# Evaluation of Implicit Reliability Level Associated with Fatigue Design Criteria of Nuclear Class-1 Piping

## Abstract

Fatigue design of Class-1 piping of NPP is carried out as par Section-III of American Society of Mechanical Engineers (ASME) Boiler and Pressure Vessel code. The fatigue design criteria of ASME are based on the concept of safety factor, which does not provide means for management of uncertainties for consistently reliable designs. In this regard, a work is taken up to estimate the implicit reliability level associated with fatigue design criteria of Class-1 piping specified by ASME Section III, NB-3650. The methodology employed for reliability evaluation is FORM, HORSM and MCS, where limit state function is derived using mean fatigue curve developed by Argonne National Laboratory. A number of important aspects related to reliability of various piping product and joints are discussed, and implicit reliability level is evaluated.

## Keywords

ASME Fatigue Implicit reliability FORM HORSM Piping## Nomenclature

*a*Constant term of polynomial

*A*,*B*,*C*Constants of Langer equation

- \( b_{ij} \)
Coefficients of univariate basis function

*C*_{q}Coefficients of multivariate basis function

*C*_{1},*C*_{2}Secondary stress indices for the specific component under investigation

*D*Expected accumulated damage ratio for the service life

- \( D_{\text{o}} \)
Outside diameter of pipe

- \( D_{f} \)
Cumulative damage ratio that leads to failure

- \( f_{{X_{i,\ldots,n} }} (x_{i} , \ldots ,x_{n} ) \)
Joint probability density function of the random variables

*X*_{ i }- \( F_{\text{en,nom}} \)
Nominal environmental fatigue correction factor

- \( F_{\text{en}} \)
Factor on life due to environmental effects

- \( F_{\text{se}} \)
Factor on life due to size effect

*F*_{sf}Factor on life due to surface finish

*F*_{def}Factor on life due to conservatism in fatigue definition

- \( g(X) \)
Limit state function

*I*Moment of inertia

*K*_{1},*K*_{2}Peak stress indices

*m*,*n*Material parameters

*M*_{i}Resultant moment due to a combination of design mechanical loads

- \( nb \)
Number of stress-range levels

- \( n_{\text{eqv}} \)
Number of equivalent full temperature load cycles

*N*Number of cycles

- \( N_{\text{air,RT}} \)
Number cycle to failure in the air environment

- \( N_{f} \)
Fatigue life or total number of cycles to failure

- \( N_{fi} \)
Number of cycles to failure in

*i*th stress-range level- \( N_{\text{water}} \)
Fatigue life in the water at service temperature

- \( O^{\prime} \)
Transformed DO levels

- \( P_{0} \)
Range of service pressure

- \( P_{f} \)
Failure probability

- \( R_{m} (x) \)
Regular polynomial

- \( S_{a} \)
Alternating stress intensity

- \( S_{m} \)
Allowable stress intensity value of the metal

- \( S_{n} \)
Primary plus secondary stress intensity value

- \( S_{p} \)
Peak stress intensity value

- \( T^{\prime} \)
Transformed temperature

*t*Nominal wall thickness of product

- \( T_{m} (x) \)
Chebyshev polynomial

- \( U_{i} \)
Usage factor at the

*i*th stress-range level- \( X_{i} \)
Random variables

*Z*Section modulus

- \( \varepsilon_{a} \)
Alternating strain amplitude

- \( \dot{\varepsilon}^{\prime} \)
Transformed strain rate

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