The stress intensity factor study of an elliptical cracked shaft

The stress intensity factors of an elliptical crack front embedded with a round bar have been evaluated by collapsed singular element with detailed mesh on crack front and appropriating adjacent area. Using newly developed model with sweeping capability, the mesh of the cracked shaft model can be easily built. The three-dimensional finite element analyses are then performed to calculate the stress intensity factors of elliptical crack front of a round bar subjected to tension and bending. The ratio of crack depth to shaft diameter is considered in the range between 0.1 and 0.6, and the elliptical ratio of crack area is in the range between 0.0 and 1.0. By comparing the stress intensity factors for different crack profiles with appropriated published results, the variation of stress intensity factors on the center and near edge location have been discussed. It also addresses the related change of the equivalent elliptical ratio of crack profile with respect to crack depth ratio. Based on stress intensity factor results, the three-parameter stress intensity factor relationships of the crack front are then determined by curve fitting technique.     

Random thermal fatigue in fast breeder reactor: a narrow-band spectrum

Thermal fatigue crack growth in a fast breeder reactor is theoretically investigated with the aid of probabilistic fracture mechanics (PFM) under the conditions that (i) the temperature variation is a narrow-band stationary process and (ii) the crack grows owing only to the peak stress variation. First, a statistical property of residual life of the component with single crack is derived in an analytical form with the aid of an extended Markov approximation method, which is an efficient mathematical technique in PFM. Next, discussion is carried out on the generalization of the primitive model to the case with plural cracks, where a stress relaxation factor is introduced to express a stress intensity factor of each crack. Finally, a numerical example is shown to examine the quantitative behavior of the component's residual life, and sensitivity analysis is performed with respect to some model parameters.     

Prediction of fatigue crack growth and experimental result on overlaod retardation

The phenomena of crack growth retardation are frequently observed under variable amplitude or irregular loading fatigue tests. This paper describes a prediction method on crack growth retardation caused by an overload during fatigue loads.The prediction reported in this paper is performed by the following procedure using the yield strength and vs. ΔK relationship of the material.

1. (1) Determination of the residual stress distribution caused by cyclic load and overload based on the Dugdale model.

2. (2) Determination of the effective residual stress intensity factor and effective stress intensity range (ΔK_eff).

3. (3) Prediction of the crack growth rate using ΔK_eff and vs. ΔK relationship of the material.

From the viewpoint to apply the prediction to a structural component, experiments have been carried out on steel pipes with an axial through thickness crack, which are subject to an overpressure during cyclic pressure. In the paper, the experimental results are compared with the prediction.     

Fatigue crack growth under continuous radiation

This paper examines the possibility that a drastic reduction of the rate of propagation of a fatigue crack can occur if a sample undergoing failure is simultaneously irradiated with high energy particles. For an effect to exist it is necessary that the rate of irradiation damage and the frequency of the cyclic stress are such that appreciable irradiation hardening occurs within the plastic crack tip zone during each stress cycle. The analysis is based on a fatigue crack growth theory of one of the authors (JW) that considers the true stress intensity factor at a fatigue crack tip. Although in a post-irradiation fatigue experiment appreciable irradiation hardening will not necessarily produce a decrease in the fatigue crack growth rate, a decrease in the fatigue crack growth rate should always occur in material with a Paris law exponent larger than two if the irradiation takes place continuously during a fatigue test that is carried out at temperatures at which annealing processes are relatively slow.     

The frequency effect on the fatigue crack growth rate of 304 stainless steel

Under cyclic loading condition, the fatigue crack growth (FCG) rate governed by stress intensity factor and stress ratio is well known; Walker’s equation, Forman’s equation and Elber’s equation are typical formulae to describe the fatigue crack growth rate. However, the loading frequency effect on the fatigue crack growth rate has yet to be explored. Recently, studies have focused on the loading frequency effect on some visco-elastic materials, and have provided a clearer understanding of the frequency effect on the fatigue crack growth rate. In a physical sense, knowledge about the loading frequency effect on the fatigue crack growth rate for 304 stainless steel is still lacking. James conducted a lot of experiments, and through data analysis, he concluded an evaluation equation which is based upon the experimental illustration. In this study, the physical properties of the material are used to illustrate the modification of fatigue crack growth rate, and a new formula which is based upon the modified Forman’s equation, is provided.     

Prediction of residual stress distributions due to surface machining and welding and crack growth simulation under residual stress distribution

In nuclear power plants, stress corrosion cracking (SCC) has been observed near the weld zone of the core shroud and primary loop recirculation (PLR) pipes made of low-carbon austenitic stainless steel Type 316L. The joining process of pipes usually includes surface machining and welding. Both processes induce residual stresses, and residual stresses are thus important factors in the occurrence and propagation of SCC. In this study, the finite element method (FEM) was used to estimate residual stress distributions generated by butt welding and surface machining. The thermoelastic-plastic analysis was performed for the welding simulation, and the thermo-mechanical coupled analysis based on the Johnson-Cook material model was performed for the surface machining simulation. In addition, a crack growth analysis based on the stress intensity factor (SIF) calculation was performed using the calculated residual stress distributions that are generated by welding and surface machining. The surface machining analysis showed that tensile residual stress due to surface machining only exists approximately 0.2 mm from the machined surface, and the surface residual stress increases with cutting speed. The crack growth analysis showed that the crack depth is affected by both surface machining and welding, and the crack length is more affected by surface machining than by welding.     

Fatigue crack growth under residual stress field in low-carbon steel

The influence of residual stress on fatigue crack growth was experimentally and analytically investigated for surface crack. Fatigue tests were performed on straight pipe components of low-carbon steel having a circumferential inner surface crack in laboratory air environment. Some of the test pipes had been subjected to special heat treatments so as to have compressive or tensile residual stresses along the inner surface.The results show that the compressive residual stress remarkably suppresses the surface crack growth while the tensile residual stress doesn't accelerate the crack growth very much.The crack growth analyses were conducted by the application of power relationship between ΔK and . The stress intensity factors due to the non-linear stress field were calculated by the weight function method. The analyses resulted in a confirmation of the behavior of the crack growth observed in the experiments.     

Crack arrest in high cycle thermal fatigue crazing

Thermal crazing in high cycle thermal fatigue due to thermal fluctuation in residual heat removal (RHR) system of some nuclear power plants is explained by crack arrest in the depth due to a decreasing stress intensity factor. This is related to high frequencies of thermal loading. An attempt has been made through a parametric study to acquire some knowledge about the loading, knowing the crack depth. For this purpose, analytical as well as finite element simulations of crack propagation in 2D- and 3D-semi-elliptical cracks have been performed. In periodic loading, bounds for the number of cycles to fatigue life are proposed. Moreover, it is shown that in the absence of mean stress, fatigue damage in RHR may be produced in the macroscopic elastic-plastic regime. Finally, it is shown by FE simulations that for a semi-elliptical crack, a small error on stress intensity factor may result in significant error on crack length at high number of cycles, due to error accumulation cycle by cycle. Moreover in this paper is given the reason as to why shielding effect has not been taken into account in the study of crack arrest in RHR.     

The effect of a single tensile overload on stress corrosion cracking growth of stainless steel in a light water reactor environment

It has been found that a single tensile overload applied during constant load amplitude might cause crack growth rate retardation in various crack propagating experiments which include fatigue test and stress corrosion cracking (SCC) test. To understand the affecting mechanism of a single tensile overload on SCC growth rate of stainless steel or nickel base alloy in light water reactor environment, based on elastic-plastic finite element method (EPFEM), the residual plastic strain in both tips of stationary and growing crack of contoured double cantilever beam (CDCB) specimen was simulated and analyzed in this study. The results of this investigation demonstrate that a residual plastic strain in the region immediately ahead of the crack tips will be produced when a single tensile overload is applied, and the residual plastic strain will decrease the plastic strain rate level in the growing crack tip, which will causes crack growth rate retardation in the tip of SCC.     

Thermoelastic stresses in pellet fragments and conditions for fragments formation

A finite element code CHICAM in which thermal and elastic effects are analysed together has been used to calculate the thermoelastic stress fields in whole and hollow pellets in a radial temperature field of approximately parabolic shape. In addition, the residual thermoelastic stresses were calculated for whole and hollow pellets containing a crack and for various geometries of pellet fragments. The residual stress fields in the pellet fragments differ very considerably from the axial symmetrical stress fields of the whole and hollow pellets. The stress intensity factor K_I is given as a function of the crack length for the whole pellet and for the half pellet showing that during the first rise to power a fuel pellet will fracture into several pie-shaped fragments not necessarily of the same angular width. The calculations show that the residual stress fields in fractured pellets cannot be simulated by a stress and strain analysis with axial symmetry.     

焊接残余应力对316LN不锈钢应力腐蚀裂纹扩展速率的影响

核电站不锈钢管道焊接过程中引入的残余应力对焊接接头的应力腐蚀开裂性能有较大影响。本文针对一AP1000主管道316LN不锈钢焊接模拟件进行残余应力分析和应力腐蚀裂纹扩展速率测量,得到了焊后原始状态和去应力热处理状态的焊接热影响区材料在高温高压水中的应力腐蚀裂纹扩展速率。实验结果表明,焊接残余应力明显提高了热影响区的应力腐蚀裂纹扩展速率,且在含氢的压水堆一回路正常水化学下焊接残余应力的影响更加显著。     

核电蒸汽发生器接管嘴外表面裂纹应力强度因子计算

核电蒸汽发生器（SG）接管嘴处由于其结构的特殊性,易在制造及服役过程中产生缺陷。为评价该处缺陷的安全性,需要工程可用的应力强度因子解。本文以核电SG接管嘴外表面裂纹为研究对象,采用有限元方法（FEM）及RSE-M规范计算获得了不同方向及尺寸裂纹在内压、弯矩和温度载荷下的等效应力强度因子值,并分析了不同载荷作用下等效应力强度因子在裂纹前沿的分布规律。将计算结果与RSE-M规范的直管应力强度因子解进行比较,发现RSE-M规范的直管应力强度因子计算方法可保守地应用于SG接管嘴处裂纹,并且随着裂纹深度的增加保守度增大。为实现SG接管嘴处缺陷安全的准确评价,基于有限元计算和RSE-M影响系数法给出了适用于SG接管嘴外表面裂纹的应力强度因子计算方法,该方法可以为SG的设计与维护提供指导。      

基于ASME和RSE-M规范的含平面缺陷奥氏体不锈钢核级管道剩余寿命预测方法的数值对比研究

核级管道在加工和安装环节可能存在不同的缺陷。此外,由于核电厂运行条件的影响,管道中可能存在少量缺陷,如裂缝。需要合理预测评估含缺陷管道的剩余寿命,以便安排更换方案,避免对核电厂的效率造成严重影响。本文根据ASME和RSE-M规范,在应力强度因子计算、裂纹扩展分析和裂纹稳定性评价等环节,通过数值对比研究了含有平面缺陷的奥氏体不锈钢核级管道的剩余寿命评估方法,为类似工作提供参考。      

Defect assessment procedures at high temperature

Within Nuclear Electric PLC, a comprehensive assessment procedure for the high-temperature response of structures is being produced. The procedure is referred to as R5 and is written as a series of step-by-step instructions in a number of volumes. This paper considers in detail those parts of R5 which address the behaviour of defects. The defect assessment procedures may be applied to defects found in service, postulated defects, or defects formed during operation as a result of creep-fatigue loading. In the last case, a method is described for deducing from endurance data the number of cycles to initiate a crack of a specified size. Under steady loading, the creep crack tip parameter C* is used to assess crack growth. Under cyclic loading, the creep crack growth during dwell periods is still governed by C* but crack growth due to cyclic excursions must also be included. This cyclic crack growth is described by an effective stress intensity factor range. A feature of the R5 defect assessment procedures is that they are based on simplified methods and approximate reference stress methods are described which enable C* in a component to be evaluated. It is shown by comparison with theoretical calculations and experimental data that reliable estimates of C* and the associated crack growth are obtained provided realistic creep strain rate data are used in the reference stress approximation.     

Primary water stress corrosion cracking behaviors in the shot-peened Alloy 600 TT steam generator tubings

The effect of compressive residual stress on the primary water stress corrosion cracking behavior was investigated, based on the J-1 and J-2 nuclear power plant data. The following analyses were performed such as: (i) Weibull slope; (ii) crack growth rate; (iii) average crack length; (iv) crack length distribution. Alloy 600 TT exhibits strong heat to heat variations in its sensitivity to PWSCC. Crack growth rate was retarded after shot-peening. The compressive residual stress induced by shot-peening was more effective on new, short cracks, than on existing, long cracks. However, whether the ‘new’ cracks were initiated after peening is an unresolved issue, due to the present ECT sensitivity limit.     

3D analyses of surface flaws in thick-walled reactor pressure-vessels using displacement-hybrid finite element method

Solutions of stress intensity factors for external and internal unpressurized and pressurized surface cracks in internally pressurized thick-walled reactor pressure vessels are determined directly by a three-dimensional displacement-hybrid finite element method. The finite element method is based on a rigorous modified variational principle of the total potential energy, with arbitrary element interior displacements, interelement boundary displacements and element boundary tractions as variables. Special crack front elements, developed using the hybrid displacement model, which contain the proper square root and inverse square root variations of displacements and stresses, are used in this analysis and the three stress intensity factors, K_I, K_II and K_III are solved directly along with the unknown nodal displacements. Stress intensity factor variations for pressurized and unpressurized semi-elliptical inner surface cracks in pressurized cylinders with crack aspect ratios of 0.2 and 1.0, crack depth to cylinder wall thickness ratios of 0.5 and 0.8 and outer to inner diameter ratios of 1.5 and 2.0, are presented. Also, for unpressurized outer surface cracks in pressurized cylinders, the solutions are presented for crack aspect ratios of 0.6 and 1.0, crack depth to cylinder wall thickness ratios of 0.4, 0.6 and 0.8, and outer to inner diameter ratio of 1.5.     

Crack growth determination on laboratory components

The present work outlines the reasoning behind the selection of laboratory component tests for the validation of design and remanent life models governing crack growth behaviour. For the case of creep crack growth a ferritic and an austenitic alloy have been studied and a reference stress based solution used to successfully relate the stress rupture behaviour of internally and externally, axially and circumferentially notched, tubular components to base line creep data. Using the same reference stress based approach, it has been demonstrated that the notched component creep crack growth rates exhibit the same C^* dependence as conventional compact tension specimens. For 316L stainless steel components subjected to thermal fatigue conditions simulative of the fusion reactor first wall, a modified version of the superposition method of Buchalet and Bamford has been applied to estimate the stress intensity range as a function of crack length during the test. By this approach the crack growth rate dependency on stress intensity range for a variety of notch geometries is seen to be broadly in line with the conventional specimen mechanical fatigue data. Recent studies of crack growth under combined creep and thermal fatigue conditions are described and some early results are reported.     

Fracture mechanics analysis of iodine-induced crack growth in Zircaloy-4 tubing between 500 and 700°C

Low ductility failure of zircaloy tubing due to iodine-induced stress corrosion cracking (SCC) can occur up to about 700°C. The time-to-failure behavior of Zircaloy-4 cladding tubes containing iodine has been described by the elastic-plastic fracture mechanics model CEPFRAME for the temperature region 500 to 700°C. The model includes an empirically-determined computation method for the incubation period of crack formation, as a portion of the time-to-failure, as well as an elastic-plastic model for describing crack growth due to iodine-induced SCC. The total life time of the cladding tube is obtained by adding the crack initiation and crack propagation periods. The incubation period is a temperature-dependent function of both the depth of surface damage (both fabrication pits and machined notches) and the applied load, and is 40 to 90% of the time-to-failure. The elastic-plastic crack growth model is a modified version of the stress intensity K_I-concept of linear-elastic fracture mechanics. The extensions of this concept take into account a plastic strain zone ahead of the crack tip, which effectively increases the crack depth, and in addition, a dynamic correction factor for the crack geometry which is essentially a function of the effective crack depth. Unstable crack growth is predicted to occur when the residual cross section reaches plastic instability.Model results show good agreement with experimental data of tube burst tests at 500, 600, and 700°C. The crack growth velocity at all three temperatures is a power function of stress intensity ahead of the crack tip; the exponent is 4.9. The model can estimate time-to-failure of as-received cladding tubes containing iodine within a factor of 2. Application of the model to temperatures below 500°C is possible in principle. Due to the increasing scatter in experimental data, the structural transformation of the cladding by recrystallization, and the growing importance of creep strain, CEPFRAME has an upper temperature limit of approximately 650°C. The model is suitable for use in computer codes describing LWR fuel rod behavior during reactor transients and accidents.     

Probabilistic fracture mechanics

This paper develops the methodology for probabilistic fracture mechanics analysis (PFM) of structural components with crack-like imperfections. Details are given for the development and application of both a simple nomographic method and a basic numerical tool for PFM applications. The tool is a computer program that uses Monte-Carlo simulation to predict the probability distribution of a structural performance parameter from known distributions of input parameters used to model the problem. The structural performance parameter might be the strength margin (strength minus stress), the life ratio (actual fatigue life divided by design fatigue life), or any other relevant model of the failure modes. Two illustrative applications based on linear elastic fracture mechanics are included to demonstrate the utility of PFM to problems of interest to the electric power generation industry.The first example selects the mean yield strength of an alloy in order to minimize the probability of failure for a hypothetical component with two failure modes, yielding and brittle fracture. The example shows that no single value of mean yield stress or of yield-related safety factor, such as specified as part of conventional engineering practice, suffices to minimize failure for all combinations of working stress and flaw size distribution. PFM analysis is required to compute the optimum value of mean yield stress for a given working stress and material quality (flaw size distribution). A second example is presented for which the residual life of a turbine rotor is assumed to be related to three parameters. The parameters are applied stress, material crack growth rate, and initial flaw size. Known variations of the input parameters are translated into variations in residual life. The residual life distribution is required to formulate improved fatigue design criteria. The effects on the turbine life distribution of mutual interdependence of the input random variables and of finite crack initiation life are examined. The second example points out the need for and current unavailability of required input data. It is recommended that data collection efforts be increased to quantify the variational characteristics of the required input parameters, as well as mean, typical, or worst-case values.     

Fatigue crack growth behavior of weld heat-affected zone of type 304 stainless steel in high temperature water

The fatigue crack growth behavior of the weld heat-affected zone (HAZ) of type 304 stainless steel in high temperature water which simulates the boiling-water reactor environment was investigated to clarify the effects of welding residual stress, cyclic frequency f and thermal aging on crack growth rate. A lower crack growth rate of the HAZ than of the base metal was observed in both the high temperature water and the ambient air caused by the compressive residual stress. The crack closure point was measured in the high temperature water. The effect of the welding residual stress on the crack growth rate of the HAZ can be evaluated separately from the environmental effect through the crack closure behavior. The high temperature water increased the crack growth rate at a cyclic frequency of 0.0167 Hz but did not affect it much at 3 and 5 Hz. The crack growth behavior of the thermally aged HAZ at 400 °C for 1800 h was almost the same as that of the unaged material tested at 0.0167 and 5 Hz in the high temperature water.