90 Changes in Elastic Properties produced by Cooling. [Aug. 11> 



lA, giving contraction in direction of X and extension in direction of Y, 

 2a „ „ „ X „ „ Z. 



A radial tension (t cases A and B) gives rise to the following two 

 shears : — 



lAB, giving extension along Y and contraction along Z, 



2ab „ „ „ Y „ ,; x. 



A circumferential tension (f case B) gives rise to the following two 

 shears : — 



Ir, giving extension along X and contraction along Y, 

 2B „ „ „ X „ ,, Z. 



It is necessary then to consider what effect these shear stresses, 

 induced by quenching, have on the behaviour of a bar subjected to a 

 tension (T) or a pressure (P) in the direction of the Z axis. 



A pull, T, in direction of the Z axis gives rise to the following two 

 shears : — 



It producing extension along Z and contraction along X, 

 2t Z Y 



-1 3J 33 35 " 53 33 33 • 



A push, P, along the Z axis produces the following tw T o shears : — 



lp giving contraction along Z and extension along X, 

 2p „ ,3 „ Z „ „ „ Y. 



It will thus be seen that the shear stresses induced in a bar of metal 

 by sudden cooling have the effect of weakening certain layers of the 

 bar as regards resistance to tension, and certain layers as regards 

 resistance to compression. For the shear stress 1 T is applied along 

 the same series of parallel planes as the stress 2a, and although the 

 stress 2 T is directly opposed by the stress Iab, the " yielding " of the 

 material must be determined by its strength in the weakest direction. 

 Similarly the stresses Ip and 2p are in the same directions as the 

 stresses 2 B , 1ab> so that the loss of elasticity exhibited by quenched 

 material both as regards tension and compression has been accounted 

 for. It may, however, be desirable to consider a little in detail what 

 ought to be the behaviour under tension of, say, a bar of iron which 

 has been subjected to the system of stresses described above. At the 

 commencement of £he loading the stress due to the applied load will 

 be uniformly distributed over the whole section, but as soon as a very 

 Small load is applied, a long cylindrical layer of material (A'), which has 

 been left by the sudden cooling under a stress of type 2 A very nearly 

 equal to the "yielding" stress of the material, will yield. This yield- 

 ing would continue to the enormous extent characteristic of a yield- 

 point were all the material in the condition A' ; but the weak layer, 

 being surrounded by stronger material, the yielding is only allowed to 

 continue to a very slight extent. This smaJl yielding will, however, 

 cause a redistribution of the internal stresses set up by quenching to 



