Short Answer:
Stress due to temperature change is the internal force developed in a material when its expansion or contraction due to a change in temperature is restricted. When a material is heated, it tends to expand, and when cooled, it tends to contract. If this movement is prevented, internal stresses are generated, known as thermal stresses or stress due to temperature change.
In simple words, when a body cannot expand or contract freely under temperature variation, compressive or tensile stresses develop inside it. This type of stress is important in components such as pipes, bridges, boilers, and machine parts that experience temperature fluctuations during operation.
Detailed Explanation:
Stress due to Temperature Change
When a material is subjected to a temperature variation, it tends to expand when heated and contract when cooled. The amount of change in its length or volume depends on the coefficient of thermal expansion of the material and the temperature difference.
If the material is allowed to freely expand or contract, no internal stress develops. However, when its movement is restricted — for example, when both ends of a bar are fixed — it cannot expand or contract freely. This resistance to movement produces internal stress, known as stress due to temperature change.
This phenomenon is very common in mechanical and civil structures that are exposed to changing temperatures, such as railway tracks, bridges, engine cylinders, and pressure vessels. The stress developed may be tensile (when the material contracts and is restricted) or compressive (when the material expands and is restricted).
Explanation of Thermal Stress Formation
Let’s consider a uniform metal bar of original length , fixed at both ends, and subjected to a temperature rise of .
- Free Expansion (Unconstrained Condition):
When the bar is free to expand, the increase in its length due to heating is given by:
where,
= coefficient of linear expansion (per °C)
= temperature change (°C)
= original length (m)
In this condition, no stress develops because the material is free to expand.
- Restrained Expansion (Constrained Condition):
When the bar is fixed at both ends, it cannot expand freely. The tendency to expand is resisted by equal and opposite forces at both ends. These forces generate compressive stress inside the bar.
The thermal strain that would have occurred due to free expansion is:
Since expansion is restricted, this strain cannot take place. The strain prevented causes internal stress, which is equal to:
where,
= thermal stress (N/m²),
= modulus of elasticity (N/m²),
= coefficient of thermal expansion,
= temperature change.
Thus, stress due to temperature change is directly proportional to the modulus of elasticity, coefficient of expansion, and temperature change.
Nature of Stress due to Temperature Change
- When the material is heated:
- The material tends to expand.
- If expansion is restricted, compressive stress develops.
- When the material is cooled:
- The material tends to contract.
- If contraction is restricted, tensile stress develops.
Hence, the direction of thermal stress depends on whether the material is heated or cooled and whether its movement is constrained.
Example of Stress due to Temperature Change
Let’s consider an example:
A steel rod of length 2 m and modulus of elasticity is fixed at both ends. The coefficient of expansion . If the temperature rises by 50°C, the stress developed is:
Thus, a compressive stress of 120 MPa develops inside the bar due to temperature rise.
Factors Affecting Stress due to Temperature Change
- Coefficient of Thermal Expansion (α):
- Materials with higher values of α (like aluminum) develop more thermal stress than those with lower α (like steel).
- Temperature Change (ΔT):
- The larger the temperature change, the greater the stress produced.
- Elastic Modulus (E):
- A material with higher elasticity (stiffness) will develop higher thermal stress.
- Restraint Condition:
- Fully fixed conditions develop maximum stress, while partially restrained conditions develop lower stress.
- Shape and Size of the Component:
- Thick components experience higher stress due to uneven temperature distribution compared to thin ones.
Effects of Stress due to Temperature Change
- Thermal Cracking:
Repeated heating and cooling cycles cause cracks due to alternating thermal stresses. - Deformation or Buckling:
Non-uniform temperature changes may cause bending or warping of components. - Material Fatigue:
Cyclic thermal stresses can weaken materials over time, leading to fatigue failure. - Failure of Joints and Connections:
Bolted or welded joints may loosen or crack under continuous temperature variations. - Distortion of Structures:
Beams, pipelines, and frames can deform or misalign if expansion is not properly accommodated.
Methods to Reduce Stress due to Temperature Change
- Use of Expansion Joints:
Expansion joints are provided in bridges, pipelines, and railway tracks to allow free expansion and contraction. - Proper Material Selection:
Choose materials with low coefficients of expansion and high ductility to minimize stress. - Controlled Heating and Cooling:
Gradual temperature changes prevent the development of large stresses. - Stress Relieving Treatments:
Heat treatment processes such as annealing can reduce residual thermal stresses. - Flexible Design:
Allowing small movements or using flexible supports in assemblies reduces stress build-up.
Conclusion
Stress due to temperature change is an internal stress that occurs when a material’s expansion or contraction due to temperature variation is restricted. It depends on the material’s modulus of elasticity, coefficient of expansion, and temperature difference. If not properly controlled, these stresses can lead to cracking, distortion, or even failure of components. Therefore, in engineering design, expansion joints, material selection, and controlled heating are used to reduce thermal stresses and ensure safe operation of machines and structures exposed to temperature changes.