PSI - Issue 57

Giovanni M. Teixeira et al. / Procedia Structural Integrity 57 (2024) 670–691 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

682

13

Equation 46 can be linearized as ( ) = ( ) − ⋅ ( ′ TMF ) (47) Which allows for the determination of parameters A and B through linear regression. From the evaluated A and B: = 1 1− − 01− 1− (48) In case only LCF and TMF tests exist ( which is more often the case ) then both parameters A and B are simply temperature independent adjustable constants and are fitted using regression analysis from all the available experiments simultaneously. In case crack growth tests exist, B can be fitted to the slope of the crack growth rate and  (beta) can be fitted to the offset of the same curve. A new dimensionless variable can be defined as: ′ = 01− (49) Which allows the equation (44) to be re-written as: = 1− − 01− 01− (1− ) 1 ′ ( ′ TMF ) − (50) Where N fc is creep-fatigue life (number of cycles), where the subscript fc evidences the contribution of creep, i.e., the DTMF in the equation above contemplates F cr as per equation 39. 2.4. The effect of Oxidation The interaction between the various damage mechanisms turns TMF into a very complex phenomenon to model. This paper discusses the mechanical, creep and oxidation contributions to TMF damage. Oxidation is a phenomenon that happens at the surface at higher temperatures. The oxide layers formed under compression ( and high temperature ) becomes brittle when temperatures decrease, originating cracks that expose the clean metal surfaces that quickly become oxidized again. Alternatively, oxide layers can be formed under tension ( and high temperature ), becoming brittle when temperatures decrease, causing delamination. In summary, oxidation happens at elevated temperatures and these oxide layers crack under subsequent straining. The damage caused by oxidation is evaluated by: | =( 1 2 ⋅ Δ ) 1 2 (51) The substitution of equation 34 into 50 yields: | = 1 4 ⋅ ( ′ ⋅ TMF ) 1 2 1 2 (52) Where the diffusion coefficient D ox is defined as: = 0 ∫ −( ) 0 (53) Rearranging equation 51: