Elastic-Plastic Analyses of Surface Flaws in a Reactor Vessel

1984 ◽  
Vol 106 (3) ◽  
pp. 247-254 ◽  
Author(s):  
W. W. Wilkening ◽  
H. G. deLorenzi ◽  
M. Barishpolsky
Keyword(s):  
Internal Pressure ◽  
Crack Front ◽  
Driving Force ◽  
Maximum Depth ◽  
Crack Driving Force ◽  
Elastic Plastic ◽  
Single Curve ◽  
Surface Flaws ◽  
Virtual Crack Extension Method ◽  
Design Pressure

Elastic-plastic analyses have been performed for the ASME Maximum Postulated Flaw and for three other semielliptical surface flaws in the beltline region of a nuclear reactor pressure vessel, with internal radius to thickness ratio, R/t, equal to 10, using nonlinear 3-D finite element methods based upon the deformation theory of plasticity. Three of the flaws had a maximum depth, a, equal to t/4, with aspect ratios, 2c/a, equal to 6 (the ASME Maximum Postulated Flaw), 4 and 3, respectively, where 2c is the surface length of the flaw. These flaws were analyzed for internal pressure varying from one to three times the design pressure, which is well into the fully plastic regime for the uncracked vessel. The fourth flaw had an aspect ratio, 2c/a, equal to 6, and its maximum depth, a, was equal to 3t/4. This deep flaw was analyzed for internal pressure varying from 60 percent of design pressure to twice the design pressure. The crack driving force was calculated as the energy release rate, J, using the virtual crack extension method. The results illustrate that, at the design pressure, plasticity near the crack front is so limited for the three flaws with a/t = 1/4 that an elastic analysis is adequate. At higher pressures, however, the elastic analyses become increasingly nonconservative and would grossly underestimate the severity of the flaws. The variation of both J and crack opening displacement, COD, along the crack front were studied. Generally, the values at the maximum depth location, denoted J* and COD*, respectively, were the maximum values, with minimum values occurring at the free surface. A simple normalization scheme was found which collapsed the J* versus pressure results for the four semielliptical flaws into a single curve. A similar normalization also collapsed the COD* versus pressure results for the four flaws into a single curve. In addition, a unique linear relationship between J* and COD* was found to apply for the results from all four sets of analyses for internal pressure levels up to at least 2.5 times the design pressure. The analyses therefore demonstrate that J and COD are equivalent measures of the crack driving force, and further demonstrate that a realistic 3-D elastic-plastic analysis is needed to properly assess the severity of surface flaws.

J and CTOD Based Tensile Strain Capacity Prediction for Pipelines with a Surface Crack in Girth Weld

2021 ◽  
Author(s):  
Youn-Young Jang ◽  
Nam-Su Huh ◽  
Ik-Joong Kim ◽  
Young-Pyo Kim
Keyword(s):  
Crack Initiation ◽  
Internal Pressure ◽  
Surface Crack ◽  
Driving Force ◽  
Tensile Strain ◽  
Structural Integrity ◽  
Accurate Estimation ◽  
Long Distance ◽  
Crack Driving Force ◽  
Girth Welding

Abstract Long-distance pipelines for the transport of oil and natural gas to onshore facilities are mainly fabricated by girth welding, which has been considered as a weak location for cracking. Pipeline rupture due to crack initiation and propagation in girth welding is one of the main issues of structural integrity for a stable supply of energy resources. The crack assessment should be performed by comparing the crack driving force with fracture toughness to determine the critical point of fracture. For this reason, accurate estimation of the crack driving force for pipelines with a crack in girth weld is highly required. This paper gives the newly developed J-integral and crack-tip opening displacement (CTOD) estimation in a strain-based scheme for pipelines with an internal surface crack in girth weld under axial displacement and internal pressure. For this purpose, parametric finite element analyses have been systematically carried out for a set of pipe thicknesses, crack sizes, strain hardening, overmatch and internal pressure conditions. Using the proposed solutions, tensile strain capacities (TSCs) were quantified by performing crack assessment based on crack initiation and ductile instability and compared with TSCs from curved wide plate tests to confirm their validity.

J-integral and crack driving force in elastic–plastic materials

2008 ◽  
Vol 56 (9) ◽  
pp. 2876-2895 ◽  
Author(s):  
N SIMHA ◽  
F FISCHER ◽  
G SHAN ◽  
C CHEN ◽  
O KOLEDNIK
Keyword(s):  
Driving Force ◽  
J Integral ◽  
Crack Driving Force ◽  
Elastic Plastic ◽  
Plastic Materials ◽  
Elastic Plastic Materials

Tensile Strain Capacity of X80 Pipeline Under Tensile Loading With Internal Pressure

2010 ◽  
Author(s):  
Satoshi Igi ◽  
Takahiro Sakimoto ◽  
Nobuhisa Suzuki ◽  
Ryuji Muraoka ◽  
Takekazu Arakawa
Keyword(s):  
Internal Pressure ◽  
Driving Force ◽  
Tensile Strain ◽  
Surface Defects ◽  
Axial Loading ◽  
Element Analysis ◽  
Crack Driving Force ◽  
Strain Capacity ◽  
High Internal Pressure ◽  
Tensile Strain Capacity

This paper presents the results of experimental and finite element analysis (FEA) studies focused on the tensile strain capacity of X80 pipelines under large axial loading with high internal pressure. Full-pipe tensile test of girth welded joint was performed using high-strain X80 linepipes. Curved wide plate (CWP) tests were also conducted to verify the strain capacity under a condition of no internal pressure. The influence of internal pressure was clearly observed in the strain capacity. Critical tensile strain is reduced drastically due to the increased crack driving force under high internal pressure. In addition, SENT tests with shallow notch specimens were conducted in order to obtain a tearing resistance curve for the simulated HAZ of X80 material. Crack driving force curves were obtained by a series of FEA, and the critical global strain of pressurized pipes was predicted to verify the strain capacity of X80 welded linepipes with surface defects. Predicted strain showed good agreement with the experimental results.

Elastic–plastic crack driving force for tubular X-joints with mismatched welds

2005 ◽  
Vol 27 (9) ◽  
pp. 1419-1434 ◽  
Author(s):  
X. Qian ◽  
Robert H. Dodds ◽  
Y.S. Choo
Keyword(s):  
Driving Force ◽  
Crack Driving Force ◽  
Elastic Plastic

Assessment of Fully Plastic J and C*-Integral Solutions for Application to Elastic-Plastic Fracture and Creep Crack Growth

1993 ◽  
Vol 115 (3) ◽  
pp. 228-234 ◽  
Author(s):  
D. R. Lee ◽  
J. M. Bloom
Keyword(s):  
Finite Element ◽  
Crack Growth ◽  
Driving Force ◽  
Creep Crack Growth ◽  
J Integral ◽  
Finite Element Program ◽  
Hardening Material ◽  
Crack Driving Force ◽  
Elastic Plastic ◽  
Creep Crack

A critical part of the assessment of defects in power plant components, both fossil and nuclear, is the knowledge of the crack driving force (K1, J, or C*). While the determination of the crack driving force is possible using finite element analyses, crack growth analyses using finite element methods can be expensive. Based on work by Il’yushin, it has been shown that for a power law hardening material, the fully plastic portion of the J-integral (or the C*-integral) is directly related to an h1 calibration function. The value of h1 is a function of the geometry and hardening exponent. The finite element program ABAQUS was used to evaluate the fully plastic J-integral and determine the h1 functions for various geometries. The Ramberg-Osgood deformation theory plasticity model, which may be used with the J-integral evaluation capability, allows the evaluation of fully plastic J solutions. Once it was established that the grid used to generate the h1 functions was adequate (based on the more recent work of Shih and Goan), additional runs were made of other configurations given in the EPRI Elastic-Plastic Fracture Handbook. Differences as great as 55 percent were found when compared to results given in the Handbook (single-edge crack plate under tension and plane stress with a/b = 0.5). Effects of errors in h1 on predicted failure load and creep crack growth are discussed.

Elastic-Plastic Analysis of the Maximum Postulated Flaw in the Beltline Region of a Reactor Vessel

1982 ◽  
Vol 104 (4) ◽  
pp. 278-286 ◽  
Author(s):  
H. G. deLorenzi
Keyword(s):  
Plastic Flow ◽  
Deformation Theory ◽  
Surface Flaw ◽  
Elastic Analysis ◽  
Elastic Plastic ◽  
Surface Flaws ◽  
Plastic Analysis ◽  
Design Calculations ◽  
Tension Loading ◽  
Design Pressure

A maximum postulated surface flaw in the beltline region of a PWR pressure vessel has been analyzed under elastic-plastic conditions. The analysis was performed using 3-D finite element methods, and the deformation theory of plasticity was used to describe the plastic flow of the material. The calculations were carried out for the internal pressure varying from the design pressure up to approximately twice the design pressure. The results show that at the design pressure the plastic flow of the material around the crack front is so small that an elastic analysis is adequate. However, the commonly used approach of treating the flaw in the vessel as a surface flaw in a flat plate under far field tension loading is nonconservative. At a pressure of approximately 50 percent over the design pressure the energy release rate derived from an elastic analysis starts to deviate from the value obtained from an elastic-plastic calculation. The elastic result now starts to be nonconservative and at twice the design pressure the elastic analysis will clearly underestimate the severity of the crack. A 2-D elastic-plastic plane strain approximation will on the other hand grossly overestimate the severity of the crack. A realistic 3-D elastic-plastic analysis is, therefore, needed to estimate the safety factors of surface flaws and to serve as benchmarks for the development of simpler design calculations.

The Influence of Residual Stresses on Small Through-Clad Cracks in Pressure Vessels

1984 ◽  
Vol 106 (4) ◽  
pp. 383-390 ◽  
Author(s):  
H. G. deLorenzi ◽  
B. I. Schumacher
Keyword(s):  
Residual Stresses ◽  
Pressure Vessel ◽  
Driving Force ◽  
Base Material ◽  
Pressure Vessels ◽  
Plastic Behavior ◽  
Material Interface ◽  
Crack Driving Force ◽  
Elastic Plastic ◽  
Stress Relieving

The influence of cladding residual stresses on the crack driving force for shallow cracks in the wall of a nuclear pressure vessel is investigated. Thermo-elastic-plastic analyses were carried out on long axial through-clad and sub-clad flaws on the inside of the vessel. The depth of the flaws were one and three times the cladding thickness, respectively. An analysis of a semielliptical axial through-clad flaw was also performed. It was assumed that the residual stresses arise due to the difference in the thermal expansion between the cladding and the base material during the cool down from stress relieving temperature to room temperature and due to the subsequent proof test before the vessel is put into service. The variation of the crack tip opening displacement during these loadings and during a subsequent thermal shock on the inside wall is described. The analyses for the long axial flaws suggest that the crack driving force is smaller for this type of flaw if the residual stresses in the cladding are taken into account than if one assumes that the cladding has no residual stresses. However, the analysis of the semielliptical flaw shows significantly different results. Here the crack driving force is higher than when the residual stresses are not taken into account and is maximum in the cladding at or near the clad/base material interface. This suggests that the crack would propagate along the clad/base material interface before it would penetrate deeper into the wall. The elastic-plastic behavior found in the analyses show that the cladding and the residual stresses in the cladding should be taken into acocunt when evaluating the severity of shallow surface cracks on the inside of a nuclear pressure vessel.

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