Section III, 1922 [293] Trans. R.S.C. 



Compressional Waves in Metals Produced by Impact 



By R. W. Boyle 



(Read May Meeting, 1922) 



I. Duration of the Impact 



In the older compressional wave theory of impact it was con- 

 sidered that when two bodies impinged on one another the com- 

 pression produced at the surface of contact gave rise to compressional 

 waves, which travelled through the length of both bodies during the 

 first half of the impact, were reflected back from the far ends as waves 

 of tension, and then on return thrust the bodies apart. 



A result of the theory would be that the duration of the impact 

 is comparable with the gravest period of free vibration in the bodies, 

 and this result is contradictory to experiment. 



A very different theory is that given by Hertz, ^ where all relations 



involving possible' vibrations set up in the bodies are disregarded, 



and the compression at the junction is treated as a purely local 



efïect in which the pressure gradually rises until the bodies are brought 



to rest and then subsides until they are separated. A necessary 



consequence is that the duration of impact should be a large multiple 



of the gravest period of free vibration in either of the impinging 



bodies; also the duration of the impact should vary inversely as the 



fifth root of the relative velocity of approach of the bodies before 



impact. Hertz himself obtained some evidence in confirmation of 



his theory, in that the linear dimensions of the compressed area at 



contact was shown to be proportional to the cube root of the pressure 



between the bodies; and quite recently Tschudi- has reported the 



results of a series of exact experiments on colliding spheres and bars, 



in which he finds, concerning the duration of impact, that in all cases 



the measured duration was much greater than the values expected 



on any theory of compressional waves. For example, taking the 



case of a moving bar of steel, 31.3 cms. long and 2. 86 cms. in diameter, 



impinging on the end of a similar bar at rest, the duration of impact 



was shown to depend on the relative velocity of approach, agreeing 



fairly well with Hertz' law. In the case of an approaching velocity 



of 50 cms. per second, the duration of impact was 3 XlO""* seconds, 



whereas on the compressional wave theory it would be 1.2X10"^ 



seconds for any ap proaching velocity. 



^Love's Mathematical Theory of Elasticity, 2nd éd., 1906, p. 195. 

 ^Physical Review, vol. xviii, Dec, 1921. 



