Visco-elastic behaviour linear

Within the region of linear visco-elastic behaviour, an imposed stress of angular frequency, u>, results in a harmonic strain of amplitude proportional to the stress amplitude, and with phase lag 8 relative to the stress, which is independent of the applied stress amplitude [Ferry, 1980],... 

The above-mentioned complexity of the relationships between the structure and properties of textiles is further complicated by the non-linear mechanical properties of individual fibres caused by their visco-elastic behaviour, friction between fibres and threads, anisotropy, and statistical distribution of all properties. Modelling such complex materials requires application of a combination of experimental, analytical, and numerical methods, which will be considered in this chapter. 

O3, h). .. etc. from this family of curves, which form the relaxation curve. Furthermore, by determining the stress which belongs to a specified strain in the relaxation test after a long test time, one can experimentally verify the only calculated tensile test stress-strain-curves for very small deformation rates. The isochronous stress-strain diagram also directly indicates the non-linearity of the visco-elastic behaviour otherwise the curves would be straight lines. 

There is strong interest to analytically describe the fzme-dependence of polymer creep in order to extrapolate the deformation behaviour into otherwise inaccessible time-ranges. Several empirical and thermo-dynamical models have been proposed, such as the Andrade or Findley Potential equation [47,48] or the classical linear and non-linear visco-elastic theories ([36,37,49-51]). In the linear viscoelastic range Findley [48] and Schapery [49] successfully represent the (primary) creep compliance D(t) by a potential equation ... 

It is a fundamental assumption of material behaviour that for short term loading the material is linear elastic to ultimate failure. Under long term loading the material is linear visco elastic with recovery on removal of load, providing the strain does not cause permanent material deterioration. 

From such experiments one obtains finally the functions Eo(23°C,e) and D2(23°C,e) at the reference temperature, e.g. Tref =23 °C, over a range of many orders of magnitude of the deformation rate. These functions, the so-called master curves for the moduli, and the time-temperature superposition principle, Eq. 4.10, fully describe the uniaxial deformation behaviour at constant deformation rate and isothermal conditions of the HDPE material in the non-linear visco-elastic range. Figure 4.3 shows the master curves. 

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