86
4
N 1 1 1 2 2
=
−
τ
τ
(4.11)
N 2
2 2
3 3
=
−
τ
τ
(4.12)
where 1 is the primary direction, 2 is the secondary direction, and 3
is the neutral direction. Two new rheological properties may be
derived based on the previous equations. They are the FNSD coefficient and the SNSD coefficient:
Ψ 1
1
2
=
=
FNSD coefficient N / 
γ
(4.13)
Ψ 2
2
2
=
=
SNSD coefficient N / 
γ
(4.14)
The relaxation time, λ, is defined as a ratio of viscosity to the rigidity
modulus:
λ
η
= G
(4.15)
The rigidity modulus is given as
Rigidity modulus G
r
N
( ) =
2
1
(4.16)
Therefore, the relaxation time may be given as
λ τγ
=
N 1
(4.17)
The relaxation time, λ, is useful to find out the time required for a
material to cool so that stresses—especially residual stresses after
moulding—are relieved. The Deborah number is ratio of relaxation
time and process time, so
N
t
t
Deb
f
p
Deborah Number
Relaxation time
Process time
= =
=
(4.18)
where
5 t f  = Characteristic fluid time
5 t p =Characteristic process time
4.1.2 Viscoelasticity
Viscoelasticity is made out of two words: viscosity and elasticity. It
is the property of materials that exhibit both viscous and elastic
characteristics when undergoing deformation. In other words, the
viscous part of a material signifies its flow under stress, whereas the
elastic part signifies the recovery of shape after stress is removed.
4.1.2.1 Model Flows
In rheology, there are two main driving forces that cause flow to
occur. These forces are pressure difference and drag force.
Chapter 4 · Rheology in Processing of Polymeric Composites