Pseudo-elastic design

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 ... 

Since these assumptions are not always justifiable when applied to plastics, the classic equations cannot be used indiscriminately. Each case must be considered on its merits, with account being taken of such factors as the time under load, the mode of deformation, the service conditions, the fabrication method, the environment, and others. In particular, it should be noted that the traditional equations are derived using the relationship that stress equals modulus times strain, where the modulus is a constant. From the review in Chapter 2 it should be clear that the modulus of a plastic is generally not a constant. Several approaches have been used to allow for this condition. The drawback is that these methods can be quite complex, involving numerical techniques that are not attractive to designers. However, one method has been widely accepted, the so-called pseudo-elastic design method. 

It is wasteful of material to design a product to be in the linear viscoelastic region. The pseudo-elastic design method, for non-linear viscoelastic materials, gives a more reasonable design. The process requires an initial design,... 

The problems of exact design for a viscoelastic polymer with non-linear properties are severe. For example, in Figure 8.1 a) the stress-strain curve is linear only at the smallest strains (below 0.2%). Most plastic parts are designed to operate at strains well above 0.2%, and in this case exact stress analysis is impossible. In practice, a safe approximate procedure known as the pseudo-elastic design method is used. The salient features of the method, which is veiy straightforward to apply, are as follows ... 

This is an example of strain-limited design. We apply the pseudo-elastic design method, specifying the duration of loading as S hours (which is 18000 seconds). In order to determine the modulus, we need the isochronous stress-strain curve for 18000 s. Substituting in the equation,... 

The pseudo-elastic design method may be used for components submitted to intermittent loading, provided that the intervals during which the material is unloaded are suffident to allow virtually complete recovery. Some manufacturers provide recovery data that enable the validity of this assumption to be tested. Altemativefy, the Boltzmann superposition prind-ple may be used to determine whether the assumption gives a satisfactory q>proximatk>n (see Oiapter 4). If not, or if die 1 is varying in a more complex manner, a more complete anafysis of deflection behaviour based upon the Boltzmaim prindple may be necessary. Linearity can be assumed for strains up n> about 0.005. 

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