## Thermal Expansion in a Glass and Aluminum Window: Part 2

Figure 1: Simplified model of an aluminum-glass window

In last week’s blog, Thermal Expansion in a Glass and Aluminum Window: Part 1, we introduced the basic concept of thermal expansion in solid materials.  Since CTE mismatch can impose extremely high stress, during mechanical engineering design one must consider the temperature exposure and expansion or contraction of a material.  In order to help the read gain insight, we used a simplified aluminum-framed window to demonstrate that a hot summer day would be enough to shatter glass if the window wasn’t equipped with a flexible gasket between the frame and the glass.  For this entry, we utilize a finite element analysis (FEA) to elucidate the stress effects caused by both high and low temperatures, as well as the effects of adding a flexible gasket.

## Mitigating CTE mismatch in a window by use of a gasket

As the energy (temperature) of molecules in an unconstrained solid part increase, the space between them increases.   However, if one constrains the solid part, as is typical in an engineered assembly, then the part is not free to expand or contract to its natural state, thus neither are the atoms.  Therefore, the energy between the atoms increases, which we refer to as stress.  One may exacerbate the increase or mitigate and reduce the stress by a clever choice of materials, each with different coefficients of thermal expansion.   The experienced design professional knows how to carefully select materials so that thermo-mechanical stresses are minimized.

In the simple aluminum-framed window example we presented last week (Figure 1), the aluminum has a  CTE of 22 × 10-6 K-1 (22 ppm), which is 2.5 times larger than that of the glass frame, 9 × 10-6 K-1 (9 ppm).  This means that as temperature increases or decreases, the aluminum wants to expand or contract at a faster rate than the glass.  Since glass also has a much lower ultimate strength than aluminum, this puts the glass at risk of shattering.  However, the engineer or designer can specify the use of a flexible gasket (usually made of a synthetic rubber like silicone or EPDM) as a thermal interface material between the two can mitigate possible damage.  This same approach can be used with many types of equipment or machinery.

## FEA of Thermal Expansion and CTE Mismatch in an Aluminum Frame Window

For the finite element analysis simulation below, we created a model of the window in Autodesk Inventor™.  We imported the model to Autodesk Simulation Mechanical™, and created four scenarios:

1. A window without a gasket at a high temperature of 45°C (115°F)
2. A window without a gasket at a low temperature of -20°C (-5°F)
3. A window with a gasket at a high temperature of 45°C (115°F)
4. A window with a gasket at a low temperature of -20°C (-5°F)

For each of the four scenarios, we present an image of the von Mises stress (or equivalent tensile stress), overlaid in color on the model.  Since different sections of these models will be experiencing tension and compression, von Mises is a useful tool for obtaining a single value for multiaxial stress conditions.  Each image is shown on the same scale, from 0-50 MPa (N/mm2), for comparison.

### Figure 2: Aluminum Window at High Temperature (45°C) and No Gasket

The window with no gasket in high heat experiences a significant amount of stress, as shown in Figure 2.  The aluminum experiences some internal stresses, but its stresses of around 50 MPa do not approach its yield strength of ultimate strength.  However, The glass easily exceeds its ultimate strength of 33 MPa in the corners.  The maximum value of 109 MPa shown in the image is present at the corners of the glass, indicating that it would have failed long before 45°C was reached.

### Figure 3: Aluminum Window at High Temperature (45°C) with a Silicone Gasket

Figure 3 shows that adding the gasket shows significant improvement for the window.  The glass pane experiences almost no stress in this scenario, as the gasket allows the aluminum to expand to whatever extent it needs.  The internal stresses in the corners of the glass are only around 1 MPa.

### Figure 4: Aluminum Window at Low Temperature (-20°C) without Gasket

Figure 4 shows the results for the gasket-less window exposed to a low temperature of -20°C.  The failure areas for the glass in the low-temperature no-gasket scenario are smaller than for the high-temperature case.

### Figure 5: Low Temperature (-20°C) with a Silicone Gasket

Figure 5 shows the low temperature gasket case.  As with the high-temperature case, adding the rubber gasket significantly decreases the stress on the glass pane.  Even in the corners, the glass stress is less than 1 MPa.

## FEA Deformation Comparison

Table 1 below shows the same von Mises stress results for each scenario, but with the addition of exaggerated deformation.  Since the maximum deformation in any scenario was always less than 1 mm, the change in shape has to be scaled up.  In this case, the deformation in each image is scaled up 150x.  The same type of change is visible in both temperatures: at high temperature, the sides of the aluminum frame are expanding, which pushes the corners away; at low temperatures, the sides are contracting, which pulls the corners in faster.

However, it’s clearly visible that the aluminum experiences more deformation in the windows with a gasket.  Aluminum has a high CTE and deforms significantly with temperature change.  One can accommodate this in the window mounting.  Since the glass is not holding the aluminum in place, it is free to expand as it needs.  This is an important consideration for an engineer who was designing such a window: the inner part of the frame should practically be considered as empty space for the purposes of stress and deformation, since the glass does not provide much support.

Table 1: von Mises stress, overlaid on model with exaggerated deformation (150x actual deformation)