PSI - Issue 13

Ho-Wan Ryu et al. / Procedia Structural Integrity 13 (2018) 1932–1939 Author name / Structural Integrity Procedia 00 (2018) 000 – 000

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Fig. 4. Typical FE mesh of the C(T) specimen used in cyclic simulation with a debonding option.

3.2. Combined hardening model Since hysteresis loops of SA312 TP316 SS shown in Fig. 1(b) and CF8A CASS shown in Fig. 2(b) show significant cyclic hardening, a combined hardening model including isotropic and nonlinear kinematic hardening rules was considered as a cyclic hardening rule. This model was mainly summarized by Chaboche (1979, 1991) and frequently used in the simulation of cyclic component. In the model, an initial yield surface, two parameters for isotropic hardening and six parameters for nonlinear kinematic hardening containing three back stresses should be determined from test results. For the isotropic hardening, the size of yield surface σ o changes due to repeated cycles can be represented as a function of cumulative plastic strain: To determine isotropic hardening parameters Q and b , cyclic stress versus strain curve should be required to determine the increasing size of yield surface. Cyclic data can be found in NUREG report by Chopra (1999): 1.94 1950 588.5 a a a    = +       (2) This cyclic stress-strain curve is the fitting line from a set of cyclic stress which corresponds to various stress amplitudes at a half of life. Originally, isotropic hardening depends on the change of linear portion in the hysteresis loop. Since the shape of hysteresis loop cannot be identified from the cyclic stress versus strain curve, the change of cyclic stress is assumed to be similar with that of linear portion in the hysteresis loop. Therefore, Q values can be determined from the difference between cyclic and monotonic stress versus strain curves at an effective strain amplitude. The value of b which means that how fast yield surface reaches to limit value Q can be determined from the fitting of peak stresses for each cycle. In the previous research, Chaboche (1979) proposed a ‘decomposed’ nonlinear kinematic hardening rule: ( ) ( ) 1 2 1 1 1 2 2 2 1 1 pl pl C e C e        − − = − = − (3) 1 Q e o o   = + −   b pl  −     (1)

3 3     = ; pl C

0

=

3