JEC COMPOSITES MAGAZINE - Issue #95 - Special JEC Europe - March 2015 - 72

design & testing
Tab. 1: Trace-normalized longitudinal elastic modulus E1* for various CFRP laminates

Laminate

[0]

[0/90]

[p/4]

Soft1

Hard1

Soft2
Soft1

Hard2
Hard1

Percent [0]

100

50

25

10

50

9

55

Percent [+-45]

Trace

0

0

50

80

40

73

36

Percent [90]

GPa

0

50

25

10

10

18

9

IM6/epoxy

232

0.87

0.46

0.34

0.23

0.52

0.23

0.55

IM7/977-3

218

0.88

0.46

0.34

0.23

0.52

0.23

0.55

T300/N5208

206

0.88

0.47

0.34

0.22

0.52

0.23

0.55

IM7/MTM45

195

0.90

0.47

0.34

0.21

0.52

0.22

0.56

IM7/8552

192

0.89

0.47

0.34

0.21

0.52

0.22

0.56

T800/Cytec

183

0.88

0.47

0.34

0.21

0.52

0.22

0.55

IM7/8552 N

180

0.88

0.47

0.34

0.22

0.52

0.22

0.56

AS4/F937

168

0.88

0.47

0.34

0.21

0.52

0.22

0.55

T800S/3900

168

0.90

0.48

0.34

0.21

0.52

0.21

0.56

T800 C-Ply 64

163

0.87

0.46

0.34

0.23

0.51

0.23

0.55

AS4/3501

162

0.85

0.46

0.34

0.24

0.51

0.23

0.54

T650/epoxy

160

0.87

0.47

0.34

0.22

0.51

0.22

0.55

T4708/MR60H

158

0.90

0.48

0.34

0.21

0.52

0.21

0.56

T700/2510

144

0.88

0.47

0.34

0.22

0.52

0.22

0.55

AS4/MTM45

143

0.89

0.47

0.34

0.21

0.52

0.21

0.55

T700 C-Ply 55

139

0.87

0.47

0.34

0.22

0.52

0.22

0.55

Median (Master Ply)

0.88

0.47

0.34

0.22

0.52

0.22

0.55

Coeff variation

1.5%

1.2%

0.3%

4.2%

0.6%

2.8%

0.7%

74.1 GPa. Thus, for the stiffness of
any CFRP, we just need to know its
trace from which the stiffness of all
laminates from this material is known
using the factors of master ply shown
in this table. We will show in the next
article that only one test at most is
sufficient to measure the trace.
With trace, material and laminate
substitution can be done by linear
scaling. For example, the factor
for [π/4] is 0.34; that for Hard1
[50/40/10] is 0.52. Thus, Hard1
is stiffer than [π/4] by 0.52/0.34 =
1.53, or 53%. Between materials, the
relative values of trace will be the
factors. In the second column, the
trace of IM6/epoxy is 232 GPa; that
of IM7/977-3, 218 GPa. Their relative stiffness is 232/218 = 1.06, or 6%

higher. So the [π/4] of the same two
materials will be different by 1.06.
Of course, we can go from IM7/9773 [π/4] to IM6/epoxy Hard1, we
will have an increase in stiffness of
1.53 x 1.06 = 1.62. This is another
simple example of how trace can
unify materials and laminates. Scaling
is linear; the predictions are better
than measurements. If measured data
do not match the predictions, the
difference can be traced to factors
involved in the quality of materials,
panel fabrication, specimen cutting,
test procedure, and so forth. There
is no mystery. Invariant trace makes
composites as simple to understand
as metals.

Failure criteria
Finally, commonly used failure crite-

72 jec composites magazine / No95 March 2015

ria can be reduced to two criteria for
the prediction of last-ply-failure: 1)
interactive Tsai-Wu; 2) non interactive maximum strain. The latter
would give the same value for Hashin
and maximum stress criteria. This
simpliication of failure criteria is
shown in Figure 1.
The omni-strain LPF envelopes
cover all ply orientations or coordinate transformation. They are thus
invariant and simple to generate
and provide a conservative basis
since the actual laminate may have a
higher strength value. The power of
the omni LPF envelope is that one
envelope shown in Figure 2 (top) can
represent all laminates in stress space
shown in Figure 2.
With invariant-defined trace for stiffness and omni FPF and LPF strain
envelopes, testing becomes extremely
simple. Such a benefit is also felt in
design and manufacturing. There is
no mystery how many tests should be
run for allowable generation and certification. We need one trace for tension and one for compression if they
are very different. Then, for LPF failure criteria, we recommend the use
of an omni envelope, which can be
defined by 2 strain values: longitudinal tensile and compressive strengths,
that appear as strain anchors in Figure
2. Design and testing are as simple
as those for metals. We do not see
the need for design allowable generation that takes months and millions
of euros. In the next article, we will
explore how testing for data generation can best be made.
Trace is the heart and soul of composite materials. We have seen in Table
1, its value, like 232 GPa for IM6/
epoxy, is used to find stiffness of all
laminates. Trace is thus the one and
only value needed. With aid of omni
envelope, one envelope in strain space
gives the conservative estimate of
all ply angles in laminates, as shown
JEC COMPOSITES MAGAZINE - Issue #95 - Special JEC Europe - March 2015

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