question_answer 2)

Fig. l shows the stress-strain curve for a given material. What are (a) Young's modulus, and (b) approximate yield strength for this material?    

Answer:

(a) From graph, for stress [therefore text{cos }!!theta!!text{  =}frac{text{x}}{l}] the corresponding strain = 0.002 Young s modulus, [T=frac{mg}{2left( x/l right)}=frac{mgl}{2x}]                                   [text{=}frac{text{T}}{text{A}}text{=}frac{text{mgl}}{text{2Ax}}]                                    (b) Approximate yield strength will be equal to the maximum stress it can sustain without crossing the elastic limit. Therefore, the approximate yield strength [text{Y=}frac{text{Stress}}{text{Strain}}text{=}frac{text{mgl}}{text{2Ax}}text{ }!!times!!text{ }frac{text{2}{{text{l}}^{text{2}}}}{{{text{x}}^{text{2}}}}text{=}frac{text{mg}{{text{l}}^{text{3}}}}{text{A}{{text{x}}^{text{3}}}}] [text{X=l}{{left[ frac{text{mg}}{text{YA}} right]}^{text{1/3}}}=0cdot 5{{left[ frac{0cdot 1times 10}{20times {{10}^{11}}times 0cdot 5times {{10}^{-6}}} right]}^{1/3}}]