Stress and Strain Curve | Explanation, Formula, Examples – Elasticity

Stress-Strain Curve Explanation:
When a wire is stretched by a load as in Fig. (a), it is seen that for small value of load, the extension produced in the wire is proportional to the load as shown in Fig. (b). Hence,

Stress ∝ Strain

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Stress and Strain Curve | Explanation, Formula, Examples – Elasticity

Beyond the limit of elasticity, the stress and strain are not proportional to each other, on increasing the load further, the wire breaks at point D, known as feature point.
Stress and Strain Curve

Stress-strain Curve Example:
The stress-strain curve illustrates the mechanical properties of materials, for example, steel, stainless steel or aluminium. This is the area in which the material is stressed beyond its elastic loadability and the first plastic deformations occur.

Breaking Stress Definition:
The minimum value of stress required to break a wire, is called breaking stress. Breaking stress is fixed for a material but breaking force varies with area of cross-section of the wire.

Safety factor = \(\frac{\text { Breaking stress }}{\text { Working stress }}\)

Elastic Relaxation Time:
The time delay in restoring the original configuration after removal of deforming force is called elastic relaxation time. For quartz and phospher bronze this time is negligible.

Elastic After Effect:
The elastic after effect shows that the temporary delay in regaining the original configuration by the elastic body after the removal of deforming force is called elastic after effect.

Elastic Fatigue Meaning:
The property of an elastic body by virtue of which its behaviour becomes less elastic under the action of repeated alternating deforming force is called elastic fatigue.

Ductile Materials are Defined as:
The materials which show large plastic range beyond elastic limits are called ductile materials.

Ductile Materials Examples

  • Copper
  • Silver
  • Iron
  • Aluminum

Ductile materials are used for making springs and sheets.

Brittle Materials Definition:
The materials which show very small plastic range beyond elastic limits are called brittle materials.

Brittle Materials Examples

  • Glass
  • Cast
  • Iron

Elastomers Definition:
The materials for which strain produced is much larger, than the stress applied, within the limit of elasticity are called elastomers.

Elastomers Examples
Rubber, the elastic tissue of arota, the large vessel carrying blood from heart etc. Elastomers have no plastic range.

When a solid is compressed, a stage is reached beyond which it cannot regains its original shape after the deforming force is removed. This quality is called malleability of solid substance.

Elastic hysteresis
As a natural consequence of the elastic after-effect, the strain in the body tends to lag behind the stress applied to the body so that during a rapidly changing stress, the strain is greater for the same value of stress. This lag of strain behind the stress is called elastic hysteresis.

Elastic Potential Energy in a Stretched Wire

The work done in stretching a wire is stored in the form of potential energy of the wire.
Potential energy

U = Average force × Increase in length = \(\frac{1}{2}\) FΔl
= \(\frac{1}{2}\) Stress × Strain × Volume of the wire

Elastic potential energy per unit volume

U = \(\frac{1}{2}\) × Stress × Strain = \(\frac{1}{2}\) (Young’s modulus) × (Strain)2

Elastic potential energy of a stretched spring = \(\frac{1}{2}\) kx2
where, k = Force constant of spring and x = Change in length.

Elasticity defines a property of an object that has the ability to regain its original shape after being stretched or compressed. Learn about the deforming force applied on an elastic object and how the stress and strain works on an object. What is a Hooke’s law and how it is applicable for the concept of elasticity.

Deforming Force Elasticity
Stress Strain
Hooke’s Law Elastic Modulus
Types of Modulus of Elasticity Poisson’s Ratio
Stress and Strain Curve Thermal Stress
Cantilever Beam Torsion of a Cylinder