(7)
where N is the number of backstresses; αk is the k-th back stress tensor;Ck and γk are the kinematic hardening parameters for the k-th back stress tensor. In this study, the isotropic and kinematic hardening parameters for Grade 91 at 600oC suggested by Kyaw et al. [47] and Saad et al. [48] were used, which are summarized in Table 3. In Fig. 5, variations of the peak stress under the 1% fatigue strain range using three hardening models used in this study are compared with the experimental result by Yaguchi and Takahashi [49] for Grade 91, used for creep-fatigue crack growth test summarized in Chapter 2. The peak stress of the kinematic hardening model is constant by definition, while those of two combined hardening models decreases with the number of cycles. The peak stress of the combined hardening model by Saad et al. is generally lower than that by Kyaw et al., but the trend of cyclic softening behaviour is almost the same with each other. The model by Kyaw et al. is closest to the experimental result.
Table 3. The parameters of Chaboche combined hardening models.