How Does Thermal Stress Affect Materials?
Before we learn what thermal stress is, it is vital to understand the fundamentals of basic stress and how it is caused.
When an external force is applied to a body, there is a high chance it can get deformed to a certain extent. How much deformation will take place relies entirely on the nature of molecular attraction of the concerned body.
As the deformation takes place, several internal forces within the body act aggressively to bring the body back to its initial state. More the deformation caused, higher will be the magnitude of these internal forces.
What is Stress?
The internal restoring force acting per unit area of a distorted body is known as stress. At an equilibrium state, these internal forces of a distorted body are always equal and opposite to the deforming forces. If this deforming force is removed, the internal force of restitution brings back the body to its original shape.
Let’s say, for a body of Area A, an external force, F is applied which expands the length of the body L by a certain measure. Let this be ΔL. As a result, an internal force of the same magnitude is created, i.e. F in the opposite direction.
So, Stress = F/A
Define Thermal Stress
When the external force applied on a body which leads to any sort of deformity is caused due to change in temperature, the resultant stress thus created can be termed as thermal stress. In other words, thermal stress definition states that formation of corresponding stress takes place when a body acquires compressive strain due to any thermal expansion or contraction.
Example of Thermal Stress
A prime example of thermal stress is the gap maintained between the outer and inner ends of rail tracks. If two such steel rods (which are usually used as rails over which trains pass) are in contact with their inner and outer ends, a high magnitude of thermal stress generated due to friction and other temperature conditions will easily bend the rods.
Before we carry on with this discussion on what is thermal stress, brush up your memory on the following topics in the Q&A section given below.
Test Your Knowledge
What are the Different Types of Stress?
Ans. There are various types of stress. Stress can be classified into 3 types based on the action of the deforming force and how it changes the orientation of a body.
These types are normal stress, tangential or shearing stress and hydrostatic or hydraulic stress. Normal stress can be further divided into tensile stress and comprehensive stress.
Check out these Questions below and Test Your Understanding
What are the Cgs and Si Units of Stress?
Ans. As per Newton’s third law of motion, the internal force of restoration is equal and opposite to the deforming force at equilibrium during thermal expansion of a material.
Hence, thermal stress or any other stress is quantitatively equal to the force of deformation acting per unit area of the concerned body.
So, the dimensional formula of stress is [ML-1T-2]. In that case, CGS and SI units of stress are dyne cm-2 and Nm-2, respectively.
What is Strain?
Ans. Due to any change in temperature, a material may undergo thermal expansion or contraction. When such a deformity takes place, the concerned material is said to be strained. It is measured as the ratio of change in orientation to the original orientation of a body.
Since strain is a ratio, it is dimensionless and therefore has no units. This is the main difference between thermal stress and strain.
Thermal Stress Formula
Let us consider that a solid rod of area A has undergone thermal expansion and its original length L0 has increased to L.
The rise in temperature is known to be ΔT due to heat applied by a certain magnitude of a force, i.e. F.
One can observe that this linear thermal expansion is directly proportional to L0 and ΔT.
So, we can conclude that –
L – L0 = L0α ΔT, where α is the coefficient of linear expansion of the material.
In that case, L = L0 (1 + α ΔT)
Hence, thermal stress = F/A = Y (L - L0) / L0 where Y is Young’s modulus of the given material.
This can be simplified into Y (α ΔT) / L0
This is considered as the thermal stress formula.
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FAQs on Thermal Stress in Physics: Concepts, Formulas & Applications
1. What exactly is thermal stress in the context of Physics?
Thermal stress is the internal restoring force per unit area that develops inside a body when its thermal expansion or contraction is prevented or restricted. If an object is free to expand or contract with temperature changes, it will experience thermal strain (a change in shape), but no thermal stress is generated. Stress only arises when this movement is constrained.
2. How is thermal stress calculated using its formula?
The formula to calculate thermal stress (σ) is:
σ = YαΔT
Where:
- Y is the Young's Modulus of the material, representing its stiffness.
- α (alpha) is the coefficient of linear thermal expansion.
- ΔT (delta T) is the change in temperature that the body undergoes.
3. What is the key difference between thermal stress and thermal strain?
The primary difference lies in their nature and units. Thermal strain is the fractional change in an object's dimension due to a temperature change (ΔL/L); it is a dimensionless quantity. Thermal stress is the internal force per unit area (N/m² or Pascals) generated only when this strain is resisted. In essence, unconstrained temperature changes cause strain, while constraining that strain causes stress.
4. What are the SI unit and dimensional formula for thermal stress?
The SI unit for thermal stress is the same as for pressure, which is Pascals (Pa) or, more fundamentally, Newtons per square metre (N/m²). The dimensional formula for thermal stress is [ML⁻¹T⁻²], derived from the formula for force divided by area.
5. Why are small gaps intentionally left between railway tracks?
This is a classic real-world example of managing thermal stress. Railway tracks are made of steel, which expands in the summer heat and contracts in the winter cold. The gaps, known as expansion joints, provide space for the tracks to expand into. Without these gaps, the expansion would be constrained, generating immense compressive thermal stress that could cause the tracks to buckle and bend, creating a severe safety hazard.
6. Does a change in temperature always cause thermal stress in an object?
No, this is a common misconception. A change in temperature only causes thermal stress if the object's natural tendency to expand or contract is externally constrained. For example, a metal rod heated in open space will simply get longer (experience thermal strain) but will have zero thermal stress. Stress is only induced if the ends of that same rod are fixed, preventing it from expanding.
7. How does a material's Young's Modulus affect the magnitude of thermal stress it experiences?
A material's Young's Modulus (Y) is a measure of its stiffness. According to the formula σ = YαΔT, thermal stress is directly proportional to Y. This means that for the same temperature change and constraint, a stiffer material (with a high Young's Modulus, like steel) will develop a much higher thermal stress than a more flexible material (with a low Young's Modulus, like rubber). The stiffer material resists deformation more strongly, leading to a greater internal force.
