Dynamic Mechanical Analysis Using Complex Waveforms

Abstract

Small-amplitude oscillatory shear is a widely used method of determining the linear viscoelastic properties of materials. In the classical version of the technique, the material is subjected to a sinusoidal shear strain of amplitude γ₀ and frequency ω, such that the shear strain as a function of time is

$$ \gamma (t) = {\gamma _0}\;\sin \left( {\omega t} \right) $$

(7.1)

If the response is linear, i.e. if the strain amplitude is sufficiently small, the resulting shear stress will also be sinusoidal:

$$ \sigma (t) = {\sigma _0}\;\sin \left( {\omega t + \delta } \right) $$

(7.2)

where δ is the phase angle or mechanical loss angle and σ₀ is the stress amplitude. Furthermore, σ₀ at a given frequency is proportional to γ₀, again if the strain is sufficiently small that the response is linear.