PSI - Issue 57

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

676

7

Fig. 6. The use of Python to calibrate Chaboche’s parameters.

Chaboche [9] argues that the calibration of both isotropic and kinematic hardening models can be done separately. He proposes an equation for the calibration of Voce’s model: , − , , − , = ∞ = 1 − (− ⋅ , ) (16) , and , are the peaks of the first and the stabilized cycle respectively. , is the maximum stress at any given time. ∞ represents the maximum expansion the elastic region can assume. , is the accumulated plastic strain and can be calculated by: , =2 Δ (17)  controls the speed of the stabilization. The higher the  the faster the hysteresis loops approach the stabilized condition. N is the number of cycles applied and pl   is the plastic strain range at every cycle. Figure 7 below is adapted from Chaboche [9]. As mentioned before SciPy can easily handle the determination of the parameter  in equation 16 through nonlinear regression. It is debatable whether isotropic hardening should be included in the finite element modeling or not, the reason being the fact that the DTMF fatigue parameters are calibrated at half-life when the size of the elastic region is already stabilized.