44 THE PLASTIC STATE. 



Thus, it will be seen that there are a number of solid 

 bodies which, under certain conditions, can be made to 

 exhibit properties in many ways similar to those of the 

 more viscous fluids. Of these solid bodies some are 

 deformed and made to flow under exceedingly small 

 stresses, often less than those induced by their own 

 weights, if these stresses are only allowed to act for a suffi- 

 ciently long time ; others require greater stress to bring 

 about the plastic phenomena ; while there are some which 

 require the application of very great stresses indeed before 

 any signs of semi-plasticity show themselves. 



18. Fluidity. When the stressupon a substance exceeds 

 a certain limiting value, the distortion or strain will take 

 place indefinitely without any further increase of stress. 

 This is seen in the case of a bar of a ductile material 

 when the breaking tensile load is nearly reached. When 

 the bar becomes plastic* a condition of unstable equili- 

 brium is reached, and a rapid extension takes place and a 

 simultaneously rapid contraction of area. As the area 

 decreases the intensity of stress on the bar increases, with 

 the result that fracture very soon takes place, being 

 generally preceded by local contraction. 



This limiting value of the stress, when plasticity is 

 reached, has been called by M. Tresca " the pressure of 

 fluidity." 



With the same notation as before, if p is the pressure of 

 fluidity the load on a tension bar, when plasticity is 

 reached, is 



Wi = pA .... (XXXII.) 



A being the area when fluidity begins. At a later stage, 

 when the area has been reduced to a, the load upon the 

 bar will be 



W z =pa . . . (XXXIII.) 

 and as 



A = L + l 

 (i L 

 we have 



Wi L-M 

 W 2 L 



TABLE III USEFUL FORMULAE. 



The following are the formulae whose use is most 

 frequently required when working out the results of test- 

 ing operations, and, in addition to those already tabulated, 

 will be found useful for reference. 



