Stress-log time curves

Strain and constant time can give respectively isometric stress-log time curves and isochronous stress-strain curves Figure 9.10). Whilst not providing any new information, such alternative presentations of the data may be preferred for certain purposes. 

Design plot, composed of stress/log time curves, for a PP copolymer (data supplied by ICI). 

A third curve can be derived from the basic family of creep curves creep modulus-time. This is a modified version of the isometric stress-log time curve, substituting creep modulus values at the intercept points for stress values. 

Figure 9.10. Presentation of creep data sections through the creep curves at constant time and constant strain give curves of isochronous stress-strain, isometric stress-log (time) and creep modulus-log (time). (From ICI Technical Service Note PES 101, reproduced by permission of ICI...

If an amorphous polymer is subjected to a stress relaxation experiment over a very long period of time, the modulus-log time curve will be similar to that shown in Fig. 5.11. There is a striking similarity in shape between the curves... 

The stress-strain-time data can be plotted as creep curves of strain vs. log time (Fig. 3.10 top view). Different methods are also used to meet specific design requirements. Examples of methods include creep curves at constant times to yield isochronous stress versus strain curves or at a constant strain, giving isometric stress versus log-time curves, as shown in the bottom views in Fig. 3.10. 

Figure 2.6 Isometric stress vs. log time curves derived from creep data...

Figure 10.2 shows relaxation modulus data obtained using several strains data for a solution of monodisperse polystyrene with cM = 5 10 [2]. The first thing that we notice is that, except at the shortest times and the smallest strains, the modulus curves drop to successively lower levels as the strain is increased. Furthermore, the shear stress versus time curves appear to be superposable by a vertical shift on this log-log plot, again except at quite short times. This... 

Stress-strain-time data are usually presented as creep curves of strain versus log time. Sets of such curves, seen in Fig. 2-27, can be produced by smoothing and interpolating data on a computer. These data may also be presented in other ways, to facilitate the selection of information to meet specific design requirements. Sections may be taken t... 

Stress relaxation master curve. For the poly-a-methylstyrene stress relaxation data in Fig. 1.33 [8], create a master creep curve at Tg (204°C). Identify the glassy, rubbery, viscous and viscoelastic regions of the master curve. Identify each region with a spring-dashpot diagram. Develop a plot of the shift factor, log (ax) versus T, used to create your master curve log (ot) is the horizontal distance that the curve at temperature T was slid to coincide with the master curve. What is the relaxation time of the polymer at the glass transition temperature ... 

For practical applications empirically determined creep data are being used, such as D(t) or, more often, E(t) curves at various levels of stress and temperature. The most often used way of representing creep data is, however, the bundle of creep isochrones, derived from actual creep curves by intersecting them with lines of constant (log) time (see Figure 7.7). These cr-e-curves should be carefully distinguished from the stress-strain diagram discussed before, as generated in a simple tensile test ... 

The first equation is much easier to manipulate than the second one. A simple check for separability of the variables is that curves of log strain vs. log time with stress as... 

Curves of stress (divided by absolute temperature) versus log time-to-break at various temperatures can be made to coincide by introducing the temperature-dependent shift factor flT. Application of the same shift factor causes the curves of the elongation at the break br versus the logarithm of time-to-break at various temperatures to coincide. A direct consequence is that all tensile strengths (divided by absolute temperature), when plotted against elongation at break, fall on a common failure envelope, independent of the temperature of testing. Fig. 13.84 shows the behaviour of Viton B elastomer. 

Fig. 11. Stress Relaxation curves for NaPOa sample of hipest molecular weight at various temperatures. log ,(t) (dynes/cm ) vs. log time (sec)...

The RPA can also do a stress relaxation test, Figure 37 shows RPA stress relaxation decay curves from three truck tread stocks of the same formulation. Each curve indicates different qualities of mix caused by variations in mixing work history (variations in total energy at Banbury dump). As the energy at dump for these tread mixes increases, the peak torque decreases, the slope of the log-log plot of the stress relaxation curve becomes steeper, the regression line intercept decreases, the integrated area under the curve decreases, and the time to a given % drop decreases [133]. Therefore a simple stress relaxation test is a fast and effective w ay to measure variations in viscoelastic properties for both raw rubber and mixed stocks. 

To test the stress—time superposition, the curve of creep strains shown in Figure 12.5 are presented as the dependence of creep compliance on log time in Figure 12.7. In the stress range from 10 to 30 MPa the difference between averaged compliance curves at different stress levels was less than the mean square error of the experimental data. Therefore, the dashed line in Figure 12.7 corresponds to the average compliance for stresses from 10 to 30 MPa. Thus, if the stress... 

The effect of nonlinearity increases gradually with increasing stress. It is seen from Figure 12.7 that the compliance curves at different stress levels are displaced relative to each other along the log time axis. These curves were shifted horizontally to produce the master curve consisting of several different symbols (see Figure 12.7) in Figure 12.8 [36]. The stress dependence of the stress shift factor is shown in an insert. The reference stress for the master curve is 30 MPa. 

Figure 12.17 shows a master stress relaxation curve, presented as ((7 — (T.)/ (T — (7j) vs. log time. The value of a. is determined for t— oo by an approximation to the experimental stress relaxation master curve. This type of plot has been recommended by one of us [52-61]. It brings out the common features of stress relaxation curves for metals, polymers and other materials. This is true not only for experimental but also for computer generated stress relaxation curves [60-62]. For a discussion of these common features see also [62]. The type of plot recommended first in [52] is also being used successfully for instance by Wortmann and coworkers [63-66]. They investigated a variety of materials including wool fibers and also very stiff aramid fibers such as Kevlar. 

The similarity is also preserved when we plot the master curves as ((7 — — (7j) vs. log time (Figure 12.20). The initial stress <7 (0)... 

A conventional creep curve as exhibited by most materials is illustrated in Fig. 2.25 although many engineers present the data using log axes to produce a graph of the form shown in Fig. 2.26. Data from families of strain-time curves at various values of constant stress are used to produce isochronous stress-strain curves (Fig. 2.27). These are obtained by cross-plotting stresses and strains at various times from the commencement of loading. The results of creep tests can also be used to derive constant strain, or isometric, curves of stress versus time, also as illustrated in Fig. 2.27. 

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. 

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