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 ... 

A typical creep-compliance curve can be divided into three principal regions (Sherman, 1970) ... 

Figure 3-41 Illustration of a Creep-Compliance Curve (Redrawn from Rao, 1992).

Sherman (1966) studied the viscoelastic properties of ice cream mix and melted ice cream. The creep-compliance curve for the ice cream mix was described by the relation ... 

Figure 6-23 Creep-Compliance Curves at 5°C of Butter (A), A Commercial Low-Fat Spread Containing Gelatin (B), and an Experimental Product with 5.2% Fat Content and Containing Maltodextrin (C) (adapted from Evageliou et al., 1997 Stanley et al., 1998).

After the stress has been removed (point D in Fig. 13A), the recovery phase follows a pattern mirroring the creep compliance curve to some degree First, there is some instantaneous elastic recovery (D-E return of spring 1 into its original shape Fig. 13A, B). Second, there is a retarded elastic recovery phase (E-F slow movement of the Kelvin unit into its original state Fig. 13A, B). However, during the Newtonian phase, links between the individual structural elements had been destroyed, and viscous deformation is non-recoverable. Hence, some deformation of the sample will remain this is in the mechanical model reflected in dash-pot 2, which remains extended (Fig. 13B). 

Before attempting to separate quantitatively the effect of the two mechanisms on the viscosity, it should be recalled that in the separation process an experimental creep compliance curve is subtracted from the lower envelope of points, the deviation being ascribed to the x mechanism. This works relatively well for all curves except those obtained at the highest temperatures. The highest temperature curve still reflects the... 

Figure 6.8 Creep compliance curve showing polymer creep-response behavior.2...

Parallel Plate. Plashchina et al. (73) studied the creep of HM pectin gels placed between two corrugated parallel plates. Creep compliance curves were obtained for 0.5 to 2.5% pectin at temperatures from 25 to 55 C. Reversible and irreversible strain components were separated. Pectin macromolecules were characterized as being very stiff and only a slight decrease in entropy was required to form a pectin gel (7 ). Mitchell and Blanshard (50) used an automated parallel plate vlscoelastometer to study the creep compliance on low methoxyl pectins. The value of these experiments was that a continuous response was obtained from the gel rather than a single point measurement. 

FIGURE 5.2 Reduced shear creep compliance curves Jp(t) cm /dyn, determined on Epon 1007/DDS at seven temperatures, as indicated, presented logarithmically as a function of logarithmic time t. 

T > To are shifted to longer times, and measurements for T < Tq aie shifted to shorter times. A well-defined reduced curve means the viscoelastic response is thermorheologically simple (Schwarzl and Staverman, 1952). It represents log Jp(t) at To over an extended time range. The time scale shift factors aj that were used in the reduction of the creep compliance curves to obtain the reduced curve constitute the temperature dependence, ar is fitted to an analytical form, which is often chosen to be the Williams-Landel-Ferry (WLF) equation (Ferry, 1980),... 

FIGURE 5.3 Reduced shear creep compliance curves Jp(f) of Epon 1007/DDS shifted to superimpose with the curve at the reference temperature 100.7°C shown logarithmically versus the logarithm of the reduced time r/aj-. 

FIGURE 5.4 Comparison of reduced shear creep compliance curves of Epon 828, 1001, 1002, 1004, and 1007/DDS plotted logarithmically against time at the reference temperatures indicated that are close to the respective TgS. 

FIGURE 5.13 The logarithm of the reduced shear creep compliance curves, Jp t) (in Pa ), for the three urethane-end Unked polybutadiene elastomers displayed as a function of the logarithm of the reduced time t/ap (in seconds). The reference temperatures of reduction are chosen so that superposition is achieved at short times in the primary softening dispersion, (o) TB-1, 74 C, ( ) TB-2, 0°C, (e) TB-3, 17°C. 

However, if the creep compliance curves are compared at their respective TgS,we see in Figure 5.16 that the softening dispersions are, within experimental uncertainty, at the same place in the time scale of response. Specifically the positions of the four Jpit/ar) curves at a compliance level of 1.0 x 10 Pa appear to be spread on a time scale by not much more than one decade of time. Relative uncertainties of Tg values of 1.5°C can account for this spread in positions. Until more precise relative TgS can be measured we can tentatively surmise that at Tg all polymers at the same rate are deep in the softening zone. This conclusion appears reasonable when we consider that short-range chain dynamics should determine both creep rates just above the glassy level as well as changes in the local liquid structure, the kinetics of which determine Tg. 

Averaged experimental creep compliance curves for the blends containing 20 wt% PLC are shown in Figure 12.9 as a series of curves D = D(log t, T). The respective diagrams for 0% PLC (= pure PP)... 

When the strains or the strain rates are sufficiently small, the creep response is linear. In this case, when the time-dependent strain is divided by the fixed stress, a unique creep compliance curve results that is, at each time there is only one value for this ratio, which is the compliance i.e., y(t)l<7o = J(t)-The unique shear creep compliance function J(t) (Pa or cm /dyne, 1 Pa" = 0.1 cm /dyne) obtained for an amorphous polymer, has the usual contributions... 

FIGURE 6 Reduced shear creep compliance curves cmVdyne, determined on Epon... 

The time-scale shift factors Ut that were determined in the reduction of the creep compliance curves to obtain the reduced curves shown in Rg. 8 are presented in Fig. 9. The logarithm of Ut are plotted as a function of the reciprocal absolute temperature. The temperature dependence data can be fitted... 

FIGURE 11 Logarithmic plot of the reduced shear creep compliance curves Jp t) (in cmVdyne = lOPa ) against the reduced time I/oy (in seconds).The reference temperature of reduction. To, is -20.0 C for all curves. Data points are shown only for Sample 11-A. 

FIGURE 20 Double logarithmic plot of the reduce shear creep compliance curves Jp(t) (in Pa" ) as a function of the logarithm of the reduced retardation time, t/Or, for five elastomers at To = 0°C. Solid line (HTPB-2), long dashed line (Viton), short dashed line (PB-2), dashed-dotted line (PB-1), dotted line (HTSBR). 

However, if the creep compliance curves are compared at their respective Tg s, we see in Fig. 21 that the softening dispersions are, within experimental... 

The extent of film viscoelasticity cannot be determined for interfaces where < 1 surface poise with the present rheometer. When is high, however, an analysis of the initial part of the creep compliance curve (1) (din J(t)/dln t) can be used to determine the extent of film viscoelasticity. Figure 1 shows the increasing viscoelastic nature of the interface across the mid pH range. This maximum in film viscoelasticity agrees well with the observed maximum in emulsion stability at this pH, and with the extent of rigid film formation (Figure 2) (1). 

The experimental procedure is illustrated in Figures 6.8 and 6.9. A series of creep compliance curves each typically extending over 2 h, so that individual tests... 

Figure 4.28. Selected creep compliance curves for a magnetic tape at a series of temperatures. The width and thickness were 8mm and 8pm, respectively. A tension film clamp was used in creep mode. In the original experiment, the temperature was stepped ia 5 °C increments from 30 °C to 165 °C. A 10 MPa creep stress was apphed for 10 min at each temperature. (Courtesy of TA Instruments.)...

Fig. 7.27 Illustration of the concept of physical aging for PMMA. Material is first rejuvenated above Tg then quenched to 15°C below Tg for isothermal aging. Creep compliance curves are obtained at each aging time and these can be shifted as shown to provide a momentary master curve. A Kohlrausch fitting function is also shown through the shifted data. (Data from Wang (2007).)...

Fig. 10.4 Shear creep compliance curves for pure torsion and torsion with superimposed tension or compression for PMMA. Change in creep compliance with multiaxial load test illustrates interaction nonlinearity (Lu and Knauss, (1999) reprinted with kind permission from Springer Science and Business Media).

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