What are Stress and Strain?
Some of the items you might have noticed can be easily stretched, for example, like a rubber band. But can you stretch an iron rod? It is impossible, right? On this page, we will learn about the properties of solids in greater detail also, how quantities like stress will help us to understand the strength of solids.
Stress and Strain are the two terms in Physics that describe the forces causing the deformation of objects. Deformation is known as the change of the shape of an object by applications of force. The object experiences it due to external forces; for example, the forces might be like squeezing, squashing, twisting, shearing, ripping, or pulling the objects apart.
Types of Strain
A person's body can be stressed in one of two ways, depending on how much stress is applied:
Tensile Strain: Tensile strain is defined as a change in the length (or area) of a body caused by tensile tension.
Compressive Strain: The change in length (or area) of a body caused by compressive strain is known as compressive strain.
Use of Stress-Strain Graph
The stress-strain diagram is a graphical representation of the material's strength and elasticity. The stress-strain diagram can also be used to study the behaviour of the materials, which simplifies the application of these materials.
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Relationship Between Stress and Strain
Stress and strain have a straight proportional relationship up to an elastic limit. The relationship between stress and strain is explained by Hooke's law. Hooke's law states that the strain in a solid is proportional to the applied stress, which must be within the solid's elastic limit.
Yield Point in Stress-Strain Graph
The yield point of a material is the point at which it begins to distort plastically. Permanent plastic deformation happens after the yield point is passed.
How to Create a Stress-Strain Curve?
The stress-strain curve is created by progressively adding load to a test coupon and monitoring the deformation, which allows the stress and strain to be calculated.
Hooke’s Law
When English scientist Robert Hooke was studying springs and elasticity in the 19th century, he observed that numerous materials had a similar feature when the stress-strain connection was analysed. Hooke's Law defined a linear zone in which the force required to stretch material was proportionate to the extension of the material.
Define Stress and Strain
The force applied per unit area in mechanics is known as stress. The following formula represents it
Σ =F/A
where,
σ is stress applied
F is force applied
A is the area of force applied
Stress is measured by unit N/m2
The ratio of internal force F, produced when a substance is deformed, to the area A where force is applied is known as stress. At equilibrium, the internal force is equal to the magnitude of the externally applied force.
The newton per square meter (Nm2) is the SI unit for stress. Dyne-cm2 is the CGS unit in which stress is measured. ML-1T-2 is the dimensional formula for stress.
What is Strain?
Strain is the ratio of the amount of deformation experienced by the body in the direction of force applied to the initial sizes of the body. The relation of deformation in terms of the length of the solid is given below
ϵ=δlL
where,
ϵ is strain due to stress applied
δl is changed in length
L is the original length of the material.
Strain is the ratio for change of shape or size to the original shape or size. It is expressed in number as it doesn't have any dimensions. Since strain defines the relative change in shape and it is a dimensionless quantity. A body can experience two types of strain depending upon the stress application.
Stress-Strain Curve Explanation
The material's stress-strain curve represents the relationship between stress and strain for materials. The strain values are plotted on the curve corresponding to the stress incurred by different loads on the object.
Explaining Stress-Strain Graph
The stress-strain diagram has different points or regions as follows:
Proportional limit
Elastic limit
Yield point
Ultimate stress point
Fracture or breaking point
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(i) Proportional Limit
The region in the stress-strain curve that observes Hooke's Law is known as the proportional limit. According to this limit, the ratio of stress and strain provides us with the proportionality constant known as young's modulus. In the graph point, OA is known as the proportional limit.
(ii) Elastic Limit
Elastic limit is the maximum stress that a substance can endure before permanently being deformed. When the load acting on the object is completely removed and the material returns to its original position, that point is known as the object's elastic limit.
(iii) Yield Point
The point at which the material starts showing to deform plastically is known as the yield point of the material. Once the yield point of an object is crossed, plastic deformation occurs. There are two types of yield points (i) upper yield point (ii) lower yield point.
(iv) Ultimate Stress Point
The point at which a material endures maximum stress before failure is known as the Ultimate Stress point. After this point, the material will break.
(v) Fracture or Breaking Point
In the stress-strain curve, the point at which the failure of the material takes place is known as the breaking point of the material.
FAQs on Stress and Strain
1. What is meant by stress and strain in Physics, and how are they measured?
Stress is the force applied per unit area within materials, causing deformation. It is measured in newtons per square meter (N/m2). Strain is the ratio of the change in dimension to the original dimension of a body, caused by the applied stress. Strain is dimensionless, as it is a ratio with no units.
2. How does Hooke's law explain the relationship between stress and strain?
Hooke’s law states that within the elastic limit, the strain produced in a material is directly proportional to the applied stress. Mathematically, this is expressed as σ ∝ ε. This linear relationship continues only up to the proportional limit of the material.
3. What are the main types of stress and how do they affect materials?
There are three main types of stress experienced by materials:
- Tensile stress: Acts to stretch the material.
- Compressive stress: Acts to compress or shorten the material.
- Shear (or tangential) stress: Acts parallel to the surface, causing the layers to slide over each other.
4. Can you explain the different types of strain with examples?
The main types of strain are:
- Longitudinal strain: Change in length divided by the original length (e.g., stretching a wire).
- Volumetric strain: Change in volume divided by original volume (e.g., compressing a rubber ball).
- Shear strain: Relative displacement between layers divided by the distance between them (e.g., sliding a deck of cards sideways).
5. What does the stress-strain curve represent and what are its key regions?
The stress-strain curve shows how a material responds to stress:
- Proportional limit: Stress is directly proportional to strain (Hooke’s law holds).
- Elastic limit: Maximum stress for complete recovery on load removal.
- Yield point: Material begins to deform plastically.
- Ultimate stress point: Maximum stress endured before failure.
- Fracture point: Material breaks.
6. Why does the area under a stress-strain curve matter in material science?
The area under the stress-strain curve indicates the material’s toughness – the total energy per unit volume that a material can absorb before rupturing. Materials with higher areas are tougher and can absorb more energy before failure.
7. How can misinterpreting the elastic limit lead to material failure in real-world applications?
If the elastic limit is exceeded, materials enter the plastic region, resulting in permanent deformation. In applications like bridges or buildings, misjudging this limit can cause catastrophic failure or unsafe structures.
8. What biological systems or everyday objects demonstrate Hooke’s law or stress-strain behavior?
Examples include:
- Tendons in the human body: Initially stretch easily, then resist further stretching (nonlinear stress-strain, but with regions following Hooke’s law).
- Springs: Extension is proportional to load within elastic range.
9. How do engineers use stress and strain data to ensure the safety of structures?
Engineers use stress-strain data to select materials with proper elastic limits and yield strengths for construction, ensuring that applied loads do not exceed safe values. This prevents permanent deformation and structural failure.
10. How does temperature affect the stress-strain behavior of a material?
Rising temperature usually decreases a material’s strength and elastic limit, making it more susceptible to deformation at lower stress levels. Conversely, some materials become more brittle at low temperatures.
