RANDOM GATE QUESTIONS

Strength Of Materials

1. The ultimate tensile strength of a material is 400 MPa and the elongation up to maximum load is 35%. If the material obeys power law of hardening, then the true stress-true strain relation (stress in MPa) in the plastic deformation range is: 

1

σ=540ϵ0.30$\sigma =540{ϵ}^{0.30}$

2

σ=775ϵ0.30$\sigma =775{ϵ}^{0.30}$

 Correct Answer

3

σ=540ϵ0.35$\sigma =540{ϵ}^{0.35}$

4

σ=775ϵ0.35

Explanation

ϵ = ln (1 + ϵo ) = ln ( 1 + 0.35 ) = 0.3

But at UTS, n = ϵ  

Hence n = ϵ = 0.3

Also σf = σo ( 1+ ϵo) = 400 ( 1 + 0.35) = 540 MPa.

Now, σf = k ϵn

540 = k (0.3) 0.3

⇒ k = 774.97

Hence σf = 775 ϵ0.3

Where, 

σf = true stress

ϵ = true strain