Oxidation is an important degradation process for materials operating in the high-temperature air or oxygen environments typical of jet turbine or rocket engines. Reaction of the combustion gases with the component material forms surface layer scales during these oxidative exposures. Typically, the instantaneous rate of reaction is inversely proportional to the existing scale thickness, giving rise to parabolic kinetics. However, more realistic applications entail periodic startup and shutdown. Some scale spallation may occur upon cooling, resulting in loss of the protective diffusion barrier provided by a fully intact scale. Upon reheating, the component will experience accelerated oxidation due to this spallation.
Cyclic-oxidation testing has, therefore, been a mainstay of characterization and performance ranking for high-temperature materials. Models simulate this process by calculating how a scale spalls upon cooling and regrows upon heating (refs. 1 to 3). Recently released NASA software (COSP for Windows) allows researchers to specify a uniform layer or discrete segments of spallation (ref. 4). Families of model curves exhibit consistent regularity and trends with input parameters, and characteristic features have been empirically described in terms of these parameters. Although much insight has been gained from experimental and model curves, no equation has been derived that can describe this behavior explicitly as functions of the key oxidation parameters.
A series summation equation has been developed to model a special case of parabolic scale growth and interfacial spallation of a constant area fraction, occurring only at the thickest portions (a deterministic interfacial cyclic-oxidation spalling model, or DICOSM, ref. 5). The input parameters are the parabolic growth rate constant kp, spall area fraction FA, oxide stoichiometry Sc, and cycle duration Dt. The output data include the net weight change, amount of oxygen and metal consumed, and amount of oxide spalled. This simplicity allows all output data and characteristic features to be represented by explicit algebraic functions (ref. 5). The net weight change can be described by the following relations, depending on whether the number of thermal-exposure cycles j is less than or greater than the number of segments no (case A or B), where no is defined as 1/FA:
![Eq. (A)--(delta W sub A)sub GSA,A approximately = F sub A times square root of k sub p times delta t times [((1/2 times 2n sub o minus S sub c) times j) to the 1/2 power plus 1/3 times ((1 minus 2S sub c) times j) to the 3/2 power]](../images/5100smialek-eqA.jpg)
![Eq. (B)--(delta W sub A)sub GSA,B approximately = F sub A times square root of k sub p times delta t times [(1 minus S sub c) times (j minus 1/2 times S sub c) (times n sub o to the 1/2 power) plus 1/3 times ((1 plus S sub c) (times n sub o to the 3/2 power)]](../images/5100smialek-eqB.gif)
Classic weight-change curves are produced with an initial maximum and final linear weight loss rate, as shown in the following figure. The maximum in weight change varied directly with the parabolic rate constant and cycle duration and inversely with the spall fraction, all to the ½ power. The number of cycles to reach maximum and zero weight change, jmax and jo, varied only with the inverse of the spall fraction, and the ratio of these is exactly 1:3.
Typical DICOSM weight-change curve, showing maximum weight, time to cross zero, and linear final slope of weight loss. Oxide stoichiometry, Sc, 2.0; parabolic growth rate constant, kp, 0.01; cycle duration, Dt, 1.0; and spall area fraction, FA, 0.006.
It was found that all variations of model parameters for one oxide type (Sc) could be represented by a single relationship. Here weight change is normalized by the weight at maximum, (DW/A)max, and cycles are normalized by the number to achieve this maximum, jmax. The result is shown in the next figure, where the universal curve (dashed line for equation shown) is unique for all oxides up to the cycle number that represents no; then a new branch is followed for each oxide type. Nevertheless, all model responses for any combination of kp, Dt, and FA have been consolidated into a single curve, indicating the universality of the key characteristics of the model.
Dimensionless DICOSM weight-change curves, normalized for all parabolic growth rate constants kp, cycle durations Dt, and spall area fractions FA.
Although net weight change is informative regarding cyclic-oxidation behavior, the ultimate figure of merit for material performance is the amount of metal reacted or consumed by oxidation. Also obtained as a normal output of these models, it too was normalized by using the
parameter 
, and the cycle number was normalized by no. Again, there are two cases depending on whether j is less than or greater than no. In the final figure, the responses for all values of Sc, kp, Dt, and FA are described by these two relations and the lines are plotted. In the extremes, it is seen that the amount of metal consumed varies with the square root of the cycle number or is linear with the cycle number. These universal constructions provide a strong indication of the regularity of model cyclic-oxidation responses. Future work is planned to categorize actual cyclic-oxidation data according to these constructions and evaluate their universality of behavior.
Dimensionless plot of metal consumed for DICOSMs, normalized for all oxide stoichiometry Sc, parabolic growth rate kp, cycle durations Dt, and spall area fraction FA, where ![Eq. (D)--sum of W sub met,u = sum of W sub met divided by [(S sub c minus 1) times (k sub p times delta t divided by F sub A)]](../images/5100smialek-eqD.gif)
Find out more about this research.
Glenn contacts: Dr. James L. Smialek, 216-433-5500, James.L.Smialek@nasa.gov
Author: Dr. James L. Smialek
Headquarters program office: OAT
Programs/Projects: Propulsion Systems R&T, UEET
Last updated: June 25, 2003
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