13th International Conference on Fracture June 16–21, 2013, Beijing, China -8- crack-growth rate on hold time and pertains to intermediate hold times and frequencies where creep-fatigue interaction is present. The coefficient C1 was adopted from literature data for 1CrMoV-steel and 304 stainless steel [11]. A value between 10-7 and 10-6 for different materials at high temperature was found to be appropriate. For further evaluations a value of 10-6 was assumed, see Table 2. The third term including the C* parameter shows a linear dependence of crack growth on hold time and corresponds to purely creep-dominated crack growth occurring at long hold times and low frequencies [11]. Using the solutions for stress intensity factor K, and C* by appropriate Norton-law coefficients, the values from Table 2 are applied for the assessment. With the accumulation rule according to Eq. (10) the results of creep-fatigue tests on P91-steel were evaluated under creep-fatigue loading and R = Fmin / Fmax=0.1. The assessment was carried out for C(T)-25 samples with a0/W – ratio of 0.55. Table 2. Material related parameters for describing the crack growth rates of P91 Fatigue Interaction Creep C0 n0 C1 m C2 m 580°C 8,85E-08 2,49 Eq. 10 600°C 8,85E-07 1,91 1E-06 0,66 4,21E-02 0,66 580°C 8,85E-08 2,49 - - Eq. 11 600°C 8,85E-07 1,91 - - 6,17E-13 0,70 The comparison between calculated and experimentally determined values is shown in Fig.8. The calculated values are overestimated for both temperatures and holding times. The creep portion is dominant in this case, so that the crack growth can be described based on creep only using C*. The biggest uncertainty here is the determination of C* with the Norton-approach, as the results are strongly influenced by changes in the Norton coefficients. a) 10 1 10 2 10-6 10-5 10-4 10-3 10-2 10-1 10 0 10 1 P91, T=580°C ∆KI (MPa m 0.5 ) da/dN (mm/cyc) Cs25-specimens R=0.1, f=0.5 Hz Experiment, HT=6 min Experiment, HT=60 min Predicted, HT=6 min Predicted, HT=60 min b) 10 1 10 2 10-6 10-5 10-4 10-3 10-2 10-1 10 0 10 1 P91, T=600°C ∆KI (MPa m 0.5 ) da/dN (mm/cyc) Cs25-specimens R=0.1, f=0.5 Hz Experiment, HT=6 min Experiment, HT=60 min Predicted, HT=6 min Predicted, HT=60 min Figure 8. Creep-fatigue crack growth rate over ∆KI for Cs25-specimens at a) T=580°C, b) T=600°C Another commonly used approach based also on simple linear superposition of creep crack growth and fatigue crack growth is the model applying the fracture mechanics parameters ∆K for fatigue load and K for creep load [7]: h m 2 n0 0 CCG FCG CFCG C ( K) C K t dt da f 1 dN da dN da ⋅ = ∆ + + ⋅ = (11) The results of the evaluation by this rule are shown in Fig. 9. It can be seen that this approach describes the behaviour under creep-fatigue loading much better, although the material is creep-ductile. At 580°C and the hold time of 6 min the influence of the fatigue proportion on the
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