Modulus creep

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...

Polymers of this type have exceptional good values of strength, stiffness and creep resistance (see Table 18.13). After 100 h at 23°C and a tensile load of 70 MPa the creep modulus drops only from 4200 to 3(K)0 MPa whilst at a tensile load of 105 MPa the corresponding figures are 3500 and 2500 MPa respectively. If the test temperature is raised to 150°C the creep modulus for a tensile load of 70 MPa drops from 2400 to 1700 MPa in 100 h. 

The creep modulus will vary with time, i.e. decrease as time increases, in a manner similar to that shown for the relaxation modulus. The classical variation of these moduli is illustrated in Fig. 2.9. On log-log scales it is observed that there is a high value of creep or relaxation modulus at short times. This is referred to as the Unrelaxed Modulus and is independent of time. Similarly at long times there is a low value Relaxed Modulus which is also independent of time. 

Occasionally in creep analysis it is convenient to use a Creep Compliance instead of the creep modulus. This is simply given by... 

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. 

To calculate 5 after 1 month it is necessary to know the 1 month creep modulus. The stresses at the centre of the cap are biaxial (radial and circumferential) both... 

This indicates an exponential increase in strain from zero up to the value, (To/, that the spring would have reached if the dashpot had not been present. This is shown in Fig. 2.37. As for the Maxwell Model, the creep modulus may be determined as... 

A plastic is stressed at a constant rate up to 30 MN/m in 60 seconds and the stress then decreases to zero at a linear rate in a further 30 seconds. If the time dependent creep modulus for the plashc can be expressed in the form... 

A plastic with a time dependent creep modulus as in the previous example is stressed at a linear rate to 40 MN/m in 100 seconds. At this time the stress in reduced to 30 MN/m and kept constant at this level. If the elastic and viscous components of the modulus are 3.5 GN/m and 50 x 10 Ns/m, use Boltzmann s Superposition Principle to calculate the strain after (a) 60 seconds and (b) 130 seconds. 

Note that in this question an alternative solution may be carried out using the creep modulus but this causes slight inaccuracies. 

Viscoelastic creep data are usually presented in one of two ways. In the first, the total strain experienced by the material under the applied stress is plotted as a function of time. Families of such curves may be presented at each temperature of interest, each curve representing the creep behavior of the material at a different level of applied stress. Below a critical stress, viscoelastic materials may exhibit linear viscoelasticity that is, the total strain at a given time is proportional to the applied stress. Above this critical stress, the creep rate becomes disproportionately faster. In the second, the apparent creep modulus is plotted as a function of time. 

The viscoelastic creep modulus may be determined at a given temperature by dividing the constant applied stress by the total strain prevailing at a particular time. Since the creep strain increases with time, the viscoelastic creep modulus must decrease with time (Fig. 2-23). Below its critical stress for linear viscoelasticity, the viscoelastic creep modulus versus time curve for a material is independent of the applied stress. In other words, the family of strain versus time curves for a material at a given temperature and several levels of applied stress may be collapsed to a single viscoelastic creep-modulus-time-curve if the highest applied stress is less than the critical value. 

Different viscoelastic materials may have considerably different creep behavior at the same temperature. A given viscoelastic material may have considerably different creep behavior at different temperatures. Viscoelastic creep data are necessary and extremely important in designing products that must bear long-term loads. It is inappropriate to use an instantaneous (short load) modulus of elasticity to design such structures because they do not reflect the effects of creep. Viscoelastic creep modulus, on the other hand, allows one to estimate the total material strain that will result from a given applied stress acting for a given time at the anticipated use temperature of the structure. 

TTie strain readings of a creep test can be more accessible to a designer if they are presented as a creep modulus. In a viscoelastic material, namely plastic, the strain continues to increase with time while the stress level remains constant. Since the creep modulus equals stress divided by strain, we thus have the appearance of a changing modulus. 

The creep modulus, also known as the apparent modulus or viscous modulus when graphed on log-log paper, is normally a straight line and lends itself to extrapolation for longer periods of time. 

Apparent creep modulus. The concept of an apparent modulus is a convenient method for expressing creep, because it takes into account the initial strain for an applied stress plus the amount of deformation or strain that occurs over time. Thus, the apparent modulus Ea is calculated in a very simplified approach as ... 

Fig. 2-32 Example of plotting the apparent creep modulus vs. log time.

The resulting data can then be presented as a series of curves much like the isometric stress curves in Fig. 2-27. A relaxation modulus similar to the creep modulus can also be derived from the relaxation data. It has been shown that using the creep modulus calculated from creep curves can approximate the decrease in load from stress relaxation. 

Second, the creep modulus, also known as the apparent modulus or viscous modulus when graphed on log-log paper, is normally a straight line and lends itself to extrapolation for longer periods of time. The apparent modulus should be differentiated from the modulus given in the data sheets, which is an instantaneous or static value derived from the testing machine, per ASTM D 638. 

There is generally a less-pronounced curvature when creep and relaxation data are plotted log-log. Tliis facilitates extrapolation and is commonly practiced, particularly with creep modulus and creep-rupture data. 

Figure 8.8 Second stage of SIM. Creep modulus (load/strain) is plotted against the logarithm of the time measured from the respective temperature change.

Figure 8.9 Third stage of SIM. The sections of the creep modulus curve are shifted parallel to the time axis to produce a single continuous curve. Small corrections are applied to allow for fibre shrinkage and for the thermal history of the material.

Figure 9.1 Schematic prediction of creep modulus of polyester fibres from time-temperature shifted data (based on information from [5])...

The CAMPUS Plastics Database, covering some 40 manufacturers grades of materials, provides data to a standard format in accordance with ISO 10350 [11] and ISO 11403 [12]. It is available from participating manufacturers and through www.campusplastics.com. Singlepoint properties listed include creep modulus after 1 h and 1,000 h and thermal expansion. Multi-point data listed include creep modulus at five temperatures. The CAMPUS website provides addresses and telephone numbers from which data to the agreed format may be obtained, and links to some manufacturers websites directly. 

Creep is the time-dependent strain induced by a constant mechanical loading. The strain is a function of the stress level, the time for which the stress is applied, and the temperature. The results can be presented graphically in various ways by combining these three parameters or in quantified forms creep modulus and creep strength, for example. 

The creep modulus for a specified stress, time and temperature is the value of the stress divided by the strain measured after the selected time. 

Creep modulus and strength values are broadly inferior to their counterparts measured by dynamometry. 

Figure 3.34. Neat thermoplastics 100 h creep modulus examples versus stress at20°C...

Figure 3.35. Reinforced thermoplastics 100h creep modulus examples versus stress at 20°C. A figure of 4 after the acronym indicates 40% glass fibre, etc.

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