Creep isometric and isochronous

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. 

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. 

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. 

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... 

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...

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. 

Curves for creep isochronous stress and isometric stress are usually produced from measurements at a fixed temperature. Complete sets of these curves are sometimes available at temperatures other than the ambient. It is common, for instance, to find creep rupture or apparent... 

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. 

Figure 9.20 Creep test results, (a) Series of creep curves, (b) Isometric stress/time curve, (c) Isochronous stress/strain curve, (d) Creep modulus/time curve. After Whelan and Craft [26].

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