Stress relaxation at different temperatures

Linear extrapolation from unified master lines with universal equations for creep and stress relaxation. In this method, the specimens are first aged at a given temperature for different times. The aged specimens are tested by creep or stress relaxation at this temperature at... 

Object in this section is to review how rheological knowledge combined with laboratory data can be used to predict stresses developed in plastics undergoing strains at different rates and at different temperatures. The procedure of using laboratory experimental data for the prediction of mechanical behavior under a prescribed use condition involves two principles that are familiar to rheologists one is Boltzmann s superposition principle which enables one to utilize basic experimental data such as a stress relaxation modulus in predicting stresses under any strain history the other is the principle of reduced variables which by a temperature-log time shift allows the time scale of such a prediction to be extended substantially beyond the limits of the time scale of the original experiment. 

To get accurate distributions of relaxation or retardation times, the expetimcntal data should cover about 10 or 15 decades of time. It is impossible to get experimental data covering such a great range of times at one temperature from a single type of experiment, such as creep or stress relaxation-t Therefore, master curves (discussed later) have been developed that cover the required time scales by combining data at different temperatures through the use of time-temperature superposition principles. 

Several attempts have been made to superimpose creep and stress-relaxation data obtained at different temperatures on styrcne-butadiene-styrene block polymers. Shen and Kaelble (258) found that Williams-Landel-Ferry (WLF) (27) shift factors held around each of the glass transition temperatures of the polystyrene and the poly butadiene, but at intermediate temperatures a different type of shift factor had to be used to make a master curve. However, on very similar block polymers, Lim et ai. (25 )) found that a WLF shift factor held only below 15°C in the region between the glass transitions, and at higher temperatures an Arrhenius type of shift factor held. The reason for this difference in the shift factors is not known. Master curves have been made from creep and stress-relaxation data on partially miscible graft polymers of poly(ethyl acrylate) and poly(mcthyl methacrylate) (260). WLF shift factors held approximately, but the master curves covered 20 to 25 decades of time rather than the 10 to 15 decades for normal one-phase polymers. 

Fig. 10. The stress relaxation at a constant length of PVA films for different D.H.s (O) 0.83 (A) 0.51 as a function of temperature...

Microstructures in deformed dolomite. The deformation characteristics of dolomite are markedly different from those of calcite and have been studied in detail by Barber, Heard, and Wenk (1981). Not only are the twin laws different, but twinning in dolomite occurs only at temperatures above about 250°C. The lower dislocation densities observed in twinned dolomite and at twin intersections is perhaps due to the greater ease of stress relaxation at the higher temperatures required for twinning. 

The second important consequence of the relaxation times of all modes having the same temperature dependence is the expectation that it should -bp possible to superimpose linear viscoelastic data taken at different temperatures. This is commonly known as the time-temperature superposition principle. Stress relaxation modulus data at any given temperature Tcan be superimposed on data at a reference temperature Tq using a time scale multiplicative shift factor uj- and a much smaller modulus scale multiplicative shift factor hf. 

Time-temperature superposition is applicable to a wide variety of viscoelastic response tests, as are creep and stress relaxation. We illustrate the principle by considering stress relaxation test data. As a result of time-temperature correspondence, relaxation curves obtained at different temperatures can be superimposed on data at a reference temperature by horizontal shifts along the time scale. This generates a simple relaxation curve outside a time range easily accessible in laboratory experiments. This is illustrated in Figure 14.13 for polyisobutylene. Here, the reference temperature has been chosen arbitrarily to be 25°C. Data obtained at temperature above 25°C are shifted to the right, while those obtained below 25°C are shifted to the left. 

When creep or stress relaxation tests are made at elevated temperatures, aging cITccts are generally present, and extrapolation to lower temperatures and longer times may be made using the techniques discussed later. It may be noted that it is fairly common to make creep tests on plastics at different temperatures, but for short times, and extrapolate using a time-temperature shift procedure. 

The practical timescale for most stress relaxation measurements ranges from 10 to 10 s but a wider range of temperamre is desirable. Such a range can be covered relatively easily by making use of the observation, first made by Leaderman, that for viscoelastic materials time is equivalent to temperature. A composite isothermal eurve eovering the required extensive time scale can then be constracted from data eolleeted at different temperatures. 

In many applications, plastic parts carry reasonably constant mechanical loads over periods up to few years. The polymer will creep during the lifetime of the part. At moderate load levels, long-term prediction of creep from short-term tests is possible, because the viscoelastic response of polymers (creep, stress relaxation) measured at different temperatures superimpose when shifted along the time axis [24]. 

The more direct identification of the molecular character of a secondary relaxation or information regarding the processes that are involved in the a-relaxation requires more information of a kinetic nature. This is accomplished by complementary experiments under different frequencies of probing to observe a temperature shift of the specific relaxation or by conducting stress-relaxation experiments at different temperatures and noting related shifts in the relaxation time of the specific transition. We explore these shifts in the following sections. 

Stress relaxation modulus observed in tension E(t) of polyisobutylene at different temperatures in the region of the glass-rubber relaxation (Tg -atW). At -83 at short time. E(t) approaches asymptotically the modulus of the glass at -40 C at long time. E(t) approaches asymptotically the modulus of the rubber. The relaxation is centred in the region of -66. Note the immense reduction in (t) of over 3 decades in a temperature rise of 43 C this behaviour is typical of amorphous polymers at the glass-rubber relaxation. 

Compressive creep tests allow measurement of strain as a function of time when a constant stress is applied. These can be conducted at several stress levels for aerogel of various densities. Loads are removed at the end of the creep test, and strains as a function of time are monitored to determine the recovery behavior. Compressive relaxation tests can be conducted at different strain levels. The relaxation functions determined at the same strain level at different temperatures can be shifted horizontally to determine whether a master curve can be formed for use to determine the long-term behavior. Recovery behavior after relaxation can also be characterized by monitoring the stress as a function of time after removing partially the step strain. For aerogels that contain polymers such as X-aerogels... 

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