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High-temperature materials and creep

Check the three stages of the creep curve, power-law and diffusion creep, deformation mechanism maps, the Larson–Miller parameter, nickel-based superalloys and single-crystal blades, thermal barrier coatings, and high-temperature oxidation and protective scales through three-choice questions.

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High-temperature materials and creep: key points

At high temperatures above about 0.4 times the melting point, creep, in which deformation proceeds with time even under a constant load, determines the life. The creep curve consists of three stages, transient, steady-state and accelerating, and design uses the steady-state creep rate. Power-law creep involving dislocation climb dominates at high stresses and diffusion creep at low stresses, and these fields are organized in a deformation mechanism map. Life is estimated with the Larson–Miller parameter, which combines temperature and time.

Jet engine turbine blades use nickel-based superalloys with a large amount of the ordered γ' phase precipitated, and single-crystal blades with no grain boundaries raise the creep strength. The surface is covered with a zirconia thermal barrier coating of low thermal conductivity to lower the metal temperature. In high-temperature oxidation, the parabolic law, in which diffusion through the scale controls growth, and the Pilling–Bedworth ratio serve as guides to protectiveness, and dense Cr₂O₃ and Al₂O₃ scales protect the alloy.

All High-temperature materials and creep questions (15)
  1. Which statement about the three stages of a creep curve (strain versus time) measured at constant load and temperature is correct?
  2. The steady-state creep rate of a heat-resistant alloy follows the power law ε̇ = Aσⁿexp(−Q/RT) with a stress exponent of n = 5. If the stress is raised by 20% at the same temperature, by roughly what factor does the steady-state creep rate increase?
  3. An alloy has a steady-state creep rate that follows ε̇ = Aσⁿexp(−Q/RT) with an activation energy of Q = 300 kJ/mol. If the temperature is raised from 1000 K to 1050 K at the same stress, by roughly what factor does the steady-state creep rate increase? Take R = 8.314 J/(mol·K).
  4. A fine-grained polycrystalline metal was creep tested at a low stress at about 0.5 times its melting point (in absolute temperature). The steady-state creep rate was nearly proportional to stress (stress exponent n ≈ 1) and nearly inversely proportional to the cube of the grain size. Which creep mechanism is most likely to be operating?
  5. Which statement about the deformation mechanism map of Ashby and coworkers (with stress normalized by the shear modulus, σ/G, on the vertical axis and homologous temperature T/Tm on the horizontal axis) is correct? Tm is the melting point in absolute temperature.
  6. At room temperature, refining the grains raises strength (the Hall–Petch relation), but components loaded for long times at high temperature often use coarse grains or single crystals. Which is the correct reason?
  7. A heat-resistant alloy ruptured by creep in 1000 h at 1000 K under a certain stress. Assuming the Larson–Miller parameter P = T(C + log₁₀t_r) (T is the absolute temperature, t_r is the rupture time in h, and C = 20) is constant at the same stress, which temperature is closest to that giving a rupture life of 10⁵ h at the same stress?
  8. Which statement about the γ' phase that provides the high-temperature strength of nickel-based superalloys is correct?
  9. Why are directionally solidified columnar-grained or single-crystal nickel-based superalloys used for jet engine turbine blades?
  10. What is the main purpose of adding a few percent of heavy elements such as rhenium (Re) to single-crystal nickel-based superalloys?
  11. When an alloy was oxidized in air at high temperature, it followed the parabolic law x² = k_p t, in which diffusion through the dense oxide scale controls the rate, and the scale was 2.0 µm thick after 100 h. Which is closest to the scale thickness after 900 h of oxidation at the same temperature?
  12. The Pilling–Bedworth ratio of a metal's oxide scale (PBR, the ratio of the volume of oxide to the volume of metal used to form it) is calculated as PBR = (M_ox ρ_M)/(n M_M ρ_ox) (M is the molar mass, ρ is the density, and n is the number of metal atoms in one formula unit of the oxide). For magnesium (24.31 g/mol, 1.74 g/cm³) and MgO (40.30 g/mol, 3.58 g/cm³, n = 1), which combination of PBR and scale behavior is correct?
  13. Which statement about the protective scales on heat-resistant alloys used in air at high temperatures above 1000 °C is correct?
  14. Which statement about the structure of a thermal barrier coating (TBC) applied to gas turbine blades is correct?
  15. A heat flux of 1.0 MW/m² passes uniformly through the thickness of the top coat of a thermal barrier coating (thickness 250 µm, thermal conductivity 1.2 W/(m·K)). Treating it as steady one-dimensional heat conduction, which is closest to the temperature difference between the two faces of the top coat?

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