Creep modulus shear

Let us remember that the properties of LCPs are dependent on processing shear and, consequently, creep modulus varies with sample geometry. 

The beauty of the linear viscoelastic analysis lies in the fact that once a viscoelastic function is known, the rest of the functions can be determined. For example, if one measures the comphance function J t), the values of the components of the complex compliance function can in principle be determined from J(t) by using Fourier transforms [Eqs. (6.30)]. On the other hand, the components of the complex relaxation moduh can be obtained from those of / (co) by using Eq. (6.50). Even more, the real components of both the complex relaxation modulus and the complex compliance function can be determined from the respective imaginary components, and vice versa, by using the Kronig-Kramers relations. Moreover, the inverse of the Fourier transform of G (m) and/or G"(co) [/ (co) and/or /"(co)] allows the determination of the shear relaxation modulus (shear creep compliance). Finally, the convolution integrals of Eq. (5.57) allow the determination of J t) and G t) by an efficient method of numerical calculation outlined by Hopkins and Hamming (13). 

Athanasopoulos, G.A., and Richait, EE. 1983a. Effect of creep on shear modulus of clays. Journal of Geotechnical Engineering, ASCE, 109, No. 10, pp. 1217-1232. 

The assessment of the asphalt performance in resistance to permanent deformation is determined with reference to either creep rate and creep modulus or creep rate and cumulative strain after n load applications, or permanent shear strain, depending on the test employed. 

Steady-state creep rate Shear modulus Hill s average shear modulus Reuss average shear modulus Voigt s average shear modulus Planck s constant... 

Fig. 3.3-ft Polyethylene, HDPE creep modulus versus Fig. 3.3-5 Polyethylene, HDPE shear modulus versus time, at 23 °C temperature...

The correspondence principle following the Boltzmann superposition principle allows the conversion of the common mechanical relationships of linear elasticity theory into linear viscoelasticity simply by replacing cr by time-dependent a t) and e by time-dependent e(t). Young s modulus E or the relaxation modulus Ej (f)= cr(f)/e is accordingly transformed to the creep modulus c(f) = cile t) orthe creep compliance/(f) = s(f)/(7,respectively. These time-dependent parameters can be determined from tensile creep and relaxation experiments. In compression or shear mode, the corresponding parameters of moduli are calculated in a similar manner. 

Equations 9 and 10 neglect shear deformation, which could give a small additional load-line displacement, causing one to underestimate the flexural creep modulus. A more exact solution by Williams[l] vdiich includes shear deformation gives the following result ... 

We shall follow the same approach as the last section, starting with an examination of the predicted behavior of a Voigt model in a creep experiment. We should not be surprised to discover that the model oversimplifies the behavior of actual polymeric materials. We shall continue to use a shear experiment as the basis for discussion, although a creep experiment could be carried out in either a tension or shear mode. Again we begin by assuming that the Hookean spring in the model is characterized by a modulus G, and the Newtonian dash-pot by a viscosity 77. ... 

The Imass Dynastat (283) is a mechanical spectrometer noted for its rapid response, stable electronics, and exact control over long periods of time. It is capable of making both transient experiments (creep and stress relaxation) and dynamic frequency sweeps with specimen geometries that include tension-compression, three-point flexure, and sandwich shear. The frequency range is 0.01—100 H2 (0.1—200 H2 optional), the temperature range is —150 to 250°C (extendable to 380°C), and the modulus range is 10" —10 Pa. 

Not only are the creep compliance and the stress relaxation shear modulus related but in turn the shear modulus is related to the tensile modulus which itself is related to the stress relaxation time 0. It is therefore in theory possible to predict creep-temperature relationships from WLF data although in practice these are still best determined by experiment. 

Throne has reported that the relationship between foam modulus and density can be generalised to other properties such as tensile strength, fatigue strength, creep properties as well as shear and compression modulus. Thus if X is the general material property then... 

The viscoelastic behavior of concentrated (20% w/w)aqueous polystryene latex dispersions (particle radius 92nm), in the presence of physically adsorbed poly(vinyl alcohol), has been investigated as a function of surface coverage by the polymer using creep measurements. From the creep curves both the instantaneous shear modulus, G0, and residual viscosity, nQ, were calculated. 

In cellulose II with a chain modulus of 88 GPa the likely shear planes are the 110 and 020 lattice planes, both with a spacing of dc=0.41 nm [26]. The periodic spacing of the force centres in the shear direction along the chain axis is the distance between the interchain hydrogen bonds p=c/2=0.51 nm (c chain axis). There are four monomers in the unit cell with a volume Vcen=68-10-30 m3. The activation energy for creep of rayon yarns has been determined by Halsey et al. [37]. They found at a relative humidity (RH) of 57% that Wa=86.6 kj mole-1, at an RH of 4% Wa =97.5 kj mole 1 and at an RH of <0.5% Wa= 102.5 kj mole-1. Extrapolation to an RH of 65% gives Wa=86 kj mole-1 (the molar volume of cellulose taken by Halsey in his model for creep is equal to the volume of the unit cell instead of one fourth thereof). 

Table 8 presents a survey of the basic elastic constants of a series of polymer fibres and the relation with the various kinds of interchain bonds. As shown by this table, the interchain forces not only determine the elastic shear modulus gy but also the creep rate of the fibre. 

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