Short Answer:
Thermal strains are the changes in the shape or size of a material caused by a change in temperature. When a material is heated, it expands, and when cooled, it contracts. This change in dimension per unit length due to temperature variation is called thermal strain.
In simple words, thermal strain is the deformation or elongation of a material that occurs because of heating or cooling. It is a result of atomic movement inside the material when temperature changes. Thermal strain is proportional to the change in temperature and depends on the material’s coefficient of thermal expansion.
Detailed Explanation:
Thermal Strains
Thermal strain refers to the deformation or change in length of a material due to a variation in temperature. When a body is heated, the distance between its atoms increases, causing the material to expand. Conversely, when cooled, the distance between atoms decreases, leading to contraction.
This dimensional change is expressed as strain, which is defined as change in length per unit original length. Therefore, when temperature changes, the resulting deformation is called thermal strain or temperature strain.
Thermal strains are very important in engineering design because most materials experience expansion or contraction with temperature changes. If such changes are restrained, they lead to thermal stresses, which may cause deformation, distortion, or even failure of the component.
Definition and Formula
If a body of original length undergoes a temperature change , then the change in its length due to thermal expansion is given by:
where,
= coefficient of linear expansion (per °C or K⁻¹),
= temperature change (°C or K),
= original length.
The thermal strain (εₜ) is the ratio of change in length to the original length:
Hence,
This means that the thermal strain is directly proportional to the temperature change and the material’s coefficient of expansion.
Explanation of Thermal Strain Formation
When temperature increases, the energy of atoms within a solid also increases. The atoms begin to vibrate more vigorously and move farther apart, leading to an increase in the overall dimensions of the material. This behavior is called thermal expansion.
Similarly, when the temperature decreases, the atomic vibrations slow down, and atoms move closer together, resulting in thermal contraction.
If the material is free to expand or contract, thermal strain occurs without producing any stress. But if the expansion or contraction is restricted, internal stresses known as thermal stresses develop.
Thus, thermal strain is a natural physical response of materials to temperature changes, while thermal stress is a secondary effect when deformation is restrained.
Types of Thermal Strains
- Linear Thermal Strain:
- Occurs along one direction (length).
- Found in uniform rods, bars, or beams subjected to temperature changes.
- Formula:
- Volumetric Thermal Strain:
- Occurs in three dimensions, affecting the volume of the material.
- For isotropic materials, volumetric strain is three times the linear strain.
- Formula:
- Area Thermal Strain:
- Occurs over two dimensions (surface area).
- Formula:
Factors Affecting Thermal Strains
- Coefficient of Thermal Expansion (α):
- The greater the coefficient, the larger the thermal strain for a given temperature change.
- For example, aluminum has a higher α than steel, so it expands more with the same temperature rise.
- Temperature Change (ΔT):
- Thermal strain is directly proportional to the difference between final and initial temperatures.
- Larger temperature differences cause greater strains.
- Material Type:
- Metals expand more than ceramics or composites.
- Some materials, like Invar alloy, have very low thermal expansion, hence low thermal strain.
- Structural Constraints:
- If a body is free to expand or contract, strain occurs without stress.
- If constrained, the same strain generates internal thermal stresses.
- Shape and Size of the Object:
- Long and thin members experience more noticeable expansion or contraction than thick ones for the same temperature change.
Example Calculation
Let’s consider a steel rod 2 m long with a coefficient of thermal expansion . If the temperature increases by 50°C, the thermal strain developed is:
Hence, the thermal strain is or 0.0006.
This means the rod elongates by 0.06% of its original length due to the temperature rise.
Importance of Thermal Strain in Engineering
- Design of Mechanical Components:
Engineers must account for thermal strain in machine parts, pipelines, and boilers that operate under temperature variation to prevent damage. - Thermal Expansion Joints:
Bridges and rail tracks are provided with expansion joints to allow free thermal expansion and prevent excessive stress. - Material Selection:
Materials are chosen based on their coefficient of thermal expansion to ensure dimensional stability in applications like engines and turbines. - Accuracy in Manufacturing:
Thermal strains affect dimensions during machining and assembly, especially when parts are exposed to different temperatures. - Prevention of Thermal Stress:
Allowing sufficient movement or using flexible joints helps prevent the development of dangerous stresses caused by thermal strain.
Practical Examples of Thermal Strains
- Railway Tracks:
During hot weather, tracks expand due to thermal strain. Gaps are provided between rails to accommodate this expansion. - Pipelines:
Long pipelines carrying hot fluids expand due to thermal strain, so expansion bends or loops are used to absorb movement. - Bridges and Buildings:
Expansion joints are provided in long structures to prevent cracking caused by temperature-induced strains. - Electronic Devices:
In semiconductors, differential thermal expansion between materials can create strains that affect performance.
Conclusion
Thermal strains are the dimensional changes that occur in materials due to variations in temperature. They arise because atoms expand when heated and contract when cooled. The amount of thermal strain depends on the coefficient of thermal expansion, temperature change, and material properties. If free expansion is restricted, these strains generate thermal stresses that can cause structural failure. Therefore, understanding and controlling thermal strains is essential in designing safe and durable mechanical components and structures.