An explicit integral expression for the stress intensity factor of a semi-elliptic surface crack subjected to thermal transient loading

An explicit integral expression for the stress intensity factor of a semi-elliptic surface crack in a plate subjected to thermal transient loading was developed. The stress intensity factor of a semi-elliptic surface crack in a plate, which is exposed to a step change of fluid temperature, was calculated on the basis of the weight function method. The change of the stress intensity factor for a semi-elliptic surface crack subjected to an arbitrary change of the boundary fluid temperature was obtained by Duhamel integration for the product of the step function result and the time varying fluid temperature. The result obtained by the present method has shown good agreement with those obtained by the influence function method. As a practical application, a parametric analysis was performed for the crack behavior during the emergency cool down of reactor coolant in the reactor pressure vessel. Also, the present expression can be effectively applied to the simulation of fatigue crack growth of a semi-elliptic surface crack subjected to various thermal transient loading.     

Development of new analytical solutions for elastic thermal stress components in a hollow cylinder under sinusoidal transient thermal loading

For the analysis of high-cycle thermal fatigue due to striping (such as has been observed due to turbulence at mixing tees of class 1–2–3 piping of nuclear power reactors) it can be necessary to consider the time-dependent temperature gradient within the pipe wall thickness rather than just at the surface. To address this, a set of analytical solutions with several new features has been developed for the temperature field and the associated elastic thermal stress distributions for a hollow circular cylinder subjected to sinusoidal transient thermal loading at the inner surface. The approach uses a finite Hankel transform and some properties of Bessel functions. The analytical predictions have been successfully benchmarked by comparison with results from finite element analysis, and also with some results of independent studies.     

The Influence of Graded Coatings on the Thermal Stress Intensity Factors of an Oblique Crack in a Semi-Infinite Substrate Subjected to Local Heating on the Boundary

Thermally induced singular behavior of an arbitrarily oriented crack in a homogeneous substrate overlaid with a functionally graded coating is considered, within the framework of linear plane thermoelasticity. It is assumed that the graded coating/substrate system is subjected to steady-state thermal loading applied over a finite region at the coating surface and the crack in the substrate is thermally insulated, disturbing the prescribed heat flow. Based on the method of Fourier integral transform and the coordinate transformations of basic field variables in thermoelasticity equations, formulation of the crack problem is reduced to two sets of Cauchy-type singular integral equations for temperature and thermal stresses in the coated medium. In the numerical results, the main emphasis is placed on the investigation of influences of loading, geometric, and material parameters of the coated system on the variations of mixed-mode thermal stress intensity factors. Further addressed are the probable cleavage angles for the incipient growth of the original crack and the corresponding values of effective tensile-mode stress intensity factors.     

Predictions for fatigue crack growth life of cracked pipes and pipe welds using RMS SIF approach and experimental validation

The objective of the present study is to understand the fatigue crack growth behavior in austenitic stainless steel pipes and pipe welds by carrying out analysis/predictions and experiments. The Paris law has been used for the prediction of fatigue crack growth life. To carry out the analysis, Paris constants have been determined for pipe (base) and pipe weld materials by using Compact Tension (CT) specimens machined from the actual pipe/pipe weld. Analyses have been carried out to predict the fatigue crack growth life of the austenitic stainless steel pipes/pipes welds having part through cracks on the outer surface. In the analyses, Stress Intensity Factors (K) have been evaluated through two different schemes. The first scheme considers the ‘K’ evaluations at two points of the crack front i.e. maximum crack depth and crack tip at the outer surface. The second scheme accounts for the area averaged root mean square stress intensity factor (K_RMS) at deepest and surface points. Crack growth and the crack shape with loading cycles have been evaluated. In order to validate the analytical procedure/results, experiments have been carried out on full scale pipe and pipe welds with part through circumferential crack. Fatigue crack growth life evaluated using both schemes have been compared with experimental results. Use of stress intensity factor (K_RMS) evaluated using second scheme gives better fatigue crack growth life prediction compared to that of first scheme. Fatigue crack growth in pipe weld (Gas Tungsten Arc Welding) can be predicted well using Paris constants of base material but prediction is non-conservative for pipe weld (Shielded Metal Arc Welding). Further, predictions using fatigue crack growth rate curve of ASME produces conservative results for pipe and GTAW pipe welds and comparable results for SMAW pipe welds.     

Simulation of thermal fatigue damage in a 316L model pipe component

To contribute to the development of improved methods for assessing possible thermal fatigue damage in nuclear plant piping systems, a unique set of crack growth data has been generated for tubular test pieces in 316L(N) stainless steel subjected to cyclic thermal loads in a specially designed rig. By accurate modelling of the thermal loads and non-linear material behaviour using the finite element method, it was possible to reliably estimate the number of cycles to initiation, using standard isothermal fatigue life curves. To simulate crack growth, an engineering method was applied using published K solutions for semi-elliptical surface cracks and via 3-D elastic–plastic cracked-body analysis of selected scenarios. It was established that conservative estimates of the thermal fatigue crack growth can be obtained using the engineering model in conjunction with an upper bound fatigue crack growth law.     

基于有限元仿真的船用单缸柴油机排气管开裂分析及改进

针对某船用单缸柴油机排气管在试验过程中出现开裂的问题,采用有限元方法,考虑材料的非线性因素,对排气管部件进行约束模态计算及热机耦合和振动疲劳计算,分析引起排气管开裂的主要原因。结果表明:排气管开裂位置受温度梯度影响,处于应力集中的薄弱区域,当振动幅度较大时,安全系数过小,易发生疲劳破坏。通过在管接部件上增加支撑提高刚度,减小排气管振动,避免了排气管疲劳开裂。后续试验验证了改进措施有效。     

Modelling crack growth for creep and fatigue loading

Estimates of creep crack growth in engineering components under steady load conditions are usually based on the application of fracture mechanics concepts. In particular the creep parameter C* has become widely used together with creep crack growth data obtained from laboratory tests. There are now a number of practical methods to utilise experimental data. For high temperature components, which are subjected to cyclic (fatigue) as well as creep loading, the estimation of the fracture mechanics parameters becomes much more difficult, and consequently the extent to which the growth of pre-existing cracks grow by creep and fatigue is difficult to quantify. In this paper the response of Type 316L stainless steel is examined. This material progressively strain hardens under reversed cyclic loading, and the creep behaviour also changes. Using uniaxial fatigue and creep results, fracture parameter maps are developed to establish the appropriate regimes for creep-fatigue crack growth. Using the maps a model is developed which can predict the combined effect of fatigue and creep on crack growth. The implications of the model are discussed in relation to the limitations of obtaining results from laboratory tests at short times, and the assessment of practical engineering components.     

Green's function approach for crack propagation problem subjected to high cycle thermal fatigue loading

An efficient numerical approach using Green's function for the analysis of crack propagation under thermal transient load has been presented. The present approach based on multi-Green's functions pre-determined for each stage of the incremental crack growth substantially shortens the calculation time of the stress intensity factor (SIF) ranges. It was shown that the Green's function method (GFM) can be efficiently used to evaluate not only thermal stresses for fatigue analysis but also the SIF for crack propagation analysis. The crack propagation analysis results have been compared with those of the actual observation for the piping structure subjected to thermal striping load in a liquid metal fast breeder reactor. It was shown that the function determined at a fixed temperature can be applied to a relatively wide range of temperatures because of the compensation effect of the material properties, that is, some properties increase while the others decrease as the temperature increases.     

Investigation Methods for Thermal Shock Crack Problems of Functionally Graded Materials–Part II: Combined Analytical-Numerical Method

Fractures phenomena can be often found in functionally graded materials (FGMs) subjected to thermal shock loadings. This paper aims to develop a set of analytical-numerical methods for analyzing the mixed-mode thermal shock crack problems of a functionally graded plate (FGP). First, a domain-independent interaction energy integral method is developed for obtaining the mixed-mode transient thermal stress intensity factors (TSIFs). A perturbation method is adopted to obtain the transient temperature field. Then an analytical-numerical method combining the interaction energy integral method, a perturbation method, and the finite element method is developed to solve the present crack problem. Particularly, the influences of the materials parameters, crack length, and crack angle on the TSIFs and the crack growth angle are investigated. The results show that the present analytical-numerical method can be used to solve the thermal shock crack problem with high efficiency. The present work will be significant for the fracture mechanics analysis and design of FGM structures.     

Transient Response of a Cracked Piezoelectric Strip Under Thermoelectric Loading

In this study, the theoretical analysis of a transient piezothermoelastic problem is developed for a piezoelectric strip with a parallel crack under static electric loading and thermal shock loading conditions. The crack faces are supposed to be insulated thermally and electrically. By using both the Laplace transform and the Fourier transform, the thermal and electromechanical problems are reduced to a system of singular integral equations, respectively, which are solved numerically. Some numerical results for the temperature change, the stress and electric displacement distributions, and the energy density factor as well as the stress and electric displacement intensity factors in a transient state are shown in figures.     

电站锅炉再热集汽箱管路的温度测量分析

为研究125MW燃煤发电机组锅炉再热器放空管和疏水管与集汽箱连接这座的角焊缝热疲劳裂纹，对一台420t/h炉再热器集汽箱的放空管和疏水这管壁温度进行了测量，证实在变工况运行时，此处的焊缝多次经受温差应力作用，便会遭受破坏而产生裂纹。在此基础上提出了预防裂纹的措施。     

CIRCUMFERENTIAL CRACK PROBLEM FOR AN FGM CYLINDER UNDER THERMAL STRESSES

The main objective of this study is to determine the stress intensity factors associated with a circumferential crack in a thin-walled cylinder subjected to quasi-static thermal loading. The cylinder is assumed to be a functionally graded material. In order to make the problem analytically tractable, the thin-walled cylinder is modeled as a layer on an elastic foundation whose thermal and mechanical properties are exponential functions of the thickness coordinate. Hence a plane strain crack problem is obtained. First temperature and thermal stress distributions for a crack-free layer are determined. Then using these solutions, the crack problem is reduced to a local perturbation problem where the only nonzero loads are the crack surface tractions. Both internal and edge cracks are considered. Stress intensity factors are computed as functions of crack geometry, material properties, and time.     

Tearing–fatigue interactions in 316L(N) austenitic stainless steel

This paper presents the results from a programme of tearing, fatigue and tearing–fatigue tests performed on specimens from a 316L(N) stainless steel plate. All tests were carried out at ambient temperature. The experimental results have been compared with assessments performed using current guidance within the R6 defect assessment method. The work has shown that there is some evidence that fatigue cycling modifies the JR-curve behaviour of this material. In most cases, the data lie approximately 20–30% above the base-line JR-curve. However, whilst there may be a modest influence of fatigue crack growth on the ductile tearing characteristics, it is difficult to separate this from experimental scatter. In tearing–fatigue tests performed at a stress ratio, R=0.2, ductile tearing reduces the fatigue crack growth rates by up to 50%. This is likely to result from the presence of a residual compressive zone at the crack-tip, and increased crack closure due to the irregular and non-matching fracture surfaces generated by the ductile crack growth mechanisms. For R=0.1 tearing–fatigue tests, fatigue crack growth rates are apparently enhanced by a factor up to of 10, particularly during the latter stages of the tests when ΔK>60 MPam. This is likely to result from: (i) loading being in the elastic–plastic regime where the J-integral (rather than K) characterises the crack-tip fields, (ii) increments of ductile tearing which may occur during each fatigue cycle, and (iii) crack blunting which reduces crack closure effects. For the R=0.2 tearing–fatigue tests, the linear summation approach described in R6 provides a consistently conservative prediction of ductile, fatigue and total crack growth during the tests. However, for the R=0.1 tearing–fatigue tests, the Paris law under-predicts fatigue crack growth rates. This may be corrected by using the Kaiser equation, which acknowledges loading in the elastic–plastic regime and incorporates incremental growth due to tearing as well as fatigue. R6 provides conservative predictions of instability for the CT specimen geometry tested in the current programme, both in terms of the critical crack growth and load required for instability to occur.     

CRACK ARREST ANALYSIS UNDER CYCLIC THERMAL SHOCK FOR AN INNER-SURFACE CIRCUMFERENTIAL CRACK IN A FINITE-LENGTH THICK-WALLED CYLINDER

This article presents a crack arrest depth analysis under cyclic thermal shock for an inner-surface circumferential crack in a finite-length thick-walled cylinder with rotation-restrained edges. The inside of the cylinder is cooled from a uniform temperature distribution. The effects of heat transfer conditions on the maximum transient stress intensity factor for the problem were investigated with systematical evaluation methods formerly developed. Then, under an assumption of a tentative threshold stress intensity range j K th together with the Paris law, the crack arrest depth under cyclic thermal stress was evaluated. The results suggested the existence of an upper limit for the normalized crack arrest depth, independent of the cylinder material in an engineering sense. Finally, the validity of applying j K max h j K th as a crack arrest criterion under cyclic thermal shock was confirmed by fatigue tests under mechanical loads equivalent to those induced by cyclic thermal shock.     

The potential drop method for monitoring crack growth in real components subjected to combined fatigue and creep conditions: application of FE techniques for deriving calibration curves

The potential drop technique is a robust method to provide continuous in situ crack growth monitoring of real power-plant components. For a correct assessment of the crack depth, accurate calibration curves for the geometry at hand are required. The problem entails determining the electrical potential field in a body usually characterised by a complicated geometry as a function of the growing crack. Finite element analysis procedures are first applied to optimise the technique (i.e. to determine the best location for the PD leads) and secondly to provide theoretical calibration curves. The validity of this procedure has been assessed in laboratory component tests under both thermal fatigue and multiaxial creep loading. Post-test measurements of the crack depth underline the accuracy of the FE calibration technique.     

Some aspects of thermal fatigue in stainless steel

This paper is concerned with the analysis of failures in the moderator circuit branch piping of the ATUCHA-1 pressurized heavy water reactor (PHWR), which is made of austenitic steel to DIN 1·4550 specification (similar to AISI 347). These failures are considered to result from thermal fatigue processes induced by fluctuations in a zone where stratified temperature layers occurred, the fluctuations being associated with variations in moderator flow.The first section evaluates the possibility of cracking due to thermal fatigue phenomena and concludes that under service conditions a crack may initiate and grow through 7 mm thickness of the branch pipe. In laboratory thermal fatigue tests that simulated the thermomechanical conditions for such a component, the number of cycles required to initiate a thermal fatigue crack in a notched modified standard fatigue specimen was about 10³. This value may be used to give a conservative prediction of the number of thermal cycles for crack initiation in actual branch pipes, including those subject to the cold plug condition which is produced in some emergency shut-down and valve testing situations.It was also demonstrated that beyond a crack depth of 7 mm stress corrosion cracking is the main process in further crack propagation. The relevance of this prediction is confirmed by microfractographic observations, since the brittle nature of the fracture surfaces under service conditions appears very different from the transgranular ductile striations found in both thermal and mechanical fatigue test specimens as a result of interacting environmental effects.     

Investigation Methods for Thermal Shock Crack Problems of Functionally Graded Materials–Part I: Analytical Method

In most published papers, in order to obtain the analytical solution of the crack problems in functionally graded materials (FGMs), the thermomechanical properties of FGMs are usually assumed to be very particular functions and, hence, may not be physically realizable for many actual material combinations. Very few analytical methods can be used to solve the thermal shock crack problem of an FGM cylindrical shell or plate with general thermomechanical properties. In this article, a set of analytical methods is proposed for the thermal shock crack problem of an FGM plate or cylindrical shell with general thermomechanical properties. The crack problem of a cylindrical shell is modeled by a plate on an elastic foundation. Greatly different from previous studies, a set of analytical methods using both the perturbation method and a piecewise model are developed to obtain the transient temperature field and thermal stress intensity factor (TSIF). The perturbation method is applied to deal with the general thermal properties and the piecewise model is used to deal with the general mechanical properties. In the analytical procedure, integral transform, the residue theorem, and the theory of singular integral equation are used. Several representative examples are considered to check the capability of the present method. The transient thermal shock behavior of a ZrO₂/Ti-6Al-4 V FGM plate with a surface crack and a Rene 41-Zirconia FGM cylindrical shell with a circumferential crack are analyzed.     

The inhibitory effect of carbon monoxide contained in hydrogen gas environment on hydrogen-accelerated fatigue crack growth and its loading frequency dependency

The effect of carbon monoxide (CO) contained in H₂ gas as an impurity on the hydrogen-accelerated fatigue crack growth of A333 pipe steel was studied in association with loading frequency dependency. The addition of CO to H₂ gas inhibited the accelerated fatigue crack growth due to the hydrogen. The inhibitory effect was affected by the CO content in the H₂ gas, loading frequency, and crack growth rate. Based on these results, it was revealed that the inhibitory effect of CO was governed by both competition between the rate of fresh surface creation by the crack growth and the rate of coverage of the surface by CO and time for hydrogen diffusion in the material to the crack tip with reduced hydrogen entry by CO.     

Thermoelasticity problem for a multilayer coating/half-space assembly with undercoat crack subjected to convective thermal loading

The transient thermal stress crack problem for a half-space with a multilayer coating under thermal surface loading containing an undercoat crack, perpendicular to the interface, is considered. The problem is solved using the principle of superposition and uncoupled quasi-static thermoelasticity. Transient temperature distribution and corresponding thermal stresses for the uncracked multilayer assembly are obtained in a closed analytical form using the model with generalized thermal boundary conditions of heat exchange of a half-space with ambient media via the coating. The crack problem is formulated as a perturbation mixed boundary value problem, in which the crack surface loading should be equal and opposite to the thermal stresses obtained for the uncracked medium, and is reduced to a singular integral equation and solved numerically. Numerical computations are performed for the analysis of influence of the coating upon thermal stresses and thermal stress intensity factor.     

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.