67
In Figure 3.16 and Figure 3.17 the error bars represent one standard
deviation for
10 simulation runs. In Figure 3.17 the error bars of the 20% control and 20% VTC
overlapped. This is because some simulated mats had no continuous layer of VTC for the
case of 20% VTC. Furthermore, the strand length of VTC was 25
mm shorter than the
normal strands in the core (see chapter 6 for effect of strand length on mechanical
properties). However, for 40% VTC, there was always continuous path through the VTC
strands on
the surface layers, which resulted in more increase in MOE. As showed in
Figure 3.17, there was no overlap of error bars between control and VTC panels.
Figure 3.17. Comparison of MPM calculation of modulus of OSB panel with 40% by
weight of VTC on the surface to the control at 20% compaction.
The 40% control MOE is higher than the 20% control MOE (see Figure 3.16 and
Figure 3.17). This is because the 40% control had more strands aligned parallel to the
axis of analysis. The 40% control is even higher than the case with 50% surface strands
in Figure 3.10. This is because the core strands in the 40% control was
randomly
oriented, thus contributed more to MOE than the 90 degree core plies in Figure 3.10.
4400
4800
5200
5600
6000
6400
6800
7200
7600
8000
0.00
0.01
0.02
0.03
0.04
0.05
1/D
t
(mm/MPa)
M
O
E
(
M
P
a
)
40% Weight VTC
Control 40%
68
Table 3.2: Experiment (in bending) and MPM simulation (in tension) moduli for control
and different weight VTC addition.
1)
Increase for VTC compared to control.
3.7 Modeling
3.7.1 Homogenized Model
A homogenized rule of mixtures (HROM) was developed to help interpret results
at different levels of compaction. The OSB composites are
approximately a three-layer
structure. For each layer, the axial modulus was replaced by an homogenized modulus by
considering the volume fraction of gaps within each layer. The moduli of the surface (
E
s
)
and core (
E
c
) layers were thus replaced by:
L
L
S
G
L
L
E
E
+
≈
and
W
R
C
G
W
W
E
E
+
≈
(3.7)
where
E
L
and
E
R
are the longitudinal and radial
modulus of the strands, <
L
> and <
W
>
are the average length and width of the strands, and <
G
L
> and <
G
W
>
are the average gaps
between strands in the surface and core layers (see “homogenize” step in Figure 3.18).
Next, it was assumed that these moduli increased uniformly due to compaction to
E
S
/(1
-
C
) and
E
C
/(1
-C
), where
C
is the fraction compaction (see last step in Figure 3.18).
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