By H. G. Hadley, T. M. Whitin

Mathematical versions of stock platforms

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16) Thus the reduction in strain gives the elastic part of the creep compliance. This result is useful under conditions where the time scale of the delayed elastic behavior is of the order of minutes, and the elastic behavior is dominated by theflow. It can be seen that the reduction in strain following removal of stress at zero time is not given by equation (16) if the steady state has not been reached at the instant of stress removal. In Section I I the recovery behavior of a noncross-linked material was described.

T h e effect of a v e r a g e m o lecular weight, molecular weight distribution, and temperature course n o t dealt w i t h b y s u c h a p h e n o m e n o l o g i c a l theory basis for the d e v e l o p m e n t are but form of m o l e c u l a r t h e o r i e s . T h e s e a s p e c t s a r e of the con- sidered in C h a p t e r 2 a n d briefly i n S e c t i o n V I . IV. M o d e l s , S p e c t r a , a n d O p e r a t o r Equations P r e v i o u s l y we h a v e been considering the r e s p o n s e of m a t e r i a l s mani- f e s t i n g l i n e a r v i s c o e l a s t i c b e h a v i o r i n s p e c i a l t y p e s of e x p e r i m e n t s .

I n m a n y c a s e s w h e r e a w i d e r a n g e of v a l u e s of t h e r e s p o n s e f u n c t i o n i s c o v e r e d , a s i n t h e c u r v e s of F i g . 2 5 , i t i s p r e f e r a b l e t o p l o t , f o r e x a m p l e , I n J ' ( ω ) i n s t e a d of «/'(co), s i n c e t h i s q u a n t i t y m a y r a n g e f r o m a b o u t 1 0 - 10 2 c m . / d y n e to 1 0 -5 49 VISCOELASTICITY PHENOMENA TABLE APPROXIMATIONS Type of test III FOR R E T A R D A T I O N Order of approximation AND R E L A X A T I O N Approximation for L(t), SPECTRA L(l/o>), H(t)y Η (l/ω) Lx(t) = (d/d In t)[J(t) - t/η] 2 L2(t/2) = [d/d In t - d / d ( l n t)*} A(t) WIL/ω) = (2/π)[Γ(ω) - 1/ωη] Creep Dynamic Z V (l/ω) = L2"(l/a>) - d / d ( l n ω) ]Β(ω) 3 3 = - [ d / d In ω - ( M ) d / d ( l n ω ) ] .

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