Development of a fundamental crack tip strain rate equation and its application to quantitative prediction of stress corrosion cracking of stainless steels in high temperature oxygenated water

A formulation for the quantitative calculation of the stress corrosion cracking (SCC) growth rate was proposed based on a fundamental-based crack tip strain rate (CTSR) equation that was derived from the time-based mathematical derivation of a continuum mechanics equation. The CTSR equation includes an uncertain parameter r₀, the characteristic distance away from a growing crack tip, at which a representative strain rate should be defined. In this research, slow strain rate tensile tests on sensitized 304L stainless steel in oxygenated high temperature water were performed. By curve fitting the experimental results to the numerically calculated crack growth rate, the parameter r₀ was determined. Then, the theoretical formulation was used to predict the SCC growth rates. The results indicate that r₀ is on the order of several micrometers, and that the application of the theoretical equation in predicting the crack growth rate provides satisfactory agreement with the available data.     

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.     

Numerical study of the effect of hydrogen on the crack propagation behavior of single crystal tungsten

An atomic model of single crystal bcc tungsten containing a pre-existing crack was built and molecular dynamics simulations were performed to investigate the crack propagation behavior with and without hydrogen atoms under uniaxial tensile load. Two kinds of crystal orientation were analyzed to study the effect of hydrogen on different crack propagation patterns. The results show that hydrogen can either improve or reduce the ductility of tungsten. High hydrogen concentration could result in the rearrangement of tungsten atoms ahead of the crack tip and reduce the stress concentration in the neighboring area around the crack tip. This will prevent the crack from propagation temporarily and therefore increase the fracture strain. Besides, hydrogen atoms can also facilitate the dislocation emission from the crack tip, which is accompanied by a larger plastic deformation. Both the mechanisms improve the ductility of tungsten. However, a void could be nucleated in a local hydrogen-rich area under tensile load. Its growth and link-up with the main crack will accelerate the crack propagation and speedup the fracture process, which diminishes the ductility of tungsten.     

Simulation of stress corrosion cracking behavior in a tube-shaped specimen of nickel-based alloy 600

Stress corrosion cracking (SCC) simulation code has been developed for the evaluation of SCC behavior in specimens in the shape of field components. The code utilizes numerical calculation of stress/strain states at a crack tip using finite element methods and a formula describing the crack tip reaction kinetics containing unknown environmental parameters. The applicability of this simulation code was investigated by applying the code to the evaluation of SCC behavior in a mock-up of a bottom mounted instrumentation tube for a pressurized water reactor subjected to complex stress/strain states. The results indicate that crack growth rate in a component suffering from certain environments can be estimated using the developed SCC simulation code with pre-determined unknown parameters, using the experimental crack growth rate data measured on other specimens in the same environment.     

Effect of welded mechanical heterogeneity on local stress and strain ahead of stationary and growing crack tips

The crack tip stress and strain condition is one of main factors affecting environmentally assisted cracking (EAC) behaviors in light water reactor (LWR). The mechanical and material properties of the base metal, weld metal and heat-affected zone (HAZ) in welded joints are heterogeneous because of the inherent characteristics of welded joint. Since the welded joint is more susceptible to EAC, to understand the effect of the strength mismatch in the welded joint on EAC growth rate, the stress and strain state in both stationary and growing crack tips of the welded joint specimen are investigated by the elastic-plastic finite element method (EPFEM) in this paper. The results indicate that the strength mismatch and sampling position in the welded joint would observably affect the stress and strain ahead of the stationary and growing crack tip, and accordingly affect the EAC growth rate.     

Measurement of plastic strain of polycrystalline material by electron backscatter diffraction

It is important to know the degree of plastic strain in order to evaluate the susceptibility and crack growth rate of stress corrosion cracking (SCC) in stainless steel and nickel based alloy, because SCC is enhanced by the cold work and causes many problems in nuclear power plant components. In this study, electron backscatter diffraction in conjunction with scanning electron microscopy is applied to measure the plastic strain imposed to stainless steel by tensile load. A new parameter, which quantifies the spread of the crystal orientation within individual grains arising due to dislocation accumulation during plastic deformation, is correlated with imposed plastic strain. The new parameter is called ‘crystal deformation’ and is determined from the spread in misorientation from the central grain orientation. It is confirmed that this parameter has a good correlation with plastic strain and is not affected by the data density of the crystal orientation map. The dislocation density distribution is also evaluated from the misorientation from the central orientation. Relatively high dislocation density was observed near grain boundaries and grain boundary triple points, which was consistent with the observed deterioration of EBSD pattern quality in those locations.     

Microstructural Characterization of SCC Crack Tip and Oxide Film for SUS 316 Stainless Steel in Simulated PWR Primary Water at 320°C

Recent studies on stress corrosion cracking (SCC) behaviors of austenitic stainless steels in hydrogenated high-temperature water show that low potential SCC (LPSCC) can occur on cold-worked SUS 316 stainless steel (hereinafter, 316SS). In this study, oxide films and crack tips on cold-worked 316SS exposed to hydrogenated high-temperature water were characterized using analytical transmission electron microscopy (ATEM), grazing incidence X-ray diffraction (GIXRD) and Auger electron spectroscopy (AES) in order to study the corrosion and SCC behaviors of these films and crack tips. A double layer structure was identified for the oxide film after a constant extension rate tensile (CERT) test. The outer layer was composed of large particles (0.2–3 μm) of Fe₃O₄ and the inner layer consisted mainly of fine particles (~10 nm) of FeCr₂O₄. In addition, nickel enrichment was identified at the metal/oxide interface. Particles of Fe₃O₄ were also identified on the crack walls. These results indicate that the same electrochemical reactions had occurred inside and outside the crack. The crack tip area was filled with corrosion products of a chromium-rich oxide. In addition, nickel enrichment was observed at the crack tip. The formation of the nickel-enriched phase indicates that a selective dissolution reaction of iron and chromium occurred at the front of the LPSCC crack.     

Evaluation of SCC crack behavior in zirconium and zircaloy-2 using nonlinear fracture mechanics parameters

Applicability of nonlinear fracture mechanics parameters, i.e. J-integral, crack tip opening displacement (CTOD), and crack tip opening angle (CTOA), to evaluation of stress corrosion crack (SCC) propagation rate was investigated using fully annealed zirconium plates and Zircaloy-2 tubing, both of which produce SCC with comparatively large plastic strain in an iodine environment at high temperatures.Tensile SCC tests were carried out at 300°C for center-notched zirconium plates and internal gas pressurization SCC tests at 350°C, for Zircaloy-2 tubing, to measure the SCC crack propagation rate. The J-integral around semi-elliptical SCC cracks produced in Zircaloy-2 tubing was calculated by a three-dimensional finite element method (FEM) code.The test results revealed that the SCC crack propagation rate dc/dt could be expressed as a function of the J-integral, which is the most frequently used parameter in nonlinear fracture mechanics, by the equation dc/dt = C · Jⁿ, where C and n were experimental constants.Among the other parameters, CTOD and CTOA, the latter appeared to be useful for assessing the crack propagation rate, because it had a tendency to hold a constant value at various crack depths.     

The iodine-induced strain rate sensitivity of Zircaloy fuel rod cladding

The strain rate sensitivities and failure times characteristic of iodine-induced stress corrosion cracking of Zircaloy fuel rod cladding are important because they can be related to certain power ramping rates which may increase fuel rod failure probabilities. The CCSCC model developed in this paper approximates these failure characteristics by simulating the transition from the slower (less observable) non-corrosive creep cracking (CC) regime to the faster (more observable) stress corrosion cracking (SCC) regime. Components of the CCSCC model include: ZrI₄ production by chemical reaction between Zircaloy and iodine; diffusion of the ZrI₄ to the crack tip; chemisorption, embrittlement, and damage accumulation at the crack tip; and crack initiation times and growth rates.Results indicate that the Zr-I₂ SCC process is dominated by competition between chemical reaction and material creep rate phenomena, rather than by stress thresholds or by the requirement that a complete monolayer of ZrI₄ form on the exposed Zircaloy surface at the crack tip. Failure times are dominated by the time required to initiate active crack growth. The SCC process is apparently not limited by diffusion kinetics on the time scale of laboratory experiments. Conflicting results were found concerning the chemical reaction rate at the crack tip.     

Numerical investigation of ductile crack growth behavior in a dissimilar metal welded joint

In this paper, the finite element method (FEM) based on GTN model is used to investigate the ductile crack growth behavior in single edge-notched bend (SENB) specimens of a dissimilar metal welded joint (DMWJ) composed of four materials in the primary systems of nuclear power plants. The J-Δa resistance curves, crack growth paths and local stress-strain distributions in front of crack tips are calculated for eight initial cracks with different locations in the DMWJ and four cracks in the four homogenous materials. The results show that the initial cracks with different locations in the DMWJ have different crack growth resistances and growth paths. When the initial crack lies in the centers of the weld Alloy182 and buttering Alloy82, the crack-tip plastic and damage zones are symmetrical, and the crack grow path is nearly straight along the initial crack plane. But for the interface cracks between materials and near interface cracks, the crack-tip plastic and damage zones are asymmetric, and the crack growth path has significant deviation phenomenon. The crack growth tends to deviate into the material whose yield stress is lower between the two materials on both sides of the interface. The different initial crack locations and mismatches in yield stress and work hardening between different materials in the DMWJ affect the local stress triaxiality and plastic strain distributions in front of crack tips, and lead to different ductile crack growth resistances and growth paths. For the accurate integrity assessment for the DMWJ, the fracture toughness data and resistance curves for the initial cracks with different locations in the DMWJ need to be obtained.     

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.     

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.     

Stress corrosion cracking countermeasure observed on Ni-based alloy welds of BWR core support structure

The effect of hydrostatic test on the residual stress re-distribution was simulated by experiment to confirm the residual stress behavior of the cone-shaped shroud support to reactor pressure vessel (RPV) weld, where a number of cracks due to stress corrosion cracking (SCC) were observed on the inner side only. Test specimen with tensile residual stress was loaded and unloaded with axial plus bending load, which simulates the hydrostatic test load, and the strain change was measured during the test to observe the residual stress behavior. The results verify that the residual stresses of the shroud support to the RPV weld were reduced and the stresses on inner and outer sides were reversed by the hydrostatic test. As the SCC countermeasure, the shot peening (SP) technology was applied. Residual stress reduction by SP on the complicated configuration, and improvement of SCC resistance and endurance of the compressive residual stress were experimentally confirmed. Then, SP treatment procedures on the actual structure were confirmed and a field application technique was established.     

Fracture mechanics investigation regarding the effects of cracks on the structural integrity of a BWR-core shroud

As a consequence of core shroud intergranular stress corrosion cracking (IGSCC) detected in the course of inservice inspections, a fracture mechanics analysis was carried out to evaluate the effects of postulated cracks on the structural integrity. In this study, critical crack sizes and crack growth were calculated. Due to the comparatively low stress acting on the core shroud during normal operation, the residual stresses in the welds make up the major proportion of the tensile stresses responsible for IGSCC. In order to consider residual stresses of the lower core support ring welds, a finite element analysis was performed at MPA Stuttgart using the FE-code ANSYS. The crack growth computed on the basis of USNRC crack growth rates da/dt demonstrated that crack growth in depth direction increases quickly at first, then retards and finally comes almost to a standstill. The cause of this ‘quasi-standstill’ is the residual stress pattern across the wall, being characterized by tensile stresses in the outer areas of the wall and compressive stresses in the middle of the wall. Crack growth in circumferential direction remains more or less constant after a slow initial phase. As the calculation of stress intensity factors K_I of surface flaws under normal conditions demonstrated, a ‘lower bound’ fracture toughness value is only exceeded in the case of very long and deep surface flaws. It can be inferred from crack growth calculations that under the assumption of intergranular stress corrosion cracking, the occurrence of such deep and at the same time long flaws is unlikely, regardless of the initial crack length. Irrespective of the above, the calculated critical throughwall crack lengths, which were determined using a ‘lower bound’ fracture toughness value, demonstrated that even long throughwall cracks will not affect the component’s integrity under full load. Moreover, it can be concluded from the studies of crack growth that—assuming intergranular stress corrosion cracking—a sufficiently long period will elapse before a crack which has just been initiated reaches a relevant size. Therefore, it can be stated that these cracks will likely be detected during periodic inservice inspections.     

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。     

Short fatigue crack propagation and effect of notch plastic field

In engineering application, almost all structures and components contain notches or holes. They often experience severe fatigue loading, and have been recognized as a potential site for small fatigue crack initiation and propagation. In this paper, the effects of notch plastic field on small fatigue crack initiation and propagation from notch member, under cyclic tensile loading control, are investigated. Experiment shows that small crack initiates from notch specimen at far higher rate than that of smooth specimen; small crack propagation is still faster than that of smooth specimen within notch plastic field, though this difference is progressively lessening; beyond notch plastic zone, small crack growth rate is approaching long crack growth rate. Analysis via finite element and analytical method reveals that notch plasticity has key influence on small crack initiation, crack tip generated plasticity has critical impact on small crack propagation within notch plastic field, while plasticity induced crack closure has dominant effect on crack propagation out of notch plastic field. A comparison between experimental and analytical results is made to identify the mechanisms of small fatigue crack initiation and propagation within notch plastic field.     

A study on the mechanism of iodine-induced stress-corrosion cracking of Zircaloy-4

The iodine-induced stress-corrosion cracking (SCC) of Zircaloy-4 plate specimens has been studied by the constant elongation rate test (CERT) and U-bend test methods. In order to systematically evaluate the effects of stress states on the SCC behavior, four kinds of specimens were prepared from as-annealed Zircaloy-4 plate specimens. The uniaxial tensile and single edge-notched (SEN) specimens fractured in the ductile manner, not by SCC. However, SCC resulted in the plane strain tensile specimens and deep-notched U-bend specimens. As the strain rate was lowered, the susceptibility to SCC increased. The stress-corrosion (SC) cracks propagated by the trans-granular brittle fracture mode for as-annealed specimens, whereas by the inter- and trans-granular mixed fracture mode for reannealed specimens. The SCC processes of Zircaloy-4 in iodine-gas are discussed in terms of effects of stress states, elongation rates and yield stresses. The present experimental results suggest that the iodine-induced SCC processes are based upon the iodine-diffusion model.     

溶解氧和溶解氢对冷变形690 MA合金应力腐蚀开裂的影响规律

采用直流电压降（DCPD）裂纹长度在线测量技术研究了溶解氧（DO）和溶解氢（DH）对冷变形690 MA合金在360 ℃水环境中应力腐蚀（SCC）裂纹扩展速率（CGR）的影响规律,并结合高分辨微观表征技术观察了裂纹尖端形貌和腐蚀产物特征,解释了溶解气体对SCC的影响机理。结果表明,DH环境下的CGR约为DO环境下的2~4倍。TEM分析表明,冷变形690 MA合金在DH和DO环境中的裂纹尖端形貌相似,裂纹尖端前端均未发现显著的晶界氧化。DH环境下CGR与晶界孔洞密度有较好的对应关系,表明介质中的DH可促进裂纹尖端前端晶界碳化物附近孔洞的生成、降低晶界结合力,进而加速裂纹扩展。     

Fatigue testing of metallurgically-bonded EBR-II superheater tubes

Fatigue crack growth tests were performed on 2¼Cr–1Mo steel specimens machined from ex-service experimental breeder reactor-II (EBR-II) superheater duplex tubes. The tubes had been metallurgically-bonded with a 100 μm thick Ni layer; the specimens incorporated this bond layer. Fatigue crack growth tests were performed at room temperature in air and at 400 °C in air and humid Ar; cracks were grown at varied levels of constant ΔK. In all conditions the presence of the Ni bond layer was found to result in a net retardation of growth as the crack passed through the layer. The mechanism of retardation was identified as a disruption of crack planarity and uniformity after passing through the porous bond layer. Full crack arrest was only observed in a single test performed at near-threshold ΔK level (12 MPa√m) at 400 °C. In this case the crack tip was blunted by oxidation of the base steel at the steel–nickel interface.     

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.