17)
5 (3 − β)
. (18)
(1 + β)
Relation (16) applies also to strain hardening solids if Σy is replaced by an
equivalent cavitation yield stress Σ ∗ y obtained by equating (6) with (1), where in
the latter Σy is replaced with Σ ∗ y. Comparison between numerical solutions of
(14)-(15) and the power expansion (16), for several metals, is shown in Figure
2 revealing excellent agreement.