Ellis 



result was merely that collapse velocity became infinite at a lower rate (pro- 

 portional to the inverse one-haLE rather than the inverse first or three-halves 

 power for the acoustic or incompressible cases, respectively). The Kirkwood- 

 Bethe hypothesis (8) was used as a basis for Gilmore's theory, and this also has 

 not been proved or universally accepted (9) for the conditions involved in cavi- 

 tation. It should also be pointed out that the radiation condition (no incoming 

 waves) which is assumed in this approximation is obviously not applicable when 

 one considers the effects of nearby boundaries. If one is interested in the study 

 of cavitation damage, then boundaries must be considered. 



There has, in the past, been an unjustified confidence in assuming that 

 cavitation damage was entirely caused by large-amplitude pressure waves in 

 the liquid due to an isolated, collapsing spherical bubble. It is true that the 

 possibility of instability of the spherical shape of a bubble has received a great 

 deal of attention in the last fifteen years or so (10,11) but true instability of an 

 initially spherical bubble isolated in an infinite medium was always the problem 

 considered. This theoretical work was a very important and basic step in the 

 progress of our understanding, but isolated bubbles by definition can hardly be 

 expected to damage anything. Of course, this isolation is relative and is as- 

 sumed only to make the theory more tractable under the assumption that the 

 radiated shock wave could travel the distance from the "isolated" bubble and 

 still be strong enough to do damage. A quantitative answer to this question is 

 therefore required before the validity of the assumption can be properly 

 assessed. Experimental answers are unfortunately still inadequate or depend- 

 ent on other assumptions, although some progress has been made (12). The 

 theoretical situation is somewhat better due to the efforts of many investigators 

 (13,14,15) as long as a spherical collapse is assumed. 



One of the most recent and best treatments is that of Hickling and Plesset 

 (16). They make the assumption that the bubble contains a small amount of gas 

 (10" ■^ or 10"^ atmosphere pressure at maximum radius). They include com- 

 pressibility and find numerical solutions including flow during rebound from a 

 Lagrangian formulation. They find the acoustic approximation to be valid at 

 high enough pressures that the peak intensity of the outgoing wave can be calcu- 

 lated. The results of these calculations are most informative and show that 

 peak pressures are very sensitive to gas content. Typical results are that at a 

 distance of the bubble maximum diameter from the collapse point the peak pres- 

 sure is 200 atmospheres for 10" -^ atmosphere initial gas content and 1000 at- 

 mospheres for 10" "^ atmospheres initial gas content when the collapsing pressure 

 at infinity is 1 atmosphere. In the author's opinion, these values are quite rea- 

 sonable and should be expected to be confirmed by experiment if it proves pos- 

 sible to obtain a spherical collapse. They are sufficient to cause the typical 

 peening appearance or depressions of relatively large curvature observed in 

 soft materials and which cannot be reasonably explained by a jet impact mecha- 

 nism because of this large curvature (17). They are also capable of causing 

 "cold work" and ultimate fatigue damage in harder materials. 



However, in view of the demonstrated violence of cavitation attack on some 

 very resistant materials it does not seem likely that the shock wave damage 

 mechanism is the only one. It might be argued that if the peak pressure has a 

 l/r dependence, then the bubble need only collapse closer to the surface to 



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