1. Comparative Study: Aluminum and Steel
Tooling and the Deformation of Co-Cured
Flexible Printed Circuit Boards
Monica Mohal, Mark Guadagni
Abstract- The effect of the mismatch of the
coefficient of thermal expansion of tooling surfaces
and carbon fiber lay-ups has been well documented
[1][2]. Co-curing is an effective joining technique
where both the curing and joining process for the
composite structure can be achieved simultaneously.
In this application a high precision flexible printed
circuit board undergoes unwanted distortions in
multiple directions during the co-cure process. This
study investigates the effect of substituting different
tooling material to mitigate the distortions seen in
the co-cured product. These results show promise for
the success of future manufacturing and packaging
of flexible printed circuit boards with carbon fiber
structures.
Introduction
The characteristics of carbon fiber, namely
long radiation length1, high thermal conductivity,
and specific modulus are particularly well suited for
high precision mechanical support structures in high
energy particle detectors. Figure 1 shows the inside
of the ATLAS experiment, a typical high energy
particle detector located in CERN, Switzerland. The
Atlas structure is gargantuan, measuring 45 meters
long, 25 meters in diameter, and weighs about 7,000
tons. The thermal properties of the carbon fiber
structure are important because vast amounts of
energy are dissipated from all the particle collisions
in the experiment.
1 Radiation Length is a characteristicof a material,
related to the energy loss of high energy,
electromagnetic-interactingparticles with it. The
longer the radiation length,the lower the energy
loss and scatteringof the radiation.
Figure 1: Part of the ATLAS experiment showing its
size in comparison to a human (on left).
The carbon fiber structure is co-cured to a
flexible printed circuit board. The flexible printed
circuit board is a composite itself, made up of
copper, aluminum, and polyimide. The flexible
printed circuit board serves as a cable to connect
multiplesilicon based particledetectors.If the solder
ports on the flexible printed circuit board, shown in
Figure 2, do not adhere to the tight tolerances, the
assembly will not fit together. Unfortunately using
the co-curing method leads to unwanted distortions
in the assembly after the cure process. The two
modes of distortion are:
 Curvature along the width of the assembly
due to dissimilar coefficients of thermal
expansion of the flexible printed circuit
board and carbon fiber structure, shown in
Figure 3.
 Stretch along the length of the flexible
printed circuit board between the solder
ports
The goal of this study was to minimize
unwanted distortion in assembly by changing the
tooling used in the co-cure process.

2. 2
Figure 2: Schematic of the flexible printed circuit
board, or “cable”, showing the nominal 98 mm
distance between the solder ports
Figure 3: Curvature of structure when preforming
the layup on just a flat plate. The flexible printed
circuit board is facing downwards.
Theory and Modeling
Our analysis began with observing that the
co-cured assembly behaved as a bi-metallic strip,
with the structure bowing towards the side with the
higher CTE, as seen above in Figure 3. The flexible
printed circuit board is heated during the curing
process, expands more than the carbon fiber
structure, sets to the carbon fiber structure, then
shrinks morethan the carbon fiber structure, leading
to the observed bowing seen in Figure 3.
The equation for the curvature of a bi-
metallic strip is as follows
Eq 1:
1
𝜌
=
6(1+𝑚)2
(𝛼2−𝛼1)(𝑇−𝑇0)
𝑡(3(1+𝑚)2+(1+𝑚𝑛)( 𝑚2 +
1
𝑚𝑛
))
Eq 2:
𝑎1
𝑎2
= 𝑚,
𝐸1
𝐸2
= 𝑛
Where E1 and E2 are the respective moduli of carbon
fiber structure and flexible printed circuit board, a1
and a2 are the respective thicknesses of the material,
t is the overall heightof the assembly,ρ is the radius
of curvature, 𝛼2 𝑎𝑛𝑑 𝛼1 are the respective
coefficient of thermal expansion of the material. T
and T0 are the final and initial temperatures
respectively.
The analytical model is an application of the
Timoshenko theory of bi-metal thermostats
(1925)[3]. The radius of curvature was empirically
found to be 12.065 cm, compared 7.02 cm from
analytical calculations using the material properties
in Table 1. The error from the analytical model is
likely from the uncertainty of what temperature the
flexibleprinted circuitboard adheres to carbon fiber
backing, and the non-uniformity thickness of
materials in the flexible printed circuit board. To
counter this curvature effect the layup was done on
the inside of a pipe of the same diameter to counter
the bowing effect.
Using the material properties shown in
Table 1, we were able to determine the equivalent
CTE of the flexible printed circuit board and
determine the amount of stretch with both a layup
on aluminum and steel tooling using material
properties and temperature data. The following
equation was used to calculate the equivalent CTE
where E is the modulus of each component, α is the
CTE, and V is the volume fraction. In our application
we replace V with the thickness of the component in
the stack-up [4]
Eq 3: 𝛼 𝑒𝑞 =
∑ 𝐸 𝑖 𝛼 𝑖 𝑉 𝑖
∑ 𝐸 𝑖 𝑉 𝑖
Table 1: Table showing material data starting from top of
the cable assembly
Material Comments Thickness
(µm)
CTE
(µm·m−1
·K−1 )
Modulus
(GPa)
Polymide [5] 25 45 3.4
Adhesive [6] Dupont 25 50 1
Aluminum 50 23.9 70
Adhesive Dupont 25 50 1
Polyimide 25 45 3.4
Adhesive Dupont 25 50 1
Copper Used
minimally
17 16.6 115
Polyimide 25 45 3.4
Carbon Fiber
[7]
Along Fiber
(2 total)
65 -0.8 320
Transverse
to fiber
65 32 7

3. 3
Figure 4: Cut-away view of the flexible printed circuit
board with thickness measured in mils. Drawing not to
scale.
Figure 4 is a detailed cut-away view of the
flexible printed circuit board. The stack-up is
analogous to Table 1 on the previous page. The
figure is not to scale. The copper, Cu, width is not to
scaleand is on the order of 100 microns. The carbon
fiber structure, CF, shown on the bottom of the stack
up is 195 microns (0.0037’’).
The first layups were done on aluminum
tooling, which has a high coefficient of thermal
expansion. This led to a large thermal distortion
along the length of the cable, resulting in a non-
linear strain distribution. To mitigate this lower CTE
tooling was used. In theory, the use of steel over
aluminum should half the amount of longitudinal
strains seen in the cable.
In order to calculate the overall
displacement, the following equation was used
where α is thermal expansion coefficient and ΔT is
the temperature change, and ϵ is the strain.
Eq 4: 𝛼 ∗ ∆𝑇 = 𝜖
Table 2: Table showing the theoretical strains
A 0-90-0 lay-up, as opposed to a 90-0-90,
was selected for the assembly because it has better
stiffness characteristicsand local bendingproperties.
Although high thermal conductivity along the width
of the structure was a goal, the stiffer layup was
chosen over the larger thermal conductivity of a 90-
0-90 lay-up.The layup,shown in Figure 4, shows that
the 0 direction goes lengthwise along the 2 meter by
10 cm assembly.Only three plies were chosen due to
radiation length concerns.
Figure 5: 0-90-0 stack-up showing the flexible printed
circuit board, or ”bus cable”, going length wise down the
length of the assembly. Figure not to scale.
Carbon fiber was also chosen because of its
long radiation length, which is desirable in particle
detector applications. Radiation length, Xo, a
characteristic of the material related to the energy
loss of high energy, electromagnetic-interacting
particles, is largely a function of the atomic number
as shown in equation 5:
Eqn 5:
where Z is the atomic number and A is the mass
number of the nucleus. The energy loss from a
particle is inversely related to radiation length:
Eqn 6:
Aluminum
Tool
Steel
Tool
Flexible
Printed
Circuit
Board
Carbon
Fiber
Backing
α
(ppm/°K)
22.2 13.0 24.07 -.5
ΔT (K) 120 120 120 120
ϵ (10-6) 2985 1605 3610 75

4. 4
Procedure
The lay-up was done on three distinct tools:
1. Flat aluminum plate
2. 12.065 cm (9.5’’) radius aluminum pipe
3. 12.065 cm (9.5’’) radius steel pipe
The lay-up was done with a 0-90-0 stacking
sequence, with the 0 direction going lengthwise
along the tube. After preforming the first layup, the
co-cured assembly exhibited the curvature of bi-
metallic strip, seen in Figure 3. The subsequent
layups were done on the inside of a pipe, with the
flexible printed circuit board facing downwards, as
seen in Figure 6. After switching to aluminum pipe
the bowing distortion issue was solve, but the
longitudinal distortions between the solder ports still
persisted. To counter this, the tooling surface was
changed from aluminumto steel, because steel has a
lower CTE.
,
Figure 6: 0-90-0 layup done on 9.5 Diameter Aluminum
pipe after being removed from Autoclave. The Kapton
bus tape is facing downwards.
Before the co-cure process, the flexible
printed circuit board was surfaced prepped. This
includes using a lightly abrasive pad to abrade the
backside of the cable and removing excess residue
with alcohol. A 25 micron layer of flash break tape
was applied to the bottom of the cable to facilitate
removal from the tooling. Flash break tape is multi-
functional polyester film that is commonly used in
the composites industry. This 25 micron layer of
flash break comes into direct contact with the
toolingsurface,and therefore is plays a major factor
in the tool-part shear interaction.
Before the flexibleprinted circuitboard was
introduced to the pre-preg carbon, the carbon
sheets were vacuumed pressed together. Then a
layer of bleeder, a fabric which allows even vacuum
pressureacross the entire surface of the part as well
as captures excess resin from the laminate, was
added to the layup. The assembly and tooling were
put under a final vacuum bag before being inserted
in the autoclave. Figure 7 shows the layup just
before being inserted in the autoclave.
Figure 6: Layup shown just before being inserted in the
autoclave. The assembly is vacuumed bagged with three
vacuum ports. The white material inside the half-pipe is a
layer of bleeder material.
The lay-up was brought up to 140°C in the
autoclave and put under a pressure of 551 KPa (80
psi) plus the pressure applied from vacuum bagging,
103.4 KPa (15 psi). Upon cooling, the pressure was
released to avoid fiber buckling from the tooling
contraction. The plot showing the exact parameters
of the cure in the autoclave can be seen in Figure 8.
The top four lines correspond to air temperature in
the autoclave, and the the dark yellow line refers to
the part temperature. The lay-up was brought up to
140o C for two hours and was allowed to cool for 12
hours.The green line corresponds to the pressue in
the autoclave and the dark marron line towards the

5. 5
bottom of the graph shows the vaccuum on the part.
Figure 8: Screen print out of autoclave temperature,
pressure and vacuum.
The flexible printed circuit board solder
ports were then measured after curing to verify the
nominal 98 mm distance between the pairs of ports
and compared to measurements before the co-cure.
The measurements were taken using a Smart Scope,
a feature driven microscope, which utilizes a xyz
stage to make measurements within accurate to 1
micron with a standard deviation of 0.5 micron. A
total of 23 measurements were taken per assembly.
Figure 9 shows the measuring set-up. The
displacements of these ports from the free cable to
the co-cured cable were used to calculate the strain
distribution. Figure 10 shows a close up the solder
ports that were measured. Each solder port was
used as a fiducial marker to characterize the
longitudinal stretch of the cable.
Figure 11 shows the final product of 5
cables that were laid up on aluminum. The carbon
fiber backing is almost entirely covered by the
flexible printed circuit board. These co-cured
assemblies served as cables for connecting the
silicon based particle detectors. These assemblies
will eventually be cured to a honey-comb cooling
structure, which is not covered in the scope of this
paper.
Figure 9: Microscope and XYZ stage used to measure the
distortions in the cable using feature driven recognition.
Figure 10: Close ups showing the solder ports that were
measured and the 98 mm nominal distance measured
between the two ports. These ports were used as fiducial
markers.
Figure 11: Photograph of five finished flexible printed
circuit boards co-cured to the carbon fiber backing. These
co-cured assemblies served as cables for connecting the
silicon based particle detectors.
98 mm

6. 6
Result and Discussion
The results from all lay-ups are shown in
Figure 12. In the aluminum lay-ups, the
accumulation of strain in the center is consistent for
each cable.After analyzingthe flexibleprinted circuit
board which serves as a cable, many hypotheses
were generated. The hypothesis that was evaluated
in this experiment was conducting the lay-up on a
steel pipe.
The most plausible reason for the
longitudinal deformation was thought to be the co-
cure process on a high CTE aluminum pipe. The cable
is held firmly against the aluminum pipe by the high
pressure of the autoclave during the heating up
period. The cable sets to the carbon fiber, making
the deformations permanent. During the cool down
process the pressure of autoclave is released, the
part starts peeling away, at the edges first, so the
center shows the most deformation.
It was concluded that the lay-up on steel
tooling reduces the level of deformation as well as
the strain accumulation in the center. This is because
the steel tooling will cause the overall assembly to
expand less due to its lower coefficient of thermal
expansion.
Conclusion
After testing the lay-up on new tooling, the
problem of deformation in the solder ports has
improved. Switching to steel reduced the amount of
strain,but did not eliminate it entirely. More data is
needed on laying up on steel tooling to confirm the
data on a lay-up using steel. Future experiments
includelayingup the flexibleprinted circuitboard (or
“cable”) carbon fiber assembly on carbon tooling, or
invar which will have close to zero CTE. This should
theoretically eliminate tool expansion and the
deformation of the flexible printed circuit board.
Funding
Lawrence Berkeley National Laboratories, Physics
Division for the ATLAS experiment at CERN.
Acknowledgements
The authors wish to acknowledge the technical
assistance provided by Professor Hari Dharan, Carl
Haber, Joe Silber, and Thomas Johnson.
References
[1] Ridgard C. Accuracy and distortion of composite
parts and tools: causes and solutions. SME tech
paper, Tooling for Composites ’93. 1993
[2] Graham Twigg, “An experimental method for
quantifying tool–part shear interaction during
composites processing” Composites Science and
Technology 63 (2003)
[3] Timoshenko, S.P. (1925), “Analysis of Bi-Metal
Thermostats,” Journal of the Optical Society of
America, Vol. 11, pp. 233-255
[4] Kattan, Peter I. and George Z.
Votiadjis. Mechanics of Composite Materials with
MATLAB. New York: Springer, 2005. Print.
[5] ShinEtsu. “Coverlays and Bonding Sheets”. CA233
Kapton datasheet.
[6] Dupont Electronic Materials. “Pyralux LF Sheet
Adhesive” LF0100 datasheet. 2002.
[7] Mitsubishi Chemical. “Coal Tar Pitch-Based
Carbon Fibers” K13C2U datasheet.
Figure 12: Plotted results showing a non-linear relationship of strain between pairs of solder ports and distance along
the cable. The strain for the aluminum tooling layup tends to accumulate in the center of the cable; The strain for the
steel tooling layup is reduced by 50% from aluminum and does not accumulate at the center of the cable.