Isochronous Creep Curves

The transition from linear to non-hnear viscoelastic behaviour and the transition threshold has been investigated with time and temperature. Thermal and mechanical tests were applied followed by isothermal creep tests at temperature steps and with differing stress levels. Isochronal creep curves were constructed to reveal the non-linearity threshold at different times and temperatures. The study was important for design and performance of elastomeric components. ... 

Isochronous creep curves at ambient and elevated temperatures and several stress levels... 

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...

Long-term deformation such as shown by creep curves and/or the derived isochronous stress-strain and isometric stress-time curves, and also by studies of recovery for deformation. 

These latter curves are particularly important when they are obtained experimentally because they are less time consuming and require less specimen preparation than creep curves. Isochronous graphs at several time intervals can also be used to build up creep curves and indicate areas where the main experimental creep programme could be most profitably concentrated. They are also popular as evaluations of deformational behaviour because the data presentation is similar to the conventional tensile test data referred to in Section 2.3. It is interesting to note that the isochronous test method only differs from that of a conventional incremental loading tensile test in that (a) the presence of creep is recognised, and (b) the memory which the material has for its stress history is accounted for by the recovery periods. 

The only unknown on the right hand side is a value for modulus E. For the plastic this is time-dependent but a suitable value may be obtained by reference to the creep curves in Fig. 2.5. A section across these curves at the service life of 1 year gives the isochronous graph shown in Fig. 2.13. The maximum strain is recommended as 1.5% so a secant modulus may be taken at this value and is found to be 347 MN/m. This is then used in the above equation. 

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 ... 

Creep data is usually obtained for a number of different stresses, as creep modulus will only be independent of stress over limited ranges. It may also be important to obtain data as a function of temperature. Commonly, isochronous stress-strain curves are derived from the creep curves at different stress levels as a useful way of displaying the information. 

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. 

The value of the simplified technique for producing isochronous stress-strain curves for non-linear isotropic materials by successive loading and unloading of a single sample have been amply demonstrated over many years and fully described elsewhere.These techniques become even more valuable in studies of anisotropy, where samples may be difficult to obtain in large numbers and where the scope of the problem is much larger. A considerable proportion of work on oriented materials reported in the literature is essentially confined to this measurement and does not include studies of time dependence of behaviour. Detailed work has been carried out validating this procedure for oriented materials by comparison of the isochronous stress-strain data with isochronous sections from families of creep curves. ... 

In studying time dependence, Le. creep behaviour, it is necessary to carry out tests at several stress levels in each direction of interest in the oriented material. I his can involve a prohibitive amount of experimental work and, in practice, little is generally lost by reducing the tests to, say, one creep curve and one isochronous stress-strain curve in each direction. The problem then becomes one of selection of the absolute value of stress for each of the creep curves and is most severe when non-linearity and its anisotropy are well developed. The choice of stress levels is arbitrary but interesting special cases are (a) equal stress levels at all angles and (b) equal strain ranges at all angles. 

The tensile creep behaviour of oriented high-density polyethylene has been studied by McCrum and coworkers " and by Ward and co-workers. " No creep curves as such are given, but the variation of isochronous modulus with temperature for specimens cut at various angles... 

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. 

Where it is necessary to compare several different materials, basic creep curves alone are not completely satisfactory. This is particularly so where the stress levels used are not the same for each material. If the stress endurance time relevant to a particular application can be agreed, a much simpler comparison of materials for a specific application can be made by means of isochronous stress-strain curves. 

Figures 18.19, 18.20, 18.21 and 18.22 show creep curves, isochronous stress-strain curves, and stress-time curves, for a typical acrylonitrile-butadiene-styrene (ABS) terpolymer and a typical unplasticised polyvinyl chloride (PVC).

Figure 10.1 Tensile creep of polypropylene at 60 °C. The stress and time dependence are approximately separable and therefore creep curves at intermediate stresses can be interpolated from a knowledge of two creep curves ( ) and the isochronous stress-strain relationship (X). (Reproduced with permission from Turner, Polym. Eng. Sci., 6, 306 (1966))...

The data in Figure 2.9 demonstrate the marked influence of density on the creep behavior of polyethylene. The curves in Figure 2.9 are relevant to a total strain of 1%, but similar plots for other permissible strains can be readily derived from the isochronous stress-strain curves. The linear relationship between creep and density for polyethylene at room temperature, irrespective of the melt index over the range investigated (i.e., 0.2-5.5), has enabled the stress-time curve of Figure 2.10 to be interpolated for the complete range of polyethylene. In this case, the data have been based on a permissible strain of 2%, but as previously explained, data for other permissible strains can be similarly interpolated from the creep curves. 

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