Creep isochrones

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 ... 

From a bundle of creep isochrones the tendency of a material to creep, can be read-off in a glance, namely from their mutual distance. Along horizontal lines of constant stress, the increase of deformation by creep can be detected. When the isochrones are straight lines, the superposition principle holds. Compliances at certain combinations of cr and t follow from the (reciprocal) slopes of connection lines to the origin. 

Creep isochrones are, sometimes, used to obtain information on stress relaxation the stresses are then read-off on a vertical line (constant strain). In general this is, however, not allowable, since E(t) in relaxation is not equal to 1 /D(t) in creep. In a linear region this objection is not too stringent for want of something better, the procedure can be used as a first approximation (data on stress relaxation are very scarce ). 

These three complications are schematically shown in Figure 7.11, using creep isochrones as a reference (a) a Kelvin-Voigt element has been chosen with a spring in series (a Burgers model without irreversible flow). 

For practical purposes the lower limit of the critical strain can be used as a criterion. This value appears, moreover, to be not much dependent on temperature, so that it can be considered as a material constant. It varies from -03% for PS to 2.2 % for PP. From creep isochrones a stress level can now quite easily be detected at which, within a given time of usage, no damage to the material is to be expected. This stress level is, of course, much lower than the one we found from Figure 7.20. 

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... 

ISOCHRONOUS STRESS - STRAIN CURVE CREEP MODULUS - TIME CURVE... 

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. 

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. 

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. 

The duration of testing is not specified, but ISO 11403-1 [36] proposes that the loads should be 20%, 40%, 60% and 80% of the maximum load for the respective temperature and that strains should be tabulated after 1,10,100,1,000 and 10,000 h (10,000 h equals 13.7 months). This data will enable creep strain curves and an isochronous diagram to be prepared (load plotted against strain for each duration) with sufficient accuracy for design. 

The isochronous stress-strain curves for the creep of PP bead foams (254) were analysed to determine the effective cell gas pressure po and initial yield stress do as a function of time under load (Figure 11). po falls below atmospheric pressure after 100 second, and majority of the cell air is lost between 100 and 10,000 s. Air loss is more rapid than in extruded PP foams, because of the small bead size and the open channels at the bead boundaries, do reduces rapidly at short yield times <1 second, due to proximity of the glass transition, and continues to fall at long times. 

Figure 7.8 gives some bundles of isochrones as supplied by a polymer manufacturer (GE). As we saw before, when comparing POM with PC, also here the higher rate of creep of a semi-crystalline polymer (PBTP), compared with the amorphous blend of PPE with PS, is obvious. 

Creep at different temperatures can be represented by separate bundles of isochrones. A simple time-temperature shift could mean that for higher temperatures shorter time values could be written at each curve. It is, however, easier to transform the stress scale. Sometimes this is possible with sufficient accuracy in those cases only one bundle of isochrones is given with different stress scales for a number of temperature levels (Figure 7.9) (see also Qu. 7.13). 

The thermal and UV stabilising action of linear, low molec.wt. unsaturated polyesters and epoxy resins in PVC was investigated using short-term tensile and long-term tensile creep testing and calculations of isochronous creep... 

Figure 2. Failure envelope for Sample A. Log percent elongation vs. log stress (engineering) for various isochrones obtained from creep data. Line a corresponds to necking, line p to the fully necked condition, and line y to fracture.

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. 

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