Availableonlineatwww.sciencedirect.com SCIENCE DIRECT E噩≈S ELSEVIER Joumal of the European Ceramic Society 25(2005)1699-1704 www.elsevier.comlocate/jeurcerams Ceramic matrix composite corrosion models Klaus. nickel University Tubingen, Institute for Geosciences, Applied Mineralogy. WilheImstr: 56. D-72074 Tuebingen, Germany ailable online 8 January 2005 Abstract This paper discusses physical and empirical models for the description of corrosion processes. Physical strict models are advantageous for simple ceramics and simple composites. In additive-containing ceramics and composites with such matrices, the transport properties will vary with time, in these cases simple physical models alone are not adequate. The use of an empirical equation of the form x kit+Kvi+ klog log(r), fitted by simple multiple linear regression, is capable to describe many versions of corrosion processes, if k allowed to become negative or positive(: scale thickness or specific mass change, t: time). The equation is recommended for complex cases, but the variability of the corrosion function makes it often necessary to have more than one parameter of evaluation of the material to deduce the most important engineering parameter, penetration depths O 2004 Elsevier Ltd. All rights reserved Keyords: Corrosion; Kinetics; Composite 1. Introduction partial pressures of oxygen calculated for the coexistence of substrate and scale material at high temperatures. An exam- Ceramic matrix composites are by definition multiphase ple is the Po, of approximately 10-28 bar at 1000.C for an materials. Every material has a specific reaction to the envi- equilibrium between Si and Sioz, calculated by a thermo- ronment it is exposed to and therefore the behavior is bound chemical program or straight from the tabulated values of to be more complex, unless a component may be treated as In this paper, we review a number of models for the de- scription of corrosion processes in view of their usefulness This situation is a classic diffusion problem for oxygen through a growing layer of silica. Relating the flux of the oxi- dant through the scale to reflect the growth in scale thickness x with time t, we derive the basic parabolic relation already 2. Models for simple mass gain or loss from Ficks first law(: effective diffusion coefficient, We begin the discussion with models for simple one-phase oxygen concentration at the scale top= solubility) materials. For oxidation as a special case of the corrosion of dr=D o=0 →|xdx=/(Dco)dr non-oxides, the modeling is often done by assuming a simple parabolic law. A simple parabolic law is the result of assum ing steady-state conditions with a constant oxygen partial (2) pressure in the atmosphere and at the gas-scale interface ap- proaching zero at the scale-substrate interface. The last as- Incorporating the factor 2 into kp we have x'=kpt,the sumption seems justified in view of the very low equilibrium simplest form of the parabolic law, which is often used in the analysis of oxidation and corrosion data Tel:+4970712976802. Deal and Grove showed that this analysis does not take E-mail address: klaus. nickelauni-tueb into account the effects of gas phase transport and chemical 0955-2219/S- see front matter 2004 Elsevier Ltd. All rights reserved doi: 10.1016/j- jeurceramsoc. 2004. 12.010Journal of the European Ceramic Society 25 (2005) 1699–1704 Ceramic matrix composite corrosion models Klaus G. Nickel∗ University T ¨ubingen, Institute for Geosciences, Applied Mineralogy, Wilhelmstr. 56, D-72074 Tuebingen, Germany Available online 8 January 2005 Abstract This paper discusses physical and empirical models for the description of corrosion processes. Physical strict models are advantageous for simple ceramics and simple composites. In additive-containing ceramics and composites with such matrices, the transport properties will vary with time; in these cases simple physical models alone are not adequate. The use of an empirical equation of the form x = klt + k p √t + klog log(t), fitted by simple multiple linear regression, is capable to describe many versions of corrosion processes, if kl is allowed to become negative or positive (x: scale thickness or specific mass change, t: time). The equation is recommended for complex cases, but the variability of the corrosion function makes it often necessary to have more than one parameter of evaluation of the material to deduce the most important engineering parameter, penetration depths. © 2004 Elsevier Ltd. All rights reserved. Keywords: Corrosion; Kinetics; Composite 1. Introduction Ceramic matrix composites are by definition multiphase materials. Every material has a specific reaction to the envi￾ronment it is exposed to and therefore the behavior is bound to be more complex, unless a component may be treated as inert. In this paper, we review a number of models for the de￾scription of corrosion processes in view of their usefulness for composite evaluation. 2. Models for simple mass gain or loss We begin the discussion with models for simple one-phase materials. For oxidation as a special case of the corrosion of non-oxides, the modeling is often done by assuming a simple parabolic law. A simple parabolic law is the result of assum￾ing steady-state conditions with a constant oxygen partial pressure in the atmosphere and at the gas–scale interface ap￾proaching zero at the scale–substrate interface. The last as￾sumption seems justified in view of the very low equilibrium ∗ Tel.: +49 7071 2976802. E-mail address: klaus.nickel@uni-tuebingen.de. partial pressures of oxygen calculated for the coexistence of substrate and scale material at high temperatures. An exam￾ple is the PO2 of approximately 10−28 bar at 1000 ◦C for an equilibrium between Si and SiO2, calculated by a thermo￾chemical program3 or straight from the tabulated values4 of the reaction: Si + O2 ⇔ SiO2 (1) This situation is a classic diffusion problem for oxygen through a growing layer of silica. Relating the flux of the oxi￾dant through the scale J to reflect the growth in scale thickness x with time t, we derive the basic parabolic relation already from Fick’s first law (D: effective diffusion coefficient, c0: oxygen concentration at the scale top = solubility): J = dx dt = Dc0 − 0 x ⇒
x dx =
(Dc0) dt ⇒ x2 = 2kpt (2) Incorporating the factor 2 into kp we have x2 = kpt, the simplest form of the parabolic law, which is often used in the analysis of oxidation and corrosion data. Deal and Grove5 showed that this analysis does not take into account the effects of gas phase transport and chemical 0955-2219/$ – see front matter © 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.jeurceramsoc.2004.12.010