Download e-book for iPad: Anelastic Relaxation in Crystalline Solids by A. S. Nowick

By A. S. Nowick

ISBN-10: 0125226500

ISBN-13: 9780125226509

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Extra resources for Anelastic Relaxation in Crystalline Solids

Example text

T o represent only t h e more specialized case of anelasticity, where we have the additional r e quirement of a u n i q u e equilibrium relationship between stress and strain, further restrictions m u s t be placed u p o n E q . 1-1). T h e n a t u r e of these restrictions will emerge later in the chapter. W e proceed to examine cases of E q . 1-1) in which all b u t a few of the coefficients Æ and bt are zero. I n doing this, it will be found that mechanical models provide a useful m e a n s for visualizing the anelastic behavior of materials, and that to every model there corresponds a u n i q u e differential stress-strain equation.

I n addition, s/ is also commonly expressed in two other u n i t s involving t h e ratio of 26 1 CHARACTERIZATION OF ANELASTIC BEHAVIOR amplitudes in decibels: j ^ ( d B c m - 1 ) = (x2 J^(dB μ 8 6 θ " 1) xJ-VO l o g 1 0[ t f ( * 0 / £ / ( * 2) ] = 8 . 6-6) W h e n e v e r t h e symbol s/ appears w i t h o u t specification of units, it will b e understood to be in nepers per centimeter. 6-2) to obtain t h e p a r a m eters and s/. I n view of t h e r e q u i r e m e n t of small d a m p i n g ( <^ 1) for the validity of E q .

2-1) by differentiating b o t h sides with respect to time. Zener (1948, C h a p t e r 5) has developed an i m p o r t a n t inequality starting from E q . 2-1). 2-3) is always negative, since it is m a d e u p of a p r o d u c t of two factors, t h e first of which is always positive and the second always negative (as can be seen from Figs. 1-2 and 1-4). 2-4) W e know, of course, that the equality in E q . 2-4) is valid b o t h for t = 0 and t = o o [see E q s . 2-9)]. F u r t h e r m o r e , P r o b l e m 2-2 shows that t h e equality holds approximately for the case of small relaxation strength, specifically, w h e n A2 <^ 1.

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Anelastic Relaxation in Crystalline Solids by A. S. Nowick

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