PSI - Issue 14

S.C.S.P. Kumar Krovvidi et al. / Procedia Structural Integrity 14 (2019) 855–863 S.C.S.P. Kumar Krovvidi / Structural Integrity Procedia 00 (2018) 000–000

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are employed in inelastic analysis for estimating total strain range. In first method, the stress range and the corresponding plastic stain range from the cyclic stress strain diagram is used to define the plastic behavior of the material. The other method employs non-linear isotropic-kinematic hardening model. The strain predicted by the inelastic analysis using cyclic stress stain diagram approach is more and hence cycle life estimated is more conservative when compared to the same estimated using detailed inelastic analysis using nonlinear isotropic kinematic hardening model. In the detailed inelastic analysis, the parameters are estimated using saturated hysteresis loop considering the hardening of the material. Hence the strain rage predicted in the detailed inelastic analysis is lesser and cycle life is more. It is found that the cycle life of the bellows estimated based on EJMA is higher compared to the same estimated based on analysis. The life of the bellows based on finite element analysis is estimated as per the design fatigue curve given in codes. The design fatigue curve consists of FOS 20 applied on number of cycles or 2 applied on the stress range, which ever gives the lower bound curve. Harvey (2001) given that out of the FOS 20 given on number of cycles, 2.5 accounts for size, a factor of 2 accounts for scatter and remaining factor 4 addresses the surface finish and environmental assisted factors. The design curve given in EJMA is a best fit curve generated based on testing of bellows without any factor of safety. Incorporation of the FOS given in codes such as ASME section-III or RCC MR in the design curve given in EJMA is not recommended as the design curves generated in ASME section-III or RCC-MR are based on the testing of smooth specimen and the design curve given in EJMA is based on component level testing (i.e testing of various configurations of bellows). Incorporation of FOS as in ASME section-III results in larger number of convolutions and the bellows will suffer squirm. From the Fig. 10, incorporation of a factor 3 shifts the life predicted as per EJMA towards that predicted as per RCC-MR using detailed inelastic analysis. Hence a factor of 2.5 on the number of cycles is recommended in the EJMA design curve to generate another lower bound curve. The life predicted by the newly made lower bound curve will have compliance with RCC-MR. Hence, the equation for the new lower bound design curve recommended is given by 6 3.4 1 1.86 10 2.5 54000 c t N S          5. Conclusions The design fatigue curves given in design codes for nuclear components such as RCC-MR and ASME section-III contain inherent factor of safety. The design of bellows for nuclear applications shall comply with the design codes for nuclear applications. Conventionally bellows are designed as per standards of EJMA. The design curve given in EJMA does not contain any factor of safety and is a best fit curve generated based on testing of various bellows configurations. Based on analysis, the life of the bellows is estimated as per RCC-MR and compared with the same estimated as per standards of EJMA. A factor of 3 on the number of cycles as per the design curve given in standards of EJMA to generate a lower bound design curve such that the life estimated as per the lower bound EJMA curve is comparable with that of the life estimated as per RCC-MR. Bellows for nuclear applications can be designed based on the lower bound EJMA curve, which is simple and has required compliance with RCC-MR code. References Kumar Krovvidi, S.C.S.P., Padmakumar, G., Bhaduri, A.K., 2017. Experience of various materials for design and manufacture of bellows for nuclear applications, Journal of Advanced materials and Proceedings 2, 156-161. Standards of Expansion Joint Manufacturers Association (EJMA)-10 th Edition, 2015. RCC-MR Section-I, Subsection-B, 2007. Roy, S.C., Goyal, S., Sandhya, R., Ray, S.K., 2012. Low cucle life prediction of SS316L(N) stainless steel based on cyclic elasto-plastic response, Nuclear Engineering and Design 253, 219-225. Harvey, J.F., 2001. Theory and design of pressure vessels, CBS Publishers, New Delhi.