__Preventing delamination in transparent armor.__
Delamination of transparent armor is an ongoing
problem. This blog post aims to explore
the subject using some technical theory, with the aim of presenting simple
solutions to minimize the problem. The
proper design of the laminate, manufacturing of the laminate and selection of
materials can all lead to a significant increase in the life of the
laminate. This post will explore some of
the issues and provide recommendations.

To start looking at the problem of delamination we want to
start with a mathematical analysis of the problem and we therefore used a
simple formula to model the stresses that cause delamination. The simplified formula is taken from the
paper “Thermal Stress in Bonded Joints” by W.T.Chen and C.W.Nelson. It examines the thermal stresses in a bonded
joint between two materials using an adhesive interlayer. The paper also gives a more complex formula for
three layers instead of two; for readers who would like to examine the formula
for three layers, the paper is easy to find by entering the title of the paper
in Google. For more complex structures
involving more than three layers, the formulas can be derived using the same
principles. The paper shows how the
following formula is derived, but for this blog post, we will just take the
formula as given. For those that prefer
to see the derivation, the paper is available to read. It is recognized that equating a laminate to
a bonded joint is somewhat simplistic, but it does give a good starting point
to analyze the problem.

The formula presented in the paper for calculating stresses
in a two-layer joint is:

**Τ=**

__(__

__α___{1 }

_{–}

_{ }

__α___{2})__T__

__G sinh (β x)__

β η cosh (β L)

β

^{2}=__G__[ (1/(E_{1}t_{1}) + (1/(E_{2}t_{2}) ]
η

Τ = Shear
Stress (Pa)

**α**= Thermal expansion coefficient of layer 1 (/C)

_{1 }**α**= Thermal expansion coefficient of layer 2 (/C)

_{2 }
T = Temperature
change (C)

x = Distance
from center of joint (mm)

L = Distance
from center of joint to end of joint (mm)

G = Shear
modulus of interlayer (Pa)

η = Thickness
of interlayer (mm)

E

_{1}= Elastic modulus of layer 1 (mm)
E

_{2}= Elastic modulus of layer 2 (mm)
t

_{1}= Thickness of layer 1 (mm)
t

_{2}= Thickness of layer 2 (mm)
The formula can be used to calculate the Shear stress at any
point in the laminate from the center to the edge. When x = L at the edge of the laminate, the
shear stress will be maximum, and:

**Τ**

_{max}=

__(__

__α___{1 }

_{–}

_{ }

__α___{2})T G
βη

This formula is somewhat intuitive. The stress will be greater if the difference
in coefficient of thermal expansion of the two materials

**α**_{1 }_{–}_{ }**α**is large. The stress will also be greater as the Temperature change T increases. Also if the interlayer is thicker (η), it allows the stresses caused by the expansion and contraction of the materials to be reduced._{2}
The first thing to note is that transparent armor is often
exposed to environmental temperature changes in military applications. ATPD.2352 requires testing over a temperature
range of -31 C to +60C or a 91 degree C temperature range. Although the laminate will not see this range
in temperature every day, it is certainly possible that it could experience
these conditions during its life.

It should be noted that if normal operating temperature is
say 15 C, this is not the temperature that has zero stresses. The temperature that has zero stresses is
much closer to the temperature during fabrication the polyurethane sets and
bonds to the glass and polycarbonate.
Depending upon the polyurethane, this temperature could be 80 C or
higher. Selection of the polyurethane
therefore has some impact on the maximum stresses that a laminate will
see. A polyurethane that sets at 120 C
will lead to much higher stresses than a polyurethane that sets up at 80C.

To illustrate this point, the maximum stress will occur in a
laminate when the temperature of the laminate is the lowest, in the case of
ATPD.2352 this will be -31C. Using a
polyurethane that sets up at 120C rather than 80C will give about (120 - -31) /
(80 - - 31) = 151/ 111 or about 36% more maximum stress in the laminate at the
interface.

It should be remembered in the selection of polyurethane,
that choosing a low melting polyurethane to minimize stresses should be done
with careful consideration of the operating and storage environment that the
laminates will see. It is extremely
counterproductive to have solar heating leading to the melting of the
polyurethane, as this will lead to melting delamination rather than thermal
stress delamination.

This problem can be made even worse by poor laminating
control. Polycarbonate expands or
contracts a lot more than glass. If the
laminate is not uniform in temperature throughout the entire thickness at the
time the Polyurethane is setting up, it is possible that some of the
polycarbonate could be at a higher temperature at its core at the time the surface
is bonding to the polyurethane. This
increased core temperature can cause increase stresses at the interface of the
polyurethane. Proper manufacturing that
allows the temperature of the laminate to stabilize throughout, just above the
temperature where the polyurethane sets up can significantly reduce stresses.

One elegant solution to the problem is to use radio
frequency lamination to lower the temperatures of the polycarbonate and glass
at the time of lamination. This type of
lamination heats only the polyurethane interlayer and can therefore reduce the
zero stress temperature well below the temperature achieved by conventional
autoclaves. We can provide laminators with
information on this process if requested.

The other item to note from the formula is that the
thickness of the polyurethane is important.
Using a thicker polyurethane can allow the stresses to be significantly
reduced. If we consider that case where
6mm glass is bonded to 6mm polycarbonate, using the above formula the stresses
can be reduced from 13.7 MPa to 6.9 MPa if using 0.075mm polyurethane rather
than 0.025mm polyurethane with a temperature swing of 111 degrees C.

Decreasing the amount of thermal stress generated will
significantly affect the life of the laminate.
Halving the stress, as in the above example, could be the difference
between delamination and no delamination.
The other factor that affects delamination is the adhesion between the
polyurethane and the other materials – glass and polycarbonate. Delamination will occur at the weakest of
these joints, which is typically the polycarbonate, polyurethane interface. Delamination will occur when the forces due
to the thermal stresses are stronger than the adhesion of the polyurethane to
the polycarbonate or glass.

One area where we have started to have some positive effects
in reducing delamination in high-end laminates is increasing the bonding
between the polyurethane and the polycarbonate.
We have been tackling this area in two ways, firstly by correct selection
of the polyurethane and secondly by modifying the chemistry of the
polycarbonate. We have recently made
available an enhanced grade of polycarbonate that has significantly higher bond
strength to polyurethane.

The next area that should be considered is the area of
laminate design. In some cases laminates
are configured only to pass ballistics specifications and little consideration
is give to how the configuration may affect stresses and delamination. To illustrate this point we will use the
three-layer formula developed in the paper that we discussed earlier. Due to the formula’s length, we will not
present it here, but again the paper can easily be found.

In the first case we will consider a two-layer laminate
consisting of 6mm Polycarbonate bonded to 6mm Glass using a 0.025 mm
polyurethane. The change in temperature
that the laminate will be exposed to will be considered to be 100 degrees
C. We have calculated that the maximum
stress will be 12.3 MPa.

If we then change the laminate configuration, with the aim
of keeping the total thickness the same, to 3mm Polycarbonate, 3mm
Polycarbonate and 6mm Glass, the total amount of polycarbonate and glass will
remain the same. In this configuration the maximum stress between the glass and
the polycarbonate will be 11.70 MPa.
Although the difference may not seem to be much, it is a 5% reduction in
the stress. In a laminate that is close
to the point of delamination, reducing the stresses by 5% could be enough to
significantly increase the life of the laminate or even prevent delamination
occurring. Reducing thermal stresses,
particularly when done in conjunction with increasing the bond strength between
the polyurethane and the polycarbonate, can be very effective in decreasing
delamination and increasing laminate life.

Other factors do affect delamination including edge seals,
chemical attack and edge finishing, but the aim of this article is mainly to
look at some of the factors associated with delamination caused by thermal
stresses.

The key points to minimize thermal stresses and reduce
delamination are:

·
Select the correct thickness of polyurethane to
minimize thermal stresses

·
Select the correct type of polyurethane to
minimize stresses and increase bonding, while also considering environmental
conditions that the laminate will be exposed to.

·
Optimize autoclave conditions to reduce thermal
stresses.

·
Improve the bond strength between the
polycarbonate and the polyurethane by using an enhanced polycarbonate designed
to increase bond strength in transparent armor.

·
Design the laminate configuration to minimize
stresses in addition to achieve ballistics requirements.