Mean characteristic time, viscoelasticity

Whether a viscoelastic material behaves as a viscous Hquid or an elastic soHd depends on the relation between the time scale of the experiment and the time required for the system to respond to stress or deformation. Although the concept of a single relaxation time is generally inappHcable to real materials, a mean characteristic time can be defined as the time required for a stress to decay to 1/ of its elastic response to a step change in strain. The... 

Chapters 5 and 6 discuss how the mechanical characteristics of a material (solid, liquid, or viscoelastic) can be defined by comparing the mean relaxation time and the time scale of both creep and relaxation experiments, in which the transient creep compliance function and the transient relaxation modulus for viscoelastic materials can be determined. These chapters explain how the Boltzmann superposition principle can be applied to predict the evolution of either the deformation or the stress for continuous and discontinuous mechanical histories in linear viscoelasticity. Mathematical relationships between transient compliance functions and transient relaxation moduli are obtained, and interrelations between viscoelastic functions in the time and frequency domains are given. 

The characteristic time of the fluid is often taken to be the largest time constant describing the slowest molecular motions or else some mean time constant determined by linear viscoelasticity. The characteristic time may also be chosen as a time constant in a constitutive equation. The characteristic time for the flow is usually taken to... 

The polymer is a branched polyethylene melt with = 1.55 x 10 and Mw/M = 11.9, flowing at 170 °C in a 3.3 1 planar contraction. The hnear viscoelastic properties and the nonlinear parameters for a four-mode PTT equation are shown in Table 10.1. Different values of e were used for each mode, but with a constant value of f = 0.08. These parameters provide a reasonable fit to the transient and steady-state shear and extensional data, although the nonlinear parameters for the two longest relaxation times cause small oscillations in startup of simple shear that are not observed experimentally using parameters that ehmi-nate the shear oscillations causes the calculated extensional stresses to be too low, and the contraction flow results are sensitive to the extensional stresses. The mean relaxation time was 1.74 s, the average velocity in the downstream channel was 7.47 mm/s, and the downstream channel half-width (the characteristic length) was 0.775 mm. The Weissenberg number based on downstream channel properties was therefore 16.8. 

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. 

A tapping mode (also called intermittent contact mode) it is a non linear resonance mode. In this case, the oscillation amplitude is larger and the mean position of the tip is closer to the surface. The tip almost touches the surface at each oscillation. In this mode, friction can be avoided as well as the sample deformation and wear. Adhesion is also avoided thanks to the extremely short time of contact . The height of the sample is generally controlled so that the oscillation amplitude remains constant. The phase shift of the oscillation is then characteristic of the system dissipation, which is very useful for characterizing viscoelastic materials. 

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