Figure 8.9 shows the strain-stress curve for a given material. What are (a) Young’s modulus and (b) approximate yield strength for this material?
Figure 8.9 shows the strain-stress curve for a given material. What are (a) Young’s modulus and (b) approximate yield strength for this material?
Solution and Explanation
It is clear from the given graph that for stress 150 × 10 6 N / m2, strain is 0.002.
∴ Young’s modulus, Y =\(\frac{ Stress }{Strain }\)
= \(\frac{150 × 10^ 6 }{0.002} \)= 7.5 × 10 10 N / m2
Hence, Young’s modulus for the given material is 7.5 ×10 10 N/m2.
The yield strength of a material is the maximum stress that the material can sustain without crossing the elastic limit. It is clear from the given graph that the approximate yield strength of this material is 300 × 106 Nm/2 or 3 × 108 N / m2 .
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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.
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