Crack initiation and growth under creep and fatigue loading of an austenitic stainless steel

Both the initiation and the propagation of macroscopic cracks have been studied in a creep ductile 316L type stainless steel at 575–650°C using various fracture mechanics specimens and a wide range of test conditions including steady load at constant or varying temperatures, varying loads at constant temperature. It is shown that, even for isothermal tests, the C^* parameter is unable to provide unique correlations for all the stages of both creep crack initiation and growth. A unique correlation nevertheless exists between C^* and the time to initiation, T_i. Large differences – either conservative or not – from a simplified linear damage cumulation rule are found when the tests are performed at two successive temperatures or two loads. Very detrimental effects of creep-fatigue loadings are shown.A simplified global approach to creep crack initiation under isothermal conditions, based on reference stress and length concept is developed. A local approach to creep cracking, in which an intergranular physical damage law determined experimentally on notched bars, and stress-strain fields obtained by analytical results is shown to provide crack growth results in good agreement with experiment.     

Defect assessment procedures at high temperature

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

Development of simplified evaluation method for creep-fatigue crack propagation

In the design assessment of fast reactor plant components, prevention of crack initiation from defect-free structures is a main concern. However, existence of initial defects such as weld defects cannot be entirely excluded and this potential cracks are to be evaluated to determine if initiated cracks do not lead to component failure instantly. Therefore, evaluation of structural integrity in the presence of crack-like defects is also important to complement the formal design assessment. The authors have been developing a guideline for assessing long-term structural integrity of fast reactor components using detailed inelastic analysis and nonlinear fracture mechanics. This guideline consists of two parts, evaluation of defect-free structures and flaw evaluation. In the latter, creep-fatigue is considered to be one of the most essential driving force for crack propagation at high operating temperature exceeding 500 °C. The uses of J-integral-type parameters (fatigue J-integral range and creep J-integral) are recommended to describe creep-fatigue crack propagation behavior in the guideline. This paper gives an outline of the simplified evaluation method for creep-fatigue crack propagation.     

Creep and creep-fatigue cracking behaviour of two structural steels

The present study deals with crack initiation and crack growth, not only under creep and creep-fatigue conditions but also under more complex thermomechanical cyclic loadings, in both 316L and 1Cr-1Mo-0.25V steel.In these creep ductile materials, most studies have focused on the creep crack growth rates, da/dt and load-geometry parameter C* correlations. In this paper, the creep crack initiation time is defined as the time T_i necessary for a defect to grow by a small critical distance X_c (X_c ≈ 50 μm for example). This initiation stage may represent a large part of the rupture life of a cracked component. The importance of such studies is discussed in the first part.In the second part, an attempt is made to present a simplified method based on the fracture mechanics of creeping solids to define the relevant load-geometry parameters for crack initiation and crack growth under creep-fatigue loadings. In particular, it is shown that da/dN-ΔK correlations apply only when the hold time t_h is smaller than the transition time t_tr between small-scale and large-scale viscoplasticity. Conversely, for long hold times, it is suggested that the T_i-C* correlation be used to predict the fatigue.     

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.     

Creep-fatigue crack propagation behavior in a surface cracked plate

A series of experiments were performed in order to clarify the surface crack growth behavior under creep-fatigue condition. Type 304 stainless steel was tested at 550°C and 650°C. Specimens were plates with a surface notch. Loading patterns were axial fatigue, bending fatigue, axial creep-fatigue and bending creep-fatigue. As results were obtained: (1) the beach mark method was available to measure the changes of the crack front shape after the test; (2) the electrical potential method was available to measure the changes of the crack front shape in real time; (3) the crack front shape was affected by the loading mode; and (4) ΔJ and ΔJ_c calculated from the proposed simplified method could characterize the surface crack growth rate.     

Applications of a fracture mechanics model of structural reliability to the effects of seismic events on reactor piping

A fracture mechanics model of structural reliability is described. The model assumes that failure occurs due to the subcritical and catastrophic growth of as-fabricated defects. The material properties, stress history, number and dimensions of the initial cracks are treated as random variables. Crack growth is calculated using fracture mechanics principles. The capability of modeling two-dimensional cracks and thickness gradients of the applied stresses represents a significant advance over previous work in this field.The model has been used to estimate the influence of earthquakes on the integrity of circumferential girth butt welds in the large (diameter greater than 30 in.) primary coolant system pipes of a commercial pressurized water reactor. In the absence of earthquakes, the probability of leaks and catastrophic double-ended guillotine breaks is estimated to be 10^?6 and 10^?12 per plant lifetime, respectively. These probabilities were only slightly increased by the occurrence of earthquakes. The cyclic stresses in the heatup-cooldown cycle had the greatest effect on the crack growth. Radial gradient thermal stresses due to temperature fluctuation of the coolant during transients have only a small effect on the amount of crack growth. Sensitivity studies show that significant changes in modeling assumptions are needed before the calculated failure probabilities are raised to the level of current estimates. This suggests that perhaps factors such as design and construction errors or stress corrosion cracking may be significant contributors to the probabilities.     

Finite element fracture mechanics analysis of creep rupture of fuel element cladding

A finite element fracture mechanics technique is applied for simulating the elevated temperature creep rupture behavior of initially defected austenitic stainless steel fuel element cladding. The basic analytical approach consists of determining total instantaneous strain energy release rates G_T, and the corresponding values of the stress intensity factor K_T from sequential linear elastic finite element solutions and relating these to either an effective creep fracture toughness parameter G_ec (or K_ec) or to creep crack growth rates , obtained from test results.An initial application of this approach has been made to simulate the creep rupture behavior of initially defected type 316 austenitic stainless steel fuel element cladding in the 20% cold worked condition, tested at 650°C. This application has provided a relationship in the simple familiar form: , where σ is the nominal loop stress, a is the initial depth of a longitudinal crack, h is the cladding thickness, t_r is the time to rupture, and q is a structure sensitive parameter which accounts for the influence of the environment. is a function, obtained from finite element solutions, which accounts for the geometric differences between the present structure and the classical Griffith plate. The function ) is obtained from creep rupture tests of cladding with varying initial flaw depths and times to rupture under corrosive as well as inert environments.Performing time-dependent analyses, a preliminary relationship is obtained between the instantaneous values G_T and K_T, and crack growth rates under corrosive and non-corrosive environments. The analytical predictions of critical combinations of cladding flaw configurations, stresses, times to rupture and crack growth rates are in good agreement with the limited test data available for comparison. Current applications are aimed at the long-term cyclic creep fracture behavior of fast reactor fuel elements, using a nonlinear finite element code. In addition, multiple intergranular fracture configurations are being investigated.     

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.     

A critical survey on the application of plastic fracture mechanics to nuclear pressure vessels and piping

Plastic fracture mechanics techniques have been developed to treat the regime where extensive plastic deformation and stable crack growth occur prior to fracture instability in the tough ductile materials used in nuclear systems. As described in this paper, a large number of crack tip parameters can be used in a plastic fracture resistance curve approach. However, applications using the J-integral currently predominate. This parameter has significant advantages. It offers computational ease and can provide a lower bound estimate of the fracture condition. But, J also has a disadvantage in that only a limited amount of stable crack growth can be accommodated. The crack tip opening angle parameter, in contrast, can be valid for extensive stable crack growth. But, with it and most other realistic alternatives, the computational convenience associated with the J-integral is lost and finite element or other numerical methods must be employed. Other possibilities such as the two-criterion approach and the critical net section stress are also described in the paper. In addition, current research work focussed upon improving the theoretical basis for the subject is reviewed together with related areas such as dynamic plastic analyses for unstable crack propagation/arrest and creep crack growth at high temperatures. Finally, an application of plastic fracture mechanics to stress corrosion cracking of nuclear piping is made which indicates the possible anti-conservative nature of the current linear elastic assessments.     

Crack growth determination on laboratory components

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

Ductile fracture of A 508 Cl 3 steel in relation with inclusion content: The benefit of the local approach of fracture and continuum damage mechanics

A new methodology for ductile fracture analysis based on the local approach of fracture, through constitutive relations that take into account void growth and damage, has been applied to three heats of A 508 Cl 3 steel with different inclusion contents in the region of 10⁻³–10⁻⁴. The ductility of the three heats is well predicted by the ductile fracture model through its parameter f₀: the initial volume fraction of voids. The model, first calibrated with the simple notched tension test, gives a good prediction of crack initiation and growth in a precracked specimen. Finally the statistical aspects in ductile fracture are briefly discussed.     

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.     

Effect of loading rate upon fracture behavior of ferritic steel under large scaled yielding

Dynamic loading to ferromagnetic materials and large scaled yielding result in peak or valley and non-linear curve, respectively, on the Direct Current Potential Drop (DCPD) versus Crack Opening Displacement (COD) plots, which make it difficult to determine the crack initiation point. In this work high intensity of current up to 100 A was applied to the specimens of SA106Gr.C ferritic steel and the crack growth behavior was directly monitored by a high speed camera to obtain the crack initiation point. The effects of loading rate up to 1200 mm min⁻¹ upon the fracture resistance were explored. As the results, it has been shown that, although no substantial difference was seen in the load–COD plots, the crack initiation and then J_i and J–R curve were quite sensitive to the loading rate. That is, under the loading rate of 300 mm min⁻¹ the material showed the worst fracture resistance than under static loading and even under the higher loading rates of 600 and 1200 mm min⁻¹. Also applying the high speed camera and high current source have been proved to be an effective way to find out the accurate crack initiation point and to compensate the pulse of DCPD due to the ferromagnetic effect.     

Application of statistical linear elastic fracture mechanics to pressure vessel reliability analysis

An evaluation of the failure probability for a pressure vessel is made on the basis of linear elastic fracture mechanics (LEFM). Failure is identified by actual crack length equal to critical crack length. The probability of failure is the joint probability that there exists a crack (i.e. K_I) greater than a given crack (i.e. K) and that the critical crack (i.e. K_IC) is smaller than that same crack, where K_I and K_IC are considered for same time and location. K_IC as well as K_I are treated as statistical variables with probability density functions (p.d.f.), which are functions of material, location and time. The variability of K_IC (that is the p.d.f. of K_IC) is a result primarily of the statistical nature of the material properties and to a lesser degree of the increasing neutron-done experienced by certain parts of the pressure vessel. The variability of K_I (that is the p.d.f. of K_I) is a result of the following parameters:

1. (1) initial distribution of cracks (that is the crack distribution at the start-up of the reactor) regarded as a statistical variable, because of the uncertainty in the non-destructive testing of the pressure vessel prior to start-up.

2. (2) stresses, regarded as a statistical variable because of the uncertainty in the stress analysis and the geometry of the vessel.

3. (3) crack growth by fatigue, which is a result of the normal (with probability equal to 1.0) and abnormal (with a p.d.f.) operational transients. The statistical nature of the crack growth is due to the statistical variation of the abnormal operational transients.

4. (4) material properties (that is K_IC, yield strength and the factors governing the fatigue crack growth) regarded as statistical variables.

The p.d.f.s of the abovementioned parameters are evaluated on the basis of the available literature. The integrated calculations of failure probability are performed by a computer program utilizing the Monte Carlo technique with importance sampling, which gives a greater freedom in selection of p.d.f.s. Calculations of failure probability for existing reactors are presented.     

A simplified analysis of creep crack growth using local approach

The use of Fracture Mechanics parameters (K, J, C^*) is subjected to serious limitations when viscoplastic strain appears in a cracked structure.It is therefore one of the cases where a local approach of fracture might be the only mean to help understand the complex mechanical phenomena which influence crack growth.Using a very simple local fracture law, called sudden damage model, various closed form solutions of creep damage zone growth are proposed. With the help of a Double Cantilever Beam (DCB) model to simplify the geometry of the cracked structure, crack initiation and growth are analytically studied.Points such as creep zone size, stress redistribution or influence of local fracture criterion are discussed using closed form solutions.     

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.     

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.     

Thermoelastic stresses in pellet fragments and conditions for fragments formation

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

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.