Viscoelasticity -time-temperature

If the modulus data of a material satisfy Equation (3.27), this material is referred to as thermorheologically simple and obeys the (viscoelastic) time-temperature superposition. 

The polymer SBR is mechanically simple, and it was found that the results for G for a given substrate could be superimposed using the Williams, Landel and Ferry (WLF) technique (see Viscoelasticity - time-temperature superposition). The master curves for each substrate were close to being parallel to each other and to a similar curve for cohesive fracture of the SBR (Fig. 1). 

For a rubber adhesive, Gent found that he could use the WLF equation to obtain a master curve of breaking stress (see Viscoelasticity - time-temperature superposition). He used a Fracture mechanics analysis to link the breaking stress to critical strain energy density. 

Viscoelasticity - time-temperature superposition D W AUBREY Shift factor, WLE equation... 

Viscoelasticity Time-temperature effects under dynamic/cyclic loading Specific heat, thermal conductivity and thermal expansion Optical properties Chemical resistance Water absorption Important process design parameters Colour, reflectance and opacity Resistance to chemical reactions during and after processing Measures material-solvent interaction... 

For a fiber immersed in water, the ratio of the slopes of the stress—strain curve in these three regions is about 100 1 10. Whereas the apparent modulus of the fiber in the preyield region is both time- and water-dependent, the equiUbrium modulus (1.4 GPa) is independent of water content and corresponds to the modulus of the crystalline phase (32). The time-, temperature-, and water-dependence can be attributed to the viscoelastic properties of the matrix phase. 

Strength and Stiffness. Thermoplastic materials are viscoelastic which means that their mechanical properties reflect the characteristics of both viscous liquids and elastic solids. Thus when a thermoplastic is stressed it responds by exhibiting viscous flow (which dissipates energy) and by elastic displacement (which stores energy). The properties of viscoelastic materials are time, temperature and strain rate dependent. Nevertheless the conventional stress-strain test is frequently used to describe the (short-term) mechanical properties of plastics. It must be remembered, however, that as described in detail in Chapter 2 the information obtained from such tests may only be used for an initial sorting of materials. It is not suitable, or intended, to provide design data which must usually be obtained from long term tests. 

When an engineering plastic is used with the structural foam process, the material produced exhibits behavior that is easily predictable over a large range of temperatures. Its stress-strain curve shows a significantly linearly elastic region like other Hookean materials, up to its proportional limit. However, since thermoplastics are viscoelastic in nature, their properties are dependent on time, temperature, and the strain rate. The ratio of stress and strain is linear at low strain levels of 1 to 2%, and standard elastic design... 

The time/temperature-dependent change in mechanical properties results from stress relaxation and other viscoelastic phenomena that are typical of these plastics. When the change is an unwanted limitation it is called creep. When the change is skillfully adapted to use in the overall design, it is referred to as plastic memory. 

Viscoelasticity A combination of viscous and elastic properties in a plastic with the relative contribution of each being dependent on time, temperature, stress, and strain rate. It relates to the mechanical behavior of plastics in which there is a time and temperature dependent relationship between stress and strain. A material having this property is considered to combine the features of a perfectly elastic solid and a perfect fluid. 

Since we are interested in this chapter in analyzing the T- and P-dependences of polymer viscoelasticity, our emphasis is on dielectric relaxation results. We focus on the means to extrapolate data measured at low strain rates and ambient pressures to higher rates and pressures. The usual practice is to invoke the time-temperature superposition principle with a similar approach for extrapolation to elevated pressures [22]. The limitations of conventional t-T superpositioning will be discussed. A newly developed thermodynamic scaling procedure, based on consideration of the intermolecular repulsive potential, is presented. Applications and limitations of this scaling procedure are described. 

Considers physics and engineering topics, including reinforcement mechanisms viscoelasticity abrasion, fatigue, adhesion rheology, mixing, and processing and the effects of time, temperature, and fluids... 

Time-temperature superposition [10] increases the accessible frequency window of the linear viscoelastic experiments. It applies to stable material states where the extent of reaction is fixed ( stopped samples ). Winter and Chambon [6] and Izuka et al. [121] showed that the relaxation exponent n is independent of temperature and that the front factor (gel stiffness) shifts with temperature... 

There are two superposition principles that are important in the theory of Viscoelasticity. The first of these is the Boltzmann superposition principle, which describes the response of a material to different loading histories (22). The second is the time-temperature superposition principle or WLF (Williams, Landel, and Ferry) equation, which describes the effect of temperature on the time scale of the response. 

Because of equipment limitations in measuring stress and strain in polymers, the time-temperature superposition principle is used to develop the viscoelastic response curve for real polymers. For example, the time-dependent stress relaxation modulus as a function of time and temperature for a PMMA resin is shown in... 

Dynamic mechanical experiments yield both the elastic modulus of the material and its mechanical damping, or energy dissipation, characteristics. These properties can be determined as a function of frequency (time) and temperature. Application of the time-temperature equivalence principle [1-3] yields master curves like those in Fig. 23.2. The five regions described in the curve are typical of polymer viscoelastic behavior. 

In Eq. (4.13) NT is the total number of internal degrees of freedom per unit volume which relax by simple diffusion (NT — 3vN for dilute solutions), and t, is the relaxation time of the ith normal mode (/ = 1,2,3NT) for small disturbances. Equation (4.13), together with a stipulation that all relaxation times have the same temperature coefficient, provides, in fact, the molecular basis of time-temperature superposition in linear viscoelasticity. It also reduces to the expression for the equilibrium shear modulus in the kinetic theory of rubber elasticity when tj = oo for some of the modes. 

It was initially stated that Cf are Cf were universal constants (Cf 17 Cf 50 K), but Cf can vary between 2 and 50 and Cf between 14 and 250 K (Mark, 1996). Epoxy values have been found in the low part of these intervals Cf 10, Cf 40 15 K (Gerard et al., 1991), whereas unsaturated polyester values can be relatively high Cf/Cf = 15-55 = 73-267 K (Shibayama and Suzuki, 1965). There is, to our knowledge, no synthetic study on the ideality and crosslinking effects on Cfand Cf. The time-temperature equivalence principles will be examined in detail in Chapter 11, which is devoted to elasticity and viscoelasticity. 

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