Medium
The figure shows the stress-strain curve for a given material. What are $(a)$ Young's modulus and $(b)$ approximate yield strength for this material?
(N/A) It is clear from the given graph that for a stress of $150 \times 10^{6} \, N/m^{2}$,the strain is $0.002$.
$(a)$ Young's modulus,$Y = \frac{\text{stress}}{\text{strain}}$
$Y = \frac{150 \times 10^{6} \, N/m^{2}}{0.002} = 7.5 \times 10^{10} \, N/m^{2}$
Hence,the Young's modulus for the given material is $7.5 \times 10^{10} \, N/m^{2}$.
$(b)$ 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 $300 \times 10^{6} \, N/m^{2}$ or $3 \times 10^{8} \, N/m^{2}$.
$(a)$ Young's modulus,$Y = \frac{\text{stress}}{\text{strain}}$
$Y = \frac{150 \times 10^{6} \, N/m^{2}}{0.002} = 7.5 \times 10^{10} \, N/m^{2}$
Hence,the Young's modulus for the given material is $7.5 \times 10^{10} \, N/m^{2}$.
$(b)$ 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 $300 \times 10^{6} \, N/m^{2}$ or $3 \times 10^{8} \, N/m^{2}$.
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In Column-$I$ there are two stress-strain graphs,and in Column-$II$ the nature of the materials is given. Match them appropriately:
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| $(a)$ Graph $A$ | $(i)$ $A$ is ductile |
| $(b)$ Graph $B$ | $(ii)$ $A$ is brittle |
| $(iii)$ $B$ is ductile | |
| $(iv)$ $B$ is brittle |
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