Modulus time curve

ISOCHRONOUS STRESS - STRAIN CURVE CREEP MODULUS - TIME CURVE... 

The viscoelastic creep modulus may be determined at a given temperature by dividing the constant applied stress by the total strain prevailing at a particular time. Since the creep strain increases with time, the viscoelastic creep modulus must decrease with time (Fig. 2-23). Below its critical stress for linear viscoelasticity, the viscoelastic creep modulus versus time curve for a material is independent of the applied stress. In other words, the family of strain versus time curves for a material at a given temperature and several levels of applied stress may be collapsed to a single viscoelastic creep-modulus-time-curve if the highest applied stress is less than the critical value. 

Plasticizer and Copolymerization change the glass transition temperature as discussed in Chapter 1. Plasticixers have little effect on Copolymerization can change although less strongly than 7 x. As a result, the basic modulus-temperature and modulus-time curves are shifted as shown in Figure 8 for different compositions. The shift in the modulus-temperature curve is essentially the same as the shift in TK. The shift in the modulus-time curve includes this plus the effect of any change in ()jr... 

A series of modulus-time curves was also made for temperatures covering the entire viscoelastic spectrum. At higher temperatures, the instrument was first allowed to reach the desired temperature and was held there for half an hour. Samples were then quickly inserted. After 10 minutes moduli were measured as a function of time up to 1000 seconds. Total measuring time for each isotherm thus was kept to less than 30 minutes to minimize chemical decomposition and plasticizer evaporation. 

Figure 2. Isothermal modulus-time curves of pure polyvinyl chloride from 41.7° to 192.0°C.

Figure 3. Isothermal modulus-time curves of plasticized polyvinyl chloride (30 wt. % dioctyl phthalate) from —42° to 168°C.

Figure 1-3. Schematic modulus-time curve for a polymer at constant temperature.

The 10-second modulus at Tg is read directly from the master curve. Now, however, the master curve can be shifted to exhibit the behavior of the polymer at some other temperature. Applying this horizontal shift, with the slight additional vertical correction, if significant, allows one to "predict" the 10-second modulus, at this new temperature from the shifted curve. This procedure is repeated until the entire modulus-time curve is generated (Figure 4-7). 

Figure 9.20 Creep test results, (a) Series of creep curves, (b) Isometric stress/time curve, (c) Isochronous stress/strain curve, (d) Creep modulus/time curve. After Whelan and Craft [26].

Stress-relaxation modulus-time curves taken at different temperatures can be related to a master curve at a specific temperature. More detailed discussion of the WLF equation and time-temperature superposition can be found in [15]. 

Figure 4.2b Tensile modulus-time curves, reduced to 100 °C.

Curve 2 shows stress-growth with low rates of deformation, during which a part of memory is lost. If the deformation is stopped and the strain is held constant, the relaxation shown by curve 5 is observed. When the deformation is carried to the steady state condition, the stress becomes constant. Curve 1. It means that stress is proportional to strain rate and no longer increases with deformation. Curve 4 is the relaxation from the steady state. It is a manifestation of the steady state memory and its dissipation with time. When the relaxation curves, 3,4 and 5, are expressed as relaxation modulus-time curves, see Figure 6.70, larger differences are observed in the shorter times, but for the longer times the curves merge. 

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