Viscoelasticity time-temperature-transformation

The shift factor is philosophically based on the concept that the viscoelastic response is a result of the ability of the polymer chains to respond to stress or deformation. Largely this response is temperature or conversely rate dependent. However, one of the factors often overlooked is that the ability of a polymer to respond is also a function of the volume available for the polymer chain to deform, which is ultimately related to density. This results in an additional vertical shift of the raw experimental data. This shift is often overlooked for two reasons. The first reason is that many practitioners are unaware that it exists and the more valid reason is that the time-temperature transformation (TTT) of the raw data is at best often only an order of magnitude predictor of the response over long times. 

In actual long term applications of polymers, however, it is well known that chemical reactions occur which actually change the viscoelastic properties of the material while it is in use. In addition, environmental factors such as exposure to solvents or even water, while not always chemically modifying a material, can have a profound influence on its viscoelastic properties in much the same way as a true chemical transformation. If predictions based exclusively on time-temperature correspondence were to be successful, the rates of all of these processes would have to vary with temperature in exactly the same m inner as does the viscoelastic spectrum. While this might be approximately true in certain special cases, it is usually not so. Thus, a more general theoretical framework is necessary to predict the properties of simultaneously chemically reacting and physically relaxing networks. 

For rubber-like materials, the viscoelastic losses vary with the strain rate and the temperature. The principle of time-temperature equivalence propose in 1955 by Williams et al (75) allows us to superimpose the experimental curves obtained at different temperatures through the known translation factor ar of the WLF transformation. As a consequence, at fixed geometry, the adherence forces provoking crack extensions at different speeds V can be studied as a function of the reduced parameter ajV. 

In addition to the Boltzmann superposition principle, the second consequence of linear viscoelasticity is the time-temperature equivalence, which will be described in greater detail later on. This equivalence implies that functions such as a=/(s), but also moduli, behave at constant temperature and various exten-sional rates similarly to analogues that are measured at constant extensional rates and various temperatures. Time- and temperature-dependent variables such as the tensile and shear moduli (E, G) and the tensile and shear compliance (D, J) can be transformed from E =f(t) into E =f(T) and vice versa, in the limit of small deformations and homogeneous, isotropic, and amorphous samples. These principles are indeed not valid when the sample is anisotropic or is largely strained. 

The quantities G, T,v) or G T,v) have all of the time-temperature superimposition properties associated with viscoelastic deformations of polymers and the WLF transform may effectively be applied to normalize G(T, v) data. Environmental changes may influence G s and thus G s is a direct scalar. " However, generally G (T,t )> G and factors of 10 to 10 are typical. 

Mechanical behaviour of asphalts is basically viscoelastic. Under high loading rates they are elastic and brittle. When the load is imposed over a long time their deformability is similar to viscous materials. With respect to temperature variations, tars behave as thermoplastics this means that with increasing temperature they are transformed gradually from brittleness to fluidity, with simultaneous decrease of material adhesion and cohesion when softening temperature is attained. That transformation is entirely reversible within a certain range of temperature. 

Gel time—the time at fixed temperature for a thermosetting material to reach the gel point, where the material transforms from a viscoelastic liquid to a crosslinked rubber. 

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