 # 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 the objects. Deformation is known as the change of the shape of an object by applications of force. Very small forces can also cause deformation. 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.

### What is Stress?

The force applied per unit area in mechanics is known as stress. The following formula represents it

σ=FA

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 length of the solid given below

ϵ=δlL

where,

ϵ is strain due to stress applied

δl is change 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

### (i) Proportional Limit

The region in the stress-strain curve that observes the Hooke's Law is known as the proportional limit. According to this limit, the ratio of stress and strain provides us 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 prior to 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.

### 1. What are the Types of Stress and Strain?

Types of Stress

• Normal Stress: The restoring force per unit area perpendicular to the body surface is known as the normal stress. It differentiated into two types: tensile and compressive stress.

•  Tangential Stress: It is called tangential stress when the elastic restoring force acts parallel to the surface area.

Types of Strain

• Longitudinal Strain: The strain produced on the body due to the deforming force, which leads to change in only the length of the object is known as longitudinal or the tensile strain.

• Volumetric Strain: This is the strain produced on the body due to the deforming force, which leads to only the change in volume of the object.

• Shear Strain: Due to the tangential stress, an angle tilt is caused in the body; this is known as shear strain.

### 2. What is the Relationship Between Stress and Strain?

Hooke's law expresses the relationship between stress and strain; it states that the strain in an object is proportionate to the stress applied within the range of elastic limit of that object.

Hooke's Law

The 19th century English scientist Robert Hooke noticed while experimenting with springs and elasticity of the materials, they exhibited a similar property when the stress-strain relationship was studied. According to Hooke's law, the linear region where the force required to stretch the material was proportionate to the extension of the material.

Mathematically, Hooke's law is commonly expressed as:

F = –k.x

Where,

F is the force

x is the extension length

k is the constant of proportionality known as spring constant in N/m

• Point A shown in the graph is the proportional limit, which exhibits the proportional relationship between stress and strain in many of the materials.

• Point B is known as the elastic limit, which is beyond the proportional limit, where an object returns to its original form when the applied stress is reversed, or the external force is removed. The proportional limit and elastic limit for many of the material is the same or equal.

• Point C in the graph is known as the yield point, where the strain increases faster than stress, and the material experiences some amount of permanent deformation.

• The stress causes a specified amount of permanent strain at the offset yield strength (point B).

• D denotes the value of the ultimate tensile strength of the material has been reached. It denotes the maximum stress that can be applied to the material before its failure occurs.