If De 5 1 we call the material a liquid; and at De 4 1 the material appears
solid. It is only if De is of order unity that we observe viscoelastic behavior.
Variation of the frequencyðoÞin dynamic tests thus amounts to varying the
Deborah number.
Nonlinearity. Many rheological measurements, e.g., virtually all
dynamic measurements, are carried out in the so-calledlinear region. This
means that the strain is proportional to the stress. In practice, however (e.g.,
during processing), large deformations are often applied, and in most
viscoelastic materials the linear region is quite small, i.e., the proportionality
of stress and strain is lost at a small value of the strain, say, between 10^4
and 0.02. Figure 5.11 gives some examples of the velocity gradientC—be it
due to shear or to elongation—resulting from applying increasing stresses
ðsÞ. Curve (a) relates to a Newtonian liquid and curve (b) to a strain rate
thinning liquid.
FIGURE5.11 Examples of the relation between velocity gradientCand stresssfor
liquidlike systems.syis yield stress. See text.