Viscoelastic behavior above dependence

In compliance with the DMA-experiments there is a distinct difference below and above the glass transition temperature. While below the glass transition temperature a strong dependency of the tangent modulus on strain can be observed, the material shows an almost linear viscoelastic behavior above the glass transition temperature within the considered region. 

As mentioned above, polishing pads show both elastic and viscoelastic behavior. Figure 4.14 shows the time-dependent behav-... 

As we have seen above, the transition that separates the glassy state from the viscous state is known as the glass-rubber transition. This transition attains the properties of a second-order transition at very slow rates of heating or cooling. In order to clearly locate the region of this transition and to provide a broader picture of the temperature dependence of polymer properties the principal regions of viscoelastic behavior of polymers will be briefly discussed. 

The above analysis shows that the nonlinear dynamic viscoelastic behavior of polymers can be resolved into three components the nonlinear elasticity resulting from the variation of modulus with the phase angle or strain during the cycle nonlinear internal friction resulting from strain and strain-rate dependence and eflFects associated with the reversible, strain-induced structural changes. 

The formulations described in the previous section show yield values coupled with viscous and viscoelastic flow, but not with thixotropy. It is possible to introduce thixotropy into plastic fluid behavior by allowing Y to depend on the history of tr dl This approach was applied to fluids with viscoelastic response above the yield value by Suetsugu and White [S26] and later by Montes and White [M35]. 

Polymers can exhibit both viscous and solid mechanical behavior this phenomenon is called viscoelasticity. For a given polymer, the degree of viscous behavior depends on temperature. Below Tg, polymers will behave more or less as elastic solids with very little viscous behavior. Above Tg,... 

The shift factor is the shift in time scale corresponding to the difference between the selected and reference temperature, and the shift factor represents the temperature dependence of the rate of the segmental motion which underlies all viscoelastic behavior the WLF equation demonstrates that all polymers, irrespective of their chemical structure, will exhibit similar viscoelastic behavior at equal temperature intervals (T-Tg) above their respective glass transition temperatures (Tg). Odian GC (2004) Principles of polymerization. John Wiley and Sons Inc., New York. Mark JE (ed) (1996) Physical properties of polymers handbook. Springer-Verlag, New York. 

This chapter deals with viscoelastic behavior in the liquid state, particular emphasis being placed upon those aspects associated with the flow properties of polymer melts and concentrated solutions. The time-dependent response of polymers in the glassy state and near the glass transition, one variety of viscoelasticity, was discussed in Chapter 2. The concern in this chapter is the response at long times and for temperatures well above the glass transition. The elastic behavior of polymer networks well above the glass transition was discussed in Chapter 1. The conditions here are similar, and elastic effects may be very important in polymeric liquids, but steady-state flow can now also occur because the chains are not linked together to form a network. All the molecules have finite sizes, and, for flexible-chain polymers, the materials of interest in this chapter, the molecules have random-coil conformations at equilibrium (see Chapters 1 and 7). 

Polymer/mbber nanocomposites exhibit enhanced mechanical, thermal stability, toughness, stiffness, and gas-barrier properties compared to those of conventional composites at same filler volume fraction [11-15]. The interaction between the filler and polymer matrix of nanocomposites at the nanometer scale enables the formation of molecular bridges in the polymer matrix. This is the basis for the enhanced mechanical properties of nanocomposite as compared to conventional microcomposites [16, 17]. Nanocomposites containing hybrid fillers add a new dimension to the above enhanced properties. These composites show more advantages to composites containing single filler as the property of the hybrid filler composite depends upon the combined effect of individual filler. The nonlinear viscoelastic behavior of nanocomposites can be influenced differently by hybrid fillers than single filler. 

The investigations of model compositions, based on linear elastomers and various fillers, have shown that the yield stress also may be characterized by the value of the complex shear modulus measured at various frequencies. The dependence of the dynamic modulus on the filler concentration characterizes critical concentrations of the filler, above which the viscoelastic behavior of composition drastically changes. Dynamic modulus corresponding to the yield stress does not depend on the matrix viscosity or its nature. This fact indicates a predominant role of the structural frame for rheological properties of filled polymers. 

In the above unsteady tests, if one keeps the level of imposed stress and strain low enough, the measured material functions show an independence from these applied stimuli levels, exhibiting only a dependence on time (or frequency). This type of response indicates linear viscoelastic behavior. The primary modes of deformation employed in these tests are either shear or extension. If there is no volume change accompanying the deformation, a single modulus or compliance, whether real or complex, but a function of time (or frequency) and temperature only, suffices to characterize the material behavior. We will define moduli and compliances further below. Let us now start examining these and other key topics in linear viscoelasticity. 

The mechanical behavior of polymer resins exhibits time and temperature dependences, called viscoelastic behavior, not only above, but also below the glass-transition temperature, T. Thus, it can be presumed that the mechanical behavior of polymer composites also depends on time and temperature even below which is within the normal operating-temperature range. Examples in this respect are given by Aboudi et al., Sullivan, Gates, and Miyano et... 

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