JEC COMPOSITES MAGAZINE - Issue #95 - Special JEC Europe - March 2015 - 75

Fig. 1: Left: Stress-strain curve of [0] for IM7/8552 and fictitious trace-based strength anchors using trace as
the slope represented as diamonds with a yellow core; Centre: Master stress-strain template using trace as
the normalizing factor for stress, and the longitudinal tensile and compressive strains at failure as the normalizing factors for strain; Right: Strengths and strain at failure predicted using master stress-strain relation and
compared to measured data (green dots). Note: (50/40/10) or (10/80/10) represent the percentages of [0], [±45]
and [90] in a laminate, respectively

needed; i.e., [0] from which X, X', ex, and
ex' can be measured. From these data, Ex
and Ex', Trace+ and Trace- can be calculated. Predicted values should be the upper
bound that does not include imperfections
in lamination, processing, curing, coupon
preparation and testing.
In Fig. 1 (right), measured data in solid
green dots with green lines for 3 laminates
(Hard1, [π/4] and Soft1) are superposed on
the master curves defined by blue lines and
maroon crosses. The uniaxial compressive
stiffness data are lower than the predictions,
while uniaxial tensile shows practically the
same data and predictions. One reason for
the lower stiffness is that the same trace was
used for both tensile and compressive loading. In fact, for this material of IM7/8552,
trace+ is 179 GPa and trace- is 158 GPa.
So there is a difference of 158/179 = 0.88.
Had we used the lower trace-, the laminate
stiffness would be 12% lower. Thus, a better
agreement between prediction and data.
Of the failure strains, the compressive
failure strains showed closer agreement
between data and predictions than tensile
failure strains. In fact, the difference can be
expressed by a conversion factor. In the tensile case, it has a value of 79% of the failure
strains measured in the laminates as com-

pared with the potentially full realization of
the fibre failure strain. The 21% discrepancy
can be caused by imperfections in materials, processing and testing as stated earlier.
Plies are not perfectly flat and fibres are not
perfectly straight in laminates. As load passes
first ply failure (FPF), there are micro-cracks
as well as delamination. All will reduce the
conversion of fibre strain capability to lower
values, such as the 79% observed for the
laminates of this material under particular
processing and consolidation.
There are also voids, resin-rich areas, damage
to coupon edges during machining, all leading to multiple in- and out-of-plane failure
modes. In the master curve, [0] coupons are
used for the basic anchor data from which
the stiffness and strength of all laminates can
be calculated. This coupon does not have
issues with most defects and imperfections
that are common in laminates cited earlier.
In fact, the estimation of laminate stiffness
and strength can be made even simpler
assuming that fibre stiffness and strength are
known. Then, we can rely on a rule-of-mixtures relation between fibre and [0] ply in
their stiffness and strength; i.e., Ex = vf × Ef;
X = vf × Xf. The trace+ = Ex/0.88; ex = X/
Ex. It can be assumed the trace- and trace+
are equal. However, an educated guess of

the compressive failure strain ex' will be
approximately 11 x 10-3. Then we can use
the master curve and generate the stiffness
and strength of all laminates with no test
at all. For some preliminary designs, such
estimates may be sufficient. Thus, our choice
of the number of tests required is between 1
and 0. Laminate tests are recommended to
calibrate quality of fabrication and testing.
In fact, the laminate panel can be one that
is as-built in the structure. It is again a good
way to determine the quality of fabrication
of the composite structure. We do not need
vf , Ey , Es , nx , any laminate, ... until we are
ready for an as-built laminate for a structural
application. This is a tremendous saving in
testing scope and time. In fact, for design
allowable generation and certification, the
master curve concept can bring testing of
composite materials in line with metals; i.e.,
one single test using [0] for trace, strength
and failure strain will be sufficient.
Using five CFRP materials, a summary of
the master curves is shown in Fig. 2. On
the left is a table showing the input data of
the five composites into the master curves.
Those with the lowest strains (lowest
conversion factors) are highlighted with yellow background. They are also noted in the
master curves.
It is interesting that the median values for all
tensile and compressive strains turned out to
be almost exactly unity. Also shown in green
dots is the specific stiffness of aluminium,
titanium and steel which happen to have
the same value (0.25 for trace-normalized
strength using the same ultimate failure
strain). A hard laminate of (50/40/10)
representing the percentages of [0], [±45]
and [90], respectively, will have twice the
stiffness of metals for the same weight, or
50% of the weight for the same stiffness.
For [π/4] with a factor of 0.34, it will be
0.35/0.25 = 1.4 or 40% stiffer for the same
weight, or 60% of the weight for the same
stiffness. Another benefit of the master
stress-strain curves is the ability to put all
CFRP data on one chart, like the one shown
in Fig. 2. For any new or improved material/
process, laminate data can be compared
directly with other material/process data.

No95 March 2015 /

jec composites magazine 75

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

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