Base Single Crystal Superalloy Research Articles

Apparent and effective creep parameters in single crystals of a nickel base superalloy—I Incubation period

During steady state creep, the effective stress σ e , acting directly on the dislocations is defined as the difference between σ a the stress applied to the sample and σ i the average internal stress resulting from the presence of all other dislocations and of a second phase in the matrix ( σ e = σ a − σ i ). The effective activation energy ( Q e = −R[∂ In ϵ ∂ ( 1 T )]σ e ) and the effective stress exponent ( n e = [∂ In ϵ ∂ Inσ s] T where ϵ is the creep rate) are the only parameters relevant to the elementary deformation processes. These effective parameters are related to their apparent counterparts ( Q a = −R[∂ In ϵ ∂ ( 1 T )] σa and n a = [∂ In ϵ t6 Inσ a] T by the following equations: Q e = Q a + RT 2n a σ ∗ i σ a(1−σ' i) and n e = n 2 σ e σ a(1−σ' i) where σ ∗ i = (∂ σ i ∂T ) σ a and σ i = (∂ σ i ∂σ a) T can be estimated experimentally. In two-phase materials, the average internal stress may be described as σ i ( σ a T) = α( σ a , T) σ a + σ c ( T) where σ c is a threshold stress resulting from the presence of the precipitates. At intermediate temperatures (700–900°C) the first stage creep of nickel base superalloy single crystals exhibits an incubation period characterized by a very low and steady creep rate (10 −6h <ϵ < 10 −5/h). During this stage the apparent parameters take on the following values: n a = 3.5 and Q a = 75 kcal/ mole whereas σ ∗ i estimates yield − 0.27 MPa/°C and σ' i = 0 for this kind of creep. The actual values of the effective parameters may be deduced from these experimental data: Q e ∼- 60 kcal/mole and n e of the order of 1. Direct observation of the dislocation structures in connection with the values of the effective parameters leads to suggest a creep model for that particular creep stage observed in superalloys. The incubation period may be described as a steady state creep rate when deformation is produced by the glide of a low density of mobile screw dislocations ( ρ m ∼- 10 −5 cm −2) bowing out between γ' precipitates. The bowing out rate and hence the creep rate are controlled by the climb of the trailing edge dislocations left at the γ-γ' interface by the leading screw segment. The effective creep parameters seem to be related to a diffusion process enhanced by pipe diffusion of Ta and Al atoms along dislocation cores.