where e is the energy density absorbed by the 

 material's plastic deformation. If e is small 

 enough, the deformation is within the elastic limit 

 and no permanent dent will be formed. When e 

 exceeds a certain limit, e^, the plastic deformation 

 of surface occurs and a pernament dent is formed. 

 Then the following relation is derived: 







for e 



465 



material such as yield strength. Young's modulus 

 etc., at the present stage, for lack of data we 

 assume the following relation. 



£ q: n '■ 



c "y 



Oy : Yield strength 



(22) 



and determine the power, n, from the erosion experi- 

 ments . 



for e > 



(18) 



The above mentioned argument is valid for the actual 

 case of erosion where many cavity bubbles collapse 

 in a certain period if e is substituted to, £, in 

 these equations. 

 Then, 



e = 



P 



E = e - E 

 P c 



for e < £ 



for £ > E 



and 



MDDR = -— £ f (e)d£ 

 ti__ I P 



(19) 



Comparison with Test Result 



The results of this theoretical model are compared 

 with the erosion test of NACA 0015 section in 

 Figure 23 where the two constants, Kj and K2 , in 

 Eq. (21) were determined using two different test 

 points. In this figure those points are shown by 

 dashed marks. The value of the power, n, was taken 

 as n = 1/4 from the experimental results. The 

 agreement between this theory and the test results 

 is satisfactory. 



The theory was also compared with Thiruvengadam' s 

 test result [Thiruvengadam (1971)]. In this case, 

 no data about the cavity was measured, so only the 

 peak value of erosion intensity was used in this 

 comparison with the present theory. The agreement 

 is almost perfect as seen in Figure 24 where one 

 set of data was used to determine two constants. 

 Photos in Figure 23 (b) also show the paint test 

 results discussed in the next section. 



H~ I '^ ~ ''c' ^'^ ^^P (-Ae)de 



V 



(20) 



Integrating Eq. (20) , 



MDDR 



Ki3 Hv 



G (a) ( 2 + 



K,e 



1 c 



pV'LF{a) 



Paint Test and Soft Aluminum Erosion Test 



Recently the paint test has been routinely used at 

 several research laboratories to predict erosion 

 intensity, in contrast to the present research using 

 the soft aluminum erosion test to predict erosion. 

 Both of these two test methods have merits and 

 demerits. The soft aliominum erosion test is some- 

 what troublesome and the surface of the material 



exp [ 



K e 



1 c 



pv2LF(a) 



(21) 



where 



F(a) s nA^o [-(a + Cp . ) ]2 

 mm 



G(a) = naSe 



Here F and G are functions of cavitation number, 

 where G is proportional to the total energy of the 

 cavity reaching to the surface, and F is related 

 to the individual energy of each cavity bubble. 



The probability of the bubble collapse on the 

 foil surface, n, is calculated using the estimated 

 mean position of collapse and its fluctuation. In 

 the case of the NACA 0015 foil section, the position 

 was estimated as 1.3 X from Figure 10 and the 

 fluctuation is assumed to be the same as the cavity's 

 fluctuations. The thickness at the end of cavity 

 is taken from Figure 8. The value of F and G for 

 NACA 0015 section were calculated at a = 4°. The 

 results are shown in Figure 22. 



While the critical value of energy density, e , 

 should be expressed by the mechanical properties of 



0.15 



0.12 



0.08 



0.01 



0.5 0.6 0.7 0.8 0.9 1.0 1.1 



Cavitation Number 



FIGURE 22. Derived F and G values for NACA 0015 foil 

 section at a = 4 deg. 



