How to perform a thermal stress analysis

The temperature distribution in a part can cause thermal stress effects (stresses caused by thermal expansion or contraction of the material).  Examples of this phenomenon include interference fit processes (also called shrink fits), where parts are mated by heating one part and keeping the other part cool for easy assembly.  Another example is thermal creep, which is permanent deformation resulting from prolonged application of a stress below the elastic limit.  An example of this is the behavior of metals exposed to mechanical loads and elevated temperatures over time.

Thermal stress effects can be simulated by coupling a heat transfer analysis (steady-state or transient) and a structural analysis (static stress with linear or nonlinear material models or Mechanical Event Simulation [MES]).  The process consists of two basic steps:

1. Perform a heat transfer analysis to determine the temperature distribution.
2. Directly input the temperature results as a load in a structural analysis to determine the stress and displacement caused by the temperature loads.

For example, a thermal stress analysis of a transistor and heat sink assembly was performed as follows:

• A steady-state heat transfer analysis was performed to obtain the temperature distribution (see Figure 1).

Figure 1:  A transistor and heat sink model with temperature distribution results from a steady-state heat transfer analysis.

• In the FEA Editor environment of Autodesk Simulation Mechanical, the analysis type was changed for a structural analysis.  In this case, static stress with linear material models was used.
• Constraints were specified for the structural analysis by fully fixing the two bottom surfaces of the model.  Additional structural loads (such as forces, pressures, and gravity) could have been added if desired; however, for this example, the only loads were the temperatures from the heat transfer analysis.
• On the "Multipliers" tab of the "Analysis Parameters" dialog, a load case multiplier of "1" was specified in the "Thermal" column so that thermal effects would be included in the structural analysis (see Figure 2).

Figure 2:   A load case multiplier was specified to include thermal effects in the structural analysis.

• On the "Thermal" tab of the "Analysis Parameters" dialog, "Another Design Scenario in loaded file" was chosen from the pull-down menu of options in the "Source of temperatures" field.  "1 – Design Scenario 1" was chosen from the pull-down menu of options in the "Use temperatures from Design Scenario" field was used to specify the location of the temperature results file from the previous steady-state heat transfer analysis (see Figure 3).

Figure 3:   The "Thermal" tab of the "Analysis Parameters" dialog was used to specify the Design Scenario that would be used as input to the static stress analysis with linear material models.

• The static stress analysis with linear material models was run and then the results, including thermal stress effects, were displayed in the Results environment (see Figure 4).

Figure 4:   Displacements (left) and stresses (right) in the transistor and heat sink assembly due to temperature loads, displayed in the Results environment.

Thus, the ability to couple heat transfer and structural analysis capabilities provides an easy and convenient way to simulate thermal stress effects. 

How to Determine the Factor of Safety

When evaluating the results of a linear static stress analysis, one can specify allowable stress values and then display factor of safety contours to see where stresses in the model are below and above those allowables. Viewing factor of safety contours can help one decide whether a design needs modification or is acceptable and is ready for manufacturing.

To display factor of safety contours, choose the "View" command in the "Safety Factor" dropdown of the “Stress” panel in the “Results Contours” tab of Autodesk Simulation (see Figure 1).

Figure 1: In the "Safety Factor" dropdown, choose the "View" command to display factor of safety contours.

When this command is activated, color-coded contours of the factor of safety for the selected stress contour will be shown (see Figure 2).

Figure 2: In the Results environment, one can specify allowable stress values and then display factor of safety contours. This contour shows a color-coded graphical display of where stresses in the model are below and above the specified allowables.

The factor of safety is the ratio of the allowable stress to the actual stress:

• A factor of safety of 1 represents that the stress is at the allowable limit.
• A factor of safety of less than 1 represents likely failure.
• A factor of safety of greater than 1 represents how much the stress is within the allowable limit.

The allowable stresses can be assigned on a per part basis by choosing the "Set Allowable Stress Values" command in the "Safety Factor" dropdown (see Figure 3).

Figure 3: Choose the "Set Allowable Stress Values" command in the "Safety Factor" dropdown to specify allowable stress values.

The "Allowable Stress Values" dialog will appear and each part will be listed in a separate row. One can specify a value in the "Allowable Stress" column or press the "Load Yield Stress" or "Load Ultimate Stress" buttons to load the values from the material library (see Figure 4). Any parts for which the allowable stress is set to 0 will be excluded from the factor of safety calculations.

Figure 4: In the "Allowable Stress Values" dialog, one can enter a value for a part in the "Allowable Stress" column or press the "Load Yield Stress" or "Load Ultimate Stress" buttons to load the values from the material library.

Thus, the ability to view factor of safety contours helps engineers determine what the results say about the adequacy of a design. For example, examining these contours can help you properly exercise engineering judgment when balancing between material cost reduction and ensuring a safe product.

How to define a local coordinate system

When setting up a model for analysis, it can be easier and more efficient to add loads and constraints in a coordinate system other than the default (particularly for off-axis loads or constraints or for curved geometry). The FEA Editor environment of Autodesk Simulation Mechanical provides the ability to define local coordinate systems (rectangular, cylindrical, or spherical with the origin located anywhere in space) and then add loads and constraints relative to them.

For example, consider a model with a cylindrical surface. To define the vector for a tangential edge force you can no longer use the global coordinate system. You will need to define a local coordinate system and use it to define your load vector.

Define a cylindrical local coordinate about the centerline of the cylinder as follows:

• In the FEA Editor environment tree view, right click on "Coordinate Systems" to access a pop-up menu of options and choose "New..."  The "Creating Coordinate System Definition" dialog will appear (see Figure 1).  This screen provides options for defining a new coordinate system.

Figure 1: The "Creating Coordinate System Definition" dialog is used to define local coordinate systems.

• Click on the "Coordinate System Type" field and choose from the pull-down menu of options.  For this example, "Cylindrical" was specified.
• Enter three sets of coordinates in the "Point A", "Point B" and "Point C" fields to define the local coordinate system per the diagram shown on the screen. 
• Alternatively, you can define coordinates by clicking on points in the model as follows:
• Click on the “Select A,” “Select B,” or “Select C” button.  Then click on a vertex in the model to define the coordinate.
• Click on the "Interactive" button. Then click on three vertices to define all three points sequentially. A graphical display of an axis will be drawn on the model to guide you as you click on the points.
• Click on the "OK" button to accept the coordinate system definition. It will then be listed in the model tree under "Coordinate Systems".

Now, you can conveniently add a force load to the model relative to the local coordinate system. 

For this example, select the edges and right click anywhere in the working area to access a pop-up menu of options. Choose "Coordinate Systems" and then the local cylindrical coordinate system to apply it to the selected edges (see Figure 2). Icons indicating the orientation of the local cylindrical coordinate system will appear on the vertices.

Figure 2: Apply the local cylindrical coordinate system to the selected edges

Right click in the working area and choose "Add" and "Edge Forces..." to access the "Creating Nodal Force Objects" dialog. Notice that the active local cylindrical coordinate system is shown in the "Coordinate System" field (see Figure 3). The axis icons on the selected vertices will indicate the direction that you should define for the force load. In this case, the Y direction was specified to designate the tangential direction.

Figure 3:  Add a force load to the selected Edges. The active local cylindrical coordinate system is shown in the "Coordinate System" field

After adding the force load, the display will show the force arrows pointing in relation to the local cylindrical coordinate system (see Figure 4).

Figure 4: The force load is applied in relation to the local cylindrical coordinate system

Thus, defining a local coordinate system in the FEA Editor can make it easier to apply loads and constraints. Local coordinate systems can either be reused in the Results environment or defined there to display results in an arbitrary orientation relative to them