Question

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. \(\sigma = 540{ \epsilon ^{0.30}}\)
2. \(\sigma = 775{ \epsilon ^{0.30}}\)
3. \(\sigma = 540{ \epsilon ^{0.35}}\)
4. \(\sigma = 775{ \epsilon ^{0.35}}\)

Answer 1

Correct Answer - Option 2 : \(\sigma = 775{ \epsilon ^{0.30}}\)

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

But at UTS, n = ϵ  

Hence n = ϵ = 0.3

Also σ_f = σ_o ( 1+ ϵ_o) = 400 ( 1 + 0.35) = 540 MPa.

Now, σ_f = k ϵⁿ

540 = k (0.3) ^0.3

⇒ k = 774.97

Hence σ_f = 775 ϵ^0.3

Where, σ_f = true strees

ϵ = true strain