Reference Stress Method Research Articles

Enhanced reference stress‐based J and crack opening displacement estimation method for leak‐before‐break analysis and comparison with GE.EPRI method

Three‐dimensional, elastic–plastic finite element analyses for circumferential through‐wall cracked pipes are performed using actual tensile data of stainless steels, for two purposes. The first one is to validate the recently proposed enhanced reference stress (ERS) method to estimate the J‐integral and rack‐opening displacement (COD) for circumferential through‐wall cracked pipes. The second one is to compare the J and COD results from the ERS method with those based on the GE/EPRI method, together with the finite element results. It is found that the GE/EPRI method generally provides poor estimations of J and COD, and such poor estimation results from the Ramberg–Osgood (R–O) fit. Moreover, the GE/EPRI results can be very sensitive to how the stress–strain data are fitted using the R–O relation. The most appropriate fitting range for the R–O fit depends on the material, and thus no specific guideline can be given. On the contrary, the J and COD estimations based on the ERS method give more accurate and robust results than the GE/EPRI estimation. The present results, together with the experimental validation presented in the previous paper, provide sufficient confidence in using the proposed method in the leak‐before‐break analysis.

Application of enhanced reference stress method to nuclear piping LBB analysis : finite element validation

Three-dimensional, elastic-plastic finite element analyses for circumferential through-wall cracked pipes are performed using actual tensile data of stainless steels, for two purposes. The first one is to validate the recently-proposed enhanced reference stress (ERS) method to estimate the J-integral and COD for circumferential through-wall cracked pipes. The second one is to compare those results with the GE/EPRI estimations. It is found that the J-integral and COD estimations according to the GE/EPRI method can be very sensitive to how the stress-strain data are fitted using the Ramberg-Osgood relation. Moreover, no tendency can be found regarding the most appropriate fitting range for the Ramberg-Osgood fit. On the contrary, the J-integral and COD estimations based on the ERS method give more accurate results than the GE/EPRI estimation. The present results provide confidence in applying the proposed method to the Leak-Before-Break(LBB) analysis.

Basic principles of analytical flaw assessment methods

Analytical flaw assessment methods play an important role in the industrial realisation of fracture mechanics application. In the field of general as well as specific standards and guidelines there have been rapid developments in recent years. This paper gives a brief review of some of the more important methods, which have been developed over the last decades. Descriptions are given of various design curves and failure assessment diagrams, net section yielding and EPRI type solutions, the reference stress method and approaches derived from it, the ETM and the recently developed European flaw assessment method SINTAP. The discussion of these approaches is restricted to the basic principles of each method.

J estimation and defect assessment for combined residual stress and mechanical loading

Procedures for dealing with residual stresses in fracture assessments are examined in this paper. Two current J estimation methods, the EPRI scheme and the reference stress method, are evaluated using the finite element approach. The treatment of secondary stresses (a category which includes residual stresses) in the R6 defect assessment procedure has also been examined. Two geometries have been analysed, a centre cracked plate with an idealised residual stress distribution and a T-plate welded joint with a measured distribution. Both components are subjected to mechanical load, the former loaded in tension, the latter in three point bend. Results show that both the EPRI and reference stress methods give conservative J-values when the mechanical load is greater than the limit load. However, when the mechanical load is less than the limit load, the conservatism of both methods is dependent on the residual stress distribution along the uncracked ligament. The results also show that the use of Appendix 4 of the current R6 procedure yields a safe assessment except for the case of a small flaw in a region of uniform tensile residual stress.

Approximate creep rupture lifetimes for butt welded ferritic steel pressurised pipes

The creep rupture of butt welded ferritic steel pipes composed of a range of weld and heat affected zone materials has been previously analysed in detail (Leckie and Hayhurst, 1994). These analyses required substantial computational resources which cannot be justified during the preliminary phases of the design process. To reduce cost and improve speed an approximate method for the analysis of kinematically determinate structures, known as the modal method (Leckie and Hayhurst, 1974), has been developed to compute creep rupture lifetimes. This paper reports an extension of the method for the analysis of multi-material structures, such as weldments, and its implementation as a post processor to a stationary state finite element creep analysis. Histories of stress and damage have been determined using the modal method for weldments with a range of heat affected zone and weld material combinations. The lifetimes determined in this way are compared with those determined using complete continuum damage mechanics analyses, and are shown to be conservative; in addition the regions of intense damage have been shown to be accurately predicted. The modal method is also shown to be superior to more approximate reference stress methods.

破壊力学 高温下における欠陥評価のためのＪ積分簡易解析法 （第１報） 高温下における欠陥評価のためのＪ積分簡易解析法の体系化

J-integral is an effective inelastic fracture parameter for the flaw evaluation of cracked components at high temperature. The evaluation of J-integral for an arbitrary crack configuration and an arbitrary loading condition can be generally accomplished by detailed numerical analysis such as finite element analysis, however, it is time-consuming and requires a high degree of expertise for its implementation. Therefore, it is important to develop simplified J-integral estimation techniques from the viewpoint of industrial requirements. In this study, a simplified J-integral evaluation method is proposed to estimate two types of J-integral parameters. One is the fatigue J-integral range to describe fatigue crack propagation behavior, and the other is the creep J-integral to describe creep crack propagation behavior. This paper presents the systematization of the simplified J-integral evaluation method incorporated with the reference stress method and the concept of elastic follow-up, and proposes a comprehensive evaluation procedure. The verification of the proposed method is presented in Part II of this paper.

On the solution of limit load and reference stress of 3-D structures under multi-loading systems

The concepts of limit load and reference stress have been widely used in structural engineering design and component integrity assessment, especially considering multi-loading systems. The limit analysis of structures and the reference stress method (RSM) have been proven to be successful in problems pertaining to two-criteria failure assessment, creep growth, rupture damage, and more recently, elastic-plastic fracture toughness. However, the determination of limit load and reference stress of 3-D structures under multi-loading systems is not a simple task. In the present paper, a solution method for radial loading is presented, the mathematical programming formulation is derived for the upper bound limit analysis of 3-D structures under multi-loading systems, and moreover, a direct iterative algorithm used to determine the reference stress is proposed which depends on the evaluation of limit load. The penalty function method is used to deal with the plastic incompressibility condition. All the numerical examples show that the proposed radial loading path scheme is reasonable and effective. The mathematical programming method without search used here can overcome the difficulties caused by the nonlinearity and nonsmoothness of the objective function and avoid the complicated computations of incremental elastic-plastic analysis.

Lower bound limit load of a circumferentially cracked pipe under combined mechanical loading

In a study on extension of the reference stress method, for J simplified assessment, to a three dimensional (3D) configuration under combined loading, lower bound limit analysis has been developed by J. Desquines. In the present paper the limit load for cracked pipe, with a 3D circumferential flaw, under pressure, tension and bending is detailed. The limit load is explicitly defined as a yield surface is the 3D space loading. A simple algorithm is proposed to solve the non linear problem associated to the reference stress calculation. Moreover, the lower bound solution is compared with Elastic Compensation Method (ECM) results computed on a 3D finite element mesh of the cracked pipe. The lower bound yield surface underestimates the numerical limit loads with a discrepancy lower than 20%.

Analysis of the Type IV creep failures of three welded ferritic pressure vessels

Creep rupture and creep crack growth assessments are performed on three 0.5Cr–0.5Mo–0.25V welded pressure vessels using reference stress methods. Each test vessel failed by steam leakage through the Type IV location of a weld. Estimated rupture times and failure locations are compared with the experimental results. The location of failure is shown to be correctly predicted and the calculated time to failure to be conservative with respect to the test results in each case. Estimates of creep crack growth from a pre-existing defect in the Type IV region of one vessel weld are also described. Conservative predictions of growth close to vessel failure are obtained.

Finite element calculation of applied J-integral for cracked ship structural details

Finite-element (FE) analysis was used to calculate the applied J-integral ( J) as a function of applied displacement for cracked full-scale test specimens which are representative of ship structural components. The specimens were welded from relatively thin (9 mm) HSLA80 (ASTM A710) and EH36 (ASTM A131) steel plates. For relatively simple CCT panels, the J calculated with FE analysis compared favorably with solutions published in the literature. Estimation schemes based on the reference stress method did not work well for the fully plastic conditions with these low-strain-hardening materials. A practical and simple model for estimating applied J was proposed which gives acceptable results. It was found that the applied J vs displacement for shell cracks bridged by stiffeners or girders can be calculated from an idealized CCT model incorporating all of the sections as if they were coplanar. The FE-calculated J was used, together with a J– R curve which was measured on small compact specimens, to model ductile crack extension.

An approximate and computationally efficient algorithm for computing reference stress for creep life assessment

One of the powerful methods that are currently available for the design and life assessment of components that operate within the creep range is the reference stress (RS) method. However, for problems for which the RS is not available from existing solutions, one usually needs to use a non-linear finite element method which is normally iterative, time-consuming and computationally expensive. An efficient and effective method for computing an approximate value for RS is described that combines a lower-bound theorem and finite-element discretization. The resulted quadratic programming is solved by an active set algorithm. The verification and application of the proposed method are also described.

Numerical analysis of limit load and reference stress of defective pipelines under multi-loading systems

The concepts of limit load and reference stress have been widely used in structural engineering design and component integrity assessment, especially in Nuclear Electric's (formerly CEGB) R5 and R6 procedures. The reference stress method has been proven to be successful in problems pertaining to creep growth, rupture damage, creep buckling, and more recently, elastic–plastic fracture toughness. An approximate method of reference stress determination relies on prior knowledge of limit loads for various configurations and loadings. However, determination of the limit loads for the problems with complicated geometric forms and loading conditions is not a simple task. In the present paper, a numerical solution method for radial loading is presented, the mathematical programming formulation is derived for the kinematic limit analysis of 3D structures under multi-loading systems, and moreover, a direct iterative algorithm used to determine the reference stress is proposed which depends on the evaluation of limit load. The numerical procedure is applied to determine the limit load and reference stress of defective pipelines under multi-loading systems. The effects of four kinds of typical part-through slots on the collapse loads of pipelines are investigated and evaluated in detail. Some typical failure modes corresponding to different configurations of slots and loading forms are studied.

Use of the reference stress method in estimating the life of pipe bends under creep conditions

The effect that the change of ovality of pipe bends, due to creep under internal pressure, has on the stationary-state stress state has been investigated using a reference stress approach. Attention has been focused on practical pipe bend geometries and loading conditions in power plant applications. Prediction of failure times based on stationary-state stresses, for cases in which ovality changes are neglected and in which ovality is included, indicate that the change of ovality can be very significant in some practical situations. Failure times obtained using a creep continuum damage mechanics approach have also been compared with those obtained using the stationary-state predictions with ovality changes included. These results indicate that even sophisticated damage mechanics analyses are inadequate unless the effects of the changing ovality which occurs are taken into account.

A French guideline for defect assessment and leak before break analysis

A large program was launched in France in order to develop defect assessment procedures and leak-before-break methods (LBB) applicable for the design and for operating FBR plants. As a result of the collaboration between CEA, EdF and Novatome, a French guideline A16 has been produced as a first step in order to produce further documents in RCC-MR for design and for in-service inspection. This paper presents the main items developed in this guide considering low and high temperature:• fatigue or creep-fatigue crack initiation based on the σd approach calculating stress and strain at a distance d=50 μm from the crack tip.• fatigue crack growth based on da/dN-δKeff relationship with a δKeff derived from a simplified estimation of δJ by reference stress.• creep-fatigue crack growth adding the fatigue crack growth and the creep crack growth during the hold time derived from a simplified evaluation of C*,• ductile tearing based on simplified estimation of J (reference stress method) and plastic collapse of the ligament with and without holdtime,• leak-before-break procedure.Some detailed examples explaining the use of this A16 guide are presented.

A numerical method for reference stress in the evaluation of structure integrity

The important concepts of reference stress has been widely used in structural component integrity assessments, both below and within the creep range of temperatures, mainly in Nuclear Electric's (fomerly CEGB) R5 an R6 procedures. The reference-stress method (RSM) has been proven to be successful in problems pertaining to creep growth, rupture damage, creep buckling, and, more recently, elastic-plastic fracture toughness. However, determination of the reference stress is not always a simple task. In the present paper, some existing methods for reference stress in evaluation of structure integrity are investigated in detail. In accordance with the relationship between the reference stress and limit load under certain applied loads or moments, a direct iterative algorithm used to determine the reference stress is proposed which depends on the solution of limit load. The penalty-function method is used to deal with the plastic-incompressibility condition. The numerical difficulties caused by the nonlinearity and nonsmoothness of the goal function are overcome. Numerical examples are given to demonstrate the applicability of the procedure.

Characterization of cyclic plastic bending of austenitic AISI 304 stainless steel

Steels used in chemical, nuclear and power industries are usually subjected to repeated loads that may induce significant inelastic deformations. Successful assessment of a component life places a great demand on understanding of material behaviour under strain histories involving cyclic plasticity under bending conditions.This work is concerned with an experimental study of low-cycle fatigue behaviour under both load and deflection controlled conditions. The tests were conducted on AISI 304 stainless steels with the objective of determining strain cycling properties under cyclic plastic bending. These properties are characterized by the cyclic stress-strain hysteresis responses obtained.The cyclic bending plasticity behaviour is investigated for beams with circular cross-section at two conditions of the material, under constant strain and under constant stress. Hysteresis loops for five different strain ranges of ±0.4%, ±0.82%, ±1.1%, ±1.33% and ±1.55% were obtained and also for different stress ranges of 730, 800, 870 and 940 MPa. The material exhibits cyclic hardening in its virgin state, the rate of hardening is very rapid at first but diminishes quickly as the stabilized condition is approached. The cyclic hardening for the constant strain condition is higher than the constant load condition.The results also confirm the applicability of the reference stress method for predicting the cyclic moment-curvature curve for beams with circular cross-sections. The observed strain values are higher in the lower strain range and lower in the higher strain. However, the correlation obtained is considered quite satisfactory in view of the nonlinearity of the problem.

Simplified stable crack growth analyses of welded CT specimens—comparison study of [formula omitted], reference stress and R6 methods

This paper describes some simplified stable crack growth analyses of two kinds of inhomogeneous CT specimens. The one is machined from a submerged are welded plate of a nuclear pressure vessel A533B Class 1 steel, while the other is machined from an electron-beam welded plate of the A533B Class 1 steel and a high strength HT80 steel. In both specimens, initial cracks are placed to be normal to the fusion line. The ratio of yield stresses of the weld metal and the base metal of the A533B Class 1 steel is about 1·15, while that of the HT80 and the A533B Class 1 steels is about 1·4. The generation phase crack growth analyses using the GE EPRI and the reference stress methods are performed, calculating an applied load ( P) and the J-value, while the application phase analyses of analyses using the R6 method are performed to calculate the maximum value of the applied load ( P max ). Finally, some modification procedures of the three simplified estimation schemes are discussed in order to apply them to inhomogeneous material regimes.

General steady creep analysis for various constitutive laws. Part 2: application and numerical examples in two dimensions

In the present paper, the general finite element method with penalty multiplier independent of the specific expression of the constitutive laws for steady creep presented in an earlier paper is applied to two-dimensional problems such as plane strain, plane stress and axisymmetry cases. In plane stress problems, it is found out that no penalty multiplier is needed. Several numerical examples are discussed to demonstrate the validity of this method. The significance of the reference stress method or R-node method has been shown in the approximate solution of the limit load. The reference stress can be obtained in two ways through several stress analyses of steady creep. One way is to perform these analyses by different constitutive laws. Another way is always to use the Norton law but with the exponent index taken as different values. The results of these two ways are consistent.

Breakdown of the skeletal stress technique for lifetime prediction of notched tension bars due to creep crack growth

The paper defines the range of applicability of the skeletal stress technique as a means of predicting the creep lifetime of a circumferentially notched tension bar subjected to steady load. The skeletal stress approach involves the quantification of the effective stress Σ c and its ratio with the maximum principal tension stress Σ l at a point, known as the skeletal point, at the throat of the notch. The stress Σ c and stress state Σ l/Σ e at the skeletal point are assumed to remain constant and to determine the notched bar lifetime, which is determined by direct integration of the constitutive equations. This paper assesses the range of validity of this technique using Continuum Damage Mechanics (CDM) calculations, based on finite element analysis techniques, to predict the exact notch behaviour for a range of material conditions appropriate to nickel superalloys. It has been shown that by reducing the ductility parameter in the constitutive equations associated with the creep constrained cavitation damage variable ω 2, the CDM computations are capable of predicting two extreme types of behaviour. Firstly, widespread CDM behaviour, and secondly CDM growth on a highly localised-planar scale which models the phenomenon of Creep Crack Growth (CCG). The reference stress method is shown to be appropriate for widespread CDM behaviour, and to progressively become valid as the material ductility is reduced. This trend is accompanied by a shift from modest notch weakening to severe notch weakening. It is also shown that the stress level applied to the bar, and the strength of the dislocation softening damage mechanism, denoted by a second damage variable ω 1, also influences the above behaviour. The paper defines bounds of applicability for the skeletal stress approach to lifetime prediction, and recommends the use of complete CDM finite clement analysis for those situations where breakdown occurs.

Design and assessment of components subjected to creep

The R5 procedure for assessing the high-temperature response of structures is described and recent progress highlighted. The scope and methodology of R5 are compared with those of existing and proposed high-temperature design codes. For defect-free components, R5 provides a shakedown approach intermediate between the elastic and inelastic routes in codes. As the codes give interaction diagrams based on shakedown concepts for particular loading circumstances, the R5 approach may be considered a generalization of existing methods. For defective components, the Reference stress methods recommended in R5 are described. Proposals for the incorporation of similar approaches in other codes are currently being considered, and these are also described.