Phenomenological Analysis of Surface Degradation of Metallic Materials in Extreme Environment

Abstract

The resistance to surface degradation in metallic alloys plays an important role for the lifetime of the components working in harsh environments. The mechanisms involved in degradation of metallic surface in a high-temperature aggressive gaseous atmosphere include the following: forming adherent to the surface multiphase oxide layer, partial spallation, and possible vaporization of formed compounds. The governing equation, which describes a parabolic growth of adherent layer, time-dependent vaporization, and cross-linked to instantaneous thickness of adherent layer spallation rate, was suggested and analyzed. The several relationships between the kinetic constants were defined from analysis of the governing equation. Design of routes for experimental procedures to determine the independent kinetic constants was discussed and an integrated simulator was used to calculate the kinetic constants based on experimental results. Two examples of high-temperature oxidation of heat-resistant Cr/Ni austenitic steel were used to illustrate the capability of the suggested method to determine the oxidation, spallation, and vaporization kinetic constants from a single experiment. The suggested methodology could be considered in future for the analysis of different types of surface degradation of solid materials in gaseous, liquid, or solid environments.

Appendix

• A1 The solution of the differential Eq. [6], under assumption X(0) = 0, links process time (τ, h) to the thickness of the oxidized adherent layer (X, cm) for the given set of kinetic coefficients for oxidation K_P (cm²/h), for vaporization K_V (cm/h), and for spallation K_S (1/h):

  $$ \tau = \frac{{K_{\text{V}} - G}}{{2K_{\text{S}} G}}ln\left( {\frac{{2K_{\text{S}} X + K_{\text{V}} - G}}{{K_{\text{V}} - G}}} \right) - \frac{{K_{\text{V}} + G}}{{2K_{\text{S}} G}}ln\left( {\frac{{2K_{\text{S}} X + K_{\text{V}} + G}}{{K_{\text{V}} + G}}} \right) $$

  (A1)

  where: $G = \sqrt {K_{\text{V}}^{2} + 2K_{\text{S}} K_{p} }$

• A2 When solid reaction product is determined at the test end (τ_f), including the weight of specimen with adherent oxide (ΔW_f), the weight of spalled oxide (${\Delta W}_{f}^{s}$), and the final thickness of adherent scale (X_f), the vaporization constant (K_V) could be calculated from a final mass balance, assuming that the metal oxide density (ρ_ox), and the weight fraction of oxygen-in oxide (f_O) are known:

  $$ K_{\text{V}} = \frac{{f_{o} X_{f} }}{{\left( {1 - f_{o} } \right)\tau_{f} }} - \frac{{\Delta W_{f}^{s} }}{{\rho_{\text{ox}} \tau_{f} }} - \frac{{\Delta W_{f} }}{{\rho_{\text{ox}} \tau_{f} \left( {1 - f_{o} } \right)}} $$

  (A2)

• A3 When all three mechanisms were involved, we have K_V > 0, K_S > 0 and for any intermediate experimental time (τ_i), instant thickness X_i of adherent layer can be analytically calculated for a known weight of specimen (ΔW_i) and a weight of spalled (${W}_{i}^{s}$) scale:

  $$ X_{i} = \frac{{\Delta W_{i} }}{{\rho _{{ox}} f_{o} }} + \frac{{K_{\text{V}} \left( {1 - f_{o} } \right)\tau _{i} }}{{f_{o} }} + \frac{{W_{i}^{s} (1 - f_{o} )}}{{\rho _{{ox}} f_{o} }} $$

  (A3)

• A4 When only specimen weight was monitored in experiments, the characteristic point of a maximal weight of specimen with adherent layer can be used for indirect analysis of surface degradation mechanisms. For the three processes described in Eq. [6], the thickness of adherent layer (X_m) at a time (τ_m) when weight change of specimen with adherent layer achieved maximum (ΔW_m) can be found:

  $$ \begin{aligned} \tau_{\text{m}} & = \frac{{K_{\text{V}} - G}}{{2K_{\text{S}} G}}\ln \left( {\frac{{G_{f} - G}}{{K_{\text{V}} - G}}} \right) - \frac{{K_{\text{V}} + G}}{{2K_{\text{S}} G}}\ln \left( {\frac{{G_{f} + G}}{{K_{\text{V}} + G}}} \right) \hfill \\ X_{\text{m}} & = \frac{{G_{f } - K_{\text{V}} }}{{2K_{\text{S}} }} \hfill \\ \end{aligned} $$

  (A4)

  where $G = \sqrt {K_{\text{V}}^{2} + 2K_{\text{S}} K_{p} } \;{\text{and}}\;G_{f} = \sqrt {K_{\text{V}}^{2} + 2K_{\text{S}} K_{p} f_{\text{O}} }.$