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Elastic–plastic J and COD estimation schemes for 90° elbow with throughwall circumferential crack at intrados under in-plane opening moment

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Abstract

Leak-before-break (LBB) assessment of primary heat transport piping of nuclear reactors involves detailed fracture assessment of pipes and elbows with postulated throughwall cracks. Fracture assessment requires the calculation of elastic–plastic J-integral and crack opening displacement (COD)1 for these piping components. Analytical estimation schemes to evaluate elastic–plastic J-integral and COD simplify the calculations. These types of estimation schemes are available for pipes with various crack configurations subjected to different types of loading. However, such schemes for elbow (or pipe bend), which is one of the important components for LBB analyses, is very meager. Recently, elastic–plastic J and COD estimation scheme has been developed for throughwall circumferentially cracked elbow subjected to closing bending moment. However, it is well known that the elbow deformation characteristics are distinctly different for closing and opening bending modes because the ovalisation patterns of elbow cross section are different under these two modes. Development of elastic–plastic J and COD estimation scheme for an elbow with throughwall circumferential crack at intrados subjected to opening bending moment forms the objective of the present paper. Experimental validation of proposed J-estimation scheme has been provided by comparing the crack initiation, unstable ductile tearing loads and crack extension at instability with the test data. The COD estimation scheme has been validated by comparing the COD of test data with the predictions of the proposed scheme.

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Abbreviations

a :

Semi-crack length

D o :

Outer diameter of elbow cross section

E :

Young’s modulus

h = t R b /R 2 :

Elbow factor or pipe bend characteristics

h 1 :

Plastic influence function to calculate plastic J-integral (Eqs.10, 18, 19)

h 2 :

Plastic influence function to calculate plastic COD (Eqs.11, 22, 23)

J :

J-integral

J avg :

Average J-integral across the thickness

J e , J p :

Elastic, Plastic J-integral

(J i )SZW :

Initiation toughness obtained from stretched zone width

J in, J mid, J out :

J-integral at inside, middle, outside surface

J p1 :

Plastic J−integral evaluated at M =  M L using Eq. 18

J p1.2 :

Plastic J-integral evaluated at M =  1.2 ×  M L using Eq. 19

K :

Stress intensity factor

M :

Moment

M 0 :

Plastic collapse moment of defect-free elbow

M L :

Plastic collapse moment of cracked elbow

n :

Ramberg–Osgood hardening exponent (Eq. 2)

R :

Mean radius of elbow cross section

R b :

Mean bend radius of elbow at crown or flank

t :

Wall thickness

t av :

Average wall thickness of elbow at crack plane

V 2 :

Elastic influence function to calculate elastic COD (Eq. 7)

X :

Weakening factor w.r.t. defect-free elbow collapse moment (Eq. 12)

α :

Ramberg–Osgood coefficient (Eq. 2)

δ :

Maximum COD at middle of crack length

δ e , δ p :

Elastic, plastic COD

δ p1 :

Plastic COD evaluated at M =  M L using Eq. 22

δ p1.2 :

Plastic COD evaluated at M =  1.2 ×  M L using Eq. 23

ε :

True strain

ε y ( = σ y /E):

Yield strain

σ :

True stress

σ y :

Yield stress

θ :

Throughwall semi-circumferential crack angle

COD:

Crack opening displacement

FE:

Finite element

FEA:

Finite element analysis

GE/EPRI:

General Electric/Electric Power Research Institute

LBB:

Leak-Before-Break

NB:

Nominal bore diameter

SIF:

Stress Intensity Factor

TCC:

Throughwall circumferentially cracked

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Authors and Affiliations

  1. Reactor Safety Division, Hall-7, Bhabha Atomic Research Centre, Mumbai, 400085, India

    J. Chattopadhyay & H. S. Kushwaha

  2. Mechanical Engineering Department, Jadavpur University, Kolkata, 700032, India

    S. Acharyya

Authors
  1. J. Chattopadhyay
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  2. S. Acharyya
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  3. H. S. Kushwaha
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Correspondence to J. Chattopadhyay.

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Chattopadhyay, J., Acharyya, S. & Kushwaha, H.S. Elastic–plastic J and COD estimation schemes for 90° elbow with throughwall circumferential crack at intrados under in-plane opening moment. Int J Fract 144, 227–245 (2007). https://doi.org/10.1007/s10704-007-9097-y

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