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.     

Creep crack growth verification testing in Alloy 800H tubular components

A method for determining the creep crack growth, CCG, and stress rupture behaviour of Alloy 800H tubular components containing longitudinal notches at 800°C is described. The presence of the notch is found to systematically weaken the tube, the degree of weakening dependent upon the notch length and depth. The creep crack growth rates, determined from a specially adapted potential drop technique are compared with those obtained from conventional compact tension type specimens. Using the stress intensity factor, K_I, and the C^* parameter as the basis of comparison it is found that the latter gives excellent correlation between the specimen and component behaviour. Finally attention is drawn to the potential dangers of predicting the component creep crack growth behaviour from the data obtained using conventional specimens for a structure sensitive material such as Alloy 800H and conversely to the advantages of the component type CCG tests developed in the present work.     

Three-dimensional interpretation of cleavage fracture tests of cladded specimens with local approach to cleavage fracture

Electricité de France has conducted during these last years an experimental and numerical research programme in order to evaluate fracture mechanics analyses used in nuclear reactor pressure vessels integrity assessment, regarding the risk of brittle fracture. Two cladded specimens made of ferritic steel A508 Cl3 with stainless steel cladding, and containing shallow subclad flaws, have been tested in four point bending at very low temperature to obtain cleavage failure. The crack instability was obtained in base metal by cleavage fracture, without crack arrest. The tests have been interpreted by local approach to cleavage fracture (Beremin model) using three-dimensional finite element computations. After the elastic–plastic computation of stress intensity factor K_J along the crack front, the probability of cleavage failure of each specimen is evaluated using m, σ_u Beremin model parameters identified on the same material. The failure of two specimens is conservatively predicted by both analyses. The elastic–plastic stress intensity factor K_J in base metal is always greater than base metal fracture toughness K_1c. The calculated probabilities of cleavage failure are in agreement with experimental results. The sensitivity of Beremin model to numerical aspects is finally exposed.     

A study of the stress intensity factors for single or multiple cracks in thick-walled cylinders

The variation of stress intensity factors of a single semi-elliptical crack and multiple semi-elliptical cracks which are radial symmetric or unsymmetric array in an internal pressurized thick-walled cylinder is studied by use of the “frozen-stress” photo-elastic method. The method of determining mixed-mode stress intensity factors K_I and K_II is given. By means of experimental results and the relative results of other authors, the approximate expression for evaluating stress intensity factors of straight border, semi-circular, semi-elliptical internal surface cracks in thick-walled cylinders are presented.     

Fatigue studies on carbon steel piping materials and components: Indian PHWRs

This paper describes the results of fatigue studies on carbon steel piping materials and components of Indian Pressurized Heavy Water Reactors (PHWRs). The piping components include pipes and elbows, of outer diameter 219 mm, 324 mm and 406 mm, made of carbon steel (SA333 Gr.6 grade) material. Tests on actual pipes and elbows with part through notch were carried out to study the behaviour of crack growth under cyclic loading for different pipe sizes, notch aspect ratios, stress ratios, etc. During the tests, numbers of cycles for crack initiation from blunt notch were recorded with an accuracy of 0.1 mm. In conjunction with component tests, the experimental studies were also conducted on standard specimens to understand the effect of different variables such as size (thickness), type of specimen and components (elbow and pipe), welding, stress ratio, notch orientation on fatigue crack growth rate. The fatigue crack growth curve (da/dN versus ΔK) obtained from three-point bend specimen and pipe was compared with that given in ASME Section XI. The comparison shows that da/dN versus ΔK curves obtained from the specimen and pipe tests are nearly same. The analytical predictions for crack initiation and crack growth for the tested components were compared with experimental results. Such comparisons validate the modeling procedure for crack initiation and growth.     

Fracture initiation and propagation in a cylindrical shell containing an initial surface flaw

The paper deals with the problem of fracture initiation, propagation, and arrest in a pressurized cylindrical vessel which contains an initial surface flaw. It is assumed that the flaw has the most unfavorable geometry and orientation, namely, it is a relatively long part-through axial crack.First we consider the problem of a crack which is sufficiently ‘shallow’ so that the plastic deformations are confined to the neighborhood of the crack border and part of the net section near the inner wall is still elastic. The plasticity-corrected stress intensity factor obtained from this analysis is the controlling load factor in failure considerations related to fatigue crack propagation, stress corrosion cracking, and static fracture (with the use of fracture toughness, COD, or a K_R curvetype failure criterion).The problem of relatively deep crack with fully-yielded net ligament is then considered. Plastic deformations are also assumed to spread around the crack ends through the entire wall thickness. A perfectly plastic strip model (with an eight order shell theory) is used to calculate the plastic zone size and the crack opening displacement along the crack border. Previous studies indicate that for the analysis of the type of stable and subsequent unstable crack propagation problems under consideration, the crack opening displacement δ is a more suitable load factor than the stress intensity factor K, or the crack extension force G. Thus, in this paper a ‘crack opening stretch’ type material characterization will be used.After the rupture of the net ligament under the crack, the axial crack propagation is accompanied by the depressurization of the vessel caused by leakage. From this point on the fracture problem is coupled with the related fluid mechanics or gas dynamics problem where the primary unknowns are the pressure and the crack length as functions of time. In the present study it is assumed that the volume of the vessel is finite and the crack propagation is quasi-static (this assumption, which is necessary to keep the problem within manageable proportions, is justified by the relatively low crack velocities, i.e. v_c < 0.25 c₂, c₂ being the shear wave velocity).     

A study on the behavior of a crack located at the striping zone in a thermally stratified pipe

The behavior of a small crack located at the thermal striping zone in a thermally stratified piping is numerically investigated. The effects of the parameters such as fluctuation frequency/ amplitude of the density interface, heat transfer coefficient near the thermal striping zone, and crack depth on the behavior of the crack are examined to identify the governing parameters. The effect of the contact surfaces on the stress intensity factor range is also examined for several levels of the internal fluid pressure. The stress intensity factor range, ΔK_I, is used to describe the crack behavior due to the thermal striping. The findings of the numerical investigation are as follows: (1) the value of ΔK_I increases up to a specific Fourier number and then decreases beyond the specific Fourier number. (2) With the increasing Biot number the value of ΔK_I increases and the Fourier number(Fo) at which the ΔK_I vs. Fo curve has a peak decreases. This means that the behavior of a crack located at the thermal striping zone has a large dependence on the oscillating frequency of the density interface and the heat transfer coefficients. (3) The value of ΔK_I increases up to a specific crack depth and then decreases beyond the specific crack depth. (4) If the fluid pressure is lower than a specific value, the value of ΔK_I decreases because of the crack surface contact.     

Effect of Stress Ratio on Crack Extension Rate of Fine-Grained Isotropic Nuclear Graphite

Effect of stress ratio on the crack extension rate da/dN was examined for an iso-tropic nuclear graphite IG-11, using tapered double cantilever beam specimens. Loads were applied to the specimens cyclically at a loading rate of 251 N/s in the load range where the stress ratio R range of 0～0.8. Here R is defined as the ratio of the minimum stress intensity factor K _min to the maximum stress intensity factor K _max. The rate da/dN was measured optically using a comparator. Conclusions derived as 1. For a given value of R, crack extension rate da/dN can be expressed as da/dN = C(ΔK)ⁿ. here, ΔK is a stress intensity factor range, i.e. ΔK = K_max ? K_min , and C and n are constants and strongly dependent on R value respectively.

2. Threshold stress intensity factor range ΔK_th which was defined as the point below which no crack extension more than 10 μm was observed after loadings of 10⁵ cycles was related with R-values as ΔK_th /ΔK_tho = (1 ? R)^0.89, (ΔK_tho = ΔK_th at R = 0).

     

New observations on the crack growth rate of low alloy nuclear grade ferritic steels under constant active load in oxygenated high-temperature water

Within the scope of reactor safety research attempts have been made over several decades to determine corrosion-assisted crack growth rates. National and international investigations have been performed on both an experimental and an analytical basis. A compilation of internationally available experimental data for ferritic steels exhibits a scatter of crack growth rates of up to 5 decades. This was one of the reasons for commencing further experimental investigations focused on the evaluation of corrosion-assisted crack growth rates. These experimental studies were performed under constant, active, external load on 2T-CT specimens of the materials 20 MnMoNi 5 5 with 0.009 and 0.020% S (similar to A508 Cl.3), 22 NiMoCr 3 7 with 0.006% S (similar to A508 Cl.2) and 17 MnMoV 6 4 with 0.017% S. The tests were carried out in deionized oxygenated high-temperature water (240°C; 0.4 and 8.0 ppm O₂). For K_I values up to 60 MPa m^1/2, the experimental results showed no significant dependence between corrosion-assisted crack growth rates and the stress intensity factor, the oxygen content of the medium or the sulphur content of the steel. Here it is important to note, that in this K_I region the high crack growth rates after the onset of cracking due to loading are decreasing and finally come to a standstill after a short period of time as compared with operational times of plants. Consequently, the determination of crack growth velocities as corrosion-assisted crack advance divided by the test duration, so far practised worldwide, results in wrong crack growth rate values in the above-mentioned range of loading up to 60 MPa m^1/2. Based on a test duration of 1000 h, the average crack growth rates are below 10⁻⁸ mm s⁻¹ for K_I ≤ 60 MPa m^1/2. When applied to a single start-up and service period of one year, this would formally lead to an average crack growth rate of 2·10⁻⁹ mm s⁻¹ (equivalent to 0.06 mm per year). At K_I values between 60 and 75 MPa m^1/2 the average corrosion-assisted crack growth rates increase significantly. It can be observed experimentally that the crack propagates during the whole period of the test. Consequently the calculation of crack growth velocities as corrosion-assisted crack advance divided by the test duration as mentioned earlier can be applied as a first estimate. Finally, for K_I values ≥ 75 MPa m^1/2 high crack growth rates up to 10⁻⁴ mm s⁻¹ can be observed. In this region the average crack growth rates are also in quite good agreement with a theoretically based crack growth model.     

Determination of more realistic Ke,r-factors for simplified elastic–plastic analysis

According to the relevant KTA-Rules, e.g. KTA 3201.2 (KTA, 1994), strain correction factors—K_e-factors—have to be used in the fatigue analysis of pressurised components if the strain intensity ranges are determined by elastic analyses, and if in this case the range of primary plus secondary stress intensity exceeds a certain limit. This limit is three times the design stress intensity value, S_m, and thus approximately corresponds to twice the value of the 0.2% strain limit. The relations given in the above-mentioned rules to determine the K_e-factors for considering plastification have proved to be very conservative in many cases compared with the strain intensity ranges that were determined by complete elastic–plastic analyses. In order to improve the validity of the fatigue analysis, the topic of ‘Performance of fundamental work to prepare concrete proposals for realistic K_e,r-factors (strain correction factors) to consider plastification at large strain amplitudes' was one of the subjects of the BMU project SR 2063. Work on this topic was jointly performed by GRS and Siemens. In summary, the result was that the proposed realistic K_e,r-factors present a real alternative to the K_e-factors of the regulations; the latter serve a mostly conservative registration of the observed elastic–plastic strain but cannot be explained in terms of physics and are not formulated in a manner adequately specific of any material. The exemplary verification calculations that have been performed so far show, furthermore, that the proposed realistic K_e,r-factors can be easily determined and also deliver sufficiently conservative results. This new method therefore has great potential which, however, still has to continue to be verified by further calculations before it can be included in the KTA-Rules.     

European experiences of the proposed ASTM test method for crack arrest toughness of ferritic materials

The proposed ASTM test method for measuring the crack arrest toughness of ferritic materials using wedge-loaded, side-grooved, compact specimens was applied to three steels: A514 bridge steel tested at −30°C (CV30–50°C), A588 bridge steel tested at −30°C (CV30–65°C), and A533B pressure vessel steel tested at +10°C (CV30-12°C) and +24°C (CV30+2°C). Five sets of results from different laboratories are discussed here; in four cases FOX DUR 500 electrodes were used for notch preparation, in the remaining case HARDEX-N electrodes were used. In all cases, notches were prepared by spark erosion, although root radii varied from 0.1–1.5 mm. Although fast fractures were successfully initiated, arrest did not occur in a significant number of cases.The results showed no obvious dependence of crack arrest toughness, K_a, (determined by a static analysis) on crack initiation toughness, K₀. It was found that K_a decreases markedly with increasing crack jump distance, Δα/W. A limited amount of further work on smaller specimens of the A533B steel showed that lower K_a values tended to be recorded.It is concluded that a number of points relating to the proposed test method and notch preparation are worthy of further consideration. It is pointed out that the proposed validity criteria may screen out lower bound data. Nevertheless, for present practical purposes, K_a values may be regarded as useful in providing an estimate of arrest toughness — although not necessarily a conservative estimate.     

Reactivity feedback coefficients of a material test research reactor fueled with high-density U3Si2 dispersion fuels

The reactivity feedback coefficients of a material test research reactor fueled with high-density U₃Si₂ dispersion fuels were calculated. For this purpose, the low-density LEU fuel of an MTR was replaced with high-density U₃Si₂ LEU fuels currently being developed under the RERTR program. Calculations were carried out to find the fuel temperature reactivity coefficient, moderator temperature reactivity coefficient and moderator density reactivity coefficient. Nuclear reactor analysis codes including WIMS-D4 and CITATION were employed to carry out these calculations. It is observed that the average values of fuel temperature reactivity feedback coefficient, moderator temperature reactivity coefficient and moderator density reactivity coefficient from 20 °C to 100 °C, at the beginning of life, followed the relationships (in units of Δk/k × 10⁻⁵ K⁻¹) −2.116 − 0.118 ρ_U, 0.713 − 37.309/ρ_U and −12.765 − 34.309/ρ_U, respectively for 4.0 ≤ ρ_U (g/cm³) ≤ 6.0.     

Mechanical integrity analysis of TMI-1 OTSG unplugged tubes

Small I.D. circumferential defects have been identified in many steam generator tubes. The origin of the cracks is known to be chemical, not mechanical. A fracture mechanics evaluation has been conducted to ascertain the stability of tube cracks under steady-state and anticipated transient conditions. A spectrum of hypothetical crack sizes was interacted with tube stresses derived from the load evaluation using the methods of linear elastic fracture mechanics (LEFM). Stress intensities were calculated for part-through wall cracks in cylinders combining components due to membrane stress, bending stress, and stresses due to internal pressure acting on the parting crack faces as the loads are cycled.The LEFM computational code, “BIGIF”, developed for EPRI, was used to integrate over a range of stress intensities following the model to describe crack growth in INCO 600 at operating temperature using the equation (ΔK)^3.5.The code was modified by applying ΔK_Th, the threshold stress intensity range. Below ΔK_Th small cracks will not propagate at all. Appropriate R ratio values were employed when calculating crack propagation due to high cycle or low cycle loading.Cracks that may have escaped detection by ECT will not jeopardize tube integrity during normal cooldown unless these cracks are greater than 180° in extent. Large non-through-wall cracks that would jeopardize tube integrity are not expected to evolve because in axi-symmetric tensile stress fields, cracks propagate preferentially through the tube wall rather than around the circumference. Tube integrity can be demonstrated for mid-span tube regions and for the transition region as well.The as-repaired transition geometry is a design no less adequate than the original. The as-repaired condition represents an improvement in the state of stress due to mechanical and thermal loads as compared to the original.     

Delayed hydride cracking in Zr-2.5Nb tube with the cooling rate and the notch tip shape

The objective of this study is to demonstrate the feasibility of the Kim’s delayed hydride cracking (DHC) model. To this end, this study has investigated the velocity and incubation time of delayed hydride cracking (DHC) for the water-quenched and furnace-cooled Zr-2.5Nb tubes with a different radius of notch tip. DHC tests were carried out at constant K_I of 20 MPa √m on cantilever beam (CB) specimens subjected to furnace cooling or water quenching after electrolytic charging with hydrogen. An acoustic emission sensor was used to detect the incubation time taken before the start of DHC. The shape of the notch tip changed from fatigue cracks to smooth cracks with its tip radius ranging from 0.1 to 0.15 mm. The DHC incubation time increased remarkably with the increased radius of the notch tip, which appeared more strikingly on the furnace-cooled CB specimens than on the water-quenched ones. However, both furnace-cooled and water-quenched CB specimens indicated little change in DHC velocity with the radius of the notch tip unless their notch tip exceeded 0.125 mm. These results demonstrate that the nucleation rate of hydrides at the notch tip determines the incubation time and the DHC velocity becomes constant after the concentration of hydrogen at the notch tip reaches terminal solid solubility for dissolution (TSSD), which agrees well with the Kim’s DHC model. A difference in the incubation time and the DHC velocity between the furnace-cooled and water-quenched specimens is attributed to the nucleation rate of reoriented hydrides at the notch tip and the resulting concentration gradient of hydrogen between the notch tip and the bulk region.     

Analysis of Novo-Voronezh NPP unit 3 radiation lifetime of the WWER-440 reactor pressure vessel given samplings

The analysis of the residual radiation lifetime of the Novo-Voronezh NPP Unit 3 reactor pressure vessel which had spherical samplings after annealing was performed for the spectrum of the ‘worst’ modes of the emergency situation category. For the residual radiation lifetime estimation within the given study, two approaches to determine stress intensity factors, K_I have been used simultaneously. The first approach included a direct numeric modelling of postulated cracks in the cut-out zone with the use of the 3D finite element method. The second approach included K₁ calculation using 3D weight functions calculated with the use of the boundary element method. For K_I, calculation flaws have been postulated as surface longitudinal semielliptical flaws located in the deepest point of a cut-out. The results of K_I calculations obtained using different methods were practically the same. The allowable critical brittleness temperature was determined as 175°C that permitted the extension of the radiation lifetime by up to 6 years after annealing.     

Fracture toughness of welded joints materials for main pipelines at Ignalina NPP

This paper deals with an investigation of mechanical and fracture toughness characteristics of welded joint materials used in Ignalina Nuclear Power Plant (NPP) reactor main circulating circuit (MCC) and steam pipelines. Basic metal of MCC group distributing header (GDH) steel 08Ch18N10T (Du-300), its weld metal welded by manual and automatic arc method using the wire SV-04Ch19N11M3 and electrodes EA-100/10U or EA-100/10T, this joint heat-affected zone metal and base metal of the main steam system—steel 16GS (DU-630) and its weld metal welded by manual arc method using the wire SV-08GS2 and electrodes UONI-13/55 were tested.Mechanical properties of welded joints materials—proportional limit (σ_pl), yield (σ_y) and ultimate (σ_u) strength, fracture stress (σ_f) and ductility (Z) (percent reduction of area) of the specimens were determined. Investigation of relative critical stress intensity factor for fixed thickness of the specimen and critical J-integral, J_IC, was performed.The probabilistic investigation of influence of the mechanical properties (σ_pl, σ_y, σ_u) onto fracture toughness characteristics and J_IC for tested materials by using linear regression model with three independent variables was performed.Research enabled to conclude that proposed multivariable regression model with 80% probability (confidence coefficient α = 0.05) has explained reasonably well the dependence of with σ_pl, σ_y, σ_u and it has shown the non-acceptability of probabilistic evaluation of the model with respect to J_IC.     

Irradiation experiments in the testing nuclear power plant VAK

Within the German Research Programme “Integrity of Components” the first two capsules were irradiated in the Testing Nuclear Power Reactor VAK. The materials are of the 22 NiMoCr 3 7 and 20 MnMoNi 5 5 types and represent the lower bound of the base material regarding upper shelf energy and chemical composition (Cu, S, P), as well as a state of material which does not meet both chemical and toughness requirements (low upper shelf test melt). Tensile, Charpy, drop-weight, and fracture mechanics specimens were irradiated up to a range of 1.5 to 2 × 10¹⁹ cm⁻² (E > 1 MeV). Despite the materials being at or beyond the specification limits, the results show irradiation sensitivity which can be predicted from the US Reg. Guide Trend Curves (1.99) and KWU Trend Curves in a conservative manner. The procedure to determine the adjusted reference temperature RT_NDT (adj.) on the basis of ΔT_41J (following ASTM E 185) could also be confirmed as conservative by comparing the different criteria derived from Charpy and drop weight tests in the unirradiated and irradiated condition.The results of fracture mechanics testing in the linear elastic range show a remarkable temperature margin to the K_Ic-curve of ASME XI.Prestrained compact tension specimens CT 40 mm made of 22 NiMoCr 3 7 material with an upper shelf energy of approx. 100 J were wedge loaded in a range up to 30 MPa m and exposed to the water environment during radiation. Macroscopic examination gave no indications of stress corrosion cracking.From tests of these specimens in the linear elastic range, a fracture toughness K_Ic^*, which was not affected by the prestrain and environment history, was found depending only on the overload applied during the prestraining procedure.