In last week’s last blog, we explored the causes and effects of thermal expansion in solid materials. The expansion and contraction of a material based with temperature must be considered in mechanical engineering design projects, since it can impose high and potentially-damaging internal stresses. We used a simplified aluminum-framed window to demonstrate mathematically 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.
Thermal Expansion and CTE Mismatch
Just as in gases and liquids, the molecules in solids increase in energy as their temperature rises and the space between them increases. Since constrained solids are not free to exand or contract to their natural state, they experience internal stresses. These stresses may be increased or reduced if multiple materials with different coefficients of thermal expansion are used together, a situation often called “CTE mismatch”. The clever 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’s CTE of 22 × 10-6 K-1 (22 ppm) is 2.5 times larger than that of the glass frame, at 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 addition 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.
FEA Window Simulation Results
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:
- A window without a gasket at a high temperature of 45°C (115°F)
- A window without a gasket at a low temperature of -20°C (-5°F)
- A window with a gasket at a high temperature of 45°C (115°F)
- 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: 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 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.
The 157 MPa maximum value shown in the image occurs on the inside corners of the aluminum frame, and is due to a stress concentration at the perfect right angle used in the CAD model.
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, but once again the corners exceed the 33 MPa limit for glass.
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. 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)
Mitigating Thermo-Mechanical Stresses
Although this was a simplified model, it clearly indicates the effectiveness of adding a rubber gasket to a metal-framed window, in order to prevent undue stresses from thermal expansion. In both high and low temperatures, the gasket reduced the internal stress on glass pane below its ultimate strength, preventing it from fracturing. Similar care must be taken on nearly every civil or mechanical engineering project that might experience temperature differences over its lifetime. The correct modeling of thermal expansion and contraction could let a semiconductor engineer avoid expensive cracks on their wafers, could help a mechanical engineer design a more efficient internal combustion engine, or could allow a structural engineer to design a skyscraper that will be 5°C cooler at the top than at the base.
© All images copyright of Glew Engineering Consulting.
- Modulus of Elasticity or Young’s Modulus – and Tensile Modulus for some common Materials. Retrieved from http://www.engineeringtoolbox.com/young-modulus-d_417.html