Abstract
When an oxidized metal is cooled from a high temperature, stresses are produced at the metal-scale interface, owing to the difference in thermal expansion rates of the oxide and metal. Such stresses become time- and temperature-dependent if the scale or underlying metal creeps as cooling occurs. A model is presented which describes thermally induced stresses in the scale and accounts for partial stress relaxation by creep of the metal substrate and/ or the scale. The expected stresses are a function of the material parameters: thermal expansion coefficients, elastic modulii, and creep rates of both metal and scale. To illustrate a range of behaviors, we have presented example calculations for three Cr2O3 forming metals, Ni-30Cr, pure Cr, and MA-754. The effect of stress relaxation during thermal cycling was also examined briefly. In these examples, creep of the Cr2O3 scale was not expected to be important.
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Abbreviations
- A :
-
A constant evaluated from experimental creep data
- δ :
-
Grain-boundary thickness
- d :
-
Grain diameter
- Δα :
-
Thermal expansion difference;a m −a ox
- Deff, v, gb :
-
Diffusion coefficient; subscript eff, defined by Eq. (6)
- υ :
-
volume
- gb :
-
grain boundary
- ɛ:
-
Strain
- Eox,m :
-
Young's modulus; subscript
- ox:
-
oxide
- m :
-
metal
- G :
-
Shear modulus
- k :
-
Boltzmann constant
- n :
-
Stress-related exponent for power-law creep
- Q p, v, gb :
-
Activation energies for creep; subscript
- p :
-
power law
- v :
-
volume diffusion
- gb :
-
grain-boundary diffusion
- R :
-
Gas constant
- R :
-
Ratio of metal-to-oxide thickness
- σ s :
-
Shear stress
- T :
-
Temperature
- t :
-
Time
- t ox,m :
-
Thickness; subscript
- ox:
-
oxide
- m :
-
metal
- Ω:
-
Atomic volume of metal
- μ :
-
Poisson's ratio
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Barnes, J.J., Goedjen, J.G. & Shores, D.A. A Model for stress generation and relief in oxide — Metal systems during a temperature change. Oxid Met 32, 449–469 (1989). https://doi.org/10.1007/BF00665449
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DOI: https://doi.org/10.1007/BF00665449