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.     

Ductile fracture parameters of RPV-materials

Ductile fracture material parameters have been determined for a reactor pressure vessel material to characterize its fracture resistance in the upper shelf toughness regime. Three different methods (the multiple specimen unloading (MSU), direct current potential drop (DCPD) and single specimen partial unloading compliance (SSPUC) methods) have been applied to test different CT-specimen geometries at temperatures between 25 and 300°C.It is shown that there are principle differences between J-R-curves measured by different experimental procedures, because of different methods for the measurement of crack lengths and crack growth. For instability analyses, using a complete J-R-curve, these differences seem to be negligible. For the determination of critical material parameters at or close to initiation of stable crack growth these differences may cause systematic errors tending to higher values for DCPD as compared to MSU-results and to lower values for SSPUC respectively.Procedures can be defined to evaluate comparable critical material parameters from the different experimental procedures, if J_i is known in a good approximation allowing to consider only the real crack extension without blunting, or if in addition the real (or realistically modelled) blunting and the effective blunting of the specific method are known. The differences in material parameters will depend quantitatively on the type of material and its toughness (slope of J-R-curve). They may be in the range of the experimental scatter observed in testing and seem to be negligible, but their systematic character should be kept in mind, e.g. when ranking different materials according to their critical parameters determined by different methods.     

Ductile fracture of cracked steel plates

A simple relationship between loading for crack initiation, or onset of ductile tear, and crack length is presented for center-cracked plates of mild steel. Formulation of the nonlinear boundary-value problem is based on incremental theory of plasticity for Prandtl-Reuss materials. Quasi-static solutions corresponding to a series of incremental loading conditions are obtained by the mothod of finite elements. Tests conducted on plates of two types of mild steel agree with numerical results.     

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.     

First spinning cylinder test analysis using a local approach to fracture

In recent years, several experimental programmes on large-scale specimens have been organized to evaluate the capabilities of the fracture mechanics concepts employed in structural integrity assessment of pressurized water reactor pressure vessels. During the first spinning cylinder test, a geometry effect was revealed experimentally showing the difficulties of transferring toughness data from small-scale to large-scale specimens. An original analysis of this test, by means of a local approach to fracture, is presented in this paper. Both compact tension specimen and spinning cylinder fracture behaviour were computed using a continuum damage mechanics model developed at EDF. We confirmed by numerical analysis that the cylinder's resistance to ductile tearing was considerably larger than in small-scale fracture mechanics specimen tests, about 50%. The final crack growth predicted by the model was close to the experimental value. Discrepancies in J R curves seemed to be due to an effect of stress triaxiality and plastic zone evolution. The geometry effect inducing differences in resistance to ductile tearing of the material involved in the specimens can be investigated and explained using a local approach to fracture methodology.     

Ductile fracture behavior of circumferentially cracked type 304 stainless steel piping under bending load

A ductile pipe fracture test program has been conducted in Japan Atomic Energy Research Institute (JAERI) to investigate the ductile fracture behavior of circumferentially cracked pipes and to demonstrate the validity of the leak before break concept in LWR pipings.In the paper are described the scope of the pipe test program and current test results for 6-inch diameter type 304 stainless steel pipes. Test pipes with a through-wall or a part-through crack in the circumferential direction were bent under low or high compliance condition, and stable or unstable pipe fracture behavior was investigated. J based tearing instability criterion and the net section collapse criterion are compared with the pipe test results, and the validity of these fracture criteria is discussed. Furthermore, geometries of acceptable flaws in pipes are evaluated considering the leak before break condition.     

Analysis of cleavage fracture potential of martensitic stainless steel fusion structures: Part I. Micromechanical models and material properties

The major disadvantage of martensitic stainless steels for structural applications in fusion reactors is currently considered to be their potential for low temperature brittle cleavage fracture. This study attempts to review the current understanding of cleavage fracture in steels and the role of microstructure in dictating material resistance to this type of fracture. A parametric analysis of cleavage fracture in a surrogate steel, A533B, is made and the results are used in conjunction with general cleavage fracture theory to establish some potential guidelines for future research in developing the martensitic stainless steels.     

Coupled phenomenological and fracture mechanics approach to assess the fracture behaviour of TWC piping component

The present study demonstrates the numerical prediction of experimental specimen J-R curve using Gurson-Tvergaard-Needleman phenomenologically based material model. The predicted specimen J-R curve is used to determine the geometric independent initiation fracture toughness (J_SZWc) value that compares well with experimental result. Using the experimentally determined and numerically predicted J_SZWc values and specimen J-R curves, the accuracy of predicting the fracture behaviour of the cracked component is judged. Thus the present study proposed a coupled phenomenological and fracture mechanics approach to predict the crack initiation and instability stages in cracked piping components using numerically predicted specimen J-R curve obtained from tensile specimens testing data.     

Prevision of the cleavage fracture properties using a local approach: Application to the welded joint of a structural C-Mn steel

The local approach of cleavage fracture developed by Beremin is applied to the weld metal of welded joints prepared with a fine-grained structural C-Mn steel. The two parameters of the model (cleavage stress and inhomogeneity exponent) are determined by tensile testing of axisymmetry notched specimens.The analytical application of this approach predicts successfully the fracture toughness values found on precracked specimens. The transition and the scatter of the fracture toughness measurements as a function of temperature are correctly estimated for very different specimen geometries (type and in-plane dimensions).It is thus shown that a realistic estimation of the statistical distribution of fracture toughness can be obtained by testing single tensile specimens.     

Application of a local approach to ductile-brittle transition in a low-alloyed steel

Both tensile tests on notched specimens and fracture mechanics experiments on axisymmetrically cracked specimens were performed on one heat of A508 steel (AFNOR: 16MND5). Tensile tests on notched geometries were made to determine the characteristic parameters used in a statistical analysis of cleavage fracture proposed previously [1]. Tests on cracked specimens were carried out between −80°C and −20°C to investigate the critical values of stable crack growth, Δa_c, occurring before unstable cleavage fracture. At a given temperature a large scatter in the values of critical crack growth, Δa_c, was observed.To interpret these results a model derived previously for cleavage crack initiation [1] is used. In this model the Weibull stress is calculated by the finite element method for three different initial crack lengths covering stable growth increments observed experimentally. It is shown that this model accounts reasonably well for the observed effects.     

Liquid metal anode X-ray sources and their potential applications

Conventional electron impact X-ray sources invariably use solid state anodes. In this article a novel type of X-ray source is described in which X-rays are produced in a turbulently flowing liquid metal separated from the vacuum region of the X-ray source by a thin foil. The three diffusion processes (electron diffusion, heat conduction and turbulent mixing) which, together with convection, are responsible for thermal transport in liquid anode sources are briefly discussed and their relative importance is quantitatively assessed.When the mean lengths of these three diffusion processes are combined into a single parameter, σ, a simple Gaussian model of the spatial dependence of the temperature profile can be used to predict the loadability (W m⁻² K⁻¹) of the LIMAX arrangement. This model suggests that a DC load of several tens of kW can be maintained on a focus of 1 mm² effective area and this estimate is confirmed by results from an experimental LIMAX apparatus.As a natural extension of this work, the combination of a LIMAX source with a secondary fluorescence target is proposed to yield a high radiance source of quasimonochromatic radiation for X-ray scatter imaging applications. A brief discussion of this proposal is given in connection with its potential applications in the fields of industrial and medical X-ray scatter imaging.     

Accuracy of dynamic calculations using shell models under local impulse loading

Depending on soil conditions and load cases in dynamic calculations of nuclear power plants today more exact mathematical models may be used. For axisymmetric structures like reactor buildings, steel containments, circular tanks or coolant towers mathematical idealisations are used which especially deal with axisymmetric shell models. The calculations for these structures mentioned above, in the last 10 years, were generally carried out by applying specialised and qualified FE-programs.In order to qualify the results obtained using axisymmetric shell models as well the approved computer program MESY (Schrader 1976, 1978) several comparisons between computation and measurements were performed. As an example for these comparisons, impulse loadings, such as aircraft impact, applied by means of a pendulum on the HDR reactor will be shown.The analytical results were obtained prior to the general tests based on a loading function measured in a preliminary test step. In these calculations 11 harmonics were considered in the frequency range up to 80 Hz.Typical results will be shown and discussed, particularly the distribution of the maximum acceleration in the meridional and circumferential direction of the building.The analytical results for the structural response obtained using axisymmetric shell models conform satisfactorily to test results, especially in the area of load introduction in both (meridian and circumferential) directions.     

Hexahedral mesh generation of nuclear structures using intelligent local approach

This paper describes an automated mesh generation method named Intelligent Local Approach (ILA), which can control size and shape of hexahedral elements. A solid model created by a commercial solid modeler is first converted to quadrilateral surface patches. Second, considering local information on geometrical constraints, local connectivity of one to few hexahedral elements is determined step by step through some pattern matching tests with an element pattern database. Finally appropriate locations of new nodes are determined through a fuzzy knowledge processing technique. Fundamental performances of the present method are demonstrated through generating hexahedral meshes of some nuclear structures.     

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.     

Diffusion models of a jet of gas-aerosol pollutant for local radiation-monitoring systems

Two operational numerical models for dissemination of gas-aerosol pollutants in the atmosphere are presented: MADJET-GA (Gaussian type) and MADJET-MM, based on the method of moments of the concentration field. It is shown that it is important to determine the input parameters of the models correctly and consistently. A comparison of the concentration of sulfur dioxide calculated using the two models and the experimental data showed satisfactory agreement: 60 and 69%, respectively, of the 73 cases examined satisfy the factor of 2 (the concentration differs by less than a factor of 2). The sensitivity of the models to the input meteorological data was estimated by comparing the pollutant concentration field at the ground, calculated from pilot-balloon measurements of the wind speed and direction at two points in the Obninsk region and its surroundings. It is shown that on the average the pollutant spots overlap by 43–86%, and the average concentration at the ground differs by a factor of 2–7. Gaussian models are least sensitive to the input meteorological data. 1 figure, 1 table, 16 references. Scientific and Industrial Association “Taifun”. Atoménergoproekt. Translated from Atomnaya énergiya, Vol. 88, No. 6, pp. 464–470, June, 2000.     

A statistical approach to the prediction of pressure tube fracture toughness

The fracture toughness of the zirconium alloy (Zr-2.5Nb) is an important parameter in determining the flaw tolerance for operation of pressure tubes in a nuclear reactor. Fracture toughness data have been generated by performing rising pressure burst tests on sections of pressure tubes removed from operating reactors. The test data were used to generate a lower-bound fracture toughness curve, which is used in defining the operational limits of pressure tubes. The paper presents a comprehensive statistical analysis of burst test data and develops a multivariate statistical model to relate toughness with material chemistry, mechanical properties, and operational history. The proposed model can be useful in predicting fracture toughness of specific in-service pressure tubes, thereby minimizing conservatism associated with a generic lower-bound approach.     

New discrete models and their application to seismic response analysis of structures

New discrete models and their application to seismic response analysis of structures is proposed in this paper. These models consist of finite number of small rigid bodies connected with springs distributed over the contact area of two neighbouring bodies. In general size of stiffness matrices of these elements are at most (6 × 6) which are equal to or even smaller than of those of conventional finite elements so that considerable reduction of computing time can be expected. Effectiveness of these elements in nonlinear structural analysis, especially dynamic response analysis of structures will be demonstrated by several numerical examples.