Analytical Determination of Stress Indices and Stress Intensification Factor for an Extruded Nozzle of Super Pipe

The super pipe nozzles in nuclear power plants are usually designed to be in compliance with the requirements of Class 2 piping of Section III of the ASME Boiler and Pressure Vessel Code. The stress indices B₂ and stress intensification factor i are required for the stress evaluation. In the past two decades, the hot extrusion forming technology has been widely used to manufacture those nozzles, instead of traditional insert weldolets. However, previous extruded nozzle stress analyses have shown B₂ that the calculated stresses may exceed the limits in some working conditions. The objective of present study is to determine the stress indices and stress intensification factor for an extruded nozzle of the supper pipe by the finite element method and to evaluate the conservatism of those factors from the ASME Code formulae. In this paper, a three-dimensional finite element model of an extruded nozzle is developed. Four load cases are considered, which are corresponding to an in-plane bending moment and an out-plane bending moment applied at the run pipe side and at the branch pipe side, respectively. The magnitude of bending moment is assumed to be 1000Nm. The stress indices B_2r, B_2b, C_2r, C_2b, K_2r and K_2b, where the subscript r and b refer to the run pipe and B_2r the branch pipe, are calculated based on the finite element analysis results. The stress intensification factor i_r and i_b are determined by the empirical formula: i_r = C_2r*K_2r/2 and i_b = C_2b*K_2b/2. Further, the developed factors are compared with those calculated from the ASME code formulae. It is found that the stress indices B_2r and B_2b obtained from the linear elastic finite element analysis are conservative. Currently, the values of B_2r and B_2b gained from the ASME code formulae are more appropriate for the stress evolution. The stress intensification factors i_r and i_b obtained from the analytical determination are lower than those calculated from the ASME code formula. For the extrude nozzle studied, the factor i_r decreases 30% and the factor i_b decreases about 3.3%.