The stress-strain graphs for materials A and B are shown in Fig. 8.10.
The graphs are drawn to the same scale.
(a) Which of the materials has the greater Young’s modulus?
(b) Which of the two is the stronger material?
The stress-strain graphs for materials A and B are shown in Fig. 8.10.
The graphs are drawn to the same scale.
(a) Which of the materials has the greater Young’s modulus?
(b) Which of the two is the stronger material?
Solution and Explanation
(a) A (b) A
For a given strain, the stress for material A is more than it is for material B, as shown the two graphs.
Young’s modulus \(= \frac{Stress }{ Strain}\)
For a given strain, if the stress for a material is more, then Young’s modulus is also greater for that material. Therefore, Young’s modulus for material A is greater than it is for material B.
The amount of stress required for fracturing a material, corresponding to its fracture point, gives the strength of that material. Fracture point is the extreme point in a stress strain curve. It can be observed that material A can withstand more strain than material B Hence, material A is stronger than material B.
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Concepts Used:
Stress Strain Curve
Stress:
The force applied per unit area in mechanics is understood as stress.
σ=FA
- σ is stress applied
- F is force applied
- A is that the area of force applied
- Stress is measured by unit N/m2
The ratio of internal force F that is produced when a substance is deformed, to the area A where force is applied is referred to as stress.
Strain:
Strain can be referred to as the ratio of the amount of deformation that the body experiences 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 shown below:
ε=δlL
where,
- ε = strain due to the stress applied
- δl = modified long
- L = the original length of the material
- Strain = the ratio for change of shape or size to the initial shape or size. It's expressed in numbers because it doesn't have any dimensions.
As strain defines the relative change in shape and it's a dimensionless quantity.
Explanation of Stress-Strain Curve:
The material's stress-strain curve delineates the connection between stress and strain for materials. In other words, a stress-strain curve is a graphical representation that shows the reaction of a material when a load is applied.