PSI - Issue 57

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

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The cyclic Ramberg-Osgood Relationship is written as: = +( ′ ) 1 ′ (37) and are the strain and stress amplitudes respectively. The plastic strain amplitude is the second term (on the right) in the equation 37 above: =( ′ ) 1 ′ (38) where is the plastic strain amplitude. Equation 38 can be easily linearized so that a simple linear regression can be used to determine ′ and ′ . Figure 9 presents an example of such linear regression. Since both Chaboche and Ramberg-Osgood models coexist in the D TMF approach, it is a sensible strategy to calibrate Chaboche’s parameters from the Ramberg-Osgood curve fit instead of the raw data.

Fig. 9. Evaluating Ramberg- Osgood parameters from linear regression. K’=192.2MPa and n’=0.186 are obtained from the available data.

A factor F can be added to the D TMF parameter to account for the damage caused by creep [17]: TMF = 1 0 (1.45 Δ 2 +2.4 Δ ⋅ Δ √1+3 ′ ) 2.3. The effect of Creep In fact, the D TMF parameter as presented in equation 39 is a generalization of the creep-fatigue parameter D CF proposed by Riedel [18]. F cr is a function of stress, temperature and time as shown in equation 40 [17]: = (1 + ∫ 0 −2 0 − ) 1 (40) Q CR is the creep activation energy. R is the gas constant (R=8.3145 J/K·mol) and T the temperature in Kelvin. n is the creep exponent ( from equation 12 ). The stress range  is defined as: = ( ) − ( 0 ) (41) t 0 is the time at the beginning of the reversal path. (39)