Probability Of Cleavage Fracture Research Articles

Effect of Neutron Irradiation on the Critical Event Size of Cleavage Fracture of the Chinese A508-3 Steel

In order to analyze the influence of neutron irradiation on the critical event of cleavage fracture for the Chinese A508-3 (RPV) steel, the fracture morphology, microstructure and grain size of the irradiated specimens are observed and analyzed by optical microscope (OM) and scanning electron microscope (SEM). The results show that with the increase of neutron doses, the fracture mode of Chinese RPV steel material changes gradually from ductile fracture to ductile-brittle mixed fracture transformation. The brittle part for fracture mode of ductile-brittle fracture is cleavage fracture, and the non-metallic inclusions, microstructure and grain size grades are not significantly different from those of the specimens without cleavage fracture. In the same material, with increasing of neutron doses, the critical event size of the cleavage fracture will be reduced, and the percentage of the grain that satisfies the grain size of the cleavage critical event will increase correspondingly, resulting in an increase of the probability of cleavage fracture of the material. The fine grain with uniform distribution can improve partly the fracture toughness of the material and withstand higher neutron doses under the same conditions.

Capturing the Temperature Dependence of Cleavage Fracture Toughness in the Ductile-to-Brittle Transition Regime in Ferritic Steels Using an Improved Engineering Local Approach

Abstract Ferritic steels, which are typically used for critical reactor components, including reactor pressure vessels (RPV), exhibit a temperature-dependent probability of cleavage fracture, termed ductile-to-brittle transition. The fracture process has been linked to the interaction between matrix plasticity and second-phase particles. Under high-enough loads, a competition exists between cleavage and ductile fracture, which results from particles rupturing to form microcracks or particles decohering to form microvoids, respectively. Currently, there is no sufficiently adequate model that can predict accurately the reduced probability of cleavage with increasing temperature and the associated increase of plastic deformation. In this work, failure probability has been estimated using a local approach to cleavage fracture incorporating the statistics of microcracks. It is shown that changes in the deformation material properties are not enough to capture the significant changes in fracture toughness. Instead, a correction to the fraction of particles converted to eligible for cleavage microcracks, with an exponential dependence on the plastic strains, is proposed. The proposed method is compared with previous corrections that incorporate the plastic strains, and its advantages are demonstrated. The method is developed for the RPV steel 22NiMoCr37 and using experimental data for a standard compact tension C(T) specimen. The proposed approach offers more accurate calculations of cleavage fracture toughness in the ductile-to-brittle transition regime using only a decoupled model, which is attractive for engineering practice.

Probability distribution on cleavage fracture in function of Jc for reactor ferritic steel in transition temperature region

This paper presents the results and methods used for determining of probability of cleavage fracture toughness of ferritic reactor steel in transition temperature area. The steel tested in this study is steel know as 20MnMoNi 55 by DIN standard, typically used for structures working at low temperatures. In addition, the effect of test specimen geometry, temperature and fatigue crack initiation rate on fracture toughness was investigated in order to predict the fracture behaviour and probability of cleavage fracture. Two main studies joined in on one are presented in this paper. Testing in both studies were performed according to ASTM 1820 standard and the Weibull distribution with regression analysis, which includes fitting the experimental results in a logarithmic coordinate system, was used to predict the Jc values. Cleavage fracture probabilities in the function of Jc for large test specimen, C(T)100 and C(T)200 were determined based on the results obtained by testing of small C(T)50 specimens, for the purpose of direct savings and decreased costs of specimen testing. Cleavage fracture probability, represented by using Weibull distribution of experimental data will provide a clear insight into material behaviour at different temperatures. The influence of ΔK values during fatigue pre-cracking procedure on the fracture toughness scatter was also presented and discussed.

Effect of Cr on the generalized stacking fault energy of impure doped Ni (111) surface: a first-principles study

In the present work, a systematic analysis of the microscopic plastic deformation mechanism and mechanical properties of interstitial impurities (H, O, N, S, and P) and Ni doped, or not doped, with Cr, was conducted based on generalized stacking fault energy curves generated via first-principles calculations. Focus has been put on the effects of Cr on plastic deformation for Ni doped interstitial impurities, upon the GPFE curve, with the aim to investigate the effects of Cr on the deformation mode and mechanical properties for doped Ni systems. It is found that a solid solution of Cr caused the tendency of partial dislocation in Ni. The evaluation of the Rice criterion reveals that Cr tends to decrease the ductility in Ni, and it cannot reverse interstitial H promoting the probability of cleavage fracture in Ni, while increases the ductility of O, P and S doped Ni, particular in O doped Ni, due to increasing the value of ductility D remarkably, so possibly changes the tendency of cleavage fracture. Besides, the solid solution of Cr is beneficial in promoting the dissociation of dislocation into fragments more easily in Ni, and enhances dislocation nucleation, while O, N, and S impurities have a slower rate of partial dislocation emission in Ni when interacting with Cr. Furthermore, Cr promotes the probability of twinning in Ni, and probably switches the deformation mechanism of H doped Ni from dislocation mediated slipping to twinning. Our study provides important insights toward the understanding and control of dislocation dynamics in doped Ni.

Weibull stress solutions for 2D cracks under mode II loading

Weibull stress is widely used to predict the probability of cleavage fracture with local approaches. However, the calculation of Weibull stress requires detailed elastic plastic finite element analyses, which limit the application of local approaches in engineering practice. In this paper, analytic and semi-analytic solutions of Weibull stress for 2D crack/notch models with elastic and elastic–plastic materials under mode II loading are obtained, which allow the Weibull stress to be estimated according to the macroscopic fracture mechanics parameters like stress intensity factor K or J integral together with material properties. The obtained Weibull stress solutions are verified by using results of finite element analyses with modified boundary layer models and a single-edge-notched specimen. The results show that the Weibull stress solutions of this paper can predict the results calculated by direct finite element analyses very well.

A combined CFD and FEM analysis of pressurized thermal shock applied to the probabilistics of cleavage fracture

In a nuclear power plant, the integrity of the pressure vessel which contains the primary water is paramount. In case of an accident involving the guillotine break of primary system piping there can be a sudden loss-of-coolant accident (LOCA). During such an incident, the reactor core needs to be cooled for some period after its shut-down (residual heat removal). The emergency core cooling is achieved by the injection of cold water in the still pressurized reactor pressure vessel (RPV). The combination of pressure and thermal stresses provides a complex stress state in the RPV wall: a pressurized thermal shock (PTS). The RPV material is generally a ferritic steel. The critical stress intensity for brittle cleavage fracture depends on the ductile to brittle transition temperature. This complex combination of stresses, absolute temperatures and temperature gradients in combination with radiation damage requires an integral approach for the evaluation of the probability for the occurrence of cleavage fracture. This problem is simulated with a combined CFD and FEM approach. A quarter of the reactor pressure wall including the cooling nozzle is simulated during the 1000 seconds of the cooling transient. This method can accurately predict the thermal profile and the corresponding stress field. This approach is applied to a reactor pressure vessel containing pre-existing semi-elliptical cracks. The stress intensities for every time step, the temperature, the effects of radiation damage, and the material properties of two types of RPV steel; (SA-508gr.3 and SA-508gr.4N) contribute to the probability for a brittle cleavage crack to form. An estimation of the probability for cleavage fracture is made through the Master Curve approach. These probabilities are calculated for different crack locations, sizes, aspect ratios and for two different grades of RPV steel. The influence of these geometric factors and material properties under the influence of radiation have been analysed. The material just below the nozzle is cooled down further and the thermal gradient is more severe. This is reflected in a higher probability for cleavage fracture. The new generation of RPV steel; SA-508gr.4N is very promising for its resistance to radiation induced embrittlement and for its higher strength, both factors leading to a lower probability of cleavage fracture in the reactor pressure vessel. Increasing the safety of the RPV.

Study on cleavage fracture probability-load curves of ferritic steel 20MnMoNi55 by using the new local approach model

In this paper, the new local approach model (NLAM) is first adopted to predict the cleavage fracture probability-load curves of notched round bar tensile specimens of ferritic steel 20MnMoNi55 at the temperatures of 123 K and 223 K. Then, based on the obtained curve, the probability density function, and the extreme value theorem of function, two significant cleavage fracture probabilities are proposed. Finally, the proposed probabilities are employed to predict the load which is most likely to cause cleavage fracture of 20MnMoNi55 steel. The results show that when the value of cleavage fracture probability is 45.29%, the corresponding predicted load is basically equal to the average fracture load of the specimens. Besides, the load corresponding to the cleavage fracture probability of 59.7% is the most likely one to induce cleavage fracture of the structure.

Weibull stress analysis in local approach to fracture

As a measure of the probability of cleavage fracture, the Weibull stress within the framework of local approach has the potential capability to predict constraint effects on fracture of structural steels. This paper mainly analyzes Weibull stress considering constraint effect using constraint parameters T-stress and Q. Weibull stress is solved with constraint effects characterized by T-stress for elastic material and Q for elastic plastic material. These solutions are verified with existing solutions for T = 0 and finite element solutions including modified boundary layer models, contact tension models and single-edge bend models. Good agreement has been obtained in all cases. The Weibull stress solutions can be further adopted to predict scale fracture toughness.

On the temperature independence of statistical model parameters for cleavage fracture in ferritic steels

The work relates to the effect of temperature on the model parameters in local approaches (LAs) to cleavage fracture. According to a recently developed LA model, the physical consensus of plastic deformation being a prerequisite to cleavage fracture enforces any LA model of cleavage fracture to observe initial yielding of a volume element as its threshold stress state to incur cleavage fracture in addition to the conventional practice of confining the fracture process zone within the plastic deformation zone. The physical consistency of the new LA model to the basic LA methodology and the differences between the new LA model and other existing models are interpreted. Then this new LA model is adopted to investigate the temperature dependence of LA model parameters using circumferentially notched round tensile specimens. With the published strength data as input, finite element (FE) calculation is conducted for elastic-perfectly plastic deformation and the realistic elastic-plastic hardening, respectively, to provide stress distributions for model calibration. The calibration results in temperature independent model parameters. This leads to the establishment of a ‘master curve’ characteristic to synchronise the correlation between the nominal strength and the corresponding cleavage fracture probability at different temperatures. This ‘master curve’ behaviour is verified by strength data from three different steels, providing a new path to calculate cleavage fracture probability with significantly reduced FE efforts.

Weibull triaxiality: A novel constraint assessment parameter for cleavage fracture in ductile to brittle transition region

AbstractThe cleavage fracture probability of ferritic and ferritic/martensitic steels is generally computed using Beremin's model. In this work, a novel approach is developed for Beremin's model to be applicable to crack tip conditions under nonself similar stress field. The modification of Beremin's model corrects the inaccurate integration of local cleavage fracture probabilities of reference volume elements due to the incorrect assumption of self similar stress field under large‐scale yielding. Under small‐scale yielding condition, where stresses remain self similar, integration of local cleavage failure probability is accurate. However, when the stresses differ along the thickness due to constraint loss, the integration of local cleavage fracture probability is inaccurate due to the fact that the stress levels are not same in all the reference volume elements. The modification developed in this work in the form of a parameter named Weibull Triaxiality, which measures the deviation of a crack tip volume from one under self similar stress field.

Prediction of steel weld HAZ Charpy impact property based on stochastic fracture model incorporating microstructural parameters

The present study proposed a model to predict Charpy impact absorbed energy for steel weld HAZ of predominantly upper bainite containing martensite-austenite constituent (MA) as a second phase. Probability distribution of local fracture stress for cleavage crack nucleation is calculated from microstructural parameters. On the other hand, local stress and strain are calculated from dynamic elastic-plastic finite-element analysis. Applying the weakest-link mechanism, probability of cleavage fracture is calculated. Charpy impact tests were conducted for steel simulated HAZ with various cooling rates. As a result, the predicted Charpy absorbed energy transition curves agreed well with the experiment and the model was validated.

A framework for statistical modelling of plastic yielding initiated cleavage fracture of structural steels

The well established consensus that cleavage fracture is preceded by plastic deformation in structural steels implies that plastic yielding is the threshold stress state for a volume element to incur cleavage fracture. An accurate compliance with this consensus underlies the normalisation of cumulative cleavage fracture probability and the justification of constraint effect on cleavage fracture. These understandings lead to the proposal of a framework for statistical modelling of cleavage fracture in structural steels. The framework takes the spatial microcrack distribution into account to formulate the cumulative failure probability model that allows for a pertinent physical interpretation of Weibull statistics, and derives the fracture probability of an elemental volume in conformity with the yielding condition from a set of commonly adopted microcrack size or strength distributions. Alternative approaches to calibrating model parameters are suggested based on frequency analysis of brittle particles as cleavage initiators and on statistical analysis of cleavage fracture stress. The strict adherence to plastic yielding as a prerequisite to cleavage fracture also reveals the probabilistic nature of notch brittleness and ductile-to-brittle transition behaviour.

Cleavage fracture assessment for surface-cracked plates fabricated from high strength steels

This paper presents a combined experimental and numerical investigation to assess the probability of cleavage fracture for surface-cracked plates, using the Weibull stress framework. The proposed procedure defines a critical crack-front segment as the fracture initiation zone using the computed energy release rate. The Weibull-stress based local approach introduces a modified constraint correction function, which allows bidirectional scaling of the fracture toughness in surface-cracked specimens and the idealized 1T small-scale yielding condition. The proposed procedure predicts closely the probability of fracture for surface-cracked specimens made of three different types of steel materials.

A statistical model of cleavage fracture in structural steels with power-law distribution of microcrack size

Based on the well-accepted physical understanding that cleavage fracture of structural steels is preceded by plastic deformation, a critical flaw in the Beremin model and its modifications is proposed, and a new statistical model with the power-law distribution of microcracks is obtained to describe the cumulative probability of cleavage fracture. A set of cleavage fracture toughness data of a nuclear pressure vessel steel is used to highlight the difference between the new model and the Beremin model.

Assessment of Cleavage Fracture in Specimens with a Curved Crack Front for High-Strength Steels in Offshore Applications

The significant petroleum reserve in the Arctic drives the need for offshore facilities in the Arctic made of ferritic structural steels. Such steel materials often exhibit a brittle fracture mode without noticeable prior plastic deformations. This paper presents a combined experimental and numerical investigation to assess the cleavage fracture failure for high-strength steels used in offshore applications. The experimental program includes a set of non-conventional, special single-edge notched bend, SSE(B) specimens, tested under a lower ambient temperature of -90 °C. In contrast to the conventional through-thickness fracture specimens, which experience an approximately uniform crack driving force along the entire crack front, the specimens with a curved crack front indicates strong variations in both the crack driving forces and constraints along the crack front. This study therefore utilizes an average toughness value calculated from the η-approach to describe the scatter observed in the fracture toughness. This study also presents a numerical investigation using the local Weibull stress approach to estimate the probability of cleavage fracture in the fracture tests. A combination of the fracture initiation zone defined by the J-integral values with a local Weibull stress driving force predicts reasonably well the probability of fracture of the experimental specimens.

The effect of subcritical ductile crack growth on cleavage fracture probability in the transition regime using continuum damage mechanics simulation

There are compelling experimental evidences that demonstrate a significant effect of specimen size, a/W ratio and ductile tearing on cleavage fracture toughness values (KJc) measured in the ductile-to-brittle transition region of materials such as ferritic steels. In this work, the influence of ductile tearing and constraint loss on Weibull stress and failure probability in ductile to brittle transition (DBT) region is investigated. The study was carried out using a modeling approach that combines the modified Beremin model (MBM) for cleavage fracture and the Bonora damage model (BDM) for ductile tearing. Here, CT and SEB, with deep and shallow crack, specimen geometries, which are characterized by different crack tip constraint, have been analyzed. Results show that the occurrence of ductile crack growth in the mid-to-upper transition region affects the nature of the stress field in the region surrounding the crack tip in terms of maximum principal stress peak, its spatial gradient – which has a direct consequence on the calculated Weibull stress – and stress triaxiality, which affects the constraint loss. This combination of effects leads to much lower fracture toughness values that those predicted by not considering ductile crack growth.

First-principles study of the effects of selected interstitial atoms on the generalized stacking fault energies, strength, and ductility of Ni

We analyze the influences of interstitial atoms on the generalized stacking fault energy (GSFE), strength, and ductility of Ni by first-principles calculations. Surface energies and GSFE curves are calculated for the 〈112̄〉 (111) and 〈101̄〉 (111) systems. Because of the anisotropy of the single crystal, the addition of interstitials tends to promote the strength of Ni by slipping along the 〈101̄〉 direction while facilitating plastic deformation by slipping along the 〈112̄〉 direction. There is a different impact on the mechanical behavior of Ni when the interstitials are located in the slip plane. The evaluation of the Rice criterion reveals that the addition of the interstitials H and O increases the brittleness in Ni and promotes the probability of cleavage fracture, while the addition of S and N tends to increase the ductility. Besides, P, H, and S have a negligible effect on the deformation tendency in Ni, while the tendency of partial dislocation is more prominent with the addition of N and O. The addition of interstitial atoms tends to increase the high-energy barrier γmax, thereby the second partial resulting from the dislocation tends to reside and move on to the next layer.

Effects of steady ductile crack growth on cleavage fracture from three-dimensional, small-scale yielding simulations

Highly refined simulations of steady, ductile crack growth in a three-dimensional small-scale yielding (SSY) framework provide detailed crack-front fields for computation of Weibull stress values in plane-sided and side-grooved configurations. The scalar Weibull stress values define a probabilistic measure for cleavage fracture with strong sensitivity to the volume of highly-stressed material – ductile crack extension subjects increasingly larger volumes of material to high stresses. The model treats all crack growth as steady-state with total Weibull stress values approximated by the value at the onset of tearing and increases caused by each increment of crack advance. The computations indicate that (1) Weibull stress values increase rapidly with steady ductile tearing, (2) side grooves slightly lower the rate of increase of Weibull stress values with crack advance – higher stresses at the root of the side-groove cannot compensate for the decreased thickness (volume loss) on the crack plane, and (3) plane-strain models remain realistic only at small load levels. Comparisons with prior analytical and experimental work indicate the model captures the increasing probability of cleavage fracture with continued crack advance. Within the restrictions of SSY, the model has particular application, for example, to low-upper shelf steels embrittled in nuclear reactor pressure vessels – materials with low-to-moderate initiation toughness, and lower resistance to ductile tearing.

Influences of crystallography and delamination on anisotropy of Charpy impact toughness in API X100 pipeline steel

The anisotropic behavior of Charpy toughness has been investigated in API X100 pipeline steel, and the combination of crystallographic textures and delamination is considered to be the reason for the observed anisotropy in Charpy toughness. The crystallographic textures can contribute to anisotropy by increasing the probability of {001} cleavage planes parallel to the fracture surfaces of the Charpy impact specimens, and biasing available slip systems for ductile fracture. Thus, the Charpy impact toughness is worst at 45° to the rolling direction, because the grains with {001} cleavage planes parallel to the Charpy specimen fracture surfaces is much more at that orientation. The existence of much more {001} cleavage planes at the 45° orientation can lead to a greater probability of cleavage fracture compared with the other orientations at the same temperature. Delamination related to elongated grain structures and {001} grain planes parallel to the rolling plane also lead to anisotropy in Charpy properties. The deep groove shape cleavage crack induced by delamination in the upper shelf region is responsible for a decrease in upper shelf energy. Delamination as a part of the fracture energy absorption process in the ductile–brittle transition region also entails additional plasticity, resulting in an increase in impact energy. Therefore, delamination can also play a role in the anisotropy of Charpy toughness.

A K0‐based calibration procedure for the Weibull stress cleavage model

ABSTRACTThis paper presents a simplified calibration procedure for the microscopic Weibull stress model to estimate the cumulative probability of cleavage fracture for ferritic steels. The proposed method requires two discrete values of the macroscopic Weibull scale parameter (K0) in contrast to the two sets of statistically significant fracture toughness data mandated in previous calibration schemes. The proposed approach predicates on the fundamental assumption that the macroscopic toughness, for specimens dominated by cleavage mechanisms, follow the three‐parameter Weibull model outlined in the testing standards. The calibration procedure thus generates two sets of fictitious toughness data corresponding to two sets of specimens with marked differences in crack‐front constraints. The calibrated Weibull parameters agree closely with the calibration results based on the conventional approach for the Euro steels. The proposed calibration also leads to an improved method to determine a limiting load level, beyond which extensive plastic deformation propagates in the specimen.