Reference Stress Concept Research Articles

On elastic-plastic and creep fracture mechanics parameters estimates of non-idealized axial through-wall crack in pressurized pipe

The present paper provides engineering estimates for plastic J-integral and crack opening displacement (COD) of a non-idealized axial through-wall crack (TWC) in pipes based on detailed 3-dimensional finite element (FE) analyses. The behaviors of plastic J-integral and COD of a non-idealized axial TWC in typical pressurized pipes in nuclear power plants were systematically investigated. The FE model and analysis procedure employed in this study were verified by comparing the present FE results with the limited existing solutions for pipes with an idealized axial TWC. Based on the FE results, the new plastic influence functions, h1 and h2, which include the effect of a non-idealized TWC on plastic J-integral and COD, are provided as tabular solutions. By employing the plastic influence functions, plastic J-integral and COD of a non-idealized axial TWC along crack front can be directly predicted based on GE/EPRI method. In the present paper, plastic J-integral and COD estimates based on the reference stress concept have also been suggested. Finally, the estimated results were compared with elastic-plastic FE results by using actual stress-strain data and Ramberg-Osgood constants for TP 316 stainless steel. In addition, the engineering estimates proposed in this study were extended to estimating the creep fracture mechanics parameters at elevated temperature. Based on Norton and RCC-MRx creep models, C*-integral and creep COD rate values predicted from the present engineering solutions were validated by comparing with creep FE results. The results provided in this paper demonstrate that the present estimates can be applied to calculating plastic J-integral and COD, C*-integral, and creep COD rate of a non-idealized axial TWC.

Engineering Approach Based on Reference Stress Concept for Calculating J and Crack Opening Displacement of Complex-Cracked Pipes

In this study, an engineering approach for estimations of fracture mechanics parameters, i.e., J-integral and crack opening displacement (COD), for complex-cracked pipes was suggested based on reference stress concept, where stress-strain data of the material was used to assess structural integrity of complex-cracked pipes. In the present study, new reference loads that can reduce the dependency on strain hardening of the material have been suggested for complex-cracked pipes under each loading mode. By using the proposed optimized reference load for complex-cracked pipes, J-integral and COD estimation procedures have been proposed based on the reference stress concept together with the elastic solutions for complex-cracked pipes. The predicted J-integrals and CODs based on the proposed method have been validated against published experimental data and FE results using actual stress–strain data. Moreover, the predictions using the proposed methods are also compared with those using the existing solutions for simple through-wall cracks (TWCs) based on reduced thickness analogy concept.

Comparison among estimation methods of C* parameter for axially oriented external surface crack in cylinders

C* is usually used to describe the creep crack growth. ASTM E1457 allows C* to be calculated from creep load line displacement rate. However in components it is difficult or impossible to measure load line displacement rate. Therefore for the components C* must be determined by finite element methods or reference stress concepts. Estimates of C* obtained by reference stress methods will depend on the collapse mechanism adopted and therefore several estimations are proposed. This paper presents a numerical study of non-linear fracture mechanics parameter predictions under elevated temperature for axially oriented external surface crack in cylinder. Comparison of C* calculated from FE analysis and different reference methods is conducted. The values of C* obtained from the API579 net section solution are also found to be slightly conservative and give the closest agreement to the F.E. contour integral C*. In addition, the comparison between C* of homogeneous material and TYPE IV cracking is conducted. The difference between homogeneous material and TYPE IV cracking is almost negligible and therefore the reference stress solutions for homogenous material could be applied to estimate C* for TYPE IV cracking.

Assessment methods for Bree-type ratcheting without the necessity of linearization of stresses and strains

This paper proposes methods for assessing Bree-type ratcheting in a cylinder subjected to constant internal pressure and cyclic thermal loading. The proposed methods are elastic analysis-route and elastic–plastic analysis-route. The former is based on the polynomial approximation of the elastic stress distributions for thermal stresses and the reference stress concept for estimating primary stress. The latter elastic–plastic route method is based on the concept of relative elastic core size. The methods proposed were validated by performing elastic–plastic finite element analyses of a smooth cylinder that exhibited Bree-type ratcheting.

Plastic Limit Loads for Slanted Through-Wall Cracks in Cylinder and Plate Based on Finite Element Limit Analyses

The plastic limit load solutions for cylinder and plate with slanted through-wall cracks (TWCs) are developed based on the systematic three-dimensional (3D) finite element (FE) limit analyses. As for loading conditions, axial tension, global bending, and internal pressure are considered for a cylinder with slanted circumferential TWC, whereas, axial tension and internal pressure are considered for a plate and a cylinder with slanted axial TWC. Then, the verification of FE model and analysis procedure employed in the present numerical work was confirmed by employing the existing solutions for both cylinder and plate with idealized TWC. Also, the geometric variables of slanted TWC which can affect plastic limit loads were considered. Based on the systematic FE limit analysis results, the slant correction factors which represent the effect of slanted TWC on plastic limit load were provided as tabulated solutions. By adopting these slant correction factors, the plastic limit loads of slanted TWC can be directly estimated from existing solutions for idealized TWC. Furthermore, the modified engineering estimations of plastic limit loads for slanted TWC are proposed based on equilibrium equation and von Mises yield criterion. The present results can be applied either to diverse structural integrity assessments or for accurate estimation of fracture mechanics parameters such as J-integral, plastic crack opening displacement (COD) and C*-integral for slanted TWC based on the reference stress concept (Kim, et al., 2002, “Plastic Limit Pressure for Cracked Pipes Using Finite Element Limit Analyse,” Int. J. Pressure Vessels Piping, 79, pp. 321–330; Kim, et al., 2001, “Enhanced Reference Stress-Based J and Crack Opening Displacement Estimation Method for Leak-Before-Break Analysis and Comparison With GE/EPRI Method,” Fatigue Fract. Eng. Mater. Struct., 24, pp. 243–254; Kim, et al., 2002, “Non-Linear Fracture Mechanics Analyses of Part Circumferential Surface Cracked Pipes,” Int. J. Fract., 116, pp. 347–375.)

High temperature initiation and propagation of cracks in 12%Cr-steel turbine disks

This work aims to study the crack propagation in 12%Cr steel for turbine disks. Creep CrackGrowth (CCG) tests on CT specimens have been performed to define the proper fracture mechanics whichdescribes the initiation of the crack propagation and the crack growth behaviour for the material at hightemperature. Results have been used to study the occurrence of crack initiation on a turbine disk at the extremeworking temperature and stress level experienced during service, and validate the use of C* integral incorrelating creep growth rate on the disk component, in case C* is numerically calculated through FEM analysisor calculated by the use of reference stress concept.

Fracture prediction in tough polyethylene pipes using measured craze strength

AbstractIn this study, an empirical model is developed that predicts the time to failure for PE pipes under combined pressure and deflection loads. The time‐dependent craze strength of different PE materials is measured using the circumferentially deep‐notched tensile (CDNT) test. In agreement with previous research, results indicate that bimodal materials with comonomer side‐chain densities biased toward high‐molecular‐weight PE molecules exhibit significantly higher long‐term craze strengths. A comparison of currently available PE materials with CDNT samples taken from a PE pipe that failed by slow crack growth in service clearly indicates the superior performance of new‐generation materials. Using measured craze strength data from the CDNT test, a simplified model for predicting failure in buried PE pipes is developed. Extending previous research, the reference stress concept is used to calculate an equivalent craze stress for a pipe subjected to combined internal pressure and deflection loads. Good agreement is obtained between the model predictions and observed failure times in an experimental test‐bed study of pipes under in‐service loading conditions. POLYM. ENG. SCI., 2008. © 2008 Society of Plastics Engineers

A perspective on the design of high-temperature boiler components

Boiler pressure parts are designed to formalize codes such as the ASME Boiler and Pressure Vessel Code. These codes employ a “design-by-rule” approach, which is based on a combination of sound structural mechanics and boiler design and operating experience. These codes have served the industry well, but the need for a number of enhancements has been highlighted by the widespread use of creep strength-enhanced steels, the advent of ultrasupercritical boilers constructed from nickel-based alloys, and the cyclic duty required for some plants. The need for these enhancements is discussed to explain their origin and key challenges that must be tackled to provide robust design methods for the future. In particular, the use of reference stress concepts and design-by-analysis are discussed to highlight some practical issues. Weldments are identified as a particular concern because they are often a life-limiting feature, and since existing code rules do not adequately consider the high-temperature creep failure modes that can arise as a function of geometry, loading and material combination. Associated with the behavior of welds, multiaxial creep rupture is also identified as a topic that requires further study. The discussion illustrates the multidisciplinary nature of design and need for the materials and structural mechanics communities to work together. This should optimize the use of advanced, expensive alloys and reduce component wall thickness, facilitating pressure part manufacture and enhancing operational flexibility without compromising safety.

Representation of the high‐temperature crack tip fields using reference stress concepts

ABSTRACTIn a previous paper, it was shown that an estimation approach to crack tip properties under cyclic creep loading conditions was described, using a methodology based on the linear matching method (LMM). The calculations revealed the possibility of obtaining the crack tip parameters, C* (n), for cracked structures subjected to both mechanical loads and temperatures, using the HRR field criterion as the crack tip condition. In this paper, those calculated values of C* (n) are re‐interpreted and presented in terms of the reference stresses, insensitive to the constitutive models and creep exponent. These reference stress values are compared with those currently used for life assessment of high‐temperature plant, showing that current practice is significantly conservative for thermal loading.

Trends in High Temperature Structural Integrity Assessment

Abstract Failure in components that may contain defects and that operate at elevated temperatures can occur by creep, fatigue, or fast fracture, or some combination of these processes. Frequently, these components include welds and repairs to welds. Codes and standards are available for assessing the structural integrity of these types of components. This paper addresses the main issues of concern in making safety assessments and reliable lifetime predictions for situations where creep processes dominate. Emphasis is placed on the creep component of cracking. Initially, models of crack initiation and growth are reviewed. The creep fracture mechanics parameter C* is used to make predictions. The influence of constraint on the mechanisms responsible for void nucleation and growth is considered and creep crack growth rate laws derived. Methods of calculating C* in components from the plastic fracture mechanics parameter J or, approximately, from stress intensity factor K and limit analysis using reference stress concepts are described. A procedure for making remaining life assessments for cracking into progressively deteriorating material is considered. Techniques for dealing with an initial transient phase, or incubation period, during which damage builds up at a crack tip are presented. An indication of the scatter to be expected in creep crack growth data, for use in sensitivity studies, is provided. The role of residual stress on the early stages of cracking and subsequent crack propagation is discussed.

복합하중이 작용하는 국부감육배관 평가법 개발

Recently authors have proposed a new method to estimate failure strength of a pipe with local wall thinning subject to either internal pressure or global bending. The proposed method was based on the equivalent stress averaged over the minimum ligament in the locally wall thinned region, and the simple scheme to estimate the equivalent stress in the minimum ligament was proposed, based on the reference stress concept. This paper extends the new method to combined internal pressure and global bending. The proposed method is validated against FE results for various geometries of local wall thinning under combined loading. The effect of internal pressure is also investigated in the present study. Comparison of maximum moments, predicted according to the proposed method, with published full-scale pipe test data for locally wall-thinned pipes under combined internal pressure and global bending, shows good agreement.

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

In the previous work carried out by the authors, a new method to estimate failure strength of a pipe with local wall thinning subject to either internal pressure or global bending has been proposed. The proposed method was based on the equivalent stress averaged over the minimum ligament in the locally wall thinned region, and the simple scheme to estimate the equivalent stress in the minimum ligament was proposed, based on the reference stress concept for creep stress analysis. This paper extends the new method to combined internal pressure and global bending. The proposed method is validated against FE results for various geometries of local wall thinning under combined loading. The effect of internal pressure is also investigated in the present study. Comparison of maximum moments, predicted according to the proposed method, with published full-scale pipe test data for locally wall thinned pipes under combined internal pressure and global bending, shows good agreement.

Analysis of cyclic creep and rupture. Part 1: bounding theorems and cyclic reference stresses

Cyclic loading on structures can produce failures not readily predicted by conventional static analysis. Ratcheting or incremental distortion leads to structural failure, and complicates the problems of creep and fatigue prediction. Predicting shakedown, ratcheting, accelerated creep and rupture, for cyclic loading, are the objectives of cyclic stress analysis. Limit load, shakedown and ratcheting analyses provide a comprehensive basis to understand static structural behaviour for ductile inelastic materials, subject to variable loading but excluding inertial dynamic effects. From them we can predict the following failure modes: – Plastic collapse. – Failure to shakedown. – Ratcheting. – Accelerated creep and rupture. This is achieved with a generalisation of the reference stress concept. Conventionally, and for steady loading, the limit load reference stress is the lowest yield stress for which the structure does not collapse. For cyclic loading two definitions are available. The more conservative is the lowest yield stress for which the structure shakes down (behaves elastically). The less conservative is the lowest yield stress for which the structure does not ratchet. They have different meanings and uses. Explaining and justifying the use of cyclic reference stresses to bound creep and rupture is the objective of Part 1. Part 2 gives examples illustrating a range of structural behaviours. The methodology of these papers involves so-called approximate methods at one level, that of inferring limiting or conservative time-dependent behaviour from time-independent elastic–plastic cyclic analyses. The elastic–plastic cyclic analyses themselves are straightforward if tedious. Some ideas and a new analysis technique are available to reduce the trial-and-error.

참조응력개념을 이용한 국부감육배관 평가법 개발

참조응력개념을 이용한 국부감육배관 평가법 개발

Elastic–plastic fracture mechanics method for finite internal axial surface cracks in cylinders

This paper provides two types of engineering J estimation equations for cylinders with finite internal axial surface cracks under internal pressure. The first type is the so-called GE/EPRI type J estimation equation based on Ramberg–Osgood (R–O) materials. Based on detailed 3-D FE results using deformation plasticity, plastic influence functions for fully plastic J components are tabulated for practical ranges of the mean radius-to-thickness ratio, the crack depth-to-length ratio, the crack depth-to-thickness ratio, the strain hardening index for the R–O material, and the location along the semi-elliptical crack front. Based on tabulated plastic influence functions, the GE/EPRI-type J estimation equation along the crack front is proposed and validated for R–O materials. For more general application, for instance, to general stress–strain laws, the developed GE/EPRI-type solutions are then re-formulated based on the reference stress concept. Such a re-formulation provides a simpler equation for J, which is then further extended to combined internal pressure and bending. The proposed reference stress based J estimation equation is compared with elastic–plastic 3-D FE results using actual stress–strain data for a Type 304 stainless steel. Good agreement between the FE results and the proposed reference stress based J estimation provides confidence in the use of the proposed method for elastic–plastic fracture mechanics of pressurised piping.

축방향 관통균열 배관의 새로운 탄소성 J-적분 및 COD 계산식

This paper proposes engineering estimation equations of elastic-plastic J and COD for axial through-wall cracked pipes under internal pressure. Based on detailed 3-D FE results based on deformation plasticity. the plastic influence functions for fully plastic J and COD solutions are tabulated as a function of the mean radius-to-thickness ratio, the normalized crack length, and the strain hardening. Based on these results, the GE/EPRI-type J and COD estimation equations are proposed and validated against the 3-D FE results based on deformation plasticity. For more general application to general stress-strain laws or to complex loading, the developed GE/EPRI-type solutions are re-formulated based on the reference stress concept. Such a re-formulation provides simpler equations for J and COD, which are then further extended to combined internal pressure and bending. The proposed reference stress based J and COD estimation equations are compared with elastic-plastic 3-D FE results using actual stress-strain data for Type 316 stainless steels. The FE results for both internal pressure cases and combined internal pressure and bending cases compare very well with the proposed J and COD estimations.

巨視的非弾性挙動を考慮した多孔板の熱疲労き裂伝ぱ評価

Crack propagation behavior of a perforated plate of normalized and tempered 2 1/4Cr-1Mo steel modeling ligament regions of boiler headers was examined under out-of-phase thermal fatigue at a maximum temperature of 600°C in the air. Inelastic analysis of the perforated plate under the thermal fatigue was carried out, and the nonlinear fracture mechanics parameters such as the J and C* integral were obtained by the line integral method for observed crack distributions. A prediction method for these parameters was proposed, which is applicable to the displacement-controlled condition such as thermal fatigue. In this method, the change of the macroscopic stress-strain relation of the perforated plate with propagating cracks was combined with the reference stress concept under the displacement-controlled condition. The predicted fracture mechanics parameters from this method coincided well with those from the inelastic analysis. The prediction of the crack propagation life on the basis of the proposed method provided a good correspondence with the test results of the perforated plate under thermal fatigue.

Elastic–plastic J and COD estimates for axial through-wall cracked pipes

This paper proposes engineering estimation equations of elastic–plastic J and crack opening displacement (COD) for axial through-wall cracked pipes under internal pressure. On the basis of detailed 3D finite element (FE) results using deformation plasticity, the plastic influence functions for fully plastic J and COD solutions are tabulated as a function of the mean radius-to-thickness ratio, the normalised crack length, and the strain hardening. On the basis of these results, the GE/EPRI-type J and COD estimation equations are proposed and validated against 3D FE results based on deformation plasticity. For more general application to general stress–strain laws or to complex loading, the developed GE/EPRI-type solutions are re-formulated based on the reference stress (RS) concept. Such a re-formulation provides simpler equations for J and COD, which are then further extended to combined internal pressure and bending. The proposed RS based J and COD estimation equations are compared with elastic–plastic 3D FE results using actual stress–strain data for Type 316 stainless steels. The FE results for both internal pressure cases and combined internal pressure and bending cases compare very well with the proposed J and COD estimates.

Crack propagation life prediction of a perforated plate under thermal fatigue

Superheater outlet headers of boilers are well known to be subjected to the cycling of high pressure and high thermal stress during plant operations. Thermal stresses during cyclic operation are generally severest on the inside surface of the ligaments between the stub-tube holes, where many examples of ligament cracking due to thermal fatigue have been found recently. A method to predict the crack propagation life of the ligaments of boiler headers under thermal fatigue has been required. Firstly in this paper, to model the crack propagation behavior of the ligament regions of boiler headers, a perforated plate of normalized and tempered 2 1/4Cr–1Mo steel was examined under out-of-phase thermal fatigue at a maximum temperature of 600°C in the air. Inelastic analysis of the perforated plate under thermal fatigue was carried out, and the nonlinear fracture mechanics parameters such as the J and C ∗ integral were obtained by the line integral for observed cracks. A simplified method was proposed for predicting these parameters under displacement-controlled conditions such as thermal fatigue. In this method, the change of the macroscopic stress–strain relation of the perforated plate with propagating cracks was combined with the reference stress concept under displacement-controlled conditions. The predicted fracture mechanics parameters from this method coincided well with those from the inelastic analysis. The prediction of the crack propagation life on the basis of the proposed method provided a good correspondence with the test results of the perforated plate under thermal fatigue.

Quantification of pressure-induced hoop stress effect on fracture analysis of circumferential through-wall cracked pipes

This paper provides engineering J and crack opening displacement (COD) estimation equations for through-wall cracked (TWC) pipes under internal pressure and under combined internal pressure and bending. Based on selected 3-D FE calculations for the TWC pipe under internal pressure using power law materials, elastic and plastic influence functions for fully plastic J and COD solutions are tabulated as a function of the normalised crack length and the mean radius-to-thickness ratio. These developed GE/EPRI-type solutions are then re-formulated based on the reference stress concept. Such re-formulation not only provides simpler equations for J and COD estimation, but also can be easily extended to combined internal pressure and bending. The proposed reference stress based J and COD estimation equations are compared with elastic–plastic 3-D FE results using actual stress–strain data for Type 316 stainless steels. The FE results for both internal pressure cases and combined internal pressure and bending cases compare very well with the proposed J and COD estimates.