A component made of a Ni-base superalloy with an average grain diameter dₒ = 10 μm is used in the hot section of a gas turbine engine at a power plant. The yield strength of this alloy is 300 MPa. However, during continuous service at 1000 °C for 100 h the grain size increases to 25 μm and σᵧ drops to 250 MPa. The acceptable σᵧ for this alloy is 200 MPa.
After how many hours of total service will the component have to be replaced? The grain size dependence on time is given by:
dⁿ – dₒⁿ = Kt,
where n=2 is a constant and K is a constant with time but depends on temperature. The Hall-Petch relationship is, σᵧ = σₒ + kᵧd^(-0.5). You may choose to solve part of this problem graphically.