Viscoelastic behavior creep compliance curves

Creep-compliance studies conducted in the linear viscoelastic range also provide valuable information on the viscoelastic behavior of foods (Sherman, 1970 Rao, 1992). The existence of linear viscoelastic range may also be determined from torque-sweep dynamic rheological experiments. The creep-compliance curves obtained at all values of applied stresses in linear viscoelastic range should superimpose on each other. In a creep experiment, an undeformed sample is suddenly subjected to a constant shearing stress, Oc. As shown in Figure 3 1, the strain (y) will increase with time and approach a steady state where the strain rate is constant. The data are analyzed in terms of creep-compliance, defined by the relation ... 

In Figure 5.8d an intermediate behavior, called viscoelastic, is depicted such a relation is often called a creep curve, and the time-dependent value of the strain over the stress applied is called creep compliance. On application of the stress, the material at first deforms elastically, i.e., instantaneously, but then it starts to deform with time. After some time the material thus exhibits flow for some materials, the strain can even linearly increase with time (as depicted). When the stress is released, the material instantaneously loses some of it deformation (which is called elastic recovery), and then the deformation decreases ever slower (delayed elasticity), until a constant value is obtained. Part of the deformation is thus permanent and viscous. The material has some memory of its original shape but tends to forget more of it as time passes. 

As the stress-strain linearity limit of most thermoplastics and their blends is very low, nonlinear viscoelastic behavior of heterogeneous blends needs to be considered in most cases. The nonlinearity is at least partly ascribed to the fact that the strain-induced expansion of materials with Poisson s ratio smaller than 0.5 markedly enhances the fractional free volume (240). Consequently, the retardation times are perpetually shortened in the course of a tensile creep in proportion to the achieved strain. Thus, knowledge of creep behavior over appropriate intervals of time and stress is of great practical importance. The handling and storage of the compliance curves D (t,a) in a graphical form is impractical, so numerous empirical functions have been proposed (241), eg. 

The steady-flow viscosity qo and the steady-state compliance can easily be determined from creep data in the region of linear viscoelastic behavior as shown-in Fig. 1-12, from equation 40 of Chapter 1, provided steady-state flow has been attained. However, it is easy to be misled into believing prematurely that the linear portion of the creep curve has been reached in general, it cannot be expected to become linear until the flow term t/vo is at least as large as the intercept / . It is always desirable to perform the recovery experiment shown in Fig. 1-12 to conflrm the calculation. 

This method can also be apphed to the extrapolation of time- and temperature-dependent creep behavior. Experimental creep curves first need to be obtained at a series of different temperatures over a specific time period, and the values of comphance plotted on a logarithmic time scale. After one creep curve at a chosen temperature is defined as reference, creep curves at other temperatures are then shifted one by one along the log time scale until they superimpose to a single curve in the ideal case. Curves above the reference temperature are shifted to the right, and those below are shifted to the left. This procedure can be apphed to predict longterm creep compliance on the basis of short-term tests at different temperature levels in the range of linear viscoelasticity. 

The DMA time temperature superposition (TTS) creep method assumes linear viscoelastic behavior with characteristic superposition [8, 9]. The Wilhams-Landel-Ferry equation describes the TTS results and is used to project time-temperature data from short term tests to generate a master curve describing the normalized time-compliance for a temperature T when a reference temperature Tj ( Tg+50°C) is set. A shift factor (aj) is used to shift the curves and is defined as... 

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