Creep-recovery curve

Assuming thai the Boltzmann superposition principle holds and that all of the creep is recoverable, what would the creep recovery curve be for I he polymer in Problem 1 if the load were removed after lO.(KM) min ... 

Figure 2 Examples of creep and creep recovery curves of gluten (Olympic x Gabo cross line -/17 + 18/-) in water and in deuterium dioxide. Temperature 35°C creep stress was 40 Pa for the sample in water and 75 Pa for the sample in D20...

On removal of the applied stress, the material experiences creep recovery. Figure 14.5 shows the creep and the creep recovery curves of the Maxwell element. It shows that the instantaneous application of a constant stress, Oo, is initially followed by an instantaneous deformation due to the response of the spring by an amount Oq/E. With the sustained application of this stress, the dashpot flows to relieve the stress. The dashpot deforms linearly with time as long as the stress is maintained. On the removal of the applied stress, the spring contracts instantaneously by an amount equal to its extension. However, the deformation due to the viscous flow of the dashpot is retained as permanent set. Thus the Maxwell element predicts that in a creep/creep recovery experiment, the response includes elastic strain and strain recovery, creep and permanent set. While the predicted response is indeed observed in real materials, the demarcations are nevertheless not as sharp. 

The creep and creep recovery curves for the Voigt elements are shown in Figure 14.8. 

Only the deformation due to the dashpot of viscosity tIj is retained as a permanent set. The creep and creep recovery curve of this model is shown in Figure 14.10. 

Figure 14 Typical creep compliance and creep recovery curve for on elastic solid and a viscoelastic fluid.

Fig. 2. Creep (curves (a) and (b)) and creep recovery (curves (a ) and (b )) for (A) an uncross-linked mbber and (B) a cross-linked mbber ( i - load applied fa - load removed)...

Thermomechanical analysis instruments are ideally suited to measure creep. In these experiments the increase in strain is measured with time following the application of a constant stress to the sample, followed by the recovery of the strain when the stress is removed. Figure 4.26 shows a typical TMA creep-recovery curve. In these experiments, an instantaneous compression or tensile stress is applied to the sample, and the time-dependent strain is measured at constant temperature. During the loading cycle, the resultant creep curve... 

Sketch creep and creep recovery curves for a VE solid and a VE fluid. Label all significant points. Also identify which curve would be expected to represent a linear polymer. Which would represent a cross-linked polymer. 

The creep portion of the creep-recovery curve was fitted to various combinations of linear viscoelastic elements illustrated in Scheme 2. 

Figure 6. Constant stress creep/creep recovery curves at 35 C for neat, polymer and rubber modified paving grade AC10-3 binders. Reference material Novaphalt AGIO.

It is important to understand the creep behavior shown in Figure 16.4 is not a simple superposition of linear elastic and viscous responses. Figure 16.5 shows the typical strain-time curves of ideal elastic material, ideal viscous material, and viscoelastic polymer fibers under constant stress. The ideal elastic material deforms instantaneously as the stress is applied and the stain remains constant with time. The removal of the stress causes the ideal elastic material to return to its original dimension. For the ideal viscous material, the strain increases linearly with time as long as the stress is applied. The removal of the stress does not return the ideal viscous material to the original dimension. This is because the eneigy introduced by the woik of the external stress is dissipated in the flow, leading to a permanent deformation. Both the ideal elastic and viscous responses contribute to the creep-recovery curve of the viscoelastic polymer fibers. However, the creep-recovery curve of viscoelastic polymer fibers is not a simple superposition of these two ideal behaviors. In addition to the ideal responses, the creep-recovery curve of the polymer fibers also includes retarded elastic response, in which... 

Figure 16.6. (A) Creep-recovery curve of a viscoelastic polymer fiber, and the corresponding (B) elastic, (C) retarded, and (D) viscous components.

Figure 16.23. Schematics of (A) the four-element model, and (B) the corresponding creep-recovery curve.

Figure 36 is representative of creep and recovery curves for viscoelastic fluids. Such a curve is obtained when a stress is placed on the specimen and the deformation is monitored as a function of time. During the experiment the stress is removed, and the specimen, if it can, is free to recover. The slope of the linear portion of the creep curve gives the shear rate, and the viscosity is the appHed stress divided by the slope. A steep slope indicates a low viscosity, and a gradual slope a high viscosity. The recovery part of Figure 36 shows that the specimen was viscoelastic because relaxation took place and some of the strain was recovered. A purely viscous material would not have shown any recovery, as shown in Figure 16b. 

First the sample, that was loaded to about 20% of its short-term yield strength or 13.8 MPa (2,000 psi), recovered almost completely one hour after the release of the load, the net strain being 0.03%. Second, the sample loaded to 66%of its short-term yield strength, or 41.4 MPa (6,000 psi), retained a strain of 0.8% at 1,000 hours after the release of the load. The initial strain was 2.8%, the strain from the 1,000 hour creep an additional 1.7%. Thus only about one-half the creep strain was recovered. Visually extrapolating the recovery curve reveals that even after a year (104 hr.), about one-third of the creep strain (0.6%) will remain. 

If the load is removed from a creep. specimen after some lime, there is a tendency for the specimen to return to its original length or shape. A recovery curve is. thus obtained if the deformation is plotted as a function of time after removal of the load,... 

Figure 4.16 The creep and recovery curve for a viscoelastic solid...

As shown by Fig. 3.11 for an applied force, the creep strain is increasing at a decreasing rate with time because the elongation of the spring is approaching the force produced by the stress. The shape of the curve up to the maximum strain is due to the interaction of the viscosity and modulus. When the stress is removed at the maximum strain, the strain decreases exponentially until at an infinite time it will again be zero. The second half of this process is often modeled as creep recovery in extruded or injection-molded parts after they cool. The creep recovery usually results in undesirable dimensional changes observed in the cooled solid with time. 

Creep measurements involve the application of a constant stress (usually a shearing stress) to the sample and the measurement of the resulting sample deformation as a function of time. Figure 9.6 shows a typical creep and recovery curve. In stress-relaxation measurements, the sample is subjected to an instantaneous predetermined deformation and the decay of the stress within the sample as the structural segments flow into more relaxed positions is measured as a function of time. 

Figure 9.6 Creep and recovery curve for a typical viscoelastic material...

Researchers have examined the creep and creep recovery of textile fibers extensively (13-21). For example, Hunt and Darlington (16, 17) studied the effects of temperature, humidity, and previous thermal history on the creep properties of Nylon 6,6. They were able to explain the shift in creep curves with changes in temperature and humidity. Lead-erman (19) studied the time dependence of creep at different temperatures and humidities. Shifts in creep curves due to changes in temperature and humidity were explained with simple equations and convenient shift factors. Morton and Hearle (21) also examined the dependence of fiber creep on temperature and humidity. Meredith (20) studied many mechanical properties, including creep of several generic fiber types. Phenomenological theory of linear viscoelasticity of semicrystalline polymers has been tested with creep measurements performed on textile fibers (18). From these works one can readily appreciate that creep behavior is affected by many factors on both practical and theoretical levels. 

If the loaded specimen is allowed to elongate for some lime and the stress is then removed, creep recovery will be observed. An uncross-linked amorphous polymer approximates a highly viscous Iluid in such a mechanical test. Hence the elongation-time curve of Fig. l-3c is fitted by an equation of the form... 

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). 

Strain from a creep experiment with constant applied stress cr followed by a creep recovery experiment (starting at t — 0) with zero applied stress, for a viscoelastic solid (lower curves) and a viscoelastic liquid (upper curves). The recoverable compliance can be determined from either creep or recovery. All deformation is recovered for solids but only the elastic part of the deformation is recovered for liquids. 

For a solid, the viscosity is infinite, and = sq all deformation in creep is subsequently recovered in creep recovery, with precisely the same time dependence, as shown in the lower curves in Fig. 7.25. In contrast, only the elastic part of the compliance of a liquid is recovered, as shown in the upper curves of Fig. 7.25 ... 

A wide variety of tests is performed in TMA, which are adapted from physical tests that were used before the instrument became commonly available. These tests may also be modeled or mimicked in TMA, such as heat distortion (Fig. 9) and softening points. Methods to obtain the modulus, compressive viscosity, and penetrative viscosity have been developed. Many of these methods, such as ASTM D648 for example, will specify the stress the sample needs to be exposed to during the run. In D684, a sample is tested at 66 and 264 psi. Most TMAs on the market today have software available that allows them to generate stress—strain curves and to run creep—recovery experiments. Some are also capable of limited types of stress relaxation studies (for example a constant gauge length test " ). 

See, for example, the product literature for Perkin Elmer s Diamond TMA and PYRIS software. The TMA and the DMA can both be used for running simple mechanical tests like stress-strain curves, creep-recovery, heat set and stress relaxation. Other vendors have similar packages. 

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