Compliance curves

A distribution obtained by the use of equation (13) is only a first approximation to the real distribution. The corresponding distribution of retardation times is designated as L(T). It may be estimated from the slope of a compliance curve D(0 or J(t), for tensile or shear creep, respectively, plotted on a logarithmic time scale according to the equation (for shear creep)-... 

One early proposal for the form of the monodisperse compliance curve, based primarily on data beyond (M )sota., was (178) ... 

In a typical indentation experiment the indenter is pressed onto the surface under investigation and the load is successively increased up to a certain maximum load. In the so-called compliance approach both load and indenter displacement are recorded and plotted as a load-displacement curve, the so-called compliance curve. If the experiment is exclusively run in the compressive load regime, the curve is also referred to as the load-penetration curve. Upon loading, elastic deformations occur succeeded by plastic ones. Upon releasing the imposed stress, elastic strain recovers immediately. 

Fig. 5a,b Schematic representation of a the tip-sample contact upon high loading b the according compliance curve. In the case of perfectly plastic response the unloading curve is identical to the vertical line intersecting with the abscissa at hmax. In general, some viscoelastic recovery occurs and the residual impression depth hy is smaller than hmax. The difference hc—hy represents the extent of viscoelastic recovery. Ap and Ae denote the dissipated and the recovered work, respectively. Ap=0 for perfect elastic behaviour, whereas Ae=0 for perfect plastic behaviour. The viscoelastic-plastic properties of the material may be described by the parameter Ap(Ap+Ae) l. The contact strain increases with the attack angle 6. Adapted from [138]... 

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). 

Fig. 22. Lower envelope of creep compliance master curve as well as experimental compliance curve for 342.2° C ( ) and 350.4° C ( ) Dashed lines represent best" straight line of slope 1 obtained by substracting lower envelope from experimental...

There is one other method of determining the activation energy for the second process. From the compliance curves due to the second meclmnism, one can calculate the viscosity as a function of temperature. A plot of the viso)sily as a function of temperature logj vs. 1/T) (not shown) yields a much higher activation energy than 50 Kcal. This is not surprising, however, because for a relaxation mechanism of the type encountered here,... 

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 4. Plot of representative compliance curves for the sample at different...

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. 

Load (P) versus depth of penetration (h) curves, also called compliance curves, are the output from a nanoindentation test. The curves are obtained as load is applied to the indenter tip up to some maximum value and then back to zero. 

Figure 16.18 shows a general compliance curve for a material that undergoes both elastic and... 

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