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 × 10⁴ and 16 × 10⁴. Determine the parameter for 20 MP_a.

Solution

Write equation

ln σ= k₁ m + c₁

where, m is Larson-Miller parameters. Use given values

ln 10 = k₁ × 18 × 10⁴ + c₁  = 2.3

By subtraction

ln 30 = k₁ × 16 × 10⁴ + c₁  = 3.4

 2 × k₁ × 10⁴  = - 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 × 10⁴  /0.55

               = 16.75 × 10⁴