Recovery, creep and

In order to obtain a general model of the creep and recovery functions we need to use a Kelvin model or a Kelvin kernel and retardation spectrum L. However, there are some additional subtleties that need to be accounted for. One of the features of a Maxwell model is that it possesses a high frequency limit to the shear modulus. This means there is an instantaneous response at all strains. The response of a simple Kelvin model is shown in Equation 4.80  

Here the term ik is the retardation time. It is given by the product of the compliance of the spring and the viscosity of the dashpot. If we examine this function we see that as t - 0 the compliance tends to zero and hence the elastic modulus tends to infinity. Whilst it is philosophically possible to simulate a material with an infinite elastic modulus, for most situations it is not a realistic model. We must conclude that we need an additional term in a single Kelvin model to represent a typical material. We can achieve this by connecting an additional spring in series to our model with a compliance Jg. This is known from the polymer literature as the standard linear solid and Jg is the glassy compliance  

We can see that as the stress is applied the strain increases up to a time t = t. Once the stress is removed we see complete recovery of the strain. All the strain stored has been recovered. The material has the properties of an elastic solid. In order to achieve viscous flow we need to include an additional term, the viscous loss term. This is known as a Burger Body  

Now as t - 0 the spectral function L reduces to the area under the distribution. This is the steady state compliance Je  

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The response of different materials to a stress applied at time t = followed by removal of that stress at t =, ie, creep and recovery, is shown in... 

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. 

Creep and Recovery Behaviour. Plastics exhibit a time-dependent strain response to a constant applied stress. This behaviour is called creep. In a similar fashion if the stress on a plastic is removed it exhibits a time dependent recovery of strain back towards its original dimensions. This is illustrated in... 

It can be seen therefore that although the relaxation behaviour of this model is acceptable as a first approximation to the actual materials response, it is inadequate in its prediction for creep and recovery behaviour. 

It may be seen that the simple Kelvin model gives an acceptable first approximation to creep and recovery behaviour but does not account for relaxation. The Maxwell model can account for relaxation but was poor in relation to creep... 

Since there can be an infinite number of combinations of creep and recovery periods it has been found convenient to express this behaviour in terms of two dimensionless variables. The first is called the Fractional Recovery, defined as... 

If there have been N cycles of creep and recovery the accumulated residual strain would be... 

Recovery is the strain response that occurs upon the removal of a stress or strain. The mechanics of the recovery process are illustrated in Fig. 2-34, using an idealized viscoelastic model. The extent of recovery is a function of the load s duration and time after load or strain release. In the example of recovery behavior shown in Fig. 2-34 for a polycarbonate at 23°C (73°F), samples were held under sustained stress for 1,000 hours, and then the stress was removed for the same amount of time. The creep and recovery strain measured for the duration of the test provided several significant points. 

Fig. 2-34 Tensile creep and recovery during the intermittent loading.

Figure 4 illustrates the creep and recovery of a four-element model with the following constants ... 

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

The applicability of the Gibson and Ashby approach, whereby deformation mechanisms are identified, to a range of thermoplastic polymer foams is explored. LDPE, EVA and PP foams were produced by the BXL Plastizote nitrogen expansion process. A full range of mechanical properties is discussed from the simpler aspects of modulus and strength to the complexities of creep and recovery performance. 8 refs. 

The response of different materials to a stress applied at time t = t0 followed by removal of that stress at t = tl, ie, creep and recovery, is shown in Figure 16 (145). For an elastic material (Fig. 16a), the resulting strain is instantaneous and constant until the stress is removed, at which time the material recovers and the strain immediately drops back to zero. In the case of the viscous fluid (Fig. 16b), the strain increases linearly with time. When the load is removed, the strain does not recover but remains constant. Deformation is permanent. The response of the viscoelastic material (Fig. 16c) draws from both kinds of behavior. An initial instantaneous (elastic) strain is followed by a time-dependent strain. When the stress is removed, the initial strain recovery is elastic, but full recovery is delayed to longer times by the viscous component. 

Dislocation climb only becomes of practical significance at elevated temperatures because of its dependence upon vacancies whose number and mobility depend very strongly on the temperature. Dislocation climb is important in high temperature creep and recovery phenomena. See Fig. 13. 

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...

Bulk creep and recovery in systems with viscosity dependent upon free volume. Trans. Soc. Rheology 5, 285—296 (1961b). 

Figure 2. Creep and recovery of ASA polymer Luran S 757R stress = 20...

The loss of modulus caused by crazing becomes less pronounced as the draw ratio is increased, especially in tests carried out at lower stress levels. This observation supports earlier conclusions drawn from creep studies on other rubber-toughened plastics (6) if the specimen can reach a strain of 5% largely or entirely by shear mechanisms, the loss of modulus resulting from the creep and recovery program is quite small if, on the other hand, crazing is the dominant mechanism, the loss in modulus is large. 

Because of the potential applications of high modulus polyethylene for reinforcement of brittle matrices, it was soon recognized that the creep and recovery behaviour should be studied in some detail. 

In the first of a series of publications. Wilding and Ward compared the creep and recovery behavimolecular weight drawn monofilaments (Rigidex 50 Grade, M, = 6,180 = 101,450) of draw ratios 10, 20 and 30 with... 

Wilding and Ward showed that the creep and recovery behaviour of the low molecular weight samples could be represented to a good approximation by the model representation shown in Fig. 35(b), which consists of a Maxwell and Voigt element in series, on the basis that the parameters E, E, r and r), are dependent on the stress level. Data for the creep response of the samples under discussion at a constant applied stress Op were therefore fitted to the equation... 

Fig. 35a-c. Mechanical models of creep and recovery, (d) Modified model for viscoelastic creep... 

Recent work has shown that the creep and recovery behaviour of ultra high modulus polypropylenes is very similar to that of LPE. Again the Sherby-Dorn plots form a good entry to the detailed examination of the creep response. Plateau creep behaviour similar to that of LPE has been observed, and the high stress process correlates well with the a-relaxation process in terms of its activation energy. 

Eedi and Morawetz (26) studied the creep and recovery of copolymers of styrene containing 2.3% methacrylic acid and their salts with Li... 

A reported dependence of on M - for narrow distribution polystyrenes recently reported by Tobocsky et al. 209a) deduced from stress relaxation measurements has not been confirmed by extensive studies of Plazek and O Rourke (180b) on the creep and recovery behavior of similar polymers. The latter found jjr cc over the interval Z, to Z 1.6 x 10, as reported in Fig. 1,... 

Fig. 1. Tensile creep and recovery of rubber-modified plastics, showing axial strain (x), lateral contraction ( ), and volume strain (o) for ASA polymer and polypropylene copolymer at 20 °C...

In the present work the effect of temperature on the rheological behaviour of wheat gluten in D20 is compared to that in water. The viscoelastic response was studied in shear by combining dynamical measurements and creep and recovery tests, in order to encompass a large timescale. 

Rheological measurements were performed in shear using a stress controlled rheometer (Carri-Med CSL 100) operating in cone-plate geometry. Each sample is submitted successively to a first frequency sweep in range 10 3-40 Hz under 3% strain, to a creep and recovery test, and finally to a second frequency sweep identical to the first one. The dynamical strain amplitude (3%) and the value of the creep stress (chosen so as to keep the maximum strain below 10%) were set in order to remain within the linear viscoelasticity domain. Creep and creep recovery were recorded during 20 h and 80 h, respectively, times which allowed the steady state to be reached in all cases. A fresh sample was used for each solvent/temperature combination. 

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