Simplified Elastic-plastic Analysis Research Articles

Consideration of Ke-Factor (Simplified Elastic-Plastic Analysis) for Calculation of Strain Rate in Environmental Fatigue Evaluation

Consideration of Ke-Factor (Simplified Elastic-Plastic Analysis) for Calculation of Strain Rate in Environmental Fatigue Evaluation

Critical Review of ASME III Plasticity Correction Factors for Fatigue Design-By-Analysis of Nuclear Power Plant Components

Abstract Despite significant technological progress in recent years, elastic–plastic fatigue analysis of pressure-retaining components remains a time-consuming venture. Accordingly, nuclear pressure vessel design codes such as ASME Section III provide simplified elastic–plastic analysis procedures as a practical alternative. This approach can be excessively conservative under certain conditions due to the bounding nature of the applied plasticity correction factor, Ke. While this over conservatism was tolerable in the past, recent technical challenges arising due to consideration of environmentally assisted fatigue and design for long-term operation have posed difficulty in achieving acceptable fatigue usage based on extant Code assessment procedures for certain components. The incorporation of more accurate Ke factors has since been identified as a nuclear industry priority. This paper presents a critical review of Ke factors within ASME Section III, with particular attention given to an approach proposed by Ranganath, which has recently been approved for publication as an ASME Section III Code Case. Correction factors adopted within other nuclear and nonnuclear codes and standards (C&S) were also considered. The code-based Ke factors were compared with Ke factors obtained directly from various elastic–plastic finite element (FE) models of representative plant components. The results revealed a considerable difference in conservatism between the code-based methods. Based on the elastic–plastic finite element analysis (FEA) results, an alternative improved plasticity correction method is proposed in this paper. The need for a harmonized approach to determining Ke based on elastic–plastic FE analysis and further development of efficient plasticity correction methods for total life assessment are highlighted as desirable industry objectives.

An efficient simplified elastic–plastic analysis procedure using engineering formulae for strain-based fatigue assessment of nuclear safety class 1 piping system subjected to severe seismic loads

This paper proposes an efficient simplified elastic–plastic analysis procedure using engineering formulas to perform strain-based fatigue design considering the plasticity that occurs in nuclear safety class 1 piping systems during severe seismic loads, and then presents the application results of the procedure to a pressurizer surge line system. The total strain amplitudes, fatigue assessment results, and total calculation time were compared between the proposed procedure and the detailed dynamic finite element elastic-plastic analysis. The comparison confirmed that the proposed analysis procedure can efficiently derive reasonable and conservative results for nuclear safety class 1 piping systems under severe seismic loads.

A modification on 3S criterion and simplified elastic-plastic ratcheting analysis in ASME VIII-2

Ratcheting is a common and important failure mode in pressure vessels. ASME VIII-2 2019 edition provides two kinds of ratcheting assessment methods——the elastic stress ratcheting assessment (paragraph 5.5.6) applied to the design by elastic stress analysis and the elastic-plastic ratcheting assessment (paragraph 5.5.7) applied to the design by elastic-plastic stress analysis. This paper focuses on the elastic stress ratcheting assessment, which includes again two methods——the elastic ratcheting analysis (paragraph 5.5.6.1), i.e. the 3S criterion, and the thermal stress ratcheting assessment (paragraph 5.5.6.3). This article reviews the development history of 3S criterion and discusses its applicable scope. The study found that the 3S criterion is not a complete elastic ratcheting assessment criterion, when the primary membrane stress range exceeds two-thirds of the cyclic yield stress, i.e. (2/3)Sy, the ratcheting assessment based on 3S criterion is unsafe for some situations. When the general primary membrane stress Pm and the local primary membrane stress PL, which allowable limit exceeds (2/3)Sy, are applied simultaneously, there is still the possibility of ratcheting failure in the structure even if the 3S criterion is met. As an extension of the 3S criterion, a complete and safe criterion on three-dimensional elastic ratcheting assessment is proposed in this paper. In order to avoid the inconvenience of partition assessment, a simplified thermal stress ratcheting assessment method based on double checking surfaces is proposed. It is a simple and conservative assessment method. Finally, elastic ratcheting analysis, thermal stress ratcheting assessment and simplified elastic-plastic analysis in ASME VIII-2 are integrated, a universal elastic stress ratcheting assessment is proposed.

Simplified elastic-plastic analysis procedure for strain-based fatigue assessment of nuclear safety class 1 components under severe seismic loads

This paper proposes a simplified elastic-plastic analysis procedure using the penalty factors presented in the Code Case N-779 for strain-based fatigue assessment of nuclear safety class 1 components under severe seismic loads such as safety shutdown earthquake and beyond design-basis earthquake. First, a simplified elastic-plastic analysis procedure for strain-based fatigue assessment of nuclear safety class 1 components under the severe seismic loads was proposed based on the analysis result for the simplified elastic-plastic analysis procedure in the Code Case N-779 and the stress categories corresponding to normal operation and seismic loads. Second, total strain amplitude was calculated directly by performing finite element cyclic elastic-plastic seismic analysis for a hot leg nozzle in pressurizer surge line subject to combined loading including deadweight, pressure, seismic inertia load, and seismic anchor motion, as well as was derived indirectly by applying the proposed analysis procedure to the finite element elastic stress analysis result for each load. Third, strain-based fatigue assessment was implemented by applying the strain-based fatigue acceptance criteria in the ASME B&PV Code, Sec. III, Subsec. NB, Article NB-3200 and by using the total strain amplitude values calculated. Last, the total strain amplitude and the fatigue assessment result corresponding to the simplified elastic-plastic analysis were compared with those using the finite element elastic-plastic seismic analysis results. As a result of the comparison, it was identified that the proposed analysis procedure can derive reasonable and conservative results.

Numerical Investigation on Plastic Strain Correction Factor in Simplified Elastic-Plastic Fatigue Analysis

A plastic strain correction factor is used in a simplified elastic-plastic fatigue analysis of nuclear power plant components. Numerical investigation on the plastic strain correction factor is presented for the case of the primary and secondary stress range exceeding three times the design stress intensity value under thermal-mechanical loadings. The plastic strain correction factor was computed separately by following the RCC-M code and applying the elastic-plastic finite element analysis. The influence of loading ratio, loading controlled mode and ambient temperature on the plastic strain correction factor was discussed. It was shown that the plastic strain correction factor computed from the RCC-M code is not as conservative as that from the complete elastic-plastic finite element analysis when the primary plus secondary stress range is close to three times the design stress intensity value. However, it is too conservative when the primary plus secondary stress range is more than three times the design stress intensity value multiplying parameter m (use in RCC-M code). Additionally, a new formula of plastic strain correction factor was proposed to provide a complete envelope curve to the entire primary plus secondary stress range.

Performance study of the simplified theory of plastic zones and the Twice-Yield method for the fatigue check

As elastic–plastic fatigue analyses are still time consuming the simplified elastic–plastic analysis (e.g. ASME Section III, NB 3228.5, the French RCC-M code, paragraphs B 3234.3, B 3234.5 and B3234.6 and the German KTA rule 3201.2, paragraph 7.8.4) is often applied. Besides linearly elastic analyses and factorial plasticity correction (Ke factors) direct methods are an option. In fact, calculation effort and accuracy of results are growing in the following graded scheme: a) linearly elastic analysis along with Ke correction, b) direct methods for the determination of stabilized elastic–plastic strain ranges and c) incremental elastic–plastic methods for the determination of stabilized elastic–plastic strain ranges.The paper concentrates on option b) by substantiating the practical applicability of the simplified theory of plastic zones STPZ (based on Zarka's method) and – for comparison – the established Twice-Yield method. The Twice-Yield method is explicitly addressed in ASME Code, Section VIII, Div. 2. Application relevant aspects are particularly addressed. Furthermore, the applicability of the STPZ for arbitrary load time histories in connection with an appropriate cycle counting method is discussed.Note, that the STPZ is applicable both for the determination of (fatigue relevant) elastic–plastic strain ranges and (ratcheting relevant) locally accumulated strains. This paper concentrates on the performance of the method in terms of the determination of elastic–plastic strain ranges and fatigue usage factors. The additional performance in terms of locally accumulated strains and ratcheting will be discussed in a future publication.

Performance study of K e factors in simplified elastic plastic fatigue analyses with emphasis on thermal cyclic loading

As code-based fully elastic plastic code conforming fatigue analyses are still time consuming, simplified elastic plastic analysis is often applied. This procedure is known to be overly conservative for some conditions due to the applied plastification (penalty) factor K e . As a consequence, less conservative fully elastic plastic fatigue analyses based on non-linear finite element analyses (FEA) or simplified elastic plastic analysis based on more realistic K e factors have to be used for fatigue design. The demand for more realistic K e factors is covered as a requirement of practical fatigue analysis. Different code-based K e procedures are reviewed in this paper with special regard to performance under thermal cyclic loading conditions. Other approximation formulae such as those by Neuber, Seeger/Beste or Kuehnapfel are not evaluated in this context because of their applicability to mechanical loading excluding thermal cyclic loading conditions typical for power plant operation. Besides the current code-based K e corrections, the ASME Code Case N-779 (e.g. Adam’s proposal) and its modification in ASME Section VIII is considered. Comparison of elastic plastic results and results from the Rules for Nuclear Facility Components and Rules for Pressure Vessels reveals a considerable overestimation of usage factor in the case of ASME III and KTA 3201.2 for the examined examples. Usage factors according to RCC-M, Adams (ASME Code Case N-779), ASME VIII (alternative) and EN 13445-3 are essentially comparable and less conservative for these examples. The K v correction as well as the applied yield criterion (Tresca or von Mises) essentially influence the quality of the more advanced plasticity corrections (e.g. ASME Code Case N-779 and RCC-M). Hence, new proposals are based on a refined K v correction.

Simplified Elastic-Plastic Analysis Methods in the JSME Rules on Design and Construction

In a fatigue analysis for Class 1 components in the Rules on Design and Construction for Nuclear Power Plants (The First Part : Light Water Reactor Structural Design Standard) in the JSME Codes for Nuclear Power Generation Facilities, a simplified elastic-plastic analysis is used when the primary plus secondary stress intensity exceeds 3 times the Design Stress Intensity. The simplified elastic-plastic analysis is to multiply elastic-analysis-based stress by a Ke-factor. It is well-known that the Ke-factor of the ASME Boiler and Pressure Vessel Code Section III has a large amount of conservatism. Hence, to develop an appropriate Ke-factor evaluation method, the Ke-factor Advisory Committee was established in June 1999 as a research committee of the Thermal and Nuclear Power Energy Society. Typical basic models were selected from actual structures. Elastic analyses and elastic-perfectly plastic analyses were performed for the basic models and the Ke-factors were calculated. equations were established by bounding the Ke-factors. The new equation was verified by using experimental data of piping. The factors for typical actual nozzles of which Ke-factors were relatively higher were directly analyzed and it was confirmed that the developed evaluation method could be higher than the Ke-factor directly analyzed. Based on those evaluations, the Ke' equation expressed by Primary + Secondary Stress Intensity (Sn) and the Ke equation expressed by Primary + Secondary + Peak Stress Intensity (Sp) were developed. The Ke' equation has been taken in the JSME Design and Construction Code and the Ke equation has been taken in the Code Case, Alternative Structural Evaluation Criteria for Class 1 Vessels based on Elastic-Plastic Finite Element Analysis.

J041013 オーステナイト系ステンレス鋼の弾塑性解析に用いる繰返し応力-ひずみ線図([J04101]工業材料の変形と強度特性及びそのモデル化(1))

When an evaluation point shows plasticity, for instance, simplified elastic-plastic analysis can be applied in accordance with the JSME Design and Construction Code (Division 1, Light Water Reactor Code). However this method is known as conservative and elastic-plastic analysis with cyclic stress-strain relation should be performed to obtain an accurate fatigue usage factor. Therefore cyclic stress-strain relation has been developed for austenitic stainless steels. Cyclic stress-strain data were collected from several Japanese reports. Two types of relationship were employed. One is power law type and the other is Ramberg-Osgood type. Those relationships were converted to bilinear type relationships with considering appropriate margin.

機械学会設計・建設規格における簡易弾塑性解析手法

In a fatigue analysis for Class 1 components in the Rules on Design and Construction for Nuclear Power Plants (The First Part : Light Water Reactor Structural Design Standard) in the JSME Codes for Nuclear Power Generation Facilities, a simplified elastic-plastic analysis is used when the primary plus secondary stress intensity exceeds 3 times the Design Stress Intensity. The simplified elastic-plastic analysis is to multiply elastic-analysis-based stress by a Ke-factor. It is well-known that the Ke-factor of the ASME Boiler and Pressure Vessel Code Section III has a large amount of conservatism. Hence, to develop an appropriate Ke-factor evaluation method, the Ke-factor Advisory Committee was established in June 1999 as a research committee of the Thermal and Nuclear Power Energy Society. Typical basic models were selected from actual structures. Elastic analyses and elastic-perfectly plastic analyses were performed for the basic models and the Ke-factors were calculated. equations were established by bounding the Ke-factors. The new equation was verified by using experimental data of piping. The factors for typical actual nozzles of which Ke-factors were relatively higher were directly analyzed and it was confirmed that the developed evaluation method could be higher than the Ke-factor directly analyzed. Based on those evaluations, the Ke' equation expressed by Primary + Secondary Stress Intensity (Sn) and the Ke equation expressed by Primary + Secondary + Peak Stress Intensity (Sp) were developed. The Ke' equation has been taken in the JSME Design and Construction Code and the Ke equation has been taken in the Code Case, Alternative Structural Evaluation Criteria for Class 1 Vessels based on Elastic-Plastic Finite Element Analysis.

Simulation of Welding Deformations of Ship Structures

Welding deformations of real structures are complicated and the accurate prediction of welding deformations has been a difficult problem. The equivalent load method is presented in this paper. The method uses the FE method combining the inherent strain theory and the experimental results for accurate and efficient analysis. A simplified elastic plastic analysis model, bar-spring model is used. It is showed that the highest temperature and the degree of restraint change the distributions of the inherent strains in the welded region. Applying the equivalent loads induced by the inherent strain on the structure, the final deformations are calculated by FE analysis. The results in this paper have been supported by the results of C.H.LEE and the experimental data.

Meaning of Ke in Design-by-Analysis Fatigue Evaluation

The ASME Section III Design-by-Analysis rules for pressure-retaining components include a detailed fatigue evaluation based on elastically predicted primary, secondary, and peak stresses. A prerequisite for the fatigue analysis is that the primary-plus-secondary stress range does not exceed 3Sm. If this limit is exceeded, the code provides “Simplified Elastic-Plastic Analysis” rules for the fatigue evaluation. A Ke penalty factor is applied to the elastically predicted alternating stress. The maximum value of Ke (3.3 or 5) is a severe design limitation. Test data indicate that the code specified maximum value of Ke is very conservative. The simplified elastic-plastic rules were originally developed for piping and published in B31.7. When the piping rules were incorporated into Section III in 1971, the B31.7 procedure was replaced by a less complex procedure. The development of the simplified elastic-plastic analysis approach is reviewed to establish the technical basis for the present code rules. The concepts of fatigue, shakedown to elastic action, thermal bending, elastic follow-up, notch factor, and strain redistribution are discussed. Recommendations for changes to the plastic strain correction factor are provided.

ASME Section III Design-By-Analysis Criteria Concepts and Stress Limits

The ASME Section III design-by-analysis approach provides stress criteria for the design of nuclear components. Stresses are calculated elastically for the most part, although plastic analysis is recognized. Limits are specified for primary, secondary, and peak stresses. Inherent in these limits are factors of safety against several modes of failure. The purpose of this paper is to explain the design-by-analysis criteria and fundamental concepts behind the approach. Topics covered include the bases for the primary stress limits, shakedown to elastic action, fatigue, simplified elastic-plastic analysis, and thermal stress ratchet. Issues that are explored are separating primary and secondary stresses in finite element analyses, material ductility requirements, and the meaning of the fatigue penalty factor.

Inelastic deformation and failure of clamped aluminium plates under pulse pressure loading

An experimental and analytical study is presented of the inelastic deformation and failure (rupture) of clamped aluminium plates measuring 0.5 m×0.5 m at the clamped edge by 1 mm thick under pulse pressure loading. The pulse loading was applied by generating a dynamic pressure gradient across the plates using a fast differential pressure device. Both static and dynamic test results are reported together with the results of an investigation of the failure surface using scanning electron microscopy. An assumed-modes, elastic–plastic analysis of the plates using a finite strip model was used to predict the maximum displacement of the plates. A simple uniaxial strain-based failure criterion was used in the analysis to predict the failure pressure of the ruptured plates. The rigid-plastic method was used to estimate the permanent deformation of some of the plates. Reasonable agreement is obtained between the predictions of the simplified elastic–plastic analysis and the experimental results. The rigid-plastic results were less accurate at predicting the permanent deformation of the plates due to the long duration of the loading relative to the fundamental natural period of the plates.

Simplified Elastic-Plastic Analysis Method Using Ke Factors Obtained for the Real Structural Model

This paper describes a new simplified elastic-plastic analysis method, which utilizes a plastic strain multiplication factor (Ke factor) obtained from elastic-plastic finite element analysis (FEA) results for the same structural model in the design stress calculation. ASME Code, Sec. III specifies a simplified elastic-plastic analysis method which can be used when PL+Q intensity exceeds the 3Sm limit, provided that the rules to prevent thermal stress ratchet are satisfied. The conventional method requires using Ke factors given by a closed-form equation having a value of PL+Q intensity as a variable. The elastically calculated peak stresses need be multiplied by the Ke factors, before performing the fatigue analysis. The Ke factors in the Code were derived from strain multiplication factors calculated for rather simple structural elements, which are assumed to cover a wide range of structural components. Consequently, although the rule can be applied safely to most of the cases, the results are usually too conservative. On the other hand, when PL+Q intensities are near 3Sm level, it has been pointed out based on experiments and analyses that the current Ke has a lack of margin. We propose to use the Ke factors obtained by FEA of the real structural model, in order to avoid the foregoing overconservatism and the lack of margin. The procedure also makes it unnecessary to extract PL+Q category, which is necessary in the conventional evaluation method. Elastic and elastic-plastic FEAs were performed for the axisymmetric nozzle in a vessel, and the effectiveness of the proposed procedure was shown in a practical case. Generalization of the procedure is also discussed.

Improvement of the strain concentration factor for simplified elastic–plastic analysis

Improvement of the strain concentration factor for simplified elastic–plastic analysis

Simplified analysis of shrinkage in pipe to pipe butt welds

Generally some shrinkage is typical of butt welding of pipes. Shrinkage due to butt welding could be more pronounced and significant in thin wall stainless steel pipes because the thermal expansion coefficient is roughly one and half times that of carbon steel. An axisymmetric finite element evaluation of hoop shrinkage associated with circumferential butt welds in thin wall stainless steel pipes was performed. Actual shrinkage data for a larger (24 in. diameter, 0.375 in. wall thickness) pipe and a smaller (4 in. diameter, 0.237 in. wall thickness) pipe were utilized. The results indicate that very localized residual stresses in excess of yield strength produced during cooldown of metal in the weld and heat affected zones cause redistribution of the stresses. A simplified elastic–plastic analysis approach was developed with adjustments for section modulus and Poisson’s ratio, and the strains due to radial shrinkage were calculated for inside and outside surfaces of the pipe at the weld center line. From the strain point of view, the strain values in the circumferential direction were about 1.4% for the larger size pipe and 3.4% for the smaller size pipe. The strain values in the axial direction were 2.5% for the larger pipe and 5.9% for the smaller pipe. It is concluded that these levels of strains are not detrimental in nature. However, for the smaller pipe they are on the high side and it is recommended not to use the pipe for elevated temperature service. Residual stresses were also calculated for inside and outside surfaces of the pipe at weld center line using a simplified elastic–plastic approach and a bilinear stress–strain curve and compared with published data indicating a general agreement.

3214 簡易弾塑性解析における応力割り増し係数の開発

In the fatigue analysis for Class 1 components in MITI Notification No.501,the simplified elastic-plastic analysis with the fatigue penalty factor (Ke factor) is applied when the primary plus secondary stress intensity exceeds 3Sm. It is known that the Ke factor has a large conservatism. Therefore, to rationalize the present Ke factor, the elastic analyses and the elastic-plastic analyses were performed, and the analyzed Ke factors were evaluated. The analyses were performed with various loading conditions and geometric models so that the analyses results could be represented for the actual design of major LWR components. And the adequacy of the rationalized Ke factor was verified with the experimental data for piping and with the evaluation results for the severest actual components from the viewpoint of the fatigue evaluation.

Determination of more realistic Ke,r-factors for simplified elastic–plastic analysis

According to the relevant KTA-Rules, e.g. KTA 3201.2 ( KTA, 1994), strain correction factors— K e-factors—have to be used in the fatigue analysis of pressurised components if the strain intensity ranges are determined by elastic analyses, and if in this case the range of primary plus secondary stress intensity exceeds a certain limit. This limit is three times the design stress intensity value, S m , and thus approximately corresponds to twice the value of the 0.2% strain limit. The relations given in the above-mentioned rules to determine the K e-factors for considering plastification have proved to be very conservative in many cases compared with the strain intensity ranges that were determined by complete elastic–plastic analyses. In order to improve the validity of the fatigue analysis, the topic of `Performance of fundamental work to prepare concrete proposals for realistic K e,r-factors (strain correction factors) to consider plastification at large strain amplitudes' was one of the subjects of the BMU project SR 2063. Work on this topic was jointly performed by GRS and Siemens. In summary, the result was that the proposed realistic K e,r-factors present a real alternative to the K e-factors of the regulations; the latter serve a mostly conservative registration of the observed elastic–plastic strain but cannot be explained in terms of physics and are not formulated in a manner adequately specific of any material. The exemplary verification calculations that have been performed so far show, furthermore, that the proposed realistic K e,r-factors can be easily determined and also deliver sufficiently conservative results. This new method therefore has great potential which, however, still has to continue to be verified by further calculations before it can be included in the KTA-Rules.