Damping Functions of Typical Polymers

Various empirical functions have been used to describe the damping function. Two popular types are shown by Eqs. 10.31 and 10.32. 

Because it leads to expressions that can be evaluated analytically, the power law function given by Eq. 10.31 has been used with integral constitutive equations to predict responses to various shear histories. We note, however, that it approaches its limiting value of one with a non-zero slope as the strain approaches zero.  

Equation 10.32 does have the correct limiting slope and is often used to describe experimental data for purposes of material characterization. The DE prediction of h( cannot be expressed in a simple explicit form, but Larson [7, p 143 ] has shown that the DE shear damping function is closely approximated by Eq. 10.32 with a = 0.2. 

The study that produced the data shown in Fig. 10.2 [2] included several other solutions, and it was found that molecular weight and concentration had little effect on the damping function for cM around 5 lO. Todemonstrate the degree of time-strain separability, the data ofFig. 10.2 are replotted in Fig. 10.5 as relaxation modulus divided by the vertical shift factor required to superpose them, i.e., The superposibility is excellent for times longer than a 

Osaki [20] summarized various reports of damping function behavior in shear as of 1993. He classified these as types A, B, or C, defined as follows. Type A behavior is in essential agreement with the DE prediction. He found that data for linear, entangled polymers with fairly narrow molecular weight distributions behaved in this manner when M/M was less than about 50. 

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