An enhanced probabilistic model for cleavage fracture assessment accounting for local constraint effects

Objective of the present study is the development of an enhanced model for the probabilistic cleavage fracture assessment of ferritic materials considering the conditions for both, nucleation and propagation of micro defects. In a first step, the local load and deformation history at the cleavage initiation spot is analysed numerically for a variety of fracture mechanics specimens. The experimental data base includes experiments on standard deep and shallow crack specimens with different geometries as well as novel small scale cruciform bending specimens. These specimens enable the application of an additional stress component along the crack front. Based on the results, a two-criteria concept for cleavage initiation is proposed, assuming that the propagation of existing micro defects is controlled by the maximum principal stress whereas the nucleation of potentially critical micro defects is governed by a combination of the local plastic strain and the local stress triaxiality at the respective material point. Based on these assumption, a probabilistic cleavage fracture model is formulated and validated against the experimental data base.     

On the change of fracture mechanism with test temperature

Three point bending (3PB) tests of precracked specimens were carried out for coarse grain C-Mn steel at three low temperatures. Details of fracture surfaces in the specimens were microscopically observed and cleavage initiation sites were located. Calculations of local critical parameters and simulations of fracture behavior were made using finite element method (FEM). The results reveal that at very low temperature (−196 °C), the critical event controlling cleavage fracture is the nucleation of crack at the precrack tip in ferrite. The critical event moves to the initiation and propagation of a second phase particle crack at moderately low temperature (−110 °C). At higher temperature (−30 °C), the critical event for cleavage fracture after a fibrous crack extends is the propagation of a grain-sized crack.     

Ductile to brittle transition of an A508 steel characterized by Charpy impact test: Part I: experimental results

This study is devoted to the ductile-brittle transition behavior of a French A508 Cl3 (16MND5) steel. Due to its importance for the safety assessment of PWR vessels, a full characterization of this steel with Charpy V-notch test in this range of temperature was undertaken. The aim of this study is to provide a wide experimental database and microstructural observations to supply, calibrate and validate models used in a local approach methodology. Mechanical and fracture properties of the steel have been investigated over a wide range of temperatures and strain-rates. Effects of impact velocity on ductile-brittle transition curve, on ductile tearing and on notch temperature rise are presented and discussed. A detailed study of ductile crack initiation and growth in Charpy specimens is also carried out. From fractographic investigations of the microvoids nucleation around carbide second phase particles, a plastic strain threshold for nucleation is determined for this material. A508 Cl3 steels undergo a transition in fracture toughness properties with temperature, due to a change in fracture mode from microvoids coalescence to cleavage fracture. A systematic investigation on the nature and the position of cleavage triggering sites and on any change in the ductile to brittle transition (DBT) range has been carried out. This leads to the conclusion that manganese sulfide inclusions do not play an increasing role with increasing test temperature as recently mentioned in other studies on A508 Cl3 steel with a higher sulfur content. In a companion paper [Tanguy et al., Engng. Fract. Mech., in press], the numerical simulation of the Charpy test in the ductile-brittle transition range using fully coupled local approach to fracture is presented.     

Conversion of transgranular to intergranular fracture in NiCr steels

The paper is focused on quantification of causes and characteristics that govern the intergranular fracture initiation and propagation of this fracture micromechanism in competition with cleavage one. A NiCr steel of commercial quality and the same steel with an increased content of impurity elements, Sn and Sb, have been used for this investigation. Step cooling annealing was applied in order to induce intergranular embrittlement and brittle fracture initiation in both steels. Standard bend and the pre-cracked Charpy type specimen geometries were both tested in three-point bending to determine the fracture toughness characteristics. Charpy V notch specimens tested statically in three-point bending supported by FEM calculation have been used for local fracture stress and other local parameters determination. Relation of cleavage fracture stress and critical stress for intergranular failure has been followed showing capability of this parameter for quantification of the transgranular/intergranular fracture conversion. In order to characterise the quantitative roughness differences in fracture surfaces fractal analysis was applied. A boundary level of fractal dimension has been determined to be 1.12 for the investigated steel; the fracture surface roughness with a higher value reflects high level of intergranular embrittlement and thus fracture toughness degradation.     

A three-dimensional numerical investigation of fracture initiation by ductile failure mechanisms in a 4340 steel

Fracture initiation in ductile metal plates occurs due to substantial tunneling of the crack in the interior of the specimen followed by final failure of side ligaments by shear lip formation. The tunneled region is characterized by a flat, fibrous fracture surface. This phenomenon is clearly exhibited in a recent experimental investigation [8] performed on pre-notched plates of a ductile heat treatment of 4340 carbon steel. Experimental evidence obtained in [8] suggests that tunneling begins at an average value of J which is significantly lower than the J value at which gross initiation is observed on the free surface. In the present work, fracture initiation in the 4340 steel specimens used in [8] is analyzed by performing a 3-dimensional numerical simulation. A damage accumulation model that accounts for the ductile failure mechanisms of void nucleation, growth, and void coalescence is employed. Results indicate that incipient Cmaterial failure at the center-plane of the 3-dimensional specimen is predicted quite accurately by this computation. Also, good agreement between results obtained at the center-plane of the 3-dimensional specimen and a plane strain analysis, suggests that a local definition of J can be used to characterize fracture initiation in the center-plane of the specimen. Finally, radial and thickness variations of the stress and porosity fields are examined with view of understanding the subsequent propagation of the failure zone.     

Radiation embrittlement modelling in multi-scale approach to brittle fracture of RPV steels

The purpose of the present article is to develop a multi-scale brittle fracture modelling for irradiated RPV materials. For this development, applicability of local brittle fracture criteria for radiation embrittlement modelling is analysed through comparison of the predicted and test results on radiation embrittlement of RPV steels in terms of ductile-to-brittle transition temperature and fracture toughness. The influence of radiation-induced defects on the processes of cleavage microcrack nucleation and propagation is clarified. The physical-and-mechanical models of the effect of irradiation-induced defects on cleavage microcrack nucleation are developed on the basis of dislocation and brittle fracture theories. Stress-and-strain controlled fracture criterion is developed that allows the adequate prediction of radiation embrittlement by various mechanisms. The differences and commonalities are revealed in the nature of material embrittlement due to cold work and neutron irradiation. The mechanism is explained of significant recovery of fracture resistance properties with simultaneous increase of fraction of intercrystalline fracture after post-irradiation annealing. Engineering approach for prediction of the temperature dependence of fracture toughness as a function of neutron fluence is justified.     

Differentiating between intergranular and transgranular fracture in polycrystalline aggregates

The competition between intergranular (IG) and transgranular (TG) fracture in fcc polycrystalline aggregates with physically representative GB misorientation distributions comprised of random low-angle, random high-angle, and coincident site lattice (CSL) GBs has been investigated. Physically-based critical conditions for IG fracture, due to the formation of dislocation pileups, and TG fracture, due to the propagation of cracks on cleavage planes, were coupled to a dislocation-density-based crystal plasticity formulation and a computational fracture scheme for crack branching to investigate how dislocation–GB interactions influence dislocation transmission, pileup formation, and local failure modes. The predictions indicate that aggregates with a large fraction of random and CSL high-angle GBs are dominated by IG fracture, as low GB transmission leads to extensive dislocation-density pileup formation and localized stress accumulations that induce IG fracture. Aggregates with a majority of low-angle GBs are dominated by TG failure, which is consistent with experimental observations. This investigation provides a fundamental understanding of the physical mechanisms governing IG and TG fracture in polycrystalline aggregates.     

ANALYZING DUCTILE FRACTURE USING DUAL DILATIONAL CONSTITUTIVE EQUATIONS

Abstract— By adopting a suggestion made by Thomason, a new failure criterion for the Gurson-Tvergaard model has been recently introduced by the authors. In this study, a method based on the Gurson-Tvergaard constitutive model and the new failure criterion is applied to the analysis of ductile fracture. The main features of the method are that the material failure is a natural process of the development of Thomason's dual dilational constitutive responses, and the void volume fraction corresponding to the failure by void coalescence is not necessarily a material constant and is not needed to be fitted beforehand. Furthermore, void nucleation parameter(s) can be numerically fitted from experimental tension results. This method has been implemented into the ABAQUS finite element program via a user material subroutine and is applied to the prediction of tension problems conducted by the authors. In the analyses, two strain-controlled void nucleation models have been studied and compared. The void nucleation parameters corresponding to the two models have been calibrated. The crack initiation of both smooth and notched axisymmetric tensile specimens are well predicted by the method. Finally, several critical issues in the analysis of ductile fracture are discussed.     

The re-characterisation of complex defects: Part I: Fatigue and ductile tearing

Defect assessment codes idealise complex defects as simple shapes which are amenable to analysis in a process known as re-characterisation. The present work examines the re-characterisation of complex defects which extend by fatigue, ductile tearing or cleavage. A family of representative defects were analysed numerically, while a related experimental programme investigated defect interaction and failure. Part I of the paper focuses on fatigue and ductile tearing. Part II examines cleavage. The numerical and experimental results are discussed within the context of the re-characterisation procedures described in BS 7910 (Guidance on methods for assessing the acceptability of flaws in metallic structures. London, UK: British Standard Institution; 1999 [Chapter 7]) and R6/4 (Assessment of the integrity of structures containing defects. Gloucester: British Energy Generation Ltd.; 2001 [Revision 4, Chapters I and II.3]).The level of conservatism of the re-characterisation procedures for fatigue and ductile tearing are discussed. A possible non-conservatism of the re-characterisation for cleavage is discussed in Part II, within the framework of constraint based statistical fracture mechanics.     

Effects of loading rate on the local cleavage fracture stress σf in notched specimens

Four point bending (4PB) notched specimens with different notch sizes are tested at various loading rates at a temperature of −110 °C for a C-Mn steel. An elastic-plastic finite element method (FEM) is used to determine the stress and strain distributions ahead of notches. By accurately measuring the distances of the cleavage initiation sites from the notch roots, the local cleavage fracture stress σ_f is measured. The results show that the local cleavage fracture stress σ_f does not essentially change with loading rate V and notch size. The reason for this is that the cleavage micromechanism does not change in the different specimens at various loading rates. The cleavage micromechanism involves competition of two critical events of crack propagation and crack nucleation in the high stress and strain volume ahead of notch root. The large scatter of σ_f and notch toughness are mainly caused by the different critical events in different specimens.     

A numerical study of fracture initiation in a ductile material containing a dual population of second-phase particles—I. Static loading

Some recent experimental studies with pre-notched bend specimens of 4340 steel under both static loading [A. T. Zehnder and A. J. Rosakis, J. appl. Mech. 57, 618–626 (1990)] and impact loading [A. T. Zehnder et al., Int. J. Fracture 42, 209–230 (1990)] have shown that considerable crack tunneling occurs in the interior of the specimens prior to gross fracture initiation on the free surfaces. The final fracture of the side ligaments happens because of shear lip formation. The tunneled region is characterized by a flat fibrous fracture surface. In this work, the above experiments are analyzed using a 2D plane-strain finite-element procedure which is expected to simulate local material failure in the center-plane of the 3D specimen accurately. The rate-independent version of the Gurson model that accounts for the ductile failure mechanisms of microvoid nucleation, growth and coalescence is employed within the framework of a finite deformation plasticity theory. Two populations of second-phase particles are considered, including large inclusions which initiate voids at an early stage, and small particles which require large strains to nucleate voids. Attention is focused on the formation of a discrete void around a simulated inclusion ahead of the notch-tip, its growth and link-up with the notch-tip via a sheet of microvoids. In Part I of the work, the results obtained from the finite-element analysis of the static fracture initiation test [A. T. Zehnder and A. J. Rosakis, J. appl. Mech. 57, 618–626 (1990)] are presented. It is found that the value of the J-integral at which material failure near the notch-tip commences in the present simulation agrees well with experimental observations regarding the onset of crack tunneling. The analysis of the impact fracture test of [A. T. Zehnder et al., Int. J. Fracture 42, 209–230 (1990)] will be taken up in Part II.     

Fracture behaviour and cleavage initiation in hypoeutectoid pearlitic steel

The paper reports on an investigation of the micromechanism of cleavage fracture in hypoeutectoid pearlitic R7T steel, commonly used for producing railway wheels. The steel possesses extensive Lüders deformation, which somewhat complicates finite element (FE) modelling and analyses of fracture behaviour. Standard Charpy V-notch specimens were used in order to analyse the fracture behaviour at quasistatic and impact loading. Finite element 3D calculations were performed and the elastic-plastic behaviour of notched bars up to the fracture was simulated. Detailed fractographic analysis was carried out on a number of Charpy V-notch specimens in order to investigate the origin site of cleavage fracture initiation and its distance from the notch root. The suitability of the three-criterion micromechanical model (Chen et al. Acta Materialia 51:1841–1855, 2003) for cleavage initiation was verified. The R7T steel under investigation exhibited a cleavage fracture stress of 1,837 MPa. Its independence on temperature evidenced the micromechanism of cleavage fracture to be microcrack propagation-controlled. For the investigated blunt-notched bend bars, an active volume exists ahead of the notch root in which pearlite colony-associated initiation sites are located. The cleavage fracture initiation of the steel is thus governed by the sites lying in the active volume. The active volume is determined by the values of three parameters. A plastic strain lying in interval from to (for the steel investigated from 0.033 to 0.108) is necessary to create a cleavage crack nucleus at any location within the active volume depending on the local pearlite properties. A stress triaxiality parameter ranging from h _min to h _max (from 0.93 to 1.39) is supposed to prevent the blunting process at the site of the cleavage nucleus. Once the main principal stress σ ₁ exceeds the local cleavage fracture stress σ _CFmin, an unstable global cleavage fracture occurs in a blunt-notched bar.     

Numerical modelling of fracture initiation in large steel specimens at impact

Dynamic mode I fracture initiation in impact loaded single edge bend specimens with a quarter notch is investigated by numerical modelling and the results are compared with sets of experimental data from two different steel qualities. The finite element analysis include 2D (two-dimensional) plane strain, 2D plane stress and 3D models. No crack growth is included in the calculations. The impact velocities are approximately 15, 30 and 45 m/s and the specimen size is 320×75 mm² with a thickness of 20 or 40 mm. Some specimens have side grooves. Details of the deflection of the specimens are accurately reproduced prior to crack initiation both by the 2D plane strain model and by the 3D model.The experiments were performed in the ductile to brittle transition region. It is assumed that cleavage fracture initiation can be predicted by the Ritchie-Knott-Rice (RKR) model, i.e. cleavage fracture initiates when the opening stress exceeds the macroscopic cleavage stress over a fixed, critical distance. At an impact velocity of 15 m/s, fracture initiation by void nucleation and growth is observed, though the RKR-conditions is seemingly fulfilled according to the computational results. Possible limitations in the use of the RKR model are discussed.     

Basic studies of ductile failure processes and implications for fracture prediction

Fracture of ductile materials has frequently been observed to result from the nucleation, growth and coalescence of microscopic voids. Experimental and analytical studies have shown that both the stress constraint factor and the effective plastic strain play a significant role in the ductile failure process. Experimental results also suggest that these two parameters are not independent of each other at failure initiation. In this study, a methodology for characterizing the effect of stress constraint A_m (which is defined to be the ratio of the mean stress and the effective stress A_m=σ_m/σ_e ) on ductile failure is proposed. This methodology is based on experimental evidence that shows the effective plastic strain at failure initiation has a one‐to‐one relationship with stress constraint. Numerical analyses based on plane strain and three‐dimensional unit‐cell models have been carried out to investigate failure initiation of the unit cell under different constraint conditions. Results from the numerical studies indicate (a) for each void volume fraction, there exists a local failure locus in terms of mesoscopic quantities, σ_m and σ_e, that adequately predict incipient local micro‐void link‐up, (b) the results are fully consistent with a failure criterion that maximizes mesoscopic effective stress for a constant level of stress constraint A_m, (c) for high to moderate constraint A_m, the link‐up envelope values for σ_m and σ_e are consistent with limit load conditions where the critical principal stress σ_1c corresponds to the maximum principal stress in the loading history and (d) for low constraint, the link‐up envelope values for σ_m and σ_e correspond to link‐up conditions having high levels of plastic strain and a principal stress σ₁ that is lower than the maximum value for this loading history. Thus, the results suggest that a two‐parameter ductile fracture criterion is plausible, such as critical crack opening displacement (COD) and stress constraint A_m, for predicting the process of stable tearing in materials undergoing ductile void growth during the fracture process.     

Quantitative acoustic emission source characterization of microcrackings in steel

Acoustic emission (AE) source wave analysis is a new NDE technique for the investigation of dynamic fracture process. We applied this technique to the quantitative characterization of crack sources in ductile fracture. Using two samples of ASTM A533B steel with different sulfur content, acoustic emissions during fracture toughness tests were detected, located, and analyzed. The detected AE signals were classified into two types according to the analyzed source waveforms. One was a signal due to microcracking at the MnS inclusion, and the other was a signal due to coalescence of the voids. The results of the source wave analysis showed that microcracking at the inclusions was due to Mode I type tension crack with sizes of 10–30 µm, and the coalescence of the voids was due to tension shear mixed cracks with sizes of 60–100 µm. It was confirmed that this technique is very effective for the quantitative evaluation of microcrackings and for the detection of the nucleation and growth of cracks.     

Effects of void damage induced by warm prestressing (WPS) on cleavage fracture of notched steel specimens

The effects of void damage induced by warm prestressing (WPS) on cleavage fracture of notched steel specimens were studied by experiments and FEM calculations. The results show that the local stress concentration around the voids promotes the cleavage initiation and decreases the notch toughness and cleavage fracture stress. The fibrous cracks ahead of notch tips caused by the ductile tearing in the WPS obviously raise the normal stress in front of their tips and decrease fracture load and notch toughness. When the beneficial effects of WPS on improving apparent fracture toughness for specimens or structures are used, the loads in WPS need to be limited so that no obvious void damage and ductile tearing are produced in front of defects.     

HXD1机车牵引电机转轴组件断裂失效分析

HXD1型电力机车的牵引电机转轴和小齿轮轴采用圆锥过盈配合传动结构(下称转轴组件),使用中该组件出现了早期断裂失效.本文通过理化检测、断口和配合面宏/微观形貌观察等失效分析技术对失效组件进行了分析.结果表明,材料成分、组织和显微硬度正常,小齿轮轴和电机转轴的失效形式分别为高周疲劳断裂和微动疲劳断裂.造成组件失效的原因和过程是,小齿轮轴近齿端油槽-油孔交界线处有较大的结构应力集中,油槽底部周向加工刀痕造成附加应力集中,在应力集中和旋转弯曲疲劳载荷作用下油孔边两个应力集中点萌生了疲劳裂纹并扩展;随小齿轮轴裂纹的不断扩展转轴组件结构刚度减小,继而诱发了与小齿轮轴匹配的电机轴配合面的微动疲劳,电机轴疲劳裂纹萌生于微动区的边缘处;电机转轴先于小齿轮轴完全断裂.基于本文的分析结果提出了提高组件抗疲劳断裂的技术措施.     

FE macro/micro analysis of thermal residual stresses and failure behaviour under transverse tensile load of VE/CF – fibre bundle composites

This paper presents a finite element analysis of a transverse fibre bundle test (TFT) using carbon fibres embedded in a vinylester urethane hybrid matrix. The evolution of thermal residual stresses, due to the cooling phase of the curing process of the model-composite and the subsequent mechanical load transverse to the fibre direction, has been investigated. The applied displacement coupling technique allowed to transfer the boundary conditions from a global model (macro model) via an intermediate model to a micro model. As a result it could be shown that the larger fraction of the total stress build up until failure occurred was due to the implicated thermal residual stresses. The micro model offered more accurate and detailed results with regard to the stress distributions on critical locations such as the fibre/matrix interface region. Generally, the results of the global model were in good agreement with the experimental data obtained. Further, the parabolic failure criterion based on experimental data of the pure matrix was used to predict time and place of failure initiation.