From Eqs. (4.334) and (4.337), we have
dσ ¼ e pdε À
1
1 À Φ
e p þ e r
WndΔγ
ð6:348Þ
From Eqs. (6.345) and (6.348), we have
C ¼
dσ
dε
¼ ~
p À
1
1ÀΦ
~
p þ~ r
À
Á
Wn
Â
à n
à 1
1ÀΦ
~
p þ~ r
À
Á
Â
Ã
m 4 þ
1
1ÀΦ
n
Ã
1 À Φ
n
Ã
!
a
Wn
m 1 m 2 H
0 Wn
&
'
ð6:349Þ
6.8 Verification Examples
6.8.1 Material Properties of ATH
ATH (particle filler) is regarded as an isotropic elastic material. The thermomechanical properties of ATH as provided by the manufacturer are as follows:
Poisson ratio of ATH: ν f ¼ 0.24
Elastic modulus of ATH: E f ¼ 70 GPa, CTE: α f ¼ 1.47 Â 10
À6 /
C
The average diameter of a filler particle is 35 μm.
6.8.2 Properties of PMMA
The matrix PMMA is a very common polymer, which has been extensively studied.
Young’s modulus of PMMA as function of temperature is as shown in Fig. 6.16
(Cheng et al. 1990a, b, c):
0
1
2
3
4
5
-50
0
50
100
150
200
Temperature
)
a
P
G
(
s
u
l
u
d
o
M
s
'
g
n
u
o
Y
Fig. 6.16 Young’s
modulus of PMMA as a
function of temperature
(Cheng et al. 1990a, b, c)
332
6 Unified Micromechanics of Particulate Composites