Chemistry Reference
In-Depth Information
12.0
7.0
Applied Strain
6.0
10.0
γ
= 0.00
γ
= 0.01
γ =0.02
γ =0.05
γ = 0.10
γ= 0.20
γ = 0.50
γ =1.00
5.0
8.0
4.0
6.0
3.0
4.0
2.0
2.0
1.0
0.0
0.0
(a)
0.001 0.01
0.1
1
10
100
1000
(b)
0.001 0.01
0.1
1
10
100
1000
time /s
time /s
35.0
non - linear model
Kreiger-Dougherty
30.0
25.0
20.0
15.0
10.0
5.0
0.0
0.01
0.1
1
10
100
1000
10
4
stress /Pa
(c)
Figure 6.3
A plot of a simple nonlinear viscoelastic response for (a) the stress
relaxation as function of the applied strain, (b) stress as a function of
time at a shear strain g
¼
1 and (c) viscosity as a function of shear stress.
(Z(0)
¼
33 Pa s, Z(N)
¼
3Pas, a
¼
1, b
¼
0.1 m
¼
0.35 and t
¼
1 s).
flow curve is plotted. This tends to generate a loop for the ''up'' and ''down''
curves and the gap between the upper and lower curve is used to measure the
''degree of thixotropy'' of the system. Figure 6.4 illustrates this. The problem
with this classification is that it is very dicult to interpret. The nonlinear
approach used here is not ideal for developing loops since by decoupling
the relaxation process from the strain they cannot allow for the recovery of the
material. They do give a qualitative indication of the behaviour. The reason for
the observed loops is associated with the form of the stress overshoot and the
relaxation rate of the material. If the sample is deformed too quickly, steady-
state equilibrium is not achieved and we will sample a portion of the stress-
growth behaviour below the maximum stress, i.e. to the left of the peak shown
in Figure 6.3(b). The increasing rate curve can appear below the decreasing one
depending on the deformation time. However, if we deform the sample so we
are at the peak or just beyond in the stress growth curve, the viscosity will show
a relative reduction and the increasing rate curve will be above the reducing
one. Clearly, a crossover of shear up and down sweeps is possible if we were to
cross from one side of the peak to the other during a sweep. The magnitude of
the stress sweeping up relative to down depends upon the rate at which the
structure breaks down relative to its ability to attain an equilibrium response.
