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### De-lamination & Thermal Stress

De-lamination 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 de-lamination we want to start with a mathematical analysis of the problem and we therefore used a simple formula to model the stresses that cause de-lamination. 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**T G sinh (β x)

_{2})β η cosh (β L)

Where:

β^{2} = G [ (1/(E_{1} t_{1}) + (1/(E_{2} t_{2}) ]

η

Τ = Shear Stress (Pa)

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

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

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 Gβη

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 de-lamination rather than thermal stress de-lamination.

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 de-lamination and no de-lamination. The other factor that affects de-lamination is the adhesion between the polyurethane and the other materials – glass and polycarbonate. De-lamination will occur at the weakest of these joints, which is typically the polycarbonate, polyurethane interface. De-lamination 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 de-lamination 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 de-lamination. 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 de-lamination, reducing the stresses by 5% could be enough to significantly increase the life of the laminate or even prevent de-lamination 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 de-lamination and increasing laminate life.

Other factors do affect de-lamination 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 de-lamination caused by thermal stresses.

The key points to minimize thermal stresses and reduce de-lamination 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.