7 Czerwiec 2021

Agnes Shin
Agnes Shin | CAE Consultant & Marketing Manager MIDAS IT Co.

Thermal Stress Analysis [Part 1]

Interpretation Theory

Structural analysis can be defined as the examination and interpretation of the stability of a structure.

If we are trying to examine the stability of a structure under a temperature change, we need more than a heat transfer analysis. Heat transfer analysis provides only the temperature distribution of the structure as a result, so thermal stress analysis must be carried out afterwards to perform a proper structural analysis for a temperature change in the structure.

Thermal stress analysis is performed by using the temperature distribution obtained through heat transfer analysis as a temperature load. Therefore, it can be interpreted as an analysis of the stability of a structure against heat.
In some cases, thermal stress analysis is considered as part of the heat transfer analysis processes. In this article, however, we will approach it as a type of structural analysis.


Let’s take a closer look into this schematic.
Why does thermal stress occur? And why should we do thermal stress analysis? Let’s examine some phenomena caused by thermal stress.


First, why is thermal stress analysis necessary?
The figure above shows what happens when an object changes temperature from high to low.
As you can see, during the cooling process, deformation or cracking occurs due to the difference between the object’s temperature and the ambient temperature. This heat-induced deformation may surface manufacturing defects. Thermal stress analysis allows us to predict the deformation and stress caused by the temperature difference and determine whether a defect will appear.
It is also important that one can also study the thermal deformation of an object during the process of thermal stress analysis.
Thermal deformations should not cause internal interference in smartphones or flat-screen TVs, and the picture quality should not be distorted even if the screen distorts to a slight degree. This is a practical example of the usability of thermal stress analysis. Or, in the case of welding, this kind of analysis is also very useful because it accounts for deformations such as bending by predicting the amount of thermal deformation caused by the heat of welding.
Now, let’s review thermal strain before looking more into its causes. Thermal strain is defined as:



Here, the thermal expansion coefficient, measured in (1/℃) is the strain per unit of temperature, and it has a unique value for each material.
When the temperature rises, the structure expands, and when it drops, it shrinks. It is natural that the rate of expansion or shrinkage is understood as thermal strain. This value is defined by multiplying the thermal expansion coefficient by the change in temperature, as shown in the formula above. Therefore, knowing the temperature change and the thermal expansion coefficient of the material used, you can find the strain. And multiplying the strain by the length of the object can provide you with the deformation.
Thermal deformation is mathematically defined as:


On the other hand, the strain can also be used to obtain the stress through the use of Hooke’s Law. The thermal stress can, therefore, be obtained by the following equation:

It can be said that thermal stress is caused by thermal strain, but thermal stress that occurs may depend also on how the product’s boundary conditions are structured. Let’s observe how this takes place in the following figure.


Thermal stress is caused by both thermal strain and boundary conditions.
In the first case, there is no thermal stress. If there is a boundary condition that allows thermal deformation to occur freely because of lack of constraints, no internal force is generated inside the object and thermal stress does not occur.
On the other hand, in the second case, the deformation is constrained, generating an internal force in the object, which causes thermal stress. In other words, deformation is limited, and only stress will occur.
Thus, thermal stresses may or may not occur depending on what the boundary conditions are when thermal deformation occurs. So, as you can see, a reasonable boundary condition setting is very important in thermal stress analysis.

Next time, we will use CAE analysis program midas MeshFree to see how each value is considered and interpreted during actual analysis.