Viscoelastic functions calculations from spectra

Distributions of relaxation or retardation times are useful and important both theoretically and practicably, because // can be calculated from /.. (and vice versa) and because from such distributions other types of viscoelastic properties can be calculated. For example, dynamic modulus data can be calculated from experimentally measured stress relaxation data via the resulting // spectrum, or H can be inverted to L, from which creep can be calculated. Alternatively, rather than going from one measured property function to the spectrum to a desired property function [e.g., Eft) — // In Schwarzl has presented a series of easy-to-use approximate equations, including estimated error limits, for converting from one property function to another (11). 

Once a relaxation (retardation) spectrum is obtained from a relaxation (creep compliance) viscoelastic function, any other function can be obtained. Alternatively, approximate methods have been developed to calculate viscoelastic functions from one another (10). By taking into account... 

Thus, once the four parameters of Eq 7.42 are known, the relaxation spectrum, and then any linear viscoelastic function can be calculated. For example, the experimental data of the dynamic storage and loss shear moduli, respectively G and G , or the linear viscoelastic stress growth function in shear or uniaxial elongation can be computed from the dependencies [Utracki and Schlund, 1987] ... 

The dynamic tests at small amplitude in parallel plates or cone-and-plate geometry are simple and reproducible. From the experimental values of storage and loss shear moduli, G and G", respectively, first the yield stress ought to be extracted and then the characteristic four material parameters in Eq. (2.13), rjo, r, mi, and m2, might be calculated. Next, knowing these parameters one may calculate the Gross frequency relaxation spectrum (see Eqs. (2.31) and (2.32)) and then other linear viscoelastic functions. 

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