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.

Comparison of Elastic-Plastic Analysis and Experimental Result for Locally Thinned Pipe

2010 ◽  
Author(s):  
Wolf Reinhardt ◽  
Xinjian Duan
Keyword(s):  
Design Method ◽  
Experimental Result ◽  
Plastic Limit ◽  
Straight Pipe ◽  
Burst Test ◽  
Elastic Plastic ◽  
Plastic Analysis ◽  
Plastic Limit Analysis ◽  
Section Viii ◽  
Design Pressure

The result of a burst test of a thinned straight pipe with local thinning is reported. The locally thinned region had a thickness well below the NB-3600 pressure based Design thickness. The burst pressure is compared with the maximum Design pressure obtained from a variety of elastic-plastic analysis methods, such as plastic limit analysis and the Section VIII Div. 2 elastic-plastic design method.

Proposal of Use of Mises Criteria for Elastic Analysis in Appendix 9 of ASME Section VIII Division 3

2020 ◽  
Author(s):  
Susumu Terada
Keyword(s):  
Flow Stress ◽  
Plastic Collapse ◽  
Elastic Analysis ◽  
Stress Evaluation ◽  
Stress Theory ◽  
Elastic Plastic ◽  
Primary Stress ◽  
Plastic Analysis ◽  
Section Viii ◽  
Von Mises

Abstract The stress evaluation by elastic analyses for protection against plastic collapse in Appendix 9 is based on maximum shear stress theory (Tresca theory). On the other hand, the stress evaluation by elastic-plastic analysis and design equations by flow stress for design pressure for cylindrical shell and spherical shell in KD-221 is based on distortion energy yield stress theory (von Mises theory). With regard to materials with low and intermediate Sy/Su, in particular the primary stress evaluation based on Tresca stress for elastic analysis in current Div.3 is much more conservative than that based on flow stress equations similar to elastic-plastic analysis from experimental results. In Section VIII Div.2, von Mises yield criterion is used for stress evaluation for elastic analysis because it matches experimental results more closely than Tresca yielding criterion and is also consistent with plasticity algorithms used in elastic-plastic analysis. Therefore in Div.3 von Mises stress should be used for elastic analysis in the same way as in Sec. VIII Div.2. For materials with high Sy/Su, the primary stress evaluation based on von Mises criterion for elastic analysis is less conservative than that based on flow stress equations similar to elastic-plastic analysis because of a difference in design factor of 1.5 for elastic analysis and 1.732 for flow stress equations. Therefore, we propose using von Mises criterion for protection against plastic collapse with design correction factor using Sy/Su in Appendix 9 in order to remove excessive conservativeness for materials with low and intermediate Sy/Su. The validity of this proposal is shown in this paper.

Effects of Flaw Shape (Idealization) on the Interaction of Co-Planar Surface Flaws

2018 ◽  
Author(s):  
Kaveh Samadian ◽  
Stijn Hertelé ◽  
Wim De Waele
Keyword(s):  
Critical Assessment ◽  
J Integral ◽  
Elastic Analysis ◽  
Planar Surface ◽  
Constant Depth ◽  
Elastic Plastic ◽  
Linear Elastic ◽  
Computational Fracture Mechanics ◽  
Surface Flaws ◽  
Flaw Shape

Engineering Critical Assessment (ECA) guidelines contain amongst others, rules to assess flaw interaction. Major flaw dimensions (depth or height and length) are typically characterized assuming the flaws to be contained entirely within a bounding rectangle through a procedure known as flaw idealization. In (computational) fracture mechanics based calculations, flaws are often assumed to be (semi-)elliptical. This paper investigates the interaction between identical co-planar surface breaking flaws. Two flaw shapes are considered and compared: “canoe-shaped” (quarter-circular ends and constant depth elsewhere) and semi-elliptical. Especially for long shallow flaws, the canoe-shaped approximates the bounding rectangle, whereas the semi-elliptical shape only touches the bounding rectangle at three points (deepest point and two points at the surface). Several flaw dimensions and spacing distances are studied through an extensive parametric study comprising elastic and elastic-plastic finite element simulations. The results, based on Stress Intensity Factor (SIF) and J-integral analysis, show how the flaw shape can affect the degree of interaction. Notably, the inconsistency is less in linear-elastic analysis, but becomes more pronounced at higher (elastic-plastic) loading levels. This work highlights a challenge of comparing analytical and numerical based evaluations of interaction with ECA guidelines.

A Shell-Element–Based Elastic Analysis Predicting Welding-Induced Distortions for Ship Panels

2007 ◽  
Vol 51 (02) ◽  
pp. 128-136
Author(s):  
Gonghyun Jung
Keyword(s):  
Numerical Model ◽  
Three Dimensional ◽  
Shell Element ◽  
Significant Loss ◽  
Buckling Analysis ◽  
Elastic Analysis ◽  
Plastic Strains ◽  
Elastic Plastic ◽  
Distortion Analysis ◽  
Plastic Analysis

A new numerical model, Q-Weld (Edison Welding Institute, Columbus, OH), which is a shell-element-based elastic analysis, is proposed for the prediction of the distortion induced in ship panels. Based on the results of the three-dimensional thermal-elastic-plastic analyses, it was found that the shell element-based model excluding the geometry of fillet welds and including only transverse and longitudinal plastic strains is valid without significant loss of accuracy. The developed Q-Weld predicts well-agreed distortions with the three-dimensional thermal-elastic-plastic analysis and demonstrates its potential in welding-induced distortion analysis, including buckling analysis.

A Simplified Technique for Shakedown Load Determination of a 90 Degree Pipe Bend Subjected to Constant Internal Pressure and Cyclic In-Plane Bending

2005 ◽  
Author(s):  
Hany F. Abdalla ◽  
Maher Y. A. Younan ◽  
Mohammed M. Megahed
Keyword(s):  
Finite Element ◽  
Cyclic Loading ◽  
Internal Pressure ◽  
High Heat ◽  
Heat Fluxes ◽  
Elastic Analysis ◽  
Pipe Bend ◽  
Elastic Plastic ◽  
Plastic Analysis ◽  
Plane Bending

In this paper a simple technique is presented to determine the shakedown load of a 90 degree pipe bend subjected to constant internal pressure and cyclic in-plane bending using the finite element method. Through the proposed technique, the shakedown load is determined without performing time consuming cyclic loading simulations or conventional iterative elastic techniques. Instead, the shakedown load is determined through performing only two analyses namely; an elastic analysis and an elastic-plastic analysis. By extracting the results of the two analyses, the shakedown load is determined through the calculation of the residual stresses developed in the pipe bend. In the elastic analysis, performed only once and stored, an in-plane closing moment is applied preserving structure stresses within the material elastic range. In the elastic-plastic analysis, a constant internal pressure, below the pressure to cause yielding, is applied in addition to an increasing moment magnitude that causes the material yield strength to be exceeded. For verification purposes, the results of the simplified technique are compared to the results of full cyclic loading finite element simulations where the pipe bend is subjected to constant internal pressure and cyclic in-plane closing moment loading. In order to have confidence in the proposed technique, it is applied beforehand on the Bree cylinder [1] subjected to constant internal pressure and cyclic high heat fluxes across its wall. The results of the proposed technique showed very good correlation with the, analytically determined, Bree diagram of the cylinder.

Study on Collapse Characteristics and CSRF Method for 45 Deg Cylinder-to-Cylinder Intersections

2012 ◽  
Author(s):  
Takuro Honda ◽  
Shunji Kataoka ◽  
Takuya Sato
Keyword(s):  
Plastic Strain ◽  
High Stress ◽  
Elastic Analysis ◽  
Collapse Pressure ◽  
Elastic Plastic ◽  
Replacement Method ◽  
Inelastic Analysis ◽  
Collapse Strength ◽  
Collapse Characteristics ◽  
Plastic Analysis

It is known that the collapse strength of complex three dimensional structures is hard to evaluate accurately with elastic analysis, and more accurate results require the use of inelastic analysis. A cylinder-to-cylinder acute lateral intersection is one of basic structures of process plants. It is known that a high stress concentration occurs at an acute lateral more than 90 deg-lateral. In general, the area replacement method and the elastic analysis are applied for the design of acute lateral. However, these results may provide overly-conservative designs. In the previous work, the authors proposed CSRF (Collapse Strength Reduction Factor) method. The CSRF was defined as a ratio of the simple cylinder collapse pressure to the cylinder-to-cylinder collapse pressure. The proposed CSRF method provided more reasonable design than the elastic analysis. In this paper, the concept of the CSRF was redefined by using the maximum allowable working pressure. The CSRF were evaluated on the 45 deg and 90 deg-laterals based on the area replacement method, the elastic analysis, the limit load analysis and the elastic plastic analysis to study the collapse characteristics of 45 deg-laterals. The 45 deg-laterals are weaker than 90 deg-laterals, and inelastic analysis provides greater strength of 45 deg-laterals than elastic analysis. The results of elastic plastic analysis showed that overly-large plastic strain occurs on 45 deg-laterals. This plastic strain should be evaluated in addition to the collapse pressure.

Elastic-Plastic Shakedown Evaluation Using ASME Code Section III and Section VIII Methods

2010 ◽  
Author(s):  
David P. Molitoris ◽  
John V. Gregg ◽  
Edward E. Heald ◽  
David H. Roarty ◽  
Benjamin E. Heald
Keyword(s):  
Elastic Analysis ◽  
Acceptance Criteria ◽  
Elastic Plastic ◽  
Division 1 ◽  
Plastic Analysis ◽  
Asme Code ◽  
Section Viii ◽  
American Society ◽  
Plastic Shakedown ◽  
Division 2

Section III, Division 1 and Section VIII, Division 2 of the American Society of Mechanical Engineers (ASME) Boiler and Pressure Vessel (B&PV) Code provide procedures for demonstrating shakedown using elastic-plastic analysis. While these procedures may be used in place of elastic analysis procedures, they are typically employed after the elastic analysis and simplified elastic-plastic analysis limits have been exceeded. In using the Section III, Division 1 and Section VIII, Division 2 procedures for elastic-plastic shakedown analyses, three concerns are raised. First, the Section III, Division 1 procedure is vague, which can result in inconsistent results between analysts. Second, the acceptance criteria contained in both procedures are vague, which can also result in inconsistent results between analysts. Lastly, differences in the procedures and acceptance criteria can result in demonstration of component elastic-plastic shakedown under Section III, Division 1 but not under Section VIII, Division 2. The authors presume that the ASME Code intends to provide similar design and analysis conclusions, which may not be a correct assumption. To demonstrate these concerns, a nozzle benchmark design subject to a representative thermal and pressure transient was evaluated using the two Code elastic-plastic shakedown procedures. Shakedown was successfully demonstrated using the Section III, Division 1 procedure. However, shakedown could not be demonstrated using the Section VIII, Division 2 procedure. The conflicting results seem to indicate that, for the nozzle design evaluated, the Section VIII, Division 2 procedure is considerably more conservative than the Section III, Division 1 procedure. To further assess the conservative nature of the Section VIII, Division 2 procedure, the nozzle benchmark design was evaluated using the same thermal transient, but without a pressure load. While shakedown was technically not observed using the Section VIII, Division 2 acceptance criteria, engineering judgment concluded that shakedown was demonstrated. Based on the results of all the evaluations, recommendations for modifications to both procedures were presented for consideration.

ASME III Fatigue Assessment Plasticity Correction Factors for Austenitic Stainless Steels

2014 ◽  
Author(s):  
Julian Emslie ◽  
Chris Watson ◽  
Keith Wright
Keyword(s):  
Preliminary Investigation ◽  
Austenitic Stainless Steels ◽  
Strain Range ◽  
Equivalent Strain ◽  
Elastic Analysis ◽  
Correction Factors ◽  
Elastic Plastic ◽  
Plastic Analysis ◽  
Asme Code ◽  
Ratio Correction

ASME III NB-3200 provides a method for carrying out fatigue calculations using a simplified elastic-plastic analysis procedure. This allows a correction to elastic analysis to be performed in place of a full elastic-plastic analysis. Two mutually exclusive factors are described: the Poisson’s ratio correction accounts for surface stress exceeding the yield strength of the material and the Ke factor accounts for gross section plasticity. The recently released ASME Code Case N-779 provides a more complex but less onerous calculation of the Ke factor. Correction factors from the JSME and RCC-M codes have also been considered in this paper. The conservatism of different plasticity correction factors has been examined by calculating a ratio between the equivalent strain range from elastic-plastic Finite Element (FE) models and the strain range from elastic FE models and comparing this to calculated plasticity correction factors. Results show the potential for both the current ASME and Code Case Ke corrections to under-predict the strains when compared to those from an elastic-plastic FE assessment. A preliminary investigation has been carried out into an alternative correction factor based on linearised stress and local thermal stress ranges. This addresses the discontinuity between the two correction methods for surface and sectional plasticity which has been identified as a feature of the ASME correction methodology.

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.

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