PSI - Issue 60

Thondamon V et al. / Procedia Structural Integrity 60 (2024) 484–493 Author name / StructuralIntegrity Procedia 00 (2019) 000 – 000

485

2

1. Introduction Elbows are very commonly used in nuclear power plant system for changing direction of flow of the liquid or gas being conveyed. Elbows are relatively more flexible than the straight portion of the piping system. Hence, they tend to deform more and absorb more energy due to thermal expansion movements or seismic displacements. They tend to undergo plastic deformation under these conditions, leading to unserviceable situation. These elbows under operating conditions are subjected to internal pressure as well. So, it is necessary to estimate the limit load capacity of the elbows. Limit load of any cracked component is generally expressed as product of limit load of defect-free component and a weakening factor due to the presence of crack. Therefore, before studying the limit load of any cracked component, one should know the limit load of a defect-free component [1]. Various researchers have performed numerical studies using finite element analysis to estimate the limit load for various loading cases of healthy elbows as well as elbows with circumferential through-wall crack, with and without internal pressure. From the results of these analyses, parameters which influence the limit load were identified. Expressions for evaluation of limit loads were proposed as a function of these identified influencing parameters. Each researcher has considered different influencing parameters for the limit load evaluation. Limit load value of healthy elbow without internal pressure was considered as the basis. Expressions for evaluation of weakening factor for effect of internal pressure and circumferential through-wall crack were proposed as well. These weakening factors were multiplied with the limit load value of healthy elbow without internal pressure based on the loading and defect. The expressions proposed by Chattopadhyay and Tomar (2006), Chang-Sik and Kim (2006) and Hong et al. (2010) have been used for estimating the limit loads in the present study. The objective of the present study is to compare the limit load obtained from the closed form solutions proposed by various researchers with Twice Elastic Slope (TES) method and with the Experimentally Measured Maximum Load (EMML). The focus of the current study is on carbon steel elbows with and without notch and with and without internal pressure. Totally seven elbows are considered for the current study. Three elbows without initial notch are considered, out of which one elbow was tested with internal pressure of 10 MPa and remaining two elbows were tested without any internal pressure. Four elbows with initial through-wall notch at the intrados in circumferential direction was considered. Out of these four elbows, two elbows were tested with internal pressure of 10 MPa and one elbow with 25 MPa and one elbow without any internal pressure. Since the notch was located at intrados and in circumferential direction, opening moment condition will be the critical loading direction.

Nomenclature h

pipe bend characteristics Limit moment of healthy elbow

R r 0

Bend radius (mm) Mean radius (mm) Thickness (mm) Notch width (mm) Yield strength (MPa) Notch length (mm) Notch angle (deg)

M 0 M X

Limit moment of elbow with through-wall notch Weakening factor due to internal pressure

t

m

w σ y 2c 2θ

OD

Outer diameter (mm) Internal pressure (MPa) Normalised internal pressure

P 0

p

2. Fracture studies on elbows The elbow specimens used in the present studies are made of SA 333 Gr. 6 carbon steel conforming to ASTM A333/A333M-18 [2]. Yield strength and ultimate strength of the material are reported as 310 MPa and 465 MPa respectively. Young’s modulus is 205 GPa and percentage elongation during tension test was 22% [3,4,5]. Geometric details of the elbows and corresponding crack parameters (applicable for elbows with initial notch) are given in Table 1. The geometric details of the elbow specimens and the crack parameters are shown in Fig. 1. The