By A. S. Nowick
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Extra resources for Anelastic Relaxation in Crystalline Solids
Comparison of 7ι(α>) and / 2 ( ω ) anelastic solid. sa functions of log 10 ωτσ for the standard Fig. 3-5 allows a comparison of the normalized function [ / ι ( ω ) Ju]ldJ with the normalized creep function ł( ) w h e n these two functions are plotted against ^ ( 1 / ω τ σ ) a n d log(r/T C T), respectively. T h e two curves are roughly similar when plotted this way, b u t it is noteworthy that the ł( ) curve lies above the normalized 7 Ø( ω ) curve. Also, t h e 54 3 MECHANICAL MODELS AND DISCRETE SPECTRA normalized J 1 function is antisymmetric about its midpoint (see Problem 3-7), while ip(t) is not.
It will be found that the simplest differential stress-strain equation capable of representing anelasticity involves three i n d e p e n d e n t parameters. Correspondingly, the equivalent model is constructed of three basic elements (two springs and a d a s h p o t ) . T h e behavior corresponding to the t h r e e - p a r a m e t e r equation or model is of such basic importance that a material exhibiting this behavior is t e r m e d a standard anelastic solid. 5) is devoted to examining the detailed behavior of such a solid.
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. 4) it will be shown t h a t the equality also holds w h e n / a n d vary relatively slowly over a b r o a d range of time, regardless of t h e m a g nitude of the relaxation strength.