JEC COMPOSITES MAGAZINE - Issue #95 - Special JEC Europe - March 2015 - 73

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Fig.1: Omni strain LPF envelopes for various CFRP based on Tsai-Wu (blue)
and Max strain failure criteria (maroon)

in Figure 1. The LPF envelopes are
anchored by the uniaxial tensile and
compressive strains to failure. The
shear strength for each material is
estimated at the interaction along the
q-axis, shown as blue rimmed circles
with yellow core.
Finally one omni strain envelope can
represent all stress-space envelopes
as shown in Figure 2. Thus the order
established by invariants in trace and
omni envelopes is the basis of our
new book. It puts priority on seemingly random collection of material
properties. Intuitively it makes sense
that for composite laminates made
with unitape, [0] is the driving force.
We need thus the stiffness and failure
strains in tension and compression of
this unitape. Other properties such
Composite Materials
Design and Testing
by Steven Tsai

An innovative invariant-based approach
developed makes
trace of the plane
stress stiffness matrix
as the heart and soul
of composite materials. It can put order in
both stiffness and strength of composite laminates. Testing unidirectional [0] specimens
should provide enough information for the

Fig.2: One omni strain-space Tsai-Wu envelope for T700/2510 can represent
multiple stress-space envelopes

the transverse and shear stiffness and
strength are of secondary importance
and can be ignored for preliminary
design, screening and rating of a
material or manufacturing process.
Resin matrix properties contribute to
12 percent of trace, thus to the laminate stiffness, and must also affect
the measured tensile and compressive failure strains in some fashion.
Concentrating only on [0] properties
should not be too upsetting because
we have never known the transverse
and shear properties of carbon fibers
and have managed to move on. We are
proposing to do the same here.

Conclusions
Trace can bring order into the design
and testing of composites. With trace,
composites are easy to understand
prediction of the failure envelope of laminates.
Then, laminates can be tested "as-built" and
data compared to the predicted properties
using a master stress-strain template, which
greatly reduces the number of tests required.
This method can be much more effective
than the traditional building block approach.
With fewer specimens to be tested, emphasis
can be placed on the quality of laminates as
reflected by the conversion of stiffness and
strength from processing and its associated
defects. Environmental effects such as hotwet conditions can also be accounted for
through their respective trace values. This

and can be used more optimally,
as demanded by Mr. Byrne. In our
book, new design and manufacturing
methods are proposed, which can
make composites much more competitive and cost-effective. Hopefully,
we will see expanding applications
in both airplanes and cars. Small companies can now demonstrate rapidly
their new or improved materials and
processes. n
More information:
stanford.edu/group/composites
Acknowledgements
The authors wish to thank
Waruna Seneviratne of Wichita
State University for his design
allowable data on the first 5 materials
shown in Figure 1.
The C-Ply data were furnished
by Philippe Sanial of Chomarat.

new approach unlocks the mystery of composites design and opens up many opportunities
in laminate design and manufacturing.

They talk about it
" ... very impressed with the underlying logic
and ingenuity ... ... offers an expedient process for introducing, evaluating and adopting
new candidate material systems without the
need for extensive and expensive testing ..."
Isaac Daniel, Northwestern University
"... a major finding in the mechanics of composites ... " Peter Linde, Airbus

No95 March 2015 / jec

composites magazine 73

http://www.stanford.edu/group/composites

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

Table of Contents for the Digital Edition of JEC COMPOSITES MAGAZINE - Issue #95 - Special JEC Europe - March 2015