Fatigue and fracture emanating from notch; the use of the notch stress intensity factor

The analysis of the stress distribution at notch tip shows a pseudo-stress singularity characterised by the notch stress intensity factor (NSIF) K_ρ. The critical value of this parameter K_ρ^ccan be used to determine the fracture toughness of very brittle materials from notched specimens. The range of the notch stress intensity factor ΔK_ρ plays an important role in initiation of fatigue emanating from notches and in the notch fatigue sensitivity index.     

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.     

Damage and fatigue crack growth of Eurofer steel first wall mock-up under cyclic heat flux loads. Part 2: Finite element analysis of damage evolution

In the preceding companion article (part 1), the experimental results of the high-heat-flux (3.5 MW/m²) fatigue tests of a Eurofer bare steel first wall mock-up was presented. The aim was to investigate the damage evolution and crack initiation feature. The mock-up used there was a simplified model having only basic and generic structural feature of an actively cooled steel FW component for DEMO reactor. In that study, it was found that microscopic damage was formed at the notch root already in the early stage of the fatigue loading. On the contrary, the heat-loaded smooth surface exhibited no damage up to 800 load cycles. In this paper, the high-heat-flux fatigue behavior is investigated with a finite element analysis to provide a theoretical interpretation. The thermal fatigue test was simulated using the coupled damage-viscoplastic constitutive model developed by Aktaa. The stresses, inelastic deformation and damage evolution at the notch groove and at the smooth surface are compared. The different damage behaviors at the notch and the surface are explained in terms of hydrostatic stress and inelastic strain fields. The effect of heating pulse length on inelastic deformation is also addressed. It is demonstrated that the predicted damage evolution feature agrees well with the experimental observation qualitatively.     

On plastic deformation and fatigue under multiaxial loading

This paper presents an experimental and theoretical investigation of deformation and fatigue behaviour under multiaxial random loading. The inelastic stress-strain response under complex loading paths has been predicted using an incremental plasticity model, which incorporates a memory rule to account for the variable-amplitude and non-proportional loading effects. Based on hysteresis strain-hardening behaviour and the history described by the memory effect under multiaxial loading, a mechanics-based cycle counting method has also been proposed for multiaxial random loading. The evaluation of cumulative damage by the cycle counting method combined with Miner's linear rule and a strain-path-dependent fatigue damage parameter is compared with experimental results of two metals under biaxial variable-amplitude loading.     

Inelastic stress-strain response for notched specimen of Cr-1Mo steel at 600°C

Following a series of cooperative studies A-I and A-II (phase III) concerning the inelastic behaviour of high temperature materials under uniform state of stress, finite element analyses were carried out on circumferential notched cylinders subjected to plasticity-creep interaction conditions. Using an electric capacitance type extensometer “Strain-Pecker”, which is capable of measuring a local strain response with a gauge length of 0.5 mm under high temperature conditions, stress-strain responses for both global and local regions near the notch root were evaluated. Ten kinds of inelastic constitutive model were introduced into a finite element code, and the responses for four kinds of loading pattern were examined for two types of notch shape.     

Probabilistic prediction of multiple fracture under service conditions

The probability of fracture initiation, propagation, and arrest is one of the important problems facing designers, analysts, and operators of modern structures including nuclear reactors. The question of fracture requires special considerations which include the random nature of the loading and the statistical nature of the material's response to fracture under the imposed service loads. In most structural applications it is essential to know not only if and when fracture will occur under normal and off-normal operating conditions, but also to have some knowledge of the fracture propagation configurations and their resulting influence on the integrity of the structure. In this paper we address the problem of multiple fracture propagation configurations in structures under service conditions. This is accomplished by introducing a generalized energy criterion for multiple brittle fracture in nonhomogeneous and anisotropic materials.The fracture criterion is expressed in terms of the so-called Hartz function H which measures the difference between the total instantaneous strain energy release rate G_T and the rate at which energy is required for the formation of new fracture surfaces R_T. Strain energy release rates are computed for a variety of symmetric as well as asymmetric fracture propagation configurations from finite element solutions of incrementally related boundary value problems. These solutions yield a deterministic influence parameter α which is used to relate the applied loading to the probabilistic expression for the strain energy release rate. A similar treatment is given to the function R_T for which the influence parameter β must be determined experimentally. The parameters, α and β, depend upon the relative locations, sizes and orientations of the primary and secondary cracks as well as flaws, and secondary imperfections present in the material. In addition the parameter β depends upon the relative values of the specific surface energy associated with the possible primary and secondary fracture paths. This is important for anisotropic materials such as ceramics mixed-oxide fuels and concrete, and for materials experiencing stress-corrosion fracture, where the energies associated with intergranular and transgranular fracture, for example, may differ significantly.From the probabilistic expressions for G_T and R_T, the Hartz function is determined as a random variable h which describes the multiple fracture process. The formulations developed in this presentation are applied to a single edge notched panel experiencing multiple fracture under assumed random loadings. Some interesting symmetric as well as asymmetric fracture configurations are studied and the results are related to reported experimental observations. The approach presented here may have applications in the areas of fatigue crack propagation, stress corrosion cracking, and fail-safe design optimization. Current studies are aimed at simulating the influence of grain structure anisotropy, intergranular corrosive attack, and creep deformation on multiple fracture in polycrystalline materials.     

Fully coupled strain and damage finite element analysis of ductile fracture

The local approach to fracture presented in this paper is based upon the continuum damage theory. The numerical implementation of this theory is made within the framework of the displacement approach of the finite element method. The fully coupled approach used to predict both initiation and propagation is described in detail. To demonstrate the usefulness of this type of local approach, it is applied to the prediction of initiation in an axisymmetrically notched tensile bar subjected to monotonous loading in ductile fracture conditions. The numerical problems arising when propagation of a localized completely damaged zone is modelled are outlined. To overcome these convergence problems, it is proposed to implement a new local fracture criterion together with a new method ensuring a C₀ continuity of the damage field throughout the finite element discretized structure.     

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.     

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.     

Transferability of post yield fracture mechanics properties from small scale specimens to large scale specimens and components

This contribution describes a method for the determination of the J-integral as a function of the load-line displacement for arbitrary specimen geometries.A correspondence could be found between the approximation method and the results determining with the Rice integral by means of a FE-calculation. Using the initiation values of the J-integral as a fracture mechanics parameter determined from the J_R-curve, correspond with failure values of double-édged notched tensile specimens and circumferentially notched round tensile specimens of which crack initiation was tantamount to instability. Consequently, it could be proved that the J-integral is a transferable parameter that may be ascertained from simple determinable deformation values. The application to real components seems to be promising, due to these good results.     

Reactor pressure vessel structural integrity research

Development continues on the technology used to assess the safety of irradiation embrittled nuclear reactor pressure vessels (RPVs) containing flaws. Fracture mechanics tests on RPV steel, coupled with detailed elastic-plastic finite element analyses of the crack-tip stress fields, have shown that (1) constraint relaxation at the crack-tip of shallow surface flaws results in increased data scatter but no increase in the lower-bound fracture toughness, (2) the nil-ductility temperature (NDT) performs better than the reference temperature for nil-ductility transition (RT_NDT) as a normalizing parameter for shallow flaw fracture toughness data, (3) biaxial loading can reduce the shallow flaw fracture toughness, (4) stress based dual-parameter fracture toughness correlations cannot predict the effect of biaxial loading on shallow flaw fracture toughness because in-plane stresses at the crack-tip are not influenced by biaxial loading, and (5) an implicit strain based dual-parameter fracture toughness correlation can predict the effect of biaxial loading on shallow flaw fracture toughness. Experimental irradiation investigations have shown that (1) the irradiation induced shift in Charpy V-notch vs. temperature behavior may not be adequate to conservatively assess fracture toughness shifts due to embrittlement, and (2) the wide global variations of initial chemistry and fracture properties of a nominally uniform material within a pressure vessel may confound accurate integrity assessments that require baseline properties.     

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.     

Creep—fatigue test of a thick-walled vessel under thermal transient loadings

To improve the damage evaluation methods in the design code for Fast Breeder Reactors (FBRs), a series of creep—fatigue tests of structural models under thermal transient loadings are going on at Oarai Engineering Center of the Power Reactor and Nuclear Fuel Development Corporation (PNC). Test models are designed to incorporate representative structures of components and pipings used in FBRs and are subjected to severer cyclic thermal transients than those experienced in FBRs. The test is planned to be continued until failure occurs. This paper describes the creep—fatigue test results and their damage evaluation for the first test model.A 40 mm thick vessel model made of SUS304 austenitic stainless steel was subjected to cyclic thermal transients, in which sodium at 600°C and 250°C flowed repeatedly. The period of each transient was 2 h. Cracks were observed at seven test portions in the model after 1002 cycles of the thermal transients.Elastic and inelastic analyses were performed to evaluate creep—fatigue damage and crack propagation. The safety margins included in the creep—fatigue design methods based on elastic analysis as well as those based on inelastic analysis are discussed. Finally fracture mechanics analyses were performed to explain the observed crack growth.     

Experimental Investigation of Strain Concentration Evaluation Based on the Stress Redistribution Locus Method

Evaluating the local strain in structural discontinuities is an important technology in high temperature design of fast reactor components because the failure mode in high-temperature fatigue or creep fatigue damage usually results from the crack initiation and growth from such locally high strained areas. A rationalized method of evaluating strain concentration that was experimentally studied is discussed. The stress redistribution locus (SRL) method had been proposed to improve the accuracy with which local stress and strain can be evaluated in the structural discontinuities. This method is based on the concept that the locus of stress redistribution from an elastic to an inelastic state, or that during relaxation, strongly depends on the structure, and the locus almost coincides with the locus obtained through elastic-creep analysis. High-temperature fatigue tests of circumferentially notched specimens were conducted accompanied by the measurement of local strain carried out with a capacitance-type strain gauge. The measured strain was compared with the predictions made with SRL, and the method's accuracy was evaluated. SRL improved the accuracy of inelastic strain estimation while remaining reasonably conservative in comparison with Neuber's rule, which is used in high temperature design codes.     

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.     

Creep anisotropy of Zircaloy-2 cladding during irradiation

A procedure is described to determine the axial-radial and circumferential-radial contractile strain ratios (the R and P factors in the Backofen modified von Mises-Hill yield criterion) from post-irradiation dimensional measurements of Zircaloy-2 of boiling water reactor fuel rods, tie rods and water rods. Values for R and P have been determined for textured cold-worked stress-relieved (CWSR) Zircaloy-2 cladding. A sensitivity study was performed to evaluate the effects of measurement uncertainties on the derived values of R and P and on the engineering application of the model to predict the in-reactor deformation of CWSR Zircaloy-2 cladding.     

Peripheral shear strength of biaxially tensioned reinforced concrete wall elements

The results of a series of tests on biaxially tensioned, orthogonally reinforced concrete panels subjected to punching shear are presented and discussed. Contrary to existing U.S. code provisions, the punching shear capacity is not reduced significantly as the biaxial tension level is increased to as much as 0.8f_y in the reinforcement. A design equation is proposed that gives 4√f′_c shear stress for zero biaxial tension and a linear decrease to 3.1√f′_c as the tension is increased to 0.9f_y.The size of the loading pad under the punching force and the shear span have little effect on the strength but the pattern of the failure crack does change with these geometric variables. The splitting crack tends to connect the edge of the loading pad and the supports.More testing is recommended to evaluate a few additional variables, such as the use of inserts which receive the punching force.     

An experimental validation of the guideline for inelastic design analysis through structural model tests

In this paper, the inelastic analysis procedures recommended to use in the advanced elevated temperature structural design guide under development in Japan for the improved design of future fast breeder reactors were validated through the structural model tests and the evaluation of the experimental results by the inelastic analyses. First, a thermal fatigue test of a 316FR hollow cylinder with two longitudinal weldments was conducted under the condition of combined constant axial load and cyclic movement of axial temperature distribution, which simulated the loading condition near the free surface of coolant sodium in the main vessel of fast breeder reactors (FBRs). In the experiments, longitudinal and radial ratcheting deformation were measured and crack initiation life was also examined. Second, the inelastic analyses were carried out in accordance with the recommended procedure by using the measured results of oscillating temperature distribution. Finally, the results of inelastic analyses were compared with the experimental results and it was validated that the recommended practice gave a conservative result for the deformation and a good estimation of strain range for the fatigue life evaluation.     

Fracture assessment of shallow-flaw cruciform beams tested under uniaxial and biaxial loading conditions

A technology to determine shallow-flaw fracture toughness of reactor pressure vessel (RPV) steels is being developed for application to the safety assessment of RPVs containing postulated shallow surface flaws. Matrices of cruciform beam tests were developed to investigate and quantify the effects of temperature, biaxial loading, and specimen size on fracture initiation toughness of two-dimensional (constant depth), shallow, surface flaws. The cruciform beam specimens were developed at Oak Ridge National Laboratory (ORNL) to introduce a far-field, out-of-plane biaxial stress component in the test section that approximates the nonlinear stresses resulting from pressurized-thermal-shock or pressure–temperature loading of an RPV. Tests were conducted under biaxial load ratios ranging from uniaxial to equibiaxial. These tests demonstrated that biaxial loading can have a pronounced effect on shallow-flaw fracture toughness in the lower transition temperature region for an RPV material. The cruciform fracture toughness data were used to evaluate fracture methodologies for predicting the observed effects of biaxial loading on shallow-flaw fracture toughness. Initial emphasis was placed on assessment of stress-based methodologies, namely, the J–Q formulation, the Dodds–Anderson toughness scaling model, and the Weibull approach. Applications of these methodologies based on the hydrostatic stress fracture criterion indicated an effect of loading-biaxiality on fracture toughness; the conventional maximum principal stress criterion indicated no effect. A three-parameter Weibull model based on the hydrostatic stress criterion is shown to correlate with the experimentally observed biaxial effect on cleavage fracture toughness by providing a scaling mechanism between uniaxial and biaxial loading states.