JEC COMPOSITES MAGAZINE - Issue #88 - April 2014 - Special JEC Americas Spring Edition - 34

C-Ply

nates B and C turned out well. Substantial
savings in layup time can be achieved if
C-Ply is used. With these master ply curves,
it is very easy to find good replacements. In
most cases, the replacement laminate can be
a few percent away from the initial laminate.
In practice, due to uncertainties in laminate
properties, it is difficult if not impossible that
tests differentiate between the original and
replacement laminates.

Strict order
A popular complaint lodged against composites is the multitude of properties from
those of plies to laminates. Stiffness and
strength have directional variations, and design and testing are random processes with
no order or preference. The lack of order in
the composites world is not true.
As a matter of fact, the stiffness and strength
of composite laminates are controlled by a
very strict order. We have the mathematical
foundation to back us. We can learn how to
test composites with no more complication
than for metals. One coupon and one test
should provide the calibration point for the
entire world of composites, just like metals.
As regards stiffness, the plane-stress stiffness
is a tensor, designated as [A°]. It has two
normal, one Poisson and one shear components. These are not separate entities but are

precisely related by strict mathematical rules.
Tensors are mathematical entities defined
by transformation relations (how their components change as the reference coordinate
axes change) and have two invariants; two
numbers that do not change. One of them
is called trace, which is the sum of A11° +
A22° + 2A66°. So Tr [A°] is the first thing
one should know about the stiffness of a
composite material. The value stays constant
for all laminates. This is order number 1.
We can test any one coupon from unidirectional to laminates with any ply combination. There is a strict relation between all
their values and a relation to trace. It turned
out that the longitudinal stiffness Ex for
all the CFRP that we have found is 88% of
trace. So if Ex is 88 GPa, the trace will be 100
GPa. We also know that A11° of [π/4] is 1/3
of trace. So its A11° is 33 GPa. For this quasiisotropic laminate, we know immediately
the shear modulus A66° is 1/6 of trace and
16.6 GPa because 1/3 + 1/3 + 2*1/6 = 1.
There are three components of trace. If two
of them are known, the third one is fixed; it
cannot change. So we will pick the components that are easy to test. Uniaxial tests
are much easier than shear tests. So once
the trace of a composite and the uniaxial
stiffness are known, it is possible to calculate
the shear. This is the practice for metals,

although we are not sure when the shear
of metal is ever measured. For [π/4], A11°
= A22°. So we only need to measure one
of them. The other two including A66° are
known.
In principle, we need only one test to know
what all the other stiffness values would be.
But the best is to test the [π/4]. From that
we can get the trace and from the trace we
can estimate the stiffness of not only the
unitape but all laminates because there is
such a strict order. A laminate stiffness has
two components: one relates to the material
(as the value of trace), and the other one to
the geometry. Different ply compositions or
stacking sequences are a function of geometry. So if we have a design, trace can be used
to go from material to material and laminate
to laminate. It is that simple. But we must
know and trust trace.
A critical matter concerns CFRP where
this strict order happens to be the same for
all such composites that we have tried. It
works well with much less errors than the
usual ones that occur in testing. Thus the
theory that spells out the strict order is more
accurate than we can test. We also know that
there are many sources of uncertainty in the
material and processing of a laminate. We
have not found the same consistency in glass
composites (GFRP) as in CFRP. We are not
sure why this is so.
The trace-based theory has been tested in
several papers in this volume, and has thus
been reasonably well substantiated. But we
are just starting on this new path and much
more work remains to be done.
The same concept was also extended to the
strength of laminates. The corresponding
tensor is the failure parameter in strain space.
The tensor is [G], which is the quadratic
term in the Tsai-Wu failure criterion. It is
sufficient to say, we have found a strict order
in strain to failure that can be traced to trace
[G]. Again, in principle, the failure can be
established from one test to determine the
strength of all CFRP and all the corresponding laminates.

Fig. 7: Using the same ply design chart, laminates A, B and C from Figure 6 can be replaced by new laminates
at lower cost

34 jec composites magazine / No88 April 2014

One more practical consequence of the trace

JEC COMPOSITES MAGAZINE - Issue #88 - April 2014 - Special JEC Americas Spring Edition

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