THE LAWS OF ELAST I CO-VISCOUS FLOW 409 



THE RETURN 



If after a time t the displacement has reached the value S and 

 the stress is released, the specimen promptly returns to a displace- 

 ment short of zero and continues much more slowly in the same 

 direction. 



If the elastico-viscous displacement at the time t is given by 



S 2 = A 2 (i-e- a ^ 1 ), 



the corresponding return displacement at the time t, counted from 

 the instant of release, will be 



R = A 2 e-«^(i-e- a ^ T °). 



To account for the viscous term, assume 



F=eS n S 



whence 



S*= 



feM 



m-\-i' 



If F= constant, and -F = the constant value of F during the pre- 

 ceding stress during the time t , 



S^KFt+FotoY-iFoioyi 



pe 



counting from the actual zero. 



As shown by the formula, if the previous strain be considerable, 

 the new strain is relatively small. This strengthening by previous 

 strain is one of the striking features of the behavior of every sub- 

 stance which exhibits viscous yield. 



If, in this expression, F represents the actual stress, it assumes 

 ' that the viscous force is proportional to the velocity, which is true 

 for fluids; but for "solid friction" the force is independent of the 

 velocity. 



It may be assumed in the present case of internal viscosity of 

 solids that the actual law may be between these two extremes, e.g., 



P=a(SY, 



* Experiment gives p = \ (o . 3-0 . 6) , which makes n = 1 . The usual assumption, 

 n = o, gives p = i. 



