Equilibrium creep curve

Assume that the creep curve J (t,t ) was measured and the shape of the equilibrium creep curve J(t,AJ is known. Shift the latter until it coincides with the measured creep curve in the short-time domain, and one gets the hypothetical creep curve J(t,Ag). Now X may be determined as a function of t for all creep times investigated. Applying Equation 13 the time-age shift function b (A,A ) can be calculated. Otherwise, we know from Figure 2 that the following is valid ... 

This leads to the following important conclusion. On the supposition that shape and time position of the equilibrium creep curve, J(t,A ), as well as the time-age shift function, b (A,A ), are known at the aging temperature, we can construct the shape of the creep curve, J(t,t ), for any preconditioning times, t [9,17-19]. As a disadvantage of this procedure we have to determine the time-age shift function experimentally from very time-consuming aging creep experiments and that has to be redone for each aging temperature. 

Figures 4 and 5 [19,26,27] show creep measurements on PS N 7000 o.W. at the aging temperatures of T = 90°C and 60°C, respectively. The creep curves for PC 2800 at T = 120°C are given in Figure 6 [12,29]. The full curve in Figure 4 represents the measured equilibrium creep curve, where the preconditioning time was chosen long enough to reach equilibrium in volume. For PS N 7000 o.W. t is about 4 months to reach equilibrium at 90°C. For PC 2800 the equilibrium creep curve at T = 142.5°C is shown (Figure 6). After completition of the various preconditioning times indicated, the ereep experiments were started.

The creep curves under progressing aging show the general shape as anticipated in Figure 2. At short creep times they have the shape of the equilibrium creep curve... 

Figure 4. Creep curves of PS N 7000 o.W. under the influence of progressive aging at = 90°C after various preconditioning times full line represents the equilibrium creep curve at T. ...

The slight time difference between the two shift functions arises from the time position of the reference equilibrium creep curve chosen for the determination of b (A,A ). This position is about 1.5 lO s for a creep compliance value of J(t)= 10 Pa" (Figure 4). Due to the long preconditioning and the long creep time, the exact position of this curve on the time scale may be somewhat uncertain. If the time position of 1.5 lO s is reduced to lO s, the two curves in Figure 9 will coincide. 

Another problem arises in measuring the equilibrium creep curves at low temperatures, which has to be done if b (A,AJ is to be determined according to Equation 16. Within a reasonable experimental time scale the equilibrium state in volume can only be reached at temperatures near T [4,6,10,28]. At T = 90°C the preconditioning time for the equilibrium creep curve is about four months, at 85°C about 30 years, and at 70°C it would be thousands of years. The problem respecting the equilibrium creep curve is solved since it has been shown in [9] that for the evaluation of the time-age shift function it is not absolutely necessary to know the exact time position of the equilibrium creep curve at the aging temperature, but it is sufficient to know the shape of this creep curve. 

Take any known equilibrium creep curve as reference. 

Apply the calculated shift function to the equilibrium creep curve and construct the desired aging creep curve by calculating the corresponding X(t) values (c.f. Equation 7). 

The present contribution has shown that the creep behavior of amorphous polymers under the influence of progressing aging can be well described and predicted under any thermal prehistory applying the multiparameter model based on free volume. The only condition necessary is the knowledge of any measured equilibrium creep curve. For each material the multiparameter model with the given set of parameters allows the prediction of the behavior in volume under any complicated thermal history as well. Introducing some additional postulations, the free volume model is adapted to work at low temperatures, i.e., at temperatures below T. Next, the theory should be extended to measurements at still lower temperatures as well as to some other amorphous polymers. 

A good diagnostic for creep and stress relaxation tests is to plot them on the same scales as a function of either compliance (J) or modulus (G), respectively. If the curves superimpose, then all the data collected is in the linear region. As the sample is overtaxed, the curves will no longer superimpose and some flow is said to have occurred. These data can still be useful as a part of equilibrium flow. The viscosity data from the steady-state part of the response are calculated and used to build the complete flow curve (see equilibrium flow test in unit hi.2). 

Figure 4.16 Creep compliance (strain per unit imposed tensile stress) versus time for glassy polyvinylchloride after aging for various times after a quench from equilibrium at 90°C to a glassy state at 20°C. The master curve with many symbols is the superposition of all the curves and is obtained by a horizontal shift. The pluses were obtained by reheating to 90 C after 1000 days of aging, and then quenching again to 20°C, followed by one day of aging. This result shows that the aging process is thermoreversible. (From Struik 1976, with permission from the New York Academy of Sciences.)...

The / = 0 intercept of the long-time creep compliance is a measure of the stored elastic energy in flow, and is called the steady state compliance J q-The time-dependent strain of a viscoelastic solid in creep is sketched as the bottom curve in Fig. 7.24. The long-time creep compliance of any solid is simply a time-independent compliance /eq that is the reciprocal of its equilibrium modulus Geq. 

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