Ductile fracture models and their potential in local approach of fracture

Since the pioneering studies conducted by McClintock, Rice and Tracey on the growth of cavities, many studies have covered modelling of ductile fracture; a non-exhaustive list is given of these studies. In the local approach of fracture, the models are used at the tip of cracks, and in the present state, only relatively simple models can be used to solve fracture problems in a complete manner, from material characterization to the analysis of cracked structures.The paper presents two types of models based on a critical ratio of cavity growth or on continuum damage mechanics. In the framework of the local approach of fracture, their possibilities are presented with constant references to experimental validation studies. This allows conclusions to be drawn regarding the effectiveness of the methods proposed and their undeniable contribution to fracture mechanics.     

Anisotropic creep damage in the framework of continuum damage mechanics

For some years various works have shown the possibility of applying continuum mechanics to model the evolution of the damage variable, initially introduced by Kachanov. Of interest here are the complex problems posed by the anisotropy which affects both the elastic behaviour and the viscoplastic one, and also the rupture phenomenon.The main concepts of the Continuum Damage Mechanics are briefly reviewed together with some classical ways to introduce anisotropy of damage in the particular case of proportional loadings. Based on previous works, two generalizations are presented and discussed, which use different kinds of tensors to describe the anisotropy of creep damage:

• - The first one, by Murakami and Ohno introduces a second-rank damage tensor and a net stress tensor through a net area definition. The effective stress-strain behaviour is then obtained by a fourth-rank tensor.

• - The second theory, by Chaboche, uses one effective stress tensor only, defined in terms of the macroscopic strain behaviour, through a fourth-order non-symmetrical damage tensor.

The two theories are compared at several levels: differences and similarities are pointed out for the damage evolution during tensile creep as well as for anisotropy effects. The possibilities are discussed and compared on the basis of some existing experimental results, especially for creep under tension-torsion, which leads to a partial validation of the two approaches.     

Evaluation of hydrogen assisted cracking: the meaning and significance of the fracture mechanics approach

Analysis of hydrogen assisted cracking is performed with emphasis on the validity of the linear elastic fracture mechanics approach. Its soundness is ensured by the uniqueness of the crack growth kinetics curve ‘crack growth rate v versus stress intensity factor K' for a material–environment system. The ability of this relationship to match the similitude of crack tip events is revised for the whole chain of process components: ‘hydrogen supply to metal—entry into and accumulation in the process zone—degradation and crack advance'. Some of the factors able to violate the uniqueness of the ‘material's' v(K)-curve are discussed: (i) the role of far field in hydrogen transportation to the fracture zone; (ii) near tip environmental interactions and process zone hydrogenation dependent on the cracking process history; (iii) mechanical nonlinear effects caused by crack tip plasticity which may be significant even under small-scale yielding. Suggestions for a refinement of the customary fracture mechanics approach are given.     

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.     

A5O8-3钢晶粒组织的细化

对 A508-3钢的原奥氏体晶粒、贝氏体束区及临界区淬火后平均晶粒的大小作了测定,并讨论了其影响因素。结果表明,低含铝量是原奥氏体晶粒出现严重混晶的原因,提高冷却速度可使贝氏体束区的尺寸变小,采用临界区淬火后晶粒组织得到大幅度的细化。     

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.     

Stress corrosion cracking in the heat-affected zone of A508 steel welds under high-temperature water

The influence of heat input on stress corrosion cracking (SCC) in the heat-affected zone (HAZ) of A508 steel welds was investigated. Constant extension rate tensile tests were conducted on notched round-bar specimens in simulated reactor coolant conditions to assess SCC performance. In multi-pass welds, the use of a low heat input resulted in a better SCC resistance than that of a high heat input due to the existence of a more refined microstructure.     

Improvement of impact toughness of the SA 508 class 3 steel for nuclear pressure vessel through steel-making and heat-treatment practices

Comparative investigations of the effects of steel-making practices on impact and fracture toughness were studied. From these examinations, impact and fracture toughness of the steels by vacuum carbon deoxidation (VCD) offered the required values; however, those of the steels by modified VCD and silicon-killing practices were secure. The fracture toughness (K_IC) was significantly improved by the silicon-killing and the modified VCD. These resulted from the fineness of austenitic grain size and reduction of sulphidic inclusion. It was observed that the grain size of steels by modified VCD and silicon-killing practices was 20 μm, while that of steel by VCD was 50 μm. The sulphidic inclusion contents were reduced in the steels by modified VCD and silicon-killing practices. Furthermore, the effects of cooling rates from austenitizing temperature on the impact toughness in the steel by VCD were also investigated. The impact toughness of the steel by VCD was closely related to the cooling rate. To obtain the secure impact toughness in the steel by VCD, it seems that the recommended minimum cooling rate from the austenitizing temperature should be 15°C min⁻¹.     

Simulation of the fracture behavior of Zircaloy-4 cladding under reactivity-initiated accident conditions with a damage mechanics model combined with fuel performance codes FEMAXI-7 and RANNS

A continuum damage mechanics model using FEM calculations was proposed to be applied to an analysis of the fuel failure due to pellet cladding mechanical interaction (PCMI) under reactivity-initiated accident conditions. The model expressed ductile fracture via two processes: damage nucleation related to void nucleation and damage evolution related to void growth and linkage. The boundary conditions for the simulations were input from the fuel performance codes FEMAXI-7 and RANNS. The simulation made reasonable predictions for the cladding hoop strain at failure and reproduced the typical fracture behavior of the fuel cladding under the PCMI loading, characterized by a ductile shear zone in the inner region of the cladding wall. It was shown that occurrence of a through-wall crack is determined at an early stage of crack propagation, and the rest of the through-wall penetration process is achieved with a negligible increment in strain. The effect of a local temperature rise in the cladding inner region on the failure strain was found to be less than 5% for the conditions investigated. Failure strains predicted under a plane strain loading were smaller by 20%–30% than those predicted under equibiaxial tensions between the hoop and the axial directions.     

Application of fracture mechanics in the design and operation of PWRs in France

Fracture mechanics techniques are used to evaluate the risks associated with material aging, the occurrence of fabrication defects or stress corrosion cracks, and to determine the margins with respect to fast fracture resulting from the design and manufacturing practices. Important programs are underway to improve the accuracy and domain of validity of the fracture mechanics methods.     

The use of fracture mechanics and non-destructive testing to reduce the risk of catastrophic failure

Structural integrity assessments involve the use of fracture mechanics together with appropriate design, quality assurance and inspection techniques. Recent application to nuclear pressure vessels has led to improvements in the fracture toughness data base, in methods for measuring fracture toughness and in the use of elastic/plastic and J?R curve concepts. Fatigue crack growth studies in water of realistic flow rate and oxygen content have shown that the effect of a PWR water environment is not as severe as previously reported and has related this to show strain rate cracking. The role of the pressure test has beenn examined, throwing emphasis on the importance of effective non-destructive inspection to detect and characterise flaws. Recent developments to improve and to validate very high levels of effectiveness of NDT are summarised.     

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.     

Determination of fracture mechanics properties of welded joints and comparison with the failure behaviour of wide plates

Fracture behaviour of different welded joints of 15 MnNi 6 3 and 20 MnMoNi 5 5 steel is studied by testing Charpy-V impact, fracture mechanics specimens as well as wide plate specimens of different sizes. The influence of welding conditions and stress relief heat treatment on the failure behaviour of the heat affected zones is examined. Fracture mechanics test data are used in order to predict failure loads of the wide plates by the R6-procedure and by FE-calculations.     

The application of the boundary-integral equation method to the solution of engineering stress analysis and fracture mechanics problems

This paper reviews the development and application of an influence function method for calculating stress intensity factors and residual fatigue life for two- and three-dimensional structures with complex stress fields and geometries. Through elastic superposition the method properly accounts for redistribution of stress as the crack grows through the structure. The analytical methods utilized and the computer programs necessary for computation and application of load independent influence functions are presented. A new exact solution is obtained for the buried elliptical crack, under an arbitrary Mode I stress field, for stress intensity factors at four positions around the crack front. The IF method is then applied to two fracture mechanics problems with complex stress fields and geometries. These problems are of current interest to the electric power generating industry and include (1) the fatigue analysis of a crack in a pipe weld under nomial and residual stresses and (2) fatigue analysis of a reactor pressure vessel nozzle corner crack under a complex bivariate stress field.     

The integration of the tensile and notch impact bend test into an experimentally validated fracture mechanics concept

A fracture concept for practical use, which is based on a correlation of the notch impact energy with the fracture mechanics characteristic quantities for crack initiation and instability, will be presented. The maximum load and crack size safety factors can be calculated by using the developed Failure Analysis Diagrams (FAD). These diagrams are also suitable for the completion of the Nuclear Technical Code with respect to the size of defects which need to be removed, the type and scope of quality assurance measures and the determination of intervals for repeated testing.     

Liquid metal embrittlement of T91 and 316L steels by heavy liquid metals: A fracture mechanics assessment

LME of the martensitic T91 and the austenitic 316L steels have been investigated in the CCT geometry in the plane-stress condition. Using such a geometry, premature cracking induced by a liquid metal (PbBi and Hg) can be studied using a fracture mechanics approach based on CTOD, J-Δa and fracture assessment diagram. One is able to measure a reduction of the crack tip blunting and a reduction of the energy required for crack propagation induced by the liquid metal. In spite of some limitations, this qualitative evaluation shows that liquid metals do not induce strong embrittlement on steels in plane-stress condition. Rather, the effect of the liquid metal seems to promote a fracture mode by plastic collapse linked with strain localization. It indicates that the materials, in spite of a potential embrittlement, should still be acceptable in terms of safety criteria.     

The use of fluorescence in the measurement of local liquid content in transient multiphase flows

The theoretical basis of a technique we proposed recently for the measurement of local-instantaneous liquid fractions in highly dispersed two-phase flows is developed. The technique is based on the measurement of ultraviolet-induced fluorescence, and the theoretical approach is to carry out numerical experiments accounting for refractions in the radiation transport path and for the randomness in the flow field (i.e., droplet positions and sizes). These numerical experiments indicate that for a properly selected measurement volume (defined by positioning of the fibers) refractions have a small impact and the measurement is predictable and robust. We also present experimental data that demonstrate this excellently predictable behavior.     

The probability of leakage in piping systems of pressurized water reactors on the basis of fracture mechanics and operating experience

Probabilities of leakages in piping systems as used in risk studies up to now do not represent the present state of the art. The goal of this investigation is to formulate a new set of probabilities of leakages in piping systems of German pressurized water reactors for the whole range of pipes which are of interest using the operating experience, the principles of the basis safety approach and fracture mechanics studies.