Thermal strain refers to the deformation of a material caused by a change in temperature. It plays a crucial role in engineering applications where temperature variations can affect structural integrity, such as bridges, pipelines, and aerospace components.
Thermal strain (εt) is caused by the expansion or contraction of a material due to a change in temperature. It is calculated as:
εt = α * ΔT
Where:
Thermal strain is dimensionless and represents the fractional change in length due to thermal effects.
When a material is constrained and cannot expand or contract freely, thermal strain induces thermal stress (σt). The relationship is given by:
σt = E * εt = E * α * ΔT
Where:
This equation shows that thermal stress depends on the material's stiffness, thermal expansion coefficient, and temperature change.
Thermal strain is critical in the following applications:
Thermal strain is measured experimentally by subjecting materials to controlled temperature changes and monitoring dimensional variations using precision instruments like strain gauges or extensometers.
Worked Example 1:
A steel rod with a length of 2 m is heated from 20°C to 120°C. The coefficient of thermal expansion for steel is 12 × 10-6 1/°C. Calculate the thermal strain.
Solution:
ΔT = 120 - 20 = 100°C
εt = α * ΔT = (12 × 10-6) * 100 = 0.0012
Thermal strain = 0.0012 (dimensionless).
Worked Example 2:
A constrained aluminum bar with a Young’s modulus of 70 GPa is subjected to a temperature increase of 50°C. The coefficient of thermal expansion for aluminum is 23 × 10-6 1/°C. Calculate the thermal stress.
Solution:
Thermal stress = 80.5 MPa.
Thermal strain is a fundamental concept in engineering that describes deformation due to temperature changes. It transitions into thermal stress when the material is constrained and cannot freely expand or contract. Understanding thermal strain is essential for designing components and structures that can withstand temperature variations without failure.
Engineers must consider both free expansion and constrained thermal effects to ensure safety and performance in real-world applications.
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