Determine the parameter - Larson-Miller parameters:
Larson-Miller parameters for an alloy at tests levels 10 MP_{a} and 30 MP_{a} are determined respectively as 18 × 10^{4 }and 16 × 10^{4}. Determine the parameter for 20 MP_{a}.
Solution
Write equation
ln σ= k_{1 }m + c_{1}
where, m is Larson-Miller parameters. Use given values
ln 10 = k_{1} × 18 × 10^{4} + c_{1} = 2.3
By subtraction
ln 30 = k_{1} × 16 × 10^{4} + c_{1} = 3.4
2 × k_{1} × 10^{4} = - 1.1
∴ k1 =- 0.55 × 10- 4
∴ c1 = 2.3 + 18 × 0.55 = 12.21
∴ ln σ= - 0.55 × 10- 4 m + 12.21
For
σ = 20 MPa
m =- ln 20 - 12.21 × 10^{4} /0.55
= 16.75 × 10^{4}