Phenomenological description of time-dependence

If the stress in a polymer is raised abruptly from zero to a value a clearly below the yield strength and then kept constant, the polymer answers with a time-dependent strain e t). The strain increases instantaneously to a value q (see figure 8.6), as in the case without time-dependent elastic behaviour, but then it further increases with time. We define the time-dependent Young s modulus at constant stress Ec t) as 

the time-dependent Young s modulus is denoted as creep modulus. The deformation, and thus Ec t), approaches a constant value if the loading time becomes large. If the load is removed after a time to, the strain decreases instantaneously by the time-independent strain eo and then reduces slowly to zero. The retardation time Tret is defined as the time needed to reduce the time-dependent part of the strain by a factor 1/e (figure 8.6). 

At small strains, polymers are linear viscoelastic An increase in stress causes a proportional increase in strain. At larger strains, this is not true anymore. 

If we prescribe the strain instead of the stress of a component, the stress in it decreases with time stress relaxation). Similar to the retardation process, the stress increases instantaneously, but then it decreases with time and approaches a constant value. Similar to the creep modulus, we can define the relaxation modulus 

As we already saw, in reality, the behaviour of a polymer is never purely viscoelastic. There is always an instantaneous elastic contribution to the deformation (without any time-dependence) and, at elevated temperatures, a plastic deformation which is irreversible. Similar to the elastic properties, the plastic properties of a polymer also strongly depend on time. Thus, polymers are viscoplastic i. e., they creep.  

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