Civil Engineering Reference
In-Depth Information
If the compliance matrix in Equation (3.1) is reduced to 2-D behavior (sheet anal-
ysis), the stress components σ
33
= τ
13
= τ
23
= 0. The third, fifth, and sixth rows and
columns are removed, yielding
1
−
ν
21
2
0
E
E
1
ε
ε
γ
σ
σ
τ
11
11
22
−
ν
1
12
1
(3.3)
=
0
22
12
E
E
2
12
1
0
0
G
12
The 2-D compliance matrix in Equation (3.3) may be inverted to yield the 2-D
stiffness matrix (Jones 1975),
E
ν
−ν ν
E
1
12
12
2
0
1
−ν ν
1
ε
ε
γ
σ
σ
τ
11
21
12
21
11
=
ν
−ν ν
E
E
(3.4)
22
21
1
2
22
12
0
1
1
−νν
12
12
21
12
21
0
0
G
12
3.6 FRP SHEET ENGINEERING CONSTANTS
FROM CONSTITUENT PROPERTIES
Using the mechanics-of-materials approach requires certain simplifying assumptions
in order to derive the mechanical properties of a unidirectional composite sheet. The
accuracy of the estimated property depends on the accuracy of the assumption made.
3.6.1 D
etermination
oF
E
1
The first modulus along the fiber direction may be determined by the rule of mix-
tures that results from the assumption of having the fiber and the matrix deform in
equal amounts along the fiber direction (Jones 1975). This assumption is known to be
very accurate, leading to an accurate estimation of the apparent Young's modulus
E
1
,
E
1
=
E
f
V
f
+
E
m
V
m
(3.5)
where
E
f
is the fiber modulus,
V
f
is the fiber volume fraction,
E
m
is the matrix modu-
lus, and
V
m
= 1 −
V
f
.
3.6.2 D
etermination
oF
E
2
The second modulus along the transverse direction is not as straightforward to
derive. One simplifying assumption can be made considering the same transverse
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