Reference Stress Method Research Articles

Evaluation of C* integral for interacting cracks in plates under tension

A closed form solution for C* integral of two interacting cracks in plates under tension is developed on the basis of reference stress method. Comprehensive finite element (FE) creep analyses are carried out to provide the benchmark of the interaction evaluation of multiple cracks. Results indicate that more pronounced interaction is observed between the C* of double cracks and that of a single crack compared to that denoted by stress intensity factor (SIF). Overall good agreement is achieved between the proposed method for C* of multiple crack interaction and the FE results which provides confidence in practical application.

参照応力J積分簡易解析法の破壊評価曲線評価への適用性の検討

In the rules on fitness-for-service for nuclear power plants of the Japan society of mechanical engineers (JSME), the two-parameter approach is prescribed for failure assessment of defects. In JSME rule, the failure assessment curve (FAC) for the two-parameter approach has to be determined using J-integral value when existing FAC is not available. The reference stress method can estimate J-integral value using stress-strain relation of the material. However, the accuracy of estimation depends on the limit load used for an evaluation of the reference stress. In this study, applicability of several limit load solutions was investigated by comparing with results of elastic-plastic finite element analyses. Pipes containing axial or circumferential flaw were analyzed under internal pressure or bending load. Appropriate limit load solutions were suggested for evaluation of FAC, based on analyses of 2880 cases for different flaw and pipe geometries and materials used in nuclear power plants.

Surface effects on time-dependent fracture parameter of subsurface crack in plates under tension

Based on the comprehensive finite element (FE) creep analyses, the influence of free surface on the time dependent fracture mechanics parameter of a crack near the free surface in plates under tension has been investigated. It is found that the time dependent fracture parameter C* increases as the crack tip closes to the free surface. Such an increment is related not only to the crack configurations but also to the material properties, especially the creep exponent n of power creep law. In addition, more pronounced interaction is observed between the C* of subsurface crack and that of a single isolated crack compared to that denoted by SIF under the linear elastic fracture condition. Under the framework of reference stress method, we also developed a closed form solution for creep interaction factor. Overall good agreement is achieved between the proposed method for the C* of subsurface crack and the FE results which provides us confidence in practical application.

Estimation of C*-Integral for Radial Cracks in Annular Discs under Constant Angular Velocity and Internal Pressure

The finite element method has been used to predict the creep rupture parameter, C*-Integral for single and double-edge cracks in eight annular rotating discs under constant angular velocity with and without internal pressure. In this study, a new dimensionless creeping crack configuration factor, Q* has been introduced. Power law creeping finite element analyses have been performed and the results are presented in the form of Q* for a wide range of components and crack geometry parameters. These parameters are chosen to be representative of typical practical situations and have been determined from evidence presented in the open literature. The extensive range of Q* obtained from the analyses are then used to obtain equivalent prediction equations using a statistical multiple non- linear regression model. The predictive equations for Q*, can also be used easily to calculate the C*- Integral values for extensive range of geometric parameters. The C*-Integral values obtained from predictive equations were also compared with those obtained from reference stress method (RSM). Finally, creep zone growth behavior was studied in the component during transient time.

Estimation of C*-Integral in Thin T-Sections Subjected to Projection and Remote Loading Base on Elastic Stress Concentration Factor

The finite element method has been used to predict the creep rupture parameter, C*-Integral of flat T-section bar subjected to loaded projection and remote loading with a crack or crack-like flaw introduced in the fillet (i.e., high stress) region of the component. In this study, a new dimensionless creeping crack configuration factor, Q* has been introduced. Power low creeping finite element analyses have been performed and the results are presented in the form of Q* for a wide range of components and crack geometric parameters. These parameters are chosen to be representative of typical practical situations and have been determined from evidence presented in the open literature. The extensive range of Q* obtained from the analyses are then used to obtain equivalent prediction equations using a statistical multiple non-linear regression model. The predictive equations for Q*, which are based on the elastic stress concentration factor, can also be used easily to calculate the C*-Integral values for extensive range of geometric parameters. The C*-Integral values obtained from predictive equations were also compared with those obtained from Reference Stress Method (RSM). Finally, creep zone growth behavior was studied in the component during transient time.

The Strain Estimation of Statically Determinate Structures Subjected to Forced Displacement by Reference Stress Method

It is well known that the inelastic strain accumulation of statically determinate structure subjected to forced displacement is caused by the elastic follow-up due to surrounding elastic region. The author once showed that the relaxation phenomenon of creeping structures during the elastic follow-up can be well estimated by the reference stress method. By applying this result, the author has proposed a simplified method to estimate the creep strain accumulated by the elastic follow-up. It has been shown that elastic follow-up factor can be calculated from the reference stress ratio, which is the ratio of Local Reference Stress and Global Reference Stress. The proposed method was applied to the elastic follow-up of 2-bar model and 2-beam model. For 2-beam model, a simple method has been proposed to estimate the stress-strain relation during the elastic follow-up, and it showed quite good agreement with FEM results. It was also shown that the proposed method can be applied to the plastic strain accumulation due to the elastic follow-up. By comparing with other strain estimation methods such as Neuber's method and Stress Relaxation Locus method, the proposed method was found to be reasonable and precise.

A205 2パラメータ評価法に対する参照応力J積分解析法の適用性の検討(材料強度評価-2,OS-6 保全・設備診断技術(3),一般講演,地球温暖化防止と動力エネルギー技術)

A205 2パラメータ評価法に対する参照応力J積分解析法の適用性の検討(材料強度評価-2,OS-6 保全・設備診断技術(3),一般講演,地球温暖化防止と動力エネルギー技術)

Use of local and global limit load solutions for plates with surface cracks under tension

Some available experimental results for the ductile failure of plates with surface cracks under tension are reviewed. The response of crack driving force, J, and the ligament strain near the local and global limit loads are investigated by performing elastic-perfectly plastic finite element (FE) analysis of a plate with a semi-elliptical crack under tension. The results show that a ligament may survive until the global collapse load is reached when the average ligament strain at the global collapse load, which depends on the uniaxial strain corresponding to the flow stress of the material and the crack geometry, is less than the true fracture strain of the material obtained from uniaxial tension tests. The FE analysis shows that ligament yielding corresponding to the local limit load has little effect on J and the average ligament strain, whereas approach to global collapse corresponds to a sharp increase in both J and the average ligament strain. The prediction of the FE value of J using the reference stress method shows that the global limit load is more relevant to J-estimation than the local one.

Assessment of the reference stress method for J-integral estimation of cracked riveted beams of an old wrought iron

This work deals with the application of the reference stress method to estimate the J-integral of cracked riveted beams of old puddle iron. The ductility of some of these materials makes it necessary to use elasto-plastic fracture criteria to assess damage tolerance. This requires a high computational effort, since it involves the determination of the J-integral in beams with plates and angles that interact by means of redundant forces dependent on crack size. The J-integral estimation method based on the reference stress could reduce this effort, provided it were shown to be valid for this type of beam. This work contributes to this end by comparing the J-integral values resultant from the reference stress method and a complete finite element modelling of a riveted beam consisting of two angles and a cracked plate made of actual puddle iron from a road bridge more than a century old but still in service. A number of samples removed from the bridge showed that this material failed in a ductile manner when it was fracture tested with fatigue precracked compact specimens, even at temperatures as low as −20 °C. The two types of J-integral values found are compared over the ranges of load and crack size explored.

Study of crystallographic creep parameters of nickel-based single crystal superalloys by indentation method

The flat cylindrical indentation creep experiment on nickel-based single crystal superalloys has been investigated with the aim of determining the crystallographic creep parameters. Theoretical analysis shows that the indentation creep exponent is equal to the crystallographic creep exponent of indented nickel-based single crystal superalloys. Two methods are explored to determine the crystallographic creep parameters with the indentation method. One is the reference stress method, which shows a general relationship between the indentation creep testing and uniaxial creep testing by two reference parameters. The second method is the reverse numerical procedure, which allows extracting the crystallographic creep parameters on the basis of two indentation creep tests with two indenter geometries and a series of finite element calculations.

On creep failure of notched bars

This paper demonstrates the application of a new multiaxial creep damage model developed by the authors to predict the failure time of components made of service aged 2.25%Cr–1%Mo, 0.5%Cr–0.5%Mo–0.25%V low alloy steels, titanium and nickel-based superalloys. The model accounts for the tertiary creep behaviour and assumes the creep damage is related to the internal energy absorbed by the material. The authors argue that the model is the most appropriate for characterizing gross creep damage from a macroscopic point of view because it takes into accounts both the multiaxial internal deformation and loading. The verification and application of the model are demonstrated by applying it to the Bridgman notched bars for which the experimental data are available. The predicted failure times by the model are compared with the experimental results and those obtained from the reference stress method. The results show that the proposed model is capable of predicting failure times of the components made of the above-mentioned materials with an accuracy of 2.2% or better. Also, it is shown that the model predicts the creep failure times of the components more accurately than the reference stress method.

Ductile Fracture Behaviour of Class 2 and 3 LWR Piping and Its Implications for Flaw Evaluation Criteria

To achieve a rational maintenance program for aged Light Water Reactor components, it is important to establish and to improve the flaw evaluation criteria. The current flaw evaluation criteria such as ASME Boiler and Pressure Vessel Code Section XI are focused on Class 1 piping which usually shows relatively higher toughness. On the other hand, flaw evaluation criteria suitable for Class 2, 3 piping with moderate-toughness are also required because some Class 2, 3 piping systems are as important to plant safety analysis as Class 1 piping. In this study, both analytical and experimental studies were conducted to provide the evaluation method of fracture loads for acceptance criteria for Class 2, 3 piping. Pipe fracture tests by four-point bending were conducted on circumferentially cracked carbon steel pipes with moderate-toughness. The Net-Section Collapse criterion overpredicted experimental maximum loads for through-wall-cracked pipes, which suggested the necessity of Z-factor. Three-dimensional finite element analysis and simplified analysis based on the reference stress method were conducted to complement the limited pipe fracture tests. It was ascertained that the reference stress method always gave moderately conservative fracture loads compared with the finite element analysis and pipe fracture tests as well. Z-factor for Class 2, 3 piping was then derived and formulated using the reference stress method. Z for Class 2, 3 piping was affected by radius-to-thickness ratio, and was higher than Z for Class 1 piping in the present codes.

352 参照応力法による変位制御型荷重を受ける静定構造物の歪推定(OS10-4 クリープ,耐震,疲労,OS10 エネルギー機器の経奪変化に関する健金性評価手法の開発とその適用(2))

352 参照応力法による変位制御型荷重を受ける静定構造物の歪推定(OS10-4 クリープ,耐震,疲労,OS10 エネルギー機器の経奪変化に関する健金性評価手法の開発とその適用(2))

A Method to Apply the Reference Stress Approach to Simplified Estimates of Inelastic J-integral Under Displacement-Controlled Loading

In the assessment of structural integrity and remaining life of a power component operated at high temperatures, evaluation of crack-like damage is frequently required. When estimating crack propagation rates under creep-fatigue loading, J-integral type inelastic fracture mechanics parameters including elastic-plastic J-integral for elastic-plastic body and creep J-integral for creeping body are needed. Although these parameters may be estimated by detailed inelastic finite element analysis of a cracked component, this kind of analysis is usually laboring and costly. Therefore, employing simplified methods such as the reference stress approach is practical. Since the reference stress approach has been developed for an inelastic body subjected to external loading, a method to apply this to a component under secondary stress has not been established. This paper proposes an approach to apply the reference stress method to a cracked component subjected to displacement-controlled loading together with a clear definition of elastic follow-up factor

Creep Crack Growth Predictions in Component Using a Damage Based Approach

Abstract This paper presents a numerical study of simulated creep crack growth (CCG) prediction in a compact tension [C(T)] specimen and a pipe component containing cracks. The results are compared to experimental data of the same consisting of creep crack growth tests of a carbon-manganese steel (C-Mn) tested at 360°C. The constitutive behavior for this steel is described by a power law creep model and the uniaxial properties are used in a damage based model to predict CCG. For comparison between CCG properties of the pipe and C(T) specimens, different reference stress methods were used to derive appropriate C* values. It has been shown that the global solution for collapse in the cracked pipes gives the best correlation with the C(T) data. On this basis CCG rates for pipe are higher than those for C(T) specimens at the same value of C*. The damage-based approach combined with a crack tip constraint model based on void growth is also used to predict the crack propagation rates in the pipe component using a two-dimensional finite elements (FE) mesh. Elastic-plastic-creep analyses are performed using a node debonding criteria to simulate and predict crack extension under plane stress and plane strain conditions. It has been found that CCG against time predicted from the FE under plane stress conditions is almost the same as those for the experimental data. Comparing C* derived from different reference stress methods to C* from FE analysis it has been found that C* from FE under plane strain condition correlates best with C* from the global reference stress solution. Consequently the main CCG difference between the C(T) and the pipe component is found to be due to the method of estimating C* and not due to constraint effects.

Time-Dependent Fracture and Defect Assessment of Welded Structures at High Temperature

The present work reports several new insights into creep crack growth performance and defect assessment of welded structures at elevated temperature. First of all, an equivalent homogeneous model based on the limit load analysis is proposed to reflect the mismatch effects of the base and weld metals, the geometrical dimension of weldment constituents and the location of the pre-existing defects. Secondly, using the proposed equivalent homogeneous model, an estimation methodology for the time-dependent fracture mechanics parameter C* is developed in conjunction with the reference stress (RS) method and the GE/EPRI scheme. Such an estimation method was validated by using nonlinear finite element analysis of 48 compact tension (CT) specimens with various degrees of mismatch in creep behavior and different width of the welding seam. After that, the applicability of C* measurement recommended in ASTM E 1457 is re-examined for the CT specimen with a mismatched cross-weld. From the limit load analysis, a series of modifications for experimental C* estimation equation from ASTM E 1457 is introduced based on the proposed equivalent homogeneous model. Finally, a failure assessment diagram (FAD)-based method is presented for the welded structures at high temperatures. The application of such an approach to a welded cylinder with an internal circumference crack under axial tension is also reported in this paper.

관통균열 세관의 파열압력 예측을 위한 탄소성 파괴역학 해석

The structural and leakage integrity of steam generator tubes should be sustained all postulated loads with appropriate margin even if a crack is present. During the past three decades, for effective integrity evaluation, several limit load solutions have been used world-widely. However, to predict accurately load carrying capacities of specific components under different conditions, the solutions have to be modified by using lots of experimental data. The purpose of this paper is to propose a new burst pressure estimation scheme based on fracture mechanics analyses for steam generator tube with an axial or circumferential through-wall crack. A series of three dimensional elastic-plastic finite element analyses were carried out and, then, closed-form estimation equations with respect to both J-integral and crack opening displacement were derived through reference stress method. The developed engineering equations were utilized for structural integrity evaluation and the resulting data were compared to the corresponding ones from experiments as well as limit load solutions. Thereafter, since the effectiveness was proven by promising results, it is believed that the proposed estimation scheme can be used as an efficient tool for integrity evaluation of cracked steam generator tubes.

変位制御弾塑性疲労条件下のき裂構造の破壊力学パラメータの推定

Quantitative prediction of crack growth under displacement-controlled conditions such as thermal fatigue is a key to the residual life prediction of plant components. In a previous paper, the authors proposed a simplified prediction method of fracture mechanics parameters such as J and C* of a perforated plate under thermal fatigue, on the basis of the reference stress approach under displacement-controlled conditions. In this paper, the fracture mechanics parameters of a CCT specimen and structural models of CrMoV cast steel under displacement-controlled conditions were experimentally and numerically examined on the basis of the proposed method. The ratio of the inelastic and the elastic crack opening displacement, as well as the ratio of the inelastic and the elastic load point displacement, was used to correlate the fracture mechanics parameters in the inelastic and elastic regions. The proposed method based on displacements was found to be insensitive to a small variation in the predicted macroscopic load in comparison with the original reference stress method, and is considered to be applicable to displacement-controlled conditions such as thermal fatigue.

반타원 표면균열 선단을 따른 참조응력 기반의 J-적분 예측

This paper discusses applicability of the enhanced reference stress method to estimate J-integral along the semi-elliptical surface crack front. It is found that angular variations of normalized J-integral are strongly dependent on the geometry, loading mode and loading magnitude. As application of the reference stress approach to semi-elliptical surface cracks implies proportional increases in the normalized J-integral, the present results pose a question in applicability of the reference stress approach. However, investigation of the error in the estimated J-integral in the present work suggests that the enhanced reference stress approach, recently proposed by authors, provides an effective engineering tool for estimating crack driving force along the semi-elliptical surface crack front.<br/>

Reference Stress Based Approach to Predict Failure Strength of Pipes With Local Wall Thinning Under Single Loading

This paper proposes a new method to estimate failure strength of a pipe with local wall thinning. The method is based on the equivalent stress averaged over the minimum ligament in the locally wall thinned region. The highlight of the proposed method is to propose a simple scheme to estimate the equivalent stress in the minimum ligament. Inspired by the reference stress method for approximate creep stress analysis, approximate estimation equations are proposed for the equivalent stress in the minimum ligament, which are then calibrated using detailed elastic-plastic three-dimensional FE analysis. Remarkably the resulting estimation equations are found to be insensitive not only to pipe and defect geometries but also to material. Comparison of failure loads, predicted according to the proposed method, with published test data for corroded pipes shows excellent agreement, which provides confidence in the use of the proposed method to assess local wall thinning in pipes. Furthermore, the proposed method is conceptually simple and thus easy to be extended to more complex situations.