Large stable crack growth in fracture mechanics specimens

According to the J concept, information is reported about the crack resistance behaviour up to 8 mm crack growth of side-grooved CT-25 as well as CCT-25 specimens made from German standard steel StE 460. Numerical simulations controlled by J_R curves make the calculation of J from the stresses and strains of specimen models during large crack growth feasible. These data allow a comparison to standards and rules describing the evaluation of J from experiments. Using stress, strain and displacement fields from a plane-strain finite-element analysis, the extended J concept is discussed concerning larger ductile crack growth. Additionally, the distribution of other fracture mechanics parameters such as the crack tip opening displacement (CTOD) and the crack tip opening angle (CTOA) are presented for larger crack growth.     

Effects of material condition on the iodine SCC susceptibility of zircaloy-2 cladding

Tube pressurization tests were conducted on two lots of Zircaloy-2 cladding to compare iodine stress corrosion cracking (SCC) susceptibilities at ˜593°K and an iodine concentration of 10⁻⁴ g/cm². Since a substantial difference in SCC behavior was observed in as-received material, a test matrix was devised to separate the effects of crystallographic texture, heat treatment, residual stress, and surface finish on SCC susceptibility. The difference in time to failure as a function of stress between the two lots is due to the substantial difference in texture where a more tangential texture results in shorter times to failure at any stress. Chemical etching and stress-relief heat treatment temperature has little effect on SCC behavior while residual stress at the levels measured in the two lots has no effect. The role of texture in the iodine SCC is discussed in terms of texture effects on mechanical properties, crack initiation, and crack propagation. It is concluded that texture influences all of these processes.     

Metallographic studies of fatigue in 20% cold-worked zircaloy-2 containing zirconium hydride

The fatigue behaviour of unhydrided and hydrided 20% cold-worked zircaloy-2 reactor pressure-vessel tubing has been studied for fluctuating tension at room-temperature and 300 °C and for reversed torsion at room-temperature. At room-temperature, high concentrations of zirconium hydride markedly reduce the critical crack length. This effect is attributed to a lowering of the fracture toughness, since hydrides fracture in the path of crack propagation and promote matrix cleavage. At 300 °C, hydride particles constrained by the matrix are plastically deformed without fracturing; the toughness is probably unaffected by the presence of hydride.     

The application of elastic-plastic fracture mechanics parameters in fracture safe design

The report summarizes some of the methods which are currently used for assessing the fracture toughness of materials under elastic and elastic-plastic conditions. The main parameters which are considered are (1) plane strain fracture toughness (K_Ic), (2) equivalent energy (K_Icd), (3) contour integral (J) and (4) crack opening displacement (COD). Gross strain crack tolerance and stress concentration methods are also discussed.It is concluded that of these parameters, the contour integral and the crack opening displacement have most potential for future development. These two parameters are shown to be equivalent, however, at the present stage of development the COD concept has several advantages over the J concept. Firstly, the COD concept is able to take into account, secondary stresses, such as welding residual stresses. Because these stresses are in equilibrium, they do not appear in energy measurements to evaluate J. Secondly, the COD value is a physical measure of the crack tip conditions which includes the effect of stress state and thickness. It is, therefore, possible to measure and calculate COD levels for cracks in real structures. It is not possible to evaluate J for real structures since J methods are appropriate only to in-plane problems. This also means that partial wall (thumbnail) flaws are better characterized by the COD concept.The COD concept has been developed to a stage where it is possible to estimate the significance of flaws in welded structures provided the toughness of the material and the acting stresses or strains are known. This development is described and the method used to analyze tests on model pressure vessels with 6″ thick walls. A comparison is made with other methods, and it is concluded that although the COD analysis gives conservative estimates of the flaw size to cause failure, further work is necessary to be able to predict vessel burst conditions when failure is preceded by extensive plasticity and stable ductile tearing. A simple nomogram to determine COD levels to ensure leak before break conditions is also developed.     

High-temperature oxidation of zircaloy-2 and zircaloy-4 in steam

At temperatures above the $\text{(α + β)}\text{β}$ transformation temperature for zirconium alloys, steam reacts with β-Zr to form a superficial layer of zirconium oxide (ZrO₂) and an intermediate layer of oxygen-stabilized α-Zr. Reaction kinetics and the rate of growth of the combined (ZrO₂ + α-Zr) layer for Zircaloy-2 and Zircaloy-4 oxidation in steam were measured over the temperature range 1050–1850°C. The reaction rates for both alloys were similar, obeyed parabolic kinetics and were not limited by gas phase diffusion. The parabolic rate constants were consistently less than those given by the Baker and Just correlation for zirconium oxidation in steam. A discontinuity was found in the temperature dependence of both the reaction rate and the rate of growth of the combined (ZrO₂ + α-Zr) layer. The discontinuity is attributed to a change in the oxide microstructure at the discontinuity temperature, an observation which is consistent with the zirconium-oxygen phase diagram.     

Classification and characterization of materials by means of fracture mechanics parameters

Within the scope of the “Integrity of Components” research project a large number of heats of reactor pressure vessel steels representing a broad quality spectrum have been investigated. In this paper the conventional and fracture mechanics parameters of four typical materials are presented. The difficulties in determining the reference temperature for nil ductility transition and the fracture mechanics parameters in the transition and upper shelf region of the Charpy energy are discussed. The technique developed at MPA for the evaluation of a physically meaningful crack initiation parameter based on the size of the stretched zone ahead of the crack tip is described, and values are reported.     

Probabilistic fracture mechanics of nuclear structural components: consideration of transition from embedded crack to surface crack

This paper describes a probabilistic fracture mechanics (PFM) analysis of aged nuclear reactor pressure vessel (RPV) material. New interpolation formulas of three-dimensional stress intensity factors are presented for both embedded elliptical surface cracks and semi-elliptical surface cracks. To investigate effects of transition from embedded crack to surface crack in PFM analyses, one of the PFM round-robin problems set by JSME-RC111 committee (i.e. aged RPV under normal and upset operating conditions) is solved, employing the interpolation formulas.     

Diffusion of tritium in zircaloy-2

The dependency of the tritium diffusion in Zircaloy-2 on the temperature as well as on the oxygen and hydrogen concentration was investigated. From the determined diffusion coefficients the following values for the frequency factor d₀ and the activation energy E_a were obtained: D₀ = (1.04^+0.28_?0.17 ) 10^?3 [cm² · s^?1 ], E_a = -42.1 ± 1.1 [kJ · mol^?1 ]. In the concentration range from 1350 to 11300 ppm oxygen and 15 to 1000 ppm hydrogen no systematic influence of these elements on the tritium diffusion coefficients was observed.     

Embrittlement behavior of zircaloy-4 cladding during oxidation and water quench

Simulated loss of coolant accident (LOCA) tests on Zircaloy-4 cladding were carried out to evaluate the thermal shock property during the injection of emergency core coolant. A Zircaloy-4 specimen was oxidized in a steam environment between 1000 and 1250 °C followed by a flooding of the cooling water. After the test, the ductility of the thermally embrittled specimen was measured by a ring-compression test and a microstructural analysis was carried out. The results showed that the threshold equivalent cladding reacted (ECR) value to cause a failure was higher than the conventional 17% criterion calculated by the Baker–Just equation. A residual metal thickness under 0.3 mm as well as a ring-compression ductility below 0.2 mm for a fracture is effective to assess the thermal shock embrittlement of Zircaloy-4 in an axially unrestrained, or even in a restrained condition.     

Application of fracture mechanics methods in safety analysis of piping components in subcreep and creep behavior

A survey and review program for the application of fracture mechanics methods in elevated temperature design analysis and safety evaluation was initiated in December 1976. The first report [1] surveyed and assembled the material for a critical review of the theories of fracture and the application of fracture mechanics methods to life prediction and safety analysis of piping components. The second report [2] provided the basic concepts and a review of the problem areas associated with the development of analytical and experimental programs for a systematic evaluation and comparison of the currently available fracture mechanics theories. The basis for such an evaluation was described in terms of a series of benchmark problems which accurately specify conditions of geometry, loading and environment characteristic of large diameter piping systems in nuclear service.The objective of this third report is to establish a data base and detail the additional analytical techniques needed to confirm the validity of existing analytical methods and improve the state of the art in current problematic areas effecting the interpretation and extension of safety evaluation methods. The need for such a program in the elevated temperature field has been demonstrated by a number of independent surveys on various safety aspects of LMFBR related structural analysis methods and matetials problems. The results of this program, however, will be applicable not only to reactor plants operating at elevated temperatures, but will also lead to improvements of light water reactor evaluation methods for operating and accident conditions.The current state of elevated temperature reactor design technology is embodied in the standards and codes which provide guidance and minimum requirements for systematic design and evaluation procedures. These, however, do not necessarily provide specific absolute values which, if satisfied in the course of design, will guarantee thirty to forty years of uninterrupted life. There are numerous assumptions and approximations embodied in these standards concerning materials behavior, damage mechanisms, and failure modes at elevated temperature. There are also numerous areas of uncertainty and conflicting opinion in the interpretation of the existing test data and in the analysis and evaluation methods. Furthermore, the standards and codes leave some areas to the judgement of the designer, some of which require explicit justifications, but no standards or rules are provided.The overall safety therefore lies, at the present time, in the combination of rigorous enforcement of current standards, judicious application of experience with high temperature equipment even if not in nuclear service, and the surveillance of actual operating conditions. In the past, one criterion proposed for elevated temperature design has been that the time for crack initiation should exceed the design life. However, due to the complexities of the piping structures and the nature of the stress history during service, the evaluation of initiation times is difficult and often leads to uneconomical designs. In addition defects may exist in the component before it enters service. Hence, the knowledge of the growth rates of cracks and the residual strength of the components containing cracks is important in a realistic design evaluation. For more brittle materials and lower temperature applications where plasticity is restricted, linear elastic fracture mechanics methods have been developed. For more ductile materials where the plastic zones near the cracks are larger, linear fracture mechanics methods are not directly applicable, but in these nonelastic cases the opening displacement and J integral methods of assessment have been proposed. In the complex situation encountered in nuclear power plant design, the analysis must also account for cyclic thermal strains, time dependent creep, and the effect of harmful environments which are not explicitly treated in the above-mentioned methods. In this report an in-depth review is presented in sufficient detail to illustrate the degree of agreement between the theoretical and empirical methods available in the literature and indicate the scope of the additional analyses and experimental work needed for the development of reliable safety evaluation methodology.For pure cylindrical bending, cracks perpendicular to the load start to grow when reaches a critical value which is generally larger than the corresponding critical uniaxial tension value. There appears to be a thickness effect in the bending case which is probably due to interference from the compressive sides of the crack.For a circular plate with lateral pressure and small lateral displacements, results agree with the bending data when using the nominal bending stress . For larger displacements when bulging occurs, the results agree with the tensile data when the nominal tensile stress is used.For curves surfaces, such as a cylinder under internal pressure, the data agree with the expression developed by Folias both for axial cracks under hoop stress σ and for circumferential cracks under axial stress σ Generally, the expressions were accurate up to , showing a tendency to be lower than the experimental data at higher values of the parameter. The parameter is a promising one.To study the influence of cracks at different angles to the applied load, analysis and data are available including the stress component parallel to the crack in the stress field around a crack tip. This, together with the concept of a critical circumferential stress at a critical distance (α = 0.1) ahead of the crack provides improved correlation with fracture predictions for both the angle of fracture and the critical stress intensity factor for the angled cracks in flat plates.For a hollow cylinder under torsion with angled cracks, the best correlation was given by the same analysis although the results were not as conclusive as for the flat plate. From elastic theory useful curves for the variation of K₁, K₂, and K₃ around the border of an elliptically shaped crack are available.In a plane stress fracture the addition of a biaxial stress produces an increase in the apparent fracture toughness compared with the uniaxial case. However, there is as yet no evidence to show that there would be the same increase in a plane strain situation. Hence, in the absence of biaxial information the uniaxial fracture data may be the most conservative for flat plates. However, for shells there will also be a curvature effect.In an analogous manner, fatigue crack propagation rates appear to be less rapid under biaxial stresses than under uniaxial stress. However, this shift is not great and generallly will be masked by other effects such as environment and temperature service situations.The analysis of cracks in weldments with residual stress effects are also available. In the case of a crack in a weld the estimated residual stress distribution agreed reasonably well with some experimental data for elastic conditions. Results indicate that there can be a tensile stress intensity factor even when the original residual stress distribution has changed to compressive. A point to remember is that residual stresses near welds can be beyond yield.An analysis based on Lagrangean mechanics is useful for indicating the different effects of liquids and gases as pressurizing media in hollow pipes. The results show that whereas gases maintain their pressure as a crack begins to propagate, the pressure in the liquid can quickly decrease so that subsequent catastrophic failure is less likely even in large diameter piping.     

Elastic-plastic FEM-analysis of a nozzle corner crack and discussion of the results by some fracture mechanics concepts

This paper presents the results of an elastic-plastic threedimensional finite element analysis for a nozzle corner crack in a pressurized reactor test vessel. The calculations were performed by the finite element program ADINA incorporating von Mises' yield condition and isotropic hardening. The crack plane was taken parallel to the axis of the vessel and the crack front straight and perpendicular to the symmetry line of the nozzle corner in order to obtain the worst position for a nozzle corner crack. The calculations were performed up to that pressure level where general yield of the ligament in the nozzle corner section takes place. The results of the finite element analysis are compared with figures obtained from analytical procedures of elastic-plastic fracture mechanics.     

Methyl iodide as a promoter of the SCC of zirconium alloys in iodine vapour

The presence of organic-iodine contaminants, or specifically methyl iodide, in the iodine environment during stress corrosion tests leads to an increased frequency of crack nucleation, and possibly a more rapid crack propagation process. The unusual fractographic features associated with these impurities suggest that they enhance the reduction in the surface energy of zirconium, cause an instability in the propagating crack front, and possibly enhance the rate of reaction to form zirconium iodides. These impurities are the most potent catalysts of iodine-induced cracking so far identified, although methyl iodide alone cannot initiate cracking.     

Failure probability assessment of wall-thinned nuclear pipes using probabilistic fracture mechanics

The integrity of nuclear piping system has to be maintained during operation. In order to maintain the integrity, reliable assessment procedures including fracture mechanics analysis, etc., are required. Up to now, this has been performed using conventional deterministic approaches even though there are many uncertainties to hinder a rational evaluation. In this respect, probabilistic approaches are considered as an appropriate method for piping system evaluation. The objectives of this paper are to estimate the failure probabilities of wall-thinned pipes in nuclear secondary systems and to propose limited operating conditions under different types of loadings. To do this, a probabilistic assessment program using reliability index and simulation techniques was developed and applied to evaluate failure probabilities of wall-thinned pipes subjected to internal pressure, bending moment and combined loading of them. The sensitivity analysis results as well as prototypal integrity assessment results showed a promising applicability of the probabilistic assessment program, necessity of practical evaluation reflecting combined loading condition and operation considering limited condition.     

Developments in fracture mechanics and non-destructive examination

The purpose of this paper is to give a brief review of the major developments and trends that have occurred in some of the technical areas covered by Division G of SMiRT since the first conference was held in Berlin in 1971. As with any human activity, time and experience produce organic change so that the technical areas covered by Division G have changed somewhat over the 18 years of its existence. As first conceived by Tom Jaeger, Division G was one of two divisions devoted to Light Water Reactor Components other than fuel and cladding. Division F was conceived with Core Structures and Piping whilst Division G was devoted to the Steel Reactor Pressure Vessels.     

Hydrogen influence on mechanical and fracture mechanics characteristics of zirconium Zr–2.5Nb alloy at ambient and elevated temperatures

This article deals with the investigation of the hydrogen concentration and temperature influence onto mechanical and fracture mechanics characteristics of RBMK-1500 Ignalina NPP unit 2 reactor fuel channel material—Zr–2.5Nb zirconium alloy (TMT-2) at temperatures from ambient up to 300 °C. The investigation of mechanical characteristics was performed on tensile specimens, fracture mechanics characteristics K_Q, , J_IC—on compact specimens (B = 4 mm) of hydrogen-free and saturated by hydrogen (52, 100 and 140 ppm) at 20, 170, 200 and 300 °C. The investigation showed that temperature increasing calls mechanical strength decreasing, whereas the reductions of area increase. Stronger influence of hydrogen concentration onto mechanical characteristics is noticed only at 20–170 °C temperature, however this influence diminishes as the temperature increases and weakest hydrogen influence is given at 300 °C. Fracture toughness characteristics K_Q, more depends on temperature than on hydrogen concentration. Critical J_IC integral values for the specimens containing hydrogen were given lowest at 20 °C, increases when temperature were raised up to 140 °C and were given highest when it reaches 300 °C.The analysis of and J_IC dependence due to the mechanical characteristics of zirconium alloy has showed that the modified plasticity Z_mod = (R_p0.2/R_m)Z satisfactorily approximates the influence of temperature and hydrogen concentration on variation of these characteristics.     

3D nonlinear finite element/fracture mechanics analysis of pressurized nuclear reactor container ring

Nuclear reactor containers, without inner liners, must withstand internal pressurization with minimal leak to the outside through the cracks. This paper reports on a 3D finite element (FE) simulation of a prestressed nuclear reactor container ring subjected to internal pressure. Discrete cracks are used, and the effect of crack surface pressurization on crack openings is investigated.It is shown that the discrete crack model can provide a suitable alternative to the smeared crack one, and that for the selected ring, the effect of additional crack pressurization is minimal.     

Morphology and composition of second phase particles in zircaloy-2

Intermetallic particles in Zircaloy-2 are analyzed for morphology (shape, size, distribution, etc.) and for crystal structure by transmission electron microscopy. Chemical composition is semi-quantitatively evaluated in a scanning transmission electron microscope. Several types of morphologically distinct particles are identified by shape, size, and substructure. All particles are found to be either nickel-bearing or chromium-bearing. Clusters containing several particles are often observed. The nickel-bearing particles are identified as a tetragonal Zr₂Ni-type phase where iron partially substitutes for some Ni giving an approximate composition of Zr₂Ni_0.4Fe_0.6. The chromium-bearing particles are found to be a hexagonal ZrCr₂-type phase where iron partially substitutes for some Cr giving an approximate composition of ZrCr_1.1Fe_0.9. Essentially all the iron is contained in these two kinds of particles, and no iron-zirconium particles are found.     

Failure analysis of a generator rotor with a deep crack detected during operation: fractographic and fracture mechanics approach

This paper reports the results of an activity of failure analysis performed on a 370 MVA generator rotor that was scrapped after about 133 000 operating hours and about 400 start-ups, when the on line monitoring system revealed a progressive increase in vibrations amplitude, due to the presence of a deep crack. It was actually detected by automated ultrasonic equipment using advanced signal processing. Failure analysis and laboratory tests demonstrated that the crack started from a forging defect located at the root of a longitudinal slot, due to the high stress range induced by oil film instability problems. During the following years the crack grew mainly during transients and not during operation.