﻿532 



Mr. S. Lees on a Simple Model 



(43), not only will T 2 become negative, but dT 2 /da; will 

 become negative and numerically increase with a or y. 

 This may be seen at once physically, or may be verified by 

 the algebra of (41) and (42). Thus a time will in general 

 arrive when d,T 2 /dcc= — J\ 1? and when this is the case, 



dF__ 2dT 2 



dx ~" * dx 



= 0. 



This would correspond to yield point, as ordinarily under- 

 stood in the testing of materials. 



With regard to the term (N — j3y 2 ) which has been fre- 

 quently utilized in this section, we can suggest a rough 

 interpretation. It is essentially to be regarded as a force 

 of cohesion. Hence the value y = \/No//3 must be regarded 

 as a slip sufficient to break down this cohesion. Thus it 

 may roughly be identified with the slip producing fracture 

 or failure. In this connexion, it should be borne in mind 

 that the model is only a rough representation o£ what is 

 essentially a statistical problem, involving a multiplicity of 

 surfaces, whose normals and corresponding cohesive forces 

 act in all directions. 



§ 11. Cyclic State for Modified Model. 

 Fig. 11. 



We proceed to discuss the nature of the hysteresis loop 

 for the model when in the cyclic condition. The appropriate 

 diagram is shown in fig. 11. The points L and J refer to 



