Viscoelastic behavior curves

The shearing characteristics of non-Newtonian fluids are illustrated in Fig. 7. Curves A and B represent viscoelastic behavior. Curve C illustrates the behavior if the fluid thins with increasing shear, generally referred to as shear thinning or pseudoplasticity. The opposite effect of shear thickening or dilatancy is shown as curve D. 

Furthermore, the magnitude of the relaxation modulus is a function of temperature to more fuUy characterize the viscoelastic behavior of a polymer, isothermal stress relaxation measurements must be conducted over a range of temperatures. Figure 15.6 is a schematic log ,(f)-versus-log time plot for a polymer that exhibits viscoelastic behavior. Curves generated at a variety of temperatures are included. Key features of this plot are that (1) the magnitude of EXt) decreases with time (corresponding to the decay of stress. Equation 15.1), and (2) the curves are displaced to lower EXt) levels with increasing temperature. 

When the magnitude of deformation is not too great, viscoelastic behavior of plastics is often observed to be linear, i.e., the elastic part of the response is Hookean and the viscous part is Newtonian. Hookean response relates to the modulus of elasticity where the ratio of normal stress to corresponding strain occurs below the proportional limit of the material where it follows Hooke s law. Newtonian response is where the stress-strain curve is a straight line. 

Contrary to the phase separation curve, the sol/gel transition is very sensitive to the temperature more cations are required to get a gel phase when the temperature increases and thus the extension of the gel phase decreases [8]. The sol/gel transition as determined above is well reproducible but overestimates the real amount of cation at the transition. Gelation is a transition from liquid to solid during which the polymeric systems suffers dramatic modifications on their macroscopic viscoelastic behavior. The whole phenomenon can be thus followed by the evolution of the mechanical properties through dynamic experiments. The behaviour of the complex shear modulus G (o)) reflects the distribution of the relaxation time of the growing clusters. At the gel point the broad distribution of... 

The viscoelastic behavior of concentrated (20% w/w)aqueous polystryene latex dispersions (particle radius 92nm), in the presence of physically adsorbed poly(vinyl alcohol), has been investigated as a function of surface coverage by the polymer using creep measurements. From the creep curves both the instantaneous shear modulus, G0, and residual viscosity, nQ, were calculated. 

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. 

Elastic behavior of liquids is characterized mainly by the ratio of first differences in normal stress, Ni, to the shear stress, t. This ratio, the Weissenberg number Wi = Nih, is usually represented as a function of the rate of shear y. Figure 7 depicts flow curves of some viscoelastic fluids, and Figure 8 presents a dimensionless standardized material function of these fluids. It again verifies that they behave similarly with respect to viscoelastic behavior under shear stress. 

Fig. 25 Viscoelastic behavior of a semi-dilute solution of DNA. Elastic modulus (G, filled symbols) and viscous modulus (G", open symbols) are plotted, together with their ratio G"IG = tan 5 (solid curve), for a 93 mg/mL DNA solution subjected to a heating-cooling cycle. The entanglement of DNA helices and, at high temperature, of single strands causes the almost monotonous increase of the dynamic moduli. Reproduced with permission from [110]...

Isothermal measurements of the dynamic mechanical behavior as a function of frequency were carried out on the five materials listed in Table I. Numerous isotherms were obtained in order to describe the behavior in the rubbery plateau and in the terminal zone of the viscoelastic response curves. An example of such data is shown in Figure 6 where the storage shear modulus for copolymer 2148 (1/2) is plotted against frequency at 10 different temperatures. 

Fig. 4. The five regions of viscoelastic behavior. All polymers exhibit these five regions, but crosslinking, crystallinity, and varying molecular weight alter the appearance of this generalized curve. The loss modulus Tg peak appears just after the storage modulus enters the glass transition region.

The deformation behavior of two pads are shown in Figure 4.14. Which pad shows greater elastic behavior Which pad shows viscoelastic behavior A CMP process is required to planarize a surface with a maximum step height of 5000 A. If the velocity of the pad is 50 cm/sec, which pad will polish faster inside a 5 pm wide trench A 10 pm wide trench A 15 pm wide trench What is the maximum width of a low region that may be planarized by each pad (Note assume that the pad relaxation and deformation behaviors (curves) are similar and symmetric.)... 

Another aspect of viscoelastic behavior is the influence of temperature and in the slow crack propagation region is has also been well documented. Marshall et al. observed that in PMMA the crack speed curves are shifted to lower Kpvalues with increasing temperature and that also Ki decreases in the temperature range from -60 Cto 80 C. 

The viscoelastic character of stratum corneum is further demonstrated by the dependence of elastic modulus on strain rate (Figure 32). Even the dry corneum 10 wt % H2O) showed significant viscoelastic behavior over the narrow range of strain rates studied. In the case of hydrated membranes, there is also a change in shape of the force-elongation curve (6, 85). 

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 this book, we review the most basic distinctions and similarities among the rheological (or flow) properties of various complex fluids. We focus especially on their linear viscoelastic behavior, as measured by the frequency-dependent storage and loss moduli G and G" (see Section 1.3.1.4), and on the flow curve— that is, the relationship between the "shear viscosity q and the shear rate y. The storage and loss moduli reveal the mechanical properties of the material at rest, while the flow curve shows how the material changes in response to continuous deformation. A measurement of G and G" is often the most useful way of mechanically characterizing a complex material, while the flow curve q(y ) shows how readily the material can be processed, or shaped into a useful product. The... 

Horizontal shifts of the isotherms obtained in aging processes combined with suitable vertical shifts give master curves that permit prediction of the viscoelastic behavior of aged systems over a wide interval of time. The timeaging time correspondence principle for poly(vinyl chloride) (26) is shown in Figure 12.23. The retardation times in these creep experiments are related to the aging time, ta, by means of the expression... 

David and Augsburger (63) studied the decay of compressional forces for a variety of excipients, compressed with flat-faced punches on a Stokes rotary press. They found that initial compressive force could be subject to a fairly rapid decay and that this rate was dependent on the deformation behavior of the excipient for the materials studied, they found that maximum loss in compression force was for compressible starch and MCC, which was followed by compressible sugar and DCP. This was attributed to differences in the extent of plastic flow. The decay curves were analyzed using the Maxwell model of viscoelastic behavior. Maxwell model implies first order decay of compression force. 

Draw a logB versus temperature plot for a linear, amorphous polymer and indicate the position and name the five regions of viscoelastic behavior. How is the curve changed if (a) the polymer is semicrystalline, (b) the polymer is cross-linked, and (c) the experiment is run faster ... 

Figure 4-1. Schematic modulus-temperature curve showing various regions of viscoelastic behavior.

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