Hookes

When the magnitude of deformation is not too great viscoelastic behavior of plastics is often observed to be linear, that is the elastic part of the response is Hookean and the viscous part is Newtonian. Hookean response relates to the modulus of elasticity where the ratio of normal stress is proportional to its corresponding strain. This action occurs below the proportional limit of the material where it follows Hooke's Law (Robert Hooks 1678). Result is a Newtonian response where the stress-strain curve is a straight-line.

From such curves, however, it would not be possible to determine whether the viscoelasticity is in fact linear. An evaluation is needed where the time effect can be isolated. Typical of such evaluation is stress relaxation. In this test, the specimen is strained to a specified magnitude at the beginning of the test and held unchanged throughout the experiment, while the monotonically decaying stress is recorded against time. The condition of linear viscoelasticity is fulfilled here if the relaxation modulus is independent of the magnitude of the strain. It follows that a relaxation modulus is a function of time only.

There are several other comparable rheological experimental methods involving linear viscoelastic behavior. Among them are creep tests (constant stress), dynamic mechanical fatigue tests (forced periodic oscillation), and torsion pendulum tests (free oscillation). Viscoelastic data obtained from any of these techniques must be consistent data from the others.

If a body were subjected to a number of varying deformation cycles, a complex time dependent stress would result. If the viscoelastic behavior is linear, this complcx stress-strain-time relation is reduced to a simple scheme by the superposition principle proposed by Boltzmann. This principle states in effect that the stress at any instant can be broken up into many parts, each of which has a corresponding part in the strain that the body is experienced. This is illustrated where the stress is shown to consist of two parts, each of which corresponds to the time axis as the temperature is changed.

It implies that all viscoelastic functions, such as the relaxation modulus, can be shifted along the logarithmic time axis in the same manner by a suitable temperature change. Thus, it is possible to reduce two independent variables (temperature and time) to a single variable (reduced time at a given temperature). Through the use of this principle of reduced variables, it is thus possible to expand enormously the time range of a viscoelastic function to many years.

The relaxation modulus (or any other viscoelastic function) thus obtained is a means of characterizing a material. In fact relaxation spectra have been found very useful in understanding molecular motions of plastics. Much of the relation between the molecular structure and the overall behavior of amorphous plastics is now known.

Mechanical properties of crystalline plastics are much more complex than those of amorphous plastics. Viscoelastic data, at least in theory, can be utilized to predict mechanical performance of a material under any use conditions. However it is seldom practical to carry out the necessarily large number of tests for the long time periods involved. Such limitations can be largely overcome by utilizing the principle of reduced variables embodying a time-temperature shift. Plastic usually exhibits not one but many relaxation times with each relaxation affected by the temperature.

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