1902.] produced by the sudden Cooling of Metals, 



89 



interior will then contract, and exert a radial pull on the outside 

 solidified layer. This will put the material into a state of circum- 

 ferential compression. If the tangential direction be called the direc- 

 tion of X, the radial direction that of Y, so that the rod considered 

 lies along the axis of Z, then the material in the outside layer of the 

 quenched rod of metal is subjected to a compressional stress in the 

 X direction. If a layer of material be considered at some distance 

 from the outside it will be found to be subjected not only to a compres- 

 sion in the X direction, but also to a tension in the Y direction. For 

 the outside solidified layers are able to resist to some extent the radial 

 pull due to contraction. A particle of material at a point such as A 

 will thus be subjected to stresses p and t in the manner illustrated in 

 the sketch. Going nearer the centre of the bar, the pull due to eon- 

 traction of the hot material may be more than balanced by the outward 

 radial pull due to the solidified material which has settled down under 

 radial tension, so there may be a resultant outward pull all round the 

 layer considered, and a particle such as B will be subjected to a circum- 



ferential pull, t\ as well as a radial pull, L There will be, of course, a 

 gradual transition from material in the one condition to material in the 

 other. 



Further, the stresses induced by sudden cooling will probably be 

 severe enough to overstrain many layers of material, and, except in the 

 case of portions which have been overstrained when quite cool, recovery 

 from overstrain will be effected, so that the material will be left in an 

 elastic condition, hardened as regards the stresses in question, and not 

 in the semi-plastic state typical of material which has been recently 

 subjected to overstrain. 



Now it is well known that when metals are deformed they alter very 

 little in volume, almost the whole strain is one due to change of shape 

 It is only necessary then to consider the shear stresses applied by the 

 systems of stresses illustrated above at A and B> A pull (t or t') is 

 equivalent to a hydrostatic tension (\t or Jf) and two shear stresses in 

 definite directions ; a push (p) gives rise to a hydrostatic pressure (\p) 

 and two shear stresses. A circumferential pressure (j) case A) gives 

 rise to the following two shears :— 



H 2 



