Isochronous curves

As indicated above, the stress-strain presentation of the data in isochronous curves is a format which is very familiar to engineers. Hence in design situations it is quite common to use these curves and obtain a secant modulus (see Section 1.4.1, Fig. 1.6) at an appropriate strain. Strictly speaking this will be different to the creep modulus or the relaxation modulus referred to above since the secant modulus relates to a situation where both stress and strain are changing. In practice the values are quite similar and as will be shown in the following sections, the values will coincide at equivalent values of strain and time. That is, a 2% secant modulus taken from a 1 year isochronous curve will be the same as a 1 year relaxation modulus taken from a 2% isometric curve. 

From the 3 year isochronous curve for polypropylene, the initial modulus, E =... 

From the 1 year isochronous curve, the initial modulus = 370 MN/m2... 

From the 1 day isochronous curve, the maximum stress at which the material is linear is 4 MN/m. TTiis may be converted to an equivalent shear stress by the relation... 

Figure 24. Measured 6 Tla) vs. Th diagram used to infer the ages of lava flows from Mt. Etna in the age range 0 to 8 ka. The eurves labeled 0, 0.5, 1... ka correspond to isochron curves. The isochron 0 is defined by the 6 Tla)o-Th correlation observed in historical lava flows of the last two millennia (Condomines et al. 1995). Five samples of previously unknown ages are reported in this diagram (Condomines et al. 1995, and unpublished results).

The optimum time step in a FEM-CVA simulation is the one that fills exactly one new control volume. Once the fill factors are updated, the simulation proceeds to solve for a new pressure and flow field, which is repeated until all fill factors are 1. While the FEM-CVA scheme does not know exactly, where the flow front lies, one can recover flow front information in post-processing quite accurately. One very common technique is for the simulation program to record the time when a node is half full, / = 0.5. This operation is performed when the nodal fill factors are updated if the node has fk <0.5 and fk+1 >0.5 then the time at which the fill factor was 0.5 is found by interpolating between tk and tk+l. These half-times are then treated as nodal data and the flow front or filling pattern at any time is drawn as a contour of the corresponding half-times, or isochronous curves. 

Figures 2.37 and 2.38, show the isochronal curves of the permittivity and loss factor for P2NBM and P3M2NBM as a function of temperature at fixed frequencies. A prominent relaxation associated with the dynamic glass transition is observed in both polymers. Clearly the effect of the methyl substitution in position 3 of the norbornyl group is to decrease the temperature of this relaxational process.

Applying the model of vacancy-controlled ordering to isochronal curves of deformed samples yielded vacancy parameters in correspondence with results on recrystallized materials and experimental results of small step aimealing. 

Isometric curves are obtained by plotting stress vs. time for a constant strain isochronous curves are obtained by plotting stress vs. strain for a constant time of loading. These curves may be obtained from the creep curves by taking a constant-strain section and a constant-time section, respectively, through the creep curves and replotting the data, as shown in Eigure 3.17. 

FIGURE 3.17 (a) Isometric and (b) isochronous curves from creep curves. 

Isochronous curves, on the other hand, are more advantageously obtained by direct experiments because they are less time consuming and require less specimen preparation than creep testing. The experiments actually involve a series of mini creep and recovery tests on the material. Thus a stress is applied to a specimen of the material, and the strain is recorded after a time t (typically 100 sec). The stress is then removed and the material is allowed to recover. This procedure is repeated unit there are sufficient points to plot the isochronous curve. 

For ease of reference, the creep data are usually replotted in one or more different ways, as Ulustrated in Figures 8.14(a) and (b). Isochronous stress-strain curves (Figure 8.14(a)), which are discussed in Chapter 4, are included in most discussions of creep characteristics. From isochronous curves of this type, the engineer can determine the secant modulus of the pofymer at any given strain or applied stress and time under load. This creep modulus E(creep compliance at the appropriate stress and time creep data is in the form of isometric curves, as shown in Figure 8.14(b), which are helpful in designing plastic components to a... 

Fig, 2.27. Isometric and isochronous curves taken from a set of creep data. (a) Isometric stress v. log time, (b) Creep curves, (c) Isochronous stress v. strain. 

Calculate the proportional limit, CTprop, by the isochronous curve. 

This viscoelastic mechanism corresponding to the transition zone (the primary or a mechanism in the language applied to classification of mechanisms m amorphous polymers as discussed in Chapter 15) can be identified only at low degrees of crystallinity. For example. Fig. 16-14 show isochronal curves for modulus and... 

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