Andrade creep

In creep experiments at the long-time end of the plateau zone where the terminal zone is being entered, it has been shown by Plazek - that the creep compliance can be described with high accuracy by the relation 

Equation 28 would imply that the creep compliance in excess of the steady-flow term increases without limit instead of approaching the customary limit J , and cannot be valid at extremely long times. However, in a range where the last two terms are of similar magnitude, it can provide a useful simplification in calculating 1)0 from creep measurements. It is not necessary to wait until J t) is a strictly linear function of time. A plot of J t) against is made, and Ja and are determined 

Andrade plot of the creep of polyfdimethyl siloxane), weight-average molecular weight 2.7 X 10 at 25°C for 36 days. The term //jjo is negligible. 

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Retardation spectra Lp were determined from the Jp(t) curves of Figure 5.10. The results reduced to Tg = -20 C are shown in Figure 5.8, where the principal maximum concentration of retardation mechanisms is shown to be at correspondingly longer times as Tg is increased with additional crosslinking. The logarithmic curves at shorter reduced times showing a slope of 1/3 for all three fluoroelastomers are consequences of the assumed Andrade creep (Plazek, 1960 Plazek and O Rourke, 1971), J(t) = Jg + at short times used to determine Jg. 

The Lo(t) that was obtained is shown in Fig. 12.22 with the retardation spectrum obtained from the shear creep compliance function, J(t). The levels of the short time behavior are matched. Three feamres should be noted. The functionality at short times is the same within experimental uncertainty. The 1/3 slope of log L(t) at short time indicates that the response is dominated by motions that contribute to Andrade creep. [66,85-87,141,142]... 

As mentioned above, if it is assumed that Andrade creep is the tme functional form exhibited by amorphous materials at short times at 7g, a common behavior is operatimially observed that can be used to determine corresponding Tg s for these materials. Since the mobility of the local mode motions determines the Tg, a kinetic characterizing variable, such as the Andrade coefficient /3, which is determined by these motions, can be associated with Tg. If we examine the glassy Andrade regions of the retardatimi spectra for many... 

Andrade creep n. A type of creep behavior in which the comphance of the sample is proportional to the cube root of the time under stress. A variety of polymers exhibit this behavior. 

See also andrade creep, delayed deformation, drift, cold flow, compression set, tension set, and strain relaxation. 

Equation (6.7), representing transient creep, is often referred to as )S-creep or Andrade creep , since Andrade [24] was the first to show that it applies to many materials. The creep behavior obeying Eq. (6.6) is often called a or logarithmic... 

In Figure 24 (90) the lowest molecular weight, narrow distribution PS depicted as A25 (M = 47,000) has only two contributions, (i) at short times a common linear portion between log A,r of — 1 and 3 with a slope of 1/3 and it is followed by (2) a S5mimetrical peak centered at log A. = 6. The short-time region reflects the presence of Andrade creep in which the recoverable creep compliance is a linear fimction of An alternative description by a generalized Andrade creep with, with Pa not necessarily equals to 1/3 and varies from one polymer to another, is possible. Actually such a generalized Andrade creep is the short-time part of the... 

Although the short-time compliance data of diverse amorphous materials can be represented by Andrade creep (eq. 32), the reason for such a universal behavior is unclear. The alternative description of the local segmental contribution by equation 29 with (1— ) = Pa not necessarily equal to 1/3 and its value dependent on the material itself offers a different possibility. The generalized Andrade creep... 

If the association is extensive enough a weak solid is formed that will exhibit a yield point. The data in Fig. 24 illustrate the properties observed with such an aggregated solution. For strains less than a critical value Yy of about 5% the creep was fully recoverable and fitted by the cube-root, or Andrade, creep relation for the compliance y(t)/a ... 

If <7 (o)) is very flat, H (which reflects the slope of G ) is small by comparison, and as a result G and G t) are almost identical, as seen in Chapter 2. Similarly, if J is very flat, it is almost identical with 7(r) — r/jjo- Another speciflc case of some interest occurs when G = G" and both are proportional to as specifled in certain theories (Chapters 9 and 10) and toughly fulfilled in the transition region between glasslike and rubberlike consistency then equation 50 reduces to G(t) = 0.79G (1 //). Still another example is given by the so-called Andrade creep behavior of cross-linked systems at long times (Chapter 13), where the compliance can be represented by the empirical equation J(t) = Ja + At an equivalent frequency oj = 1 /r, the dynamic compliances are then given by ... 

Plazek, D.J. (1960) Dynamic mechanical and creep properties of a 23% cellulose nitrate solution Andrade creep in polymeric systems. J. Colloid. Sci., 15, 50. 

Figure 5.10 Retardation spectrum of the poly(vinyl acetate) of Figs. 5.7 and 5.8 versus reduced time (logarithmic scales). The slope is 1/3 in the glassy region reflecting Andrade creep.The plateau zone is between the two peaks, the second of which marks the start of the terminal zone. It was not possible to obtain superposition using a single reference temperature, and different values were used in short and long-time zones.This is reflected in the difference between the curves obtained with = 35 X (dashed line) and with 60 X (points). From Plazek [31].

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