Assessment of the role of micro defect nucleation in probabilistic modeling of cleavage fracture

The present study is concerned with an experimental and numerical investigation of the local conditions for initiation of cleavage failure in ferritic steels. In the experimental analysis, a variety of SE(B), C(T) and CC(T) specimens has been tested. The cleavage triggering sites and the fracture mechanisms were determined in a subsequent fractographic investigation. In a finite element analysis, the local mechanical field quantities at the cleavage initiation spots at the instant of fracture were investigated. Based on the results, an enhanced local concept for cleavage assessment is proposed, accounting for both, the nucleation of critical micro defects and their possible instability due to local overloading. Together with a comparison to the prediction of previous probabilistic models for cleavage failure assessment, the results reveal the importance of considering the nucleation of possibly critical micro defects due to plastic straining as a second necessary criterion for cleavage fracture.     

A probabilistic model for cleavage fracture with a length scale - Parameter estimation and predictions of growing crack experiments

A probabilistic model for the cumulative probability of failure by cleavage fracture was applied to experimental results where cleavage fracture was preceded by ductile crack growth. The model, introduced by Kroon and Faleskog [Kroon M, Faleskog J. A probabilistic model for cleavage fracture with a length scale - influence of material parameters and constraint. Int J Fract 2002;118:99-118], includes a non-local stress with an associated material related length scale, and it also includes a strain measure to account for the number of nucleated cleavage initiation sites. The experiments were performed on single edge cracked bend test specimens with three different crack lengths at the temperature 85 °C, which is in the upper transition region for the steel in question. The ductile rupture process is modelled using the cell model for nonlinear fracture mechanics. The original cleavage fracture model had to be modified in order to account for the substantial number of cleavage initiators being consumed by the ductile process. With this modification, the model was able to accurately capture the experimental failure probability distribution.     

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.     

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.     

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.     

Damage tolerance reliability analysis of automotive spot-welded joints

This paper develops a damage tolerance reliability analysis methodology for automotive spot-welded joints under multi-axial and variable amplitude loading history. The total fatigue life of a spot weld is divided into two parts, crack initiation and crack propagation. The multi-axial loading history is obtained from transient response finite element analysis of a vehicle model. A three-dimensional finite element model of a simplified joint with four spot welds is developed for static stress/strain analysis. A probabilistic Miner's rule is combined with a randomized strain-life curve family and the stress/strain analysis result to develop a strain-based probabilistic fatigue crack initiation life prediction for spot welds. Afterwards, the fatigue crack inside the base material sheet is modeled as a surface crack. Then a probabilistic crack growth model is combined with the stress analysis result to develop a probabilistic fatigue crack growth life prediction for spot welds. Both methods are implemented with MSC/NASTRAN and MSC/FATIGUE software, and are useful for reliability assessment of automotive spot-welded joints against fatigue and fracture.     

A probabilistic model for cleavage fracture with a length scale--parameter estimation and predictions of stationary crack experiments

This study presents a large experimental investigation in the transition temperature region on a modified A508 steel. Tests were carried out on single-edge-notch-bend specimens with three different crack depth over specimen width ratios to capture the strong constraint effect on fracture toughness. Three test temperatures were considered, covering a range of 85 °C. All specimens failed by cleavage fracture prior to ductile tearing. A recently proposed probabilistic model for the cumulative failure by cleavage was applied to the comprehensive sets of experimental data. This modified weakest link model incorporates a length scale, which together with a threshold stress reduce the scatter in predicted toughness distributions as well as introduces a fracture toughness threshold value. Model parameters were estimated by a robust procedure, which is crucial in applications of probabilistic models to real structures. The conformity between predicted and experimental toughness distributions, respectively, were notable at all the test temperatures.     

A criterion for low-stress brittle fracture of notched specimens based on combined micro- and macro fracture mechanics—1

Based on the combined micro- and macro fracture mechanics, the two requisites necessary for the crack propagation, that is, the energy unstable requisite and the critical local stress requisite, are derived for the low-stress brittle fracture of notched specimens. Thus the fracture criterion was obtained. The criterion is compared with the experimental data, such as on the relationships between the fracture stress or the fracture toughness and the grain size diameter, the crack length, the notch tip radius or the yield stress. The good agreement is obtained.     

Fracture behaviour of 8%Ni 980 MPa high strength steel at various temperatures Part 3 – Four-point notched bend tests

Abstract

Based on the results of four-point notched bend tests together with detailed microscopic observations of fracture surfaces and crack configurations below the unbroken notch roots of double notch specimens, the fracture mechanisms in notched specimens of 8%Ni high strength (980 MPa) steel have been observed to be as follows. A fibrous crack initiates in the bainitic matrix at the notch root and then develops into a cleavage crack at a critical length. The cleavage crack propagates in an unstable manner and causes the final fracture of specimen. The critical event controlling the cleavage fracture is the propagation of the bainitic packet-sized crack, and the local fracture stress is measured as around 1845–2200 MPa.     

Micromechanism of cleavage fracture in fully pearlitic steels

Abstract

The micromechanism of cleavage fracture in a fully pearlitic steel has been investigated. Uniaxial tensile and compression test specimens, together with single notched bend (SNB) and double notched bend (DNB) specimens, were heat treated such that the prior austenite grain size remained constant while the pearlite interlamellar spacing was varied. The SNB specimens were used to determine the cleavage fracture stress σ_fM, over the temperature range ?25 to ?196°C. The DNB specimens were used to study the initial stages of crack nucleation. The results indicate that pearlite can exhibit two different cleavage mechanisms which are dependent on the strength of the steel. For cleavage fracture stresses below about 2100 MN m^?2, fracture is nucleation controlled and involves shear linking of carbide nucleated microcracks before unstable cleavage can occur. Under these conditions, the cleavage fracture stress is dependent on temperature and is proportional to the uniaxial proof stress. For cleavage fracture stresses above 2100 MN m^?2, cracked carbides act directly as cleavage nuclei. Fracture is then propagation controlled and the cleavage fracture stress is independent of temperature. The transition from nucleation–controlled to propagation–controlled cleavage may be achieved by either a reduction in pearlite interlamellar spacing or a reduction in testing temperature.

MST/355     

Cleavag Fracture Criterion of Low Alloy Steal and Weld Metal in Notched Specimens

The cleavage fracture criterion of low alloy steel and weld metal in notched specimens is investigated in detail based on a great number of experimental data. It has been found that the most cleavage fractures initiate at a distance shorter (left side) than that of the peak stress location below a notch root, and the cleavage fracture in notched specimens must satisfy a dual criterion, i.e., a critical plastic strain (ε_p ≥ ε_pc) for initiating a crack nucleus, and a critical tensile stress (σ_yy ≥ σ_f) for its propagation. According to the dual criterion model, the great number of experimental data of 4PB (four-point bending) tests for the low alloy steel and weld metal and their statistical distribution are explained. The effects of temperature , the local fracture stress σ_f and the critical plastic strain ε_pc on the locations of cleavage initiation sites and the controlling steps of cleavage fracture process are discussed. This revised version was published online in August 2006 with corrections to the Cover Date.     

低碳钢解理裂缝源的微观分析

本文通过对低碳钢光滑拉伸试样及缺口弯曲试样在低温下断裂的断口表面形貌及其纵剖面金相所进行的SEM观察,揭示了解理裂缝萌生及扩展的随机性,分析了解理断裂过程的控制因素。建立了“解理裂缝源”的概念以与“解理初裂缝”相区别,据此并结合显微组织特点,指出了低碳钢解理断裂的微观机制。     

Finite element simulation of fracture behaviour for aged duplex stainless steels

In this paper, the local approach model developed by Gurson–Tvergaard has been applied to simulate both the crack initiation and the crack growth of aged duplex stainless steel. The parameters of the Gurson–Tvergaard model have been obtained, from axisymmetric notched specimen testing, as a function of the ageing time at 400°C, the ferrite content of the steel and the stress triaxiality. After that, to simulate the fracture of CT specimens, finite element (FE) calculations have been effected in order to obtain the stress triaxiality value at each point on the process zone ahead of the crack tip of these specimens. The adequate damage parameters concerning triaxiality are determined from the ones obtained at the notched specimens, in order to be used in FE simulations of fracture behaviour. With them, the corresponding J−Δa curves have been simulated as representative of both the crack initiation and crack propagation stages, and compared with experimental results in order to validate the methodology proposed.     

FATIGUE BEHAVIOUR OF STEEL CASTINGS CONTAINING NEAR-SURFACE DEFECTS

Manufacturing defects in the near-surface region of 2¼% Cr 1% Mo castings were investigated in a joint research programme. After ultrasonic testing and X-ray inspection, large push-pull specimens (cross section 1000 mm²) were taken from castings in regions with indications of defects and tested under fully reversed loading in the elastic and elastic plastic region up to predetermined levels of defect growth. The defects are micropores, pin holes, slag and oxide layers or inclusions, hot tears and small micro cracks in welds. The initiation of crack growth was analysed by two methods, namely (a) the local strain concept with idealization of defects as three-dimensional elliptical notches and (b) by the fracture mechanics concept with idealization of defects as two-dimensional elliptical cracks. The main results can be summarized as follows: 1. The local strain concept describes the crack initiation potential of the defects more accurately than the fracture mechanics concept. 2. Interpretation of casting defects as cracks produces very conservative estimates in many cases. 3. Analytical evaluation of crack growth behaviour using the fracture mechanics approach for defects experiencing crack growth of at least 1 mm is much more accurate than when defects having a smaller extent of crack growth are included in the analysis. Additional evaluations of crack growth behaviour of hot tears by fracture mechanics show that crack growth starting from open and partially closed hot tears must be subjected to a larger number of cycles than normal fatigue cracks of sound material. Partially closed hot tears in the vicinity of the crack front additionally delay crack propagation.     

Change of fracture mode in Charpy toughness transition temperature range

Abstract

A transition layer of width 5 - 10 μm was found on the boundary between ductile and brittle fracture for Charpy V notch specimens in the transition temperature range of a structural steel having a microstructure of polygonal ferrite -pearlite. The fracture mode in the transition layer was shearing with occasional submicrometre dimples. From tensile tests on notched specimens, the cleavage fracture stress and flow stress by ductile decohesion were determined. Based on the experimental data and the assumption that the volume of metal involved in the plastic deformation during fracture was related to the volume of the dimples, it was deduced that the transition layer width represents the size of the plastic zone immediately before cleavage initiation. The crack opening displacement and the crack tip radius for the change of fracture mode were calculated.     

Constraint effects on probabilistic analysis of cracks in ductile solids

This paper presents a method for evaluating constraint effects on probabilistic elastic–plastic analysis of cracks in ductile solids. It is based on fracture parameters J and Q , correlation between Q and J– resistance curve of the material, and J -tearing theory for predicting fracture initiation and instability in cracked structures. Based on experimental data from small-scale fracture specimens, correlation equations were developed for fracture toughness at crack initiation and the slope of the J– resistance curve as a function of constraint condition. The random parameters may involve crack geometry, tensile and fracture toughness properties of the material, and applied loads. Standard reliability methods were applied to predict probabilistic fracture response and reliability of cracked structures. The results suggest that crack-tip constraints have little effect on the probability of crack initiation. However, the probability of fracture instability can be significantly reduced when constraint effects are taken into account. Hence, for a structure where some amount of stable crack-growth can be tolerated, crack-tip constraints should be considered for probabilistic fracture-mechanics analysis.     

Numerical modelling of damage behaviour of laser-hybrid welds

The effect of laser-hybrid welds on deformation and failure behaviour of fracture mechanics specimens is investigated in order to provide quantitative prediction of damage tolerance and residual strength. The simulation of crack initiation and crack extension in hybrid welds is performed by applying GTN damage model. The identification of damage parameters requires combined numerical and experimental analyses. The tendency to crack path deviation during crack growth depends strongly on the constraint development at the interface between base and weld metal. In order to quantify the influence of local stress state on the crack path deviation, the initial crack location is varied. Finally, the results from fracture mechanics tests are compared to real component, beam-column-connection, with respect to fracture resistance.     

The Effect of Stress Triaxiality on the Local Cleavage Fracture Stress in a Granular Bainitic Weld Metal

The local cleavage fracture stress σ_F measured at the cleavage initiation sites of a granular bainitic weld metal is only an apparent fracture parameter dependent on stress triaxialities at the local sites in the propagation controlled cleavage regime. This dependence can be explained by the stress triaxiality modified Smith equation in which the intrinsic cleavage fracture stress σ _F ⁰ is introduced, considered to be an invariant characterizing a material's fracture property. In the nucleation controlled cleavage regime σ_F is temperature dependent and coincident with the local yield stresses defined by Von Mises criterion at the local sites. It is suggested that the modified Smith model would provide a unified physical basis for the intrinsic correlation among various macroscopic fracture properties as well as their temperature transition behaviors from the temperature dependence of material's yield strength. This revised version was published online in August 2006 with corrections to the Cover Date.     

High-temperature ultra-high cycle fatigue damage of notched single crystal superalloys at high mean stresses

Blade nickel superalloy CMSX-4 widely used in the aero industry and its potential low cost alternative, superalloy CM186LC intended for use in the industrial gas turbines, were subjected to ultra-high-cycle fatigue at high mean stresses to model the effect of vibrations superimposed on sustained load. Circumferentially notched cylindrical specimens of single crystals with the axis orientation of [001] were tested at 850 °C in air. For small amplitudes of the cyclic stress superimposed on the sustained stress the time to fracture is slightly increasing with increasing stress amplitude. This trend is reversed for higher stress amplitudes where the time to fracture quickly decreases with increasing stress amplitude. Fatigue crack initiation and following crack propagation are here the decisive failure mechanisms. Cyclic stress component leads to the formation of persistent slip bands running through the γ matrix and the γ′ precipitates. These bands represent sites for the initiation (in interaction with casting pores and other defects) and early propagation of fatigue cracks. The early crack propagation along the slip planes is later replaced by non-crystallographic propagation of the dominant crack.     

A simple damage-accumulation model for constraint effects on ductile fracture

A simple model is presented to account for the effects of void-type damage on crack initiation and propagation in ductile steels under plane strain conditions by virtue of elementary fracture mechanics solutions. Multiple primary voids from large inclusions are uniformly distributed ahead of the crack tip. The growth of these primary voids is followed by nucleation of a large population of secondary voids from second-phase particles. A critical accumulative damage based on the length ratio of the damage zone to the spacing of primary voids, is employed as a failure criterion, including contributions from two populations of voids. Damage accumulation depends much on the strain and stress states such as stress triaxilities, which are extracted from existing results instead of detailed computation. Results show the dependence of fracture toughness on the size of damage zones associated with constraints. Initiation of crack growth is insensitive to the constraints since nucleation of fine voids is determined by local deformation. The model captures the transition in mechanisms from void-by-void growth to multiple void interactions in terms of a decreasing trend in the slopes of fracture resistance curves. At high constraints and large damage zone, a steady-state crack advance is identified with constant toughness. Damage accumulation from the growth of primary voids determines subsequent crack growth resistance and the study demonstrates its dependences on the crack-tip constraints.