Stress and Strain-Definition, Curve or Diagram, Formula, PDF

Amrit Kumar
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Stress and Strain Definition:

In engineering, stress has been defined is:

when an external force applied to the object(made of an elastic material), they produce a change in shape and size of the object.

Stress is defined as, the deformation force per unit area of the body or material.
Stress is the internal force(per unit area) associated with the strain.
It is ratio of force applied on the system to the per unit area of the body.

To find the stress of an object which is displaced (after applying force on it). The formula is,

Stress(σ)= Force(F) / (A)Cross-sectional Area

Whereas, σ= Stress in N/M2 or Pascal.

F= Force applied on the system which is in Newton (N).

A= Cross-sectional area of the object in M2.

The types of stresses are like

  1. Tensile stress,
  2. Compressive stress,
  3. Torsional stress.

The Tensile stress is like pulling the material on each side or might one side as figures shown below,

The Compressive stress is like pushing the material on each side or might one side as figures shown below,

compressive force

The Torsional stress is like there are two forces applied on the object and the forces are opposite to each other. The figure is shown below,

Torsional force

Whereas Strain is defined as

The ratio of change in length to the original length of an object or body is called as Strain.
Strain is relative change in shape or size of an object due to externally applied forces.

To find the strain of an object which is displaced (after applying force on it). The formula is,

Strain(∈)= Change in length (Li) / Original length (L0)

The standard unit of strain is dimensionless. It has no units.

=Strain.

Li = Change in length in Meters.

L0 = Original length in Meters.

Stress and Strain Curves or Diagram:

This curve is a behavior of the material when it is subjected to load.

The stress-strain curve depends on two types of material.

1. Ductile Material:

Ductile materials are materials that can be plastically twisted with no crack. They have the tendency to hold the deformation that occurs in the plastic region.

The ductile material is- Aluminium, Copper, Steel and more.

2. Brittle Material:

A material is brittle if, when subjected to stress, it breaks without significant plastic deformation. Brittle materials absorb relatively little energy prior to fracture, even those of high strength.

The brittle material is: Cast Iron, Concrete, Some glass product and more.

To draw the stress-strain curve of any material the mechanical point or properties includes,

  • Proportional Limit
  • Elastic Limit
  • Yield Point
  • Ultimate Stress Point
  • Breaking Point

Taking an example to understand the curve :

Stress-Strain curve for Mild steel (Ductile Material):

Stress Strain curve for Mild steel

Young's Modulus:

The Young's modulus is defined as the ratio of the stress of the object to the strain of the object or body.

Young's Modulus= Stress / Strain

The SI unit of  Young's Modulus is N/M2 or Pascal.

Limit of proportionality or Proportionality limit (A):

The proportional limit is the point on the curve up to which the value of stress and strain remains proportional.

From the diagram point, A is called the proportional limit point or it can also be known as the limit of proportionality.

The stress up to this point can be also be known as proportional limit stress.

Elastic limit:

Elastic limit is the limiting value of stress up to which the material is perfectly elastic.

Yield Stress (B-C):

  • B-upper yield value
  • C-lower yield value

Yield stress is defined as the stress after which material extension takes place more quickly with no or little increase in load. Point (B-C) is the yield point on the graph and stress associated with this point is known as yield stress.

Ultimate Stress Point (D):

Ultimate stress point is the maximum strength that material has to bear stress before breaking.

It can also be defined as the ultimate stress corresponding to the peak point on the stress-strain graph.

Breaking Stress Point or Fracture Point (E):

Breaking point or breaking stress or Fracture point is the point where the strength of material breaks.

The stress associated with this point known as breaking strength. On the stress-strain curve, point E is the breaking stress point or Fracture point.

Differences between Stress and Strain:

  • The force applied to object, the object gets displaced that is stress and Strain is the change in the form or shape of the object or physical body on which stress is applied.
  • Stress can occur without strain, but strain cannot occur with the absence of stress.
  • The stress and strain can be calculated. Stress has a dimensional unit but the strain has no dimensional unit.

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