Effective creep modulus

Equation 2a for creep compliance can be inverted to give an effective creep modulus which may be more easily compared to the relaxation modulus, or... 

While the standard linear model does not precisely describe creep or stress relaxation behavior because of the assumption of a single relaxation time, the above arguments still ly to actual polymer behavior, where Dc (t) < Dr ) . Thus, for constant load applications, the creep compliance or its inverse, the so-called effective creep modulus should be used, whereas for constant displacement (e.g., a plastic nut and bolt), the relaxation modulus should be used. 

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. 

Physical properties of CSA-containing concretes (compressive strength, creep, modulus of elasticity and durability) are comparable to those of corresponding Portland cement concretes, especially when CSA is used at dosages of 8-11%. When the dosage exceeds the ranges mentioned above and no restraint is provided either internally (by reinforcement) or externally, a point is reached when the expansion will have a disruptive effect on mechanical... 

Craze growth at the crack tip has been qualitatively interpreted as a cooperative effect between the inhomogeneous stress field at the crack tip and the viscoelastic material behavior of PMMA, the latter leading to a decrease of creep modulus and yield stress with loading time. If a constant stress on the whole craze is assumed then time dependent material parameters can be derived by the aid of the Dugdale model. An averaged curve of the creep modulus E(t) is shown in Fig. 13 as a function of time, whilst the craze stress is shown in Fig. 24. 

An example of this effect is given in where the time to failure of a polymeric adhesive is measured for various applied Gi values. The corresponding creep modulus values for the various times were then obtained. From Eq. (37) ... 

In common with other plastics the effective modulus (deflection under load) of PAEK will change as a function of time, load and temperature. Creep modulus data in the form of strain measured as a function of time and temperature under a particular stress should be available from all suppliers of PAEK. The ratio of stress to strain then... 

Copolymer type and melt flow rate also influenee the creep behaviour. Copolymer grades of PP have substantially lower ereep modulus than the homopolymer grades. PP has a similar modulus to high density PE, but its resistance to creep is much better and, at a equivalent time under similar load, the creep modulus of PP is more than that of high density PE. However, the ereep resistance of amorphous plastics is much better than the semi-crystalline plastics such as PP and PE. Creep resistance of PP could be further improved by addition of fillers or reinforcements. The creep behaviour of moulded artefacts is affected by the residual stress or orientation effect in the moulded article. 

In a set of similar creep tests on the same material where the level of applied stress is varied at constant temperature, the effect of increasing stress normally is to decrease the creep modulus at corresponding test times. This is consistent with experience and with the theory of linear viscoelasticity. However, experimental data occasionally will show the opposite efl ect, or the creep curves at different stress levels will cross. This is probably due to experimental variation, and in such cases the experimental data may be regarded collectively as estimates of creep behavior over the range of the applied stesses involved. 

The creep modulus is directly affected by the increase in the level of stress and temperature. With the exception of extremely low strains around 1 percent or less, the creep modulus decreases as the amount of stress is increased. This effect is illustrated in Figure 2-32. In a very similar manner, as the temperature is increased, the creep modulus significantly decreases. Figure 2-33 shows the creep modulus versus time plotted at different temperatures. As one would expect, the combined effect of increasing stress level and temperature on creep modulus is much more severe and should not be overlooked. 

Figure 2-32. Effect of stress on creep modulus. (Reprinted with permission of McGraw-Hill Company.)...

To cope with the effect of stress level the designer has two alternatives. If the design problem is such that the stress level is predetermined, the designer should select the creep modulus curve whose stress level is the closest. If the stress level is not known beforehand, the designer should choose a creep modulus curve at a conservative stress level and check the choice after calculating a stress level. 

Even though torsion pendulum tests run at elevated temperatures provide very useful information regarding the dynamic mechanical properties of plastics, one must not forget that it is, nevertheless, a short-term test. The data obtained from creep modulus and creep rupture tests conducted at elevated temperatures must be relied on for long-term effects. 

Since extrapolation to a 50 year creep compliance or creep modulus depends critically on the short-term behavior, the moisture effects can potentially give significant errors, particularly if there is a one-time absorption of moisture into initially dry specimens. In tensile creep tests conducted over a two-year time period [7], the moisture fluctuations in the... 

In the derivation of equations 24—26 (60) it is assumed that the cylinder is made of a material which is isotropic and initially stress-free, the temperature does not vary along the length of the cylinder, and that the effect of temperature on the coefficient of thermal expansion and Young s modulus maybe neglected. Furthermore, it is assumed that the temperatures everywhere in the cylinder are low enough for there to be no relaxation of the stresses as a result of creep. 

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