Stress and strain are two quantities that are used to define the nature of the applied force and resulting deformation.
Stress is defined as the internal restoring force applied per unit area of the deformed body.
Stress developed in a body depending upon how much external force acted on it.
Stress Formula:
It is measured as the external force applied per unit area of the body i.e,
- Stress = External deforming force (F)/Area (A)
- Its SI unit is Nm-2 or N/m2.
- Its dimensional formula is [ML-1T-2].
E.g., If the applied force is 10N and the area of cross section of the wire is 0.1m2, then stress = F/A = 10/0.1 = 100N/m2.
Types of Stress:
There are mainly 3 types of stresses:
- Tensile stress
- Compressive stress
- Tangential stress
Tensile stress: Tensile stress is defined as the increase in the length of the body due to applied force.
Compressive stress: It is defined as the decrease in the length of the body due to applied force.
Tangential stress: It is defined as the deforming force applied per unit area.
Strain Definition:
Strain is defined as the change in shape or size of a body due to deforming force applied to it.
We can say that a body is strained due to stress.
Strain Formula:
Its symbol is (∈).
Strain is measured by the ratio of change in dimension to the original dimension. i.e,
Strain (∈) = Change in dimension / Original dimension
Since it is the ratio of two similar quantities, it is a pure number.
Therefore, Strain has no SI unit. It is dimensionless.
Types of strain:
Strain also has 3 types:
- Longitudinal strain
- Volumetric strain
- Shearing strain
Longitudinal strain: When the deforming force makes a change in length alone, the strain produced is called longitudinal strain.
It is measured as the ratio of change in length to its original length.
Volumetric strain: When the deforming force makes a change in volume, the strain is called volumetric strain.
It is measured by the ratio of change in volume to the original volume.
Shearing strain: When the deforming force makes a change in the shape of the body, the strain is called shearing strain.
It is measured as the ratio of the displacement of the surface that is in direct contact with the applied shear stress from its original position.
Stress and Strain Curve for an Elastic Material:
Suppose a wire of uniform cross-section is suspended from a rigid support. When the load on the other side is increased gradually, then the length of the wire goes on increasing.
If we plot the graph between stress and strain, then the shape of the curve will be as shown in fig just below:
Let us describe all the points of the graph:
Portion O-A (Elastic Behavior):
The portion OA of the graph is a straight line showing that up to point A, Stress produced in the wire is directly proportional to the strain i.e., stress-strain.
In this portion, Hooke’s law is obeyed by the material of the wire. Point A is termed the Limit of Proportionality.
The proportionality of the limit is the maximum stress that a material can hold without departure from a linear stress-strain relation. If the applied force from any point between O and A is removed, then the wire will regain its original length.
Portion A-B:
In Portion AB of the graph, stress is not directly proportional to the strain of the material.
Note that the slope of the graph is decreased; this means that strain increases more rapidly with strain. Point B is termed as Elastic limit.
The elastic limit of a body is the maximum stress which a body can sustain and still regain its original shape and size if the load is removed.
Portion B-C:
If the load is increased beyond the elastic limit, a point C is reached at which there is a marked increase in extension. Point C is termed Yield Point.
Between B and C, the material becomes plastic i.e., if the applied force is removed from any point between B and C, the material will not regain its original shape and size.
The extension is not recoverable after the removal of applied force is called a permanent set. Here OO’ is the permanent set.
Portion C-D:
If stress is increased beyond C, the wire lengthens rapidly until we reach point D at the top of the curve. Point D is termed the Ultimate strength or Breaking stress.
Point E:
It is the fracture or breaking point of the material. Beyond point D, even stress smaller than at C may continue to stretch the wire until it breaks.
The breaking point or fracture point is the point where a material loses its strength and breaks.
Reference [External Links]:
S. Chand s Principles Of Physics
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