Creep curve

The creep curves will depend not only on stress but also on  

ISOCHRONOUS STRESS - STRAIN CURVE CREEP MODULUS - TIME CURVE 

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Creep curves Creep experiments Creep resistance C9 reformate Cremin... 

Fig. 3. The idealized creep curve where the distance from A to B represents the initial elongation on loading. See text.

Fig. 36. Typical creep curve for a viscoelastic material. Stress applied at time and removed at...

Figure 36 is representative of creep and recovery curves for viscoelastic fluids. Such a curve is obtained when a stress is placed on the specimen and the deformation is monitored as a function of time. During the experiment the stress is removed, and the specimen, if it can, is free to recover. The slope of the linear portion of the creep curve gives the shear rate, and the viscosity is the appHed stress divided by the slope. A steep slope indicates a low viscosity, and a gradual slope a high viscosity. The recovery part of Figure 36 shows that the specimen was viscoelastic because relaxation took place and some of the strain was recovered. A purely viscous material would not have shown any recovery, as shown in Figure 16b. 

Viscoelasticity can also be determined by a controlled stress rheometer. The shape of a creep curve can show that a fluid is viscoelastic, and the amount of recovery after the stress is removed gives a measure of elasticity. 

Creep tests require careful temperature control. Typically, a specimen is loaded in tension or compression, usually at constant load, inside a furnace which is maintained at a constant temperature, T. The extension is measured as a function of time. Figure 17.4 shows a typical set of results from such a test. Metals, polymers and ceramics all show creep curves of this general shape. 

Like metals, ceramics creep when they are hot. The creep curve (Fig. 17.4) is just like that for a metal (see Book 1, Chapter 17). During primary creep, the strain-rate decreases with time, tending towards the steady state creep rate... 

Major polymer manufacturers can usually supply creep data on those of their polymers which are likely to be subjected to long-term loads. A typical set of such curves is given in Figure 9.9. Sections through the creep curves at constant... 

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...

The theory relating stress, strain, time and temperature of viscoelastic materials is complex. For many practical purposes it is often better to use an ad hoc system known as the pseudo-elastic design approach. This approach uses classical elastic analysis but employs time- and temperature-dependent data obtained from creep curves and their derivatives. In outline the procedure consists of the following steps ... 

The appropriate figure for stress, modulus etc. is taken from the creep curve or a derivative curve. This is then inserted into the formula. 

A blow-moulded container, cylindrical in shape but with one spherical end, is prepared from the polysulphone whose creep curves at 20°C are illustrated in Figure 9.9. The cylindrical part of the container has an outside diameter of 200 mm and is required to withstand a constant internal pressure of 7 MPa at 20°C. It is estimated that the required service lifetime of the part will be one year and the maximum allowable strain is 2%. What will be the minimum wall thickness for satisfactory operation ... 

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. 

Occasionally creep curves are plotted as log (strain) against log (time). This is convenient because quite often this results in straight line plots suggesting that the creep behaviour can be described by an equation of the type... 

The most common method of displaying the interdependence of stress, strain and time is by means of creep curves. However, it should be realised that these... 

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. 

Once the limiting strain is known, design methods based on the creep curves are quite straightforward and the approach is illustrated in the following... 

Example 2.1 A ball-point pen made from polypropylene has the clip design shown in Fig. 2.11. When the pen is inserted into a pocket, the clip is subjected to a deflection of 2 mm at point A. If the limiting strain in the material is to be 0.5% calculate (i) a suitable thickness, d, for the clip (ii) the initial stress in the clip when it is first inserted into the pocket and (iii) the stress in the clip when it has been in the pocket for 1 week. The creep curves in Fig. 2.5 may be used and the short-term modulus of polypropylene is 1.6 GN/m. ... 

Example 2.2 A polypropylene beam is 100 mm long, simply supported at each end and is subjected to a load W at its mid-span. If the maximum permissible strain in the material is to be 1.5%, calculate the largest load which may be applied so that the deflection of the beam does not exceed 5 mm in a service life of 1 year. For the beam / = 28 mm and the creep curves in Fig. 2.5 should be used. 

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. 

As before, a similar result could have been achieved by taking a section across the creep curves at 1.5% strain, plotting an isometric graph (or a 1.5% modulus/time graph) and obtaining a value for modulus at 1 year (see Fig. 2.8)... 

For some plastics, particularly nylon, the moisture content can have a significant effect on the creep behaviour. For such plastics, creep curves are normally available in the wet and dry states and a knowledge of the service conditions enables the appropriate data to be used. 

For convenience so far we have referred generally to creep curves in the above examples. It has been assumed that one will be using the conect curves for the particular loading configuration. In practice, creep curves obtained under tensile and flexural loading conditions are quite widely available. Obviously it is important to use the creep curves which are appropriate to the particular loading situation. Occasionally it is possible to obtain creep curves for compressive or shear loading but these are less common. 

If only one type of data is available (e.g. tensile creep curves) then it is possible to make conversions to the other test modes. It should always be remembered, however, that these may not always be absolutely accurate for plastics under all situations. 

Example 23 A cylindrical polypropylene tank with a mean diameter of 1 m is to be subjected to an internal pressure of 0.2 MN/m. If the maximum strain in the tank is not to exceed 2% in a period of 1 year, estimate a suitable value for its wall thickness. AVhat is the ratio of the hoop strain to the axial strain in the tank. The creep curves in Fig. 2.5 may be used. 

This is a stress relaxation problem and strictly speaking stress relaxation data should be used. However, for most purposes isometric curves obtained from the creep curves are sufficiently accurate. By considering the 1.5% isometric curve shown in Fig. 2.8 it may be seen that the initial stress is 16 MN/m2 and the stress after 1 week is 7 MN/m2. 

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