Time-age shift function

J(A.,T, ) has known the meaning of the creep function at constant temperature as a function of the effective time A.. All these results may be transferred immediately to the problem of viscoelastic behavior under the influence of aging at constant temperature [9,15]. The temperature history has to be replaced by the degree of aging. A, of the sample and the time-temperature shift function, a(T,T ), by the time-age shift function, b (A,A ). The degree of aging, also called the age of the sample, defines the time elapsed from the last quench from the equilibrium state down to the aging temperature so far A, can then be expressed ... 

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. 

If these physical aging effects that occur during creep measurements are due to the decrease of free volume, the time-age shift function must be directly related to the change in free volume. In recent years several expressions have been proposed to describe volume recovery behavior [4,5,8,20-25] in which the temperature and structure dependence of the retardation times is based on activation processes [21], configurational entropy [22,23] or free volume [4,5,8,20,24,25]. 

The necessity to find an adequate reduction method for the creep curves in the short-time region is obvious if we try to construct the function b (A,A ) from Figures 5 and 7 for creep times smaller than 0.1-0.3 t. Due to the extremely flat course of the creep curves at low temperatures, the time-age shift function without vertical shift is only accessible at very long creep times, i.e., at 50°C for creep times longer than 5 lO s. 

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. 

Calculate the time-age shift function a, according to Equation 25 with respect to the f and S values obtained from step 2. 

The effects of a number of environmental factors on viscoelastic material properties can be represented by a time shift and thus a shift factor. In Chapter 10, a time shift associated with stress nonlinearities, or a time-stress-superposition-principle (TSSP), is discussed in detail both from an analytical and an experimental point of view. A time scale shift associated with moisture (or a time-moisture-superposition-principle) is also discussed briefly in Chapter 10. Further, a time scale shift associated with several environmental variables simultaneously leading to a time scale shift surface is briefly mentioned. Other examples of possible time scale shifts associated with physical and chemical aging are discussed in a later section in this chapter. These cases where the shift factor relationships are known enables the constitutive law to be written similar to Eq. 7.53 with effective times defined as in Eq. 7.54 but with new shift factor functions. This approach is quite powerful and enables long-term predictions of viscoelastic response in changing environments. 

Class 2 capacitors are based on ferroelectric materials with considerably higher dielectric constants such as those listed in Table 3.10. These materials exhibit shifts in dielectric constant as a function of time (aging). This phenomenon is a result of ferroelectric domain movement over time. A typical aging curve is shown in Fig. 3.27. The application of heat. 

Figure 11.7. A. NMR spectra of an Al-Mg alloy containing zinc, showing the signal from the matrix (upper) and from the precipitate, represented by stoichiometric MgnAli2 (lower). The 2 middle spectra show the effect of aging time at 200°C on the relative amounts of matrix and precipitate phases. B. Knight shift of the matrix of binary Mg-Al alloys as a function of aluminium content. C. Knight shift of the precipitate phase in Mg-Al alloys doped with zinc as a function of the Zn content. From Celotto and Bastow (2001) by permission of Elsevier Science.

Fig. 22 Steady state incoherent intermediate scattering functions (z) measured in the vorticity direction as functions of accumulated strain jf for various shear rates y data from molecular dynamics simulations of a supercooled binary Lenard-Jones mixture below the glass transition ate taken from [91]. These collapse onto a yield scaling function at long times. The wavevector is q = 3.55/R (at the peak of Sq). The quiescent curve, shifted to agree with that at the highest y, shows ageing dynamics at longer times outside the plotted window. The apparent yielding master function from simulation is compared to those calculated in ISHSM for glassy states at or close to the transition (separation parameters s as labeled) and at nearby wave vectors (as labeled). ISHSM curves were chosen to match the plateau value fq, while strain parameters yc = 0.083 at = 0 solid line) and y, = 0.116 at e = 10 dashed line) were used from [45]...

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