1921] on Elasticity 393 



into wire or tube. The stresses produced by hammering are shear 

 and volume compression, while in drawing they are shear and volume 

 extension. 



Hence it may be concluded that in a material which is malleable 

 but not ductile, the limit of strain for volume expansion is less 

 than the rigidity limit, and also, that body which is ductile is also 

 malleable, but that the converse is not true. 



Plastic bodies are those which when distorted do not rupture but 

 retain their distorted shapes, and this implies that the elastic limits 

 for rigidity are small, but that the limit for permanent set are large. 



I will conclude by showing a few experiments designed to illus- 

 trate fracture by volume extension and fracture by shear. 



I have here some brass rings over which damp paper has been 

 stretched. The contraction of this paper as it is dried by the heat 

 of the lantern will be sufficient to cause rupture. 



In the stress due to contraction volume extension is predominant 

 in the proportion of two to one. 



It is impossible to foretell in what position or direction the break 

 will occur. In an isotropic material this would be a matter of pure 

 chance, but in the present case some irregularity in cementing the 

 paper to the ring or in the structure of the paper itself will decide. 



In the next experiment a sheet of brittle material will be broken 

 by shear. The material used is a square of dried sheet gelatine, two 

 of whose opposite edges are gripped by clamps, which are then made 

 to slide parallel to one another at a constant distance. 



If the sheet were thick enough to withstand edgeway pressure 

 without folding, the applied stress would be a simple shear, and in 

 the actual case shear is predominant. The direction of the fracture, 

 as will be seen, is nearly at right angles to the extended diagonal. 



Lastly, I will break some of the same gelatine which has had its 

 limits of shear increased by the absorption of water, and draw your 

 attention to the shape of the termination of the cracks which have 

 been started. 



At the end of a spreading crack the material is undergoing 

 intense distortion, and when the limit for shear strain is much in 

 excess of the volume strain limit, the termination of the crack is, as 

 in the present instance, rounded. 



In a note appended to this lecture the effect of the relative 

 magnitude of the elastic constants and their limits on the character 

 of permanent set and fracture is considered in somewhat greater 

 detail. The subject is one on which much useful work might be done. 



In conclusion, I wish to give my best thanks to the Director 

 of the Davy Faraday Laboratory, where the greater part of the 

 experiments on Rigidity have been carried out. The experiments, in 

 fact, could not have been made without the facilities for dealing with 

 low temperatures which the Davy Faraday Laboratory has afforded. 



[A. M.] 



