PSI - Issue 13

Takehiro Shimada et al. / Procedia Structural Integrity 13 (2018) 1873–1878 Author name / Structural Integrity Procedia 00 (2018) 000 – 000

1877

5

fatigue condition, the stress level during dwell is adequately high (Wen et al., 2016) and the drop of ductile elongation was not seen in the pure creep test at the stress level conducted in the creep-fatigue test. Therefore, the ductile elongation is considered as a constant.

t

=   

in dt  

3

d

(10)

c

f

t

2

4.3. Modified ductile exhaustion method based on non-unified constitutive model Priest and Ellison (1981) considered that the matrix damage designated to "fatigue damage" and the grain boundary damage designated to "creep" damage. In this method, it is assumed that the visco-plastic strain which denotes the glide deformation caused by the motion of dislocation induce only matrix damage. On the other hand, it is assumed that the “ creep strain ” under tensile stress loading is the only factor of the “ creep damage ” . Therefore, the fatigue damage and the creep damage per cycle can be obtained from equation (11) and (12) respectively.

2 3

vp   =

vp vp

) vp m −

− ε ε

( f d B  = 

,

(11)

5

3

t

=   

cr dt  

4

d

(12)

c

f

t

1

5. Results and discussion

Figure 5 shows the comparison of experimental number of cycles to failure and predicted number of cycles to failure. The definition of failure cycles in the experiment is the number of cycles to give a 25% drop in the peak stress. The time friction rule estimates the creep-fatigue damage conservatively as hold time becomes longer. This conservative estimation is probably because of the cyclic hardening effect on creep strain. In creep-fatigue test of 316H stainless steel, the creep strain rate drop occurs due to the dislocation pinning during the cyclic loading. As a consequent, the time friction rule, where the creep strain rate drop is not considered, overestimates the creep damage in the creep-fatigue tests. The ductile exhaustion method estimates the creep-fatigue damage more conservatively as mechanical strain range becomes smaller. On the other hand, the modified ductile exhaustion method can predict the creep-fatigue damage precisely for all experiments conducted in this study. This might indicate that the visco-plastic strain, which is a part of inelastic strain during dwell, does not affect to grain boundary damage. Therefore, it can be said that it is necessary to decompose the inelastic strain into the visco plastic strain and the creep strain and the visco-plastic strain and the creep strain is used to estimate fatigue damage and creep damage, respectively. 6. Conclusions In this paper, non-unified constitutive model is proposed to estimate the creep-fatigue damage. The model can predict the stress and strain state precisely and therefore it is implemented in FEMmodel to estimate the creep damage and the fatigue damage precisely. The time fraction rule and the ductile exhaustion model give overly conservative estimation of creep-fatigue damage in some cases. On the other hand, the modified ductile exhaustion method using non-unified constitutive model can estimate creep-fatigue damage for all the test condition conduced in this study precisely. References

ASME Boiler and Pressure Vessel Code Case Section Ⅲ Division 1 sub-section NH,2010, ASME Chaboche, J, L., 2008, A review of Some Plasticity and Viscoplasticity Constitutive Theories, International Journal of Plasticity,24 ,1642-1693