JEC COMPOSITES MAGAZINE - Issue #102 - January/February 2016 - 43

trace

A miracle in trace:
Too good to be true! But it is truly true
Trace, the sum of the diagonal components of the
stiffness matrix of composites, is the one and only
one material property that is needed to determine
not only the stiffness of laminates but also their
weight savings and cost. That is truly true!

Fig. 2: Values of 2D and 3D trace for carbon/epoxy composites

For 2D trace, there are three stiffness components. Their percentage
fraction of trace is shown in Figure 3 for carbon, Kevlar and glass/
epoxy composites.

By
stePhen W. tsai
DePartment of aeronautics & astronautics
stanforD university

T

race is an invariant of tensorial transformation. Figure 1
shows examples of trace. There are many other invariants,
but trace is unique in that it has a physical meaning that
can guide composites design and testing. It remains the same
regardless if the laminate is stretched or twisted, or symmetric
or unsymmetric. No other property of composites is so unifying and universal. It is truly a miracle.

Fig. 3: Components in percentage of trace

In all three material systems, Qxx is the fibre dominant component.
In practice, only this component needs to be measured, i.e. trace =
Ex/0.88 for CFRP and Kevlar (for highly anisotropic composites,
Qxx = Ex). Glass fibre being less stiff, the magic factor is 0.70. Such
simplicity made possible with a single constant is truly true.

Universal laminates
Fig. 1: Definition of trace for stress, strain and stiffness

What are the values of trace for most common carbon/epoxy composites in 2-dimensional (plane stress) and 3D stiffness matrices?
They are shown in Figure 2.

In Figure 4, the longitudinal stiffness E1 shown on the left appears
totally random. For each material listed in the first column, the
longitudinal stiffness is different for each of the six laminates in the
first row. Thus, the usual procedure for laminate selection is to select
one material, say IM7/8552, and to find the best laminate for a given
set of loading conditions. In fact, for a structure that has multiple
laminates in a mosaic pattern, the optimum weight and cost savings

No102 January - February 2016 /

jec composites magazine 43



Table of Contents for the Digital Edition of JEC COMPOSITES MAGAZINE - Issue #102 - January/February 2016

Cover
Edito
Point of view : additive manufacturing
Contents
COMPANY & BUSINESS
DSM Composite Resins to be renamed Aliancys
Aerion and Airbus announce expanded collaboration on supersonic AS2
Agenda of Events
APPLICATIONS
Defence
Sports & leisure
MARKET
Overview
FEATURE AUTOMOTIVE
CFRP
Natural fibres
Prepreg
Thermoplastic
PUR
Phenolic
Process
RESEARCH & DEVELOPMENT
Impact resistance
Trace
TECHNOLOGY & INNOVATIONS
Control
Quality
Automation
Thermoplastic
Nano
Compound
Index
In the world
JEC COMPOSITES MAGAZINE - Issue #102 - January/February 2016 - Cover
JEC COMPOSITES MAGAZINE - Issue #102 - January/February 2016 - 2
JEC COMPOSITES MAGAZINE - Issue #102 - January/February 2016 - Edito
JEC COMPOSITES MAGAZINE - Issue #102 - January/February 2016 - Point of view : additive manufacturing
JEC COMPOSITES MAGAZINE - Issue #102 - January/February 2016 - 5
JEC COMPOSITES MAGAZINE - Issue #102 - January/February 2016 - Contents
JEC COMPOSITES MAGAZINE - Issue #102 - January/February 2016 - 7
JEC COMPOSITES MAGAZINE - Issue #102 - January/February 2016 - DSM Composite Resins to be renamed Aliancys
JEC COMPOSITES MAGAZINE - Issue #102 - January/February 2016 - Aerion and Airbus announce expanded collaboration on supersonic AS2
JEC COMPOSITES MAGAZINE - Issue #102 - January/February 2016 - Agenda of Events
JEC COMPOSITES MAGAZINE - Issue #102 - January/February 2016 - 11
JEC COMPOSITES MAGAZINE - Issue #102 - January/February 2016 - pub1
JEC COMPOSITES MAGAZINE - Issue #102 - January/February 2016 - pub2
JEC COMPOSITES MAGAZINE - Issue #102 - January/February 2016 - Defence
JEC COMPOSITES MAGAZINE - Issue #102 - January/February 2016 - Sports & leisure
JEC COMPOSITES MAGAZINE - Issue #102 - January/February 2016 - 14
JEC COMPOSITES MAGAZINE - Issue #102 - January/February 2016 - Overview
JEC COMPOSITES MAGAZINE - Issue #102 - January/February 2016 - 16
JEC COMPOSITES MAGAZINE - Issue #102 - January/February 2016 - 17
JEC COMPOSITES MAGAZINE - Issue #102 - January/February 2016 - CFRP
JEC COMPOSITES MAGAZINE - Issue #102 - January/February 2016 - 19
JEC COMPOSITES MAGAZINE - Issue #102 - January/February 2016 - 20
JEC COMPOSITES MAGAZINE - Issue #102 - January/February 2016 - 21
JEC COMPOSITES MAGAZINE - Issue #102 - January/February 2016 - 22
JEC COMPOSITES MAGAZINE - Issue #102 - January/February 2016 - Natural fibres
JEC COMPOSITES MAGAZINE - Issue #102 - January/February 2016 - 24
JEC COMPOSITES MAGAZINE - Issue #102 - January/February 2016 - 25
JEC COMPOSITES MAGAZINE - Issue #102 - January/February 2016 - 26
JEC COMPOSITES MAGAZINE - Issue #102 - January/February 2016 - Prepreg
JEC COMPOSITES MAGAZINE - Issue #102 - January/February 2016 - Thermoplastic
JEC COMPOSITES MAGAZINE - Issue #102 - January/February 2016 - 29
JEC COMPOSITES MAGAZINE - Issue #102 - January/February 2016 - 30
JEC COMPOSITES MAGAZINE - Issue #102 - January/February 2016 - PUR
JEC COMPOSITES MAGAZINE - Issue #102 - January/February 2016 - Phenolic
JEC COMPOSITES MAGAZINE - Issue #102 - January/February 2016 - 33
JEC COMPOSITES MAGAZINE - Issue #102 - January/February 2016 - 34
JEC COMPOSITES MAGAZINE - Issue #102 - January/February 2016 - Impact resistance
JEC COMPOSITES MAGAZINE - Issue #102 - January/February 2016 - Process
JEC COMPOSITES MAGAZINE - Issue #102 - January/February 2016 - 37
JEC COMPOSITES MAGAZINE - Issue #102 - January/February 2016 - 38
JEC COMPOSITES MAGAZINE - Issue #102 - January/February 2016 - 39
JEC COMPOSITES MAGAZINE - Issue #102 - January/February 2016 - 40
JEC COMPOSITES MAGAZINE - Issue #102 - January/February 2016 - 41
JEC COMPOSITES MAGAZINE - Issue #102 - January/February 2016 - 42
JEC COMPOSITES MAGAZINE - Issue #102 - January/February 2016 - Trace
JEC COMPOSITES MAGAZINE - Issue #102 - January/February 2016 - 44
JEC COMPOSITES MAGAZINE - Issue #102 - January/February 2016 - 45
JEC COMPOSITES MAGAZINE - Issue #102 - January/February 2016 - Control
JEC COMPOSITES MAGAZINE - Issue #102 - January/February 2016 - 47
JEC COMPOSITES MAGAZINE - Issue #102 - January/February 2016 - 48
JEC COMPOSITES MAGAZINE - Issue #102 - January/February 2016 - Quality
JEC COMPOSITES MAGAZINE - Issue #102 - January/February 2016 - 50
JEC COMPOSITES MAGAZINE - Issue #102 - January/February 2016 - 51
JEC COMPOSITES MAGAZINE - Issue #102 - January/February 2016 - Automation
JEC COMPOSITES MAGAZINE - Issue #102 - January/February 2016 - Thermoplastic
JEC COMPOSITES MAGAZINE - Issue #102 - January/February 2016 - 54
JEC COMPOSITES MAGAZINE - Issue #102 - January/February 2016 - Nano
JEC COMPOSITES MAGAZINE - Issue #102 - January/February 2016 - Compound
JEC COMPOSITES MAGAZINE - Issue #102 - January/February 2016 - Index
JEC COMPOSITES MAGAZINE - Issue #102 - January/February 2016 - In the world
JEC COMPOSITES MAGAZINE - Issue #102 - January/February 2016 - 59
JEC COMPOSITES MAGAZINE - Issue #102 - January/February 2016 - 60
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