Derivation of the Equation Expressing Weight Loss by Fretting Corrosion

7 DERIVATION OF THE EQUATION EXPRESSING WEIGHT LOSS BY FRETTING CORROSION 

The corresponding amount of oxide W removed by one asperity plowing out a path / long and c wide depends on the amount of oxide formed in time t. For thin-film oxidation, the logarithmic equation is obeyed (see Section 11.4.1)  

Preliminary to oxidation, we can also consider the situation of oxygen adsorbing rapidly as physically adsorbed gas, followed by conversion at a slower rate to chemisorbed oxygen atoms. The chemisorbed oxygen, in turn, reacts with underlying metal to form metal oxide, a reaction that is activated mechanically by asperities moving over the metal surface. Chemisorption limits the amount of oxide that is formed in such a process, the rate of chemisorption following an equation identical in form to that of (29.57) [6]. Hence, whichever process apphes, the form of the final equation is essentially the same.  

Assuming that relative motion of the two surfaces is sinusoidal, 21 is the total length of travel in any one cycle and x, the linear displacement from the midpoint of travel at time t, is given by 

If/represents constant linear frequency, this is related to constant angular velocity by the expression 

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