Probability Of Cleavage Fracture Research Articles

Study on Fracture Toughness Prediction of Non Power Law Hardening Material by Using Local Approach

A new method of fracture toughness K1C prediction of non power law hardening material by using cleavage fracture local approach is proposed in this paper. The fracture toughness of A508-Ⅲ 16MnR at different cleavage fracture probability are predicted by using the method. To most of pressure vessel carbon-manganese steels, cleavage fracture is likely to occur at the load corresponding to 62% cleavage fracture probability. Hence, the fracture toughness corresponding to the load is the most possible fracture toughness of the steels. The values of fracture toughness corresponding to 62% cleavage fracture probability is close to that of testing fracture toughness. The work of this paper expends the application of Beremin cleavage fracture model in predicting fracture toughness.

An Enhanced Local Approach Model for the Assessment of Brittle Fracture Based on Micromechanical Investigations

The objective of the present study is the development of a micromechanically based probabilistic model for the assessment of the cleavage fracture probability of ferritic steels. Brittle fracture of ferritic steels is a probabilistic process, triggered by the failure of randomly distributed brittle particles. These particles fracture due to plastic deformation of the surrounding matrix, resulting in the nucleation of micro-cracks. Once nucleated, the local stress state controls the possible instability of the defects. In this context, the local stress-triaxiality is assumed to govern the blunting of freshly nucleated micro-defects. The local approach models available in literature account for the above-mentioned correlations only in a simplified manner. Based on Representative Volume Elements (RVE) of the microstructure, accounting for the grain-structure as well as for the brittle particles, the cleavage initiation process was modelled in order to investigate the relevant parameters and their interactions. The RVE’s were loaded according to the local mechanical field quantities determined numerically for a variety of specimen types at the cleavage-origins. Thus, the behaviour of the particles against the micromechanical conditions could be specified, resulting in a better understanding of the processes at cleavage fracture initiation. Based on the results, an enhanced probabilistic cleavage model is proposed.

Temperature and Geometry Dependence of Fracture Toughness in "Euro Fracture Dataset"

Reliable prediction of fracture conditions is a major concern in the integrity assessment of structural components. This is specifically critical within the transition regime where there is a significant scatter in fracture test data. In recent years local stress based approaches that use a "Weibull distribution function" have been examined to predict probability of cleavage fracture at lower shelf temperature. Furthermore the role of constraint in toughness prediction has been noted. An extensive experimental programme known as "Euro fracture dataset" aimed at characterisation of the "Ductile-to-Brittle" transition (DBT) behaviour of ferritic steels. Recently this data set was used by authors to propose a set of "Global" equations for determination of temperature and thickness dependence of Weibull distribution parameters. In this paper finite element simulations of fracture tests are carried out firstly to verify the experimental findings and secondly to examine and validate the proposed "Global" equations. This objective has been achieved through the comparison between the experimental data, predictions of "Global" curves and the results of performed finite element simulations.

Study on Fracture of Notch Bars at Low Temperature with Local Approach

Fracture test and finite element analysis of two different sized notched tensile bars at low temperature are carried out. It shows that cleavage fracture initiates from the location ahead of the notch,not from the root of notch where the elastic stress is maximal. The stress distribution isn't elastic at fracture but elastic-plastic,so the result of elastic finite element analysis is contrary to the experimental results,otherwise,the result of elastic-plastic finite element analysis accords with the experimental results. Based on cleavage fracture local approach theory,numerical simulation method is used to predict cleavage fracture probability-load curves of notch bars with different radius. The study shows that the predicted load value corresponding to 44% cleavage fracture probability of a structure is almost equal to the average value of actual cleavage fracture load. Based on this,the variation trend of cleavage fracture load vs. different notch radius is predicted and verified by test.

Weibull Stress Analysis for an Embedded Crack in Reactor Pressure Vessels under Pressurized Thermal Shock

This paper describes the Weibull stress approach in predicting the cumulative probability of cleavage fracture for an axially embedded crack in the wall of a reactor pressure vessel (RPV) subjected to a thermal-mechanical transient typical for an accidental, pressurized thermal shock (PTS) event. This study demonstrates the need for detailed elastic-plastic analyses in the integrity assessment of RPVs under PTS loadings, and proposes both a simplified approach and a refined approach to assess the probability of fracture for RPVs subjected to such events.

Introducing Heterogeneity into Brittle Fracture Modeling of a 22NiMoCr37 Ferritic Steel Ring Forging

Abstract Microstructural observations of the 22NiMoCr37 “EURO” reactor pressure vessel (RPV) steel ring forging reveal that there is a banded structure along the radial direction, composed of alternate layers rich in bainite and ferrite of wavelength ∼1.5 ±0.75 mm. Heterogeneity at this meso (millimetre)-scale as well as at the micro (micrometre)-scale is currently not considered by conventional fracture mechanics. This paper describes the development of two numerical approaches aimed at incorporating such heterogeneity into the Beremin local approach model of cleavage failure, a model that has been used extensively for predicting the brittle fracture of ferritic RPV steels. The approaches developed combine the crystal plasticity finite element method (CPFEM) with continuum finite element analysis (FEA). CPFEM is applied to predict stress distributions at the microscale and to obtain phase-specific yield and flow properties for continuum FEA that derives stresses at the mesoscale. The results confirm that deformation heterogeneity on the micro- and mesoscales influences the local development of stress. At the microscale, the stress distribution within a representative volume of material located within the crack-tip plastic zone is shown to follow a normal distribution with a ratio of mean stress to standard deviation tending towards 0.1. These results indicate local stress levels that are within approximately ±20 % of those derived using continuum FEA. At the mesoscale, a periodic variation of stress is predicted within the larger representative volume. This variation is less dramatic than that observed at the microscale, though it still gives a spatial variation in maximum principal stress of approximately ±7 % between bainite- and ferrite-rich microstructural regions. These results suggest a significant influence of deformation heterogeneity on local stress levels, particularly at the microscale. However, the conventional Beremin cleavage fracture model, modified to account for microscale stress distribution, predicts only a modest influence of deformation heterogeneity on cleavage fracture probability, increasing Pf by just 5 %. This highlights the need to account for both the spatial variation in cleavage initiation sites as well as the distribution in stress throughout the microstructure. The paper describes one approach for this development.

Cleavage fracture of RPV steel following warm pre‐stressing: micromechanical analysis and interpretation through a new model

ABSTRACTIn this paper, the warm pre‐stress (WPS) effect on the cleavage fracture of an 18MND5 (A533B) RPV steel is investigated. This effect, which describes the effective enhancement of the cleavage fracture toughness at low temperature following a prior loading at high temperature, has received great interest in light of its significance in the integrity assessment of structures, such as nuclear pressure vessels, subjected to thermal transients. Several loading cycles between room temperature (RT) and −150 °C are considered: Load‐Unload‐Cool‐Fracture (LUCF), Load‐Cool‐Fracture (LCF) and Load‐Cool with Increasing K‐Fracture (LCIKF). All experiments complied with the conservative principle, which states that no fracture will occur if the applied stress intensity factor (SIF) decreases (or is held constant) while the temperature at the crack‐tip decreases, even if the fracture toughness of the virgin material is exceeded. The experimental results indicate that an effective WPS effect is present even at small pre‐load (Kwps= 40 MPa√m), and that a minimum critical slope (−ΔK/ΔT) in the LCIKF cycle has to be exceeded to induce cleavage fracture between RT and −150 °C. Numerical modelling was performed using mixed isotropic and kinematic hardening laws identified on notched tensile (NT) specimens, tested in tension to large strains (up to 40%), followed by large compressive strains. Detailed microstructural investigations on compact tensile (CT) and NT fracture test specimens were performed so as to determine the nature of the cleavage initiation sites, as well as the local mechanical conditions at fracture. Based on this local information, a new cleavage model was calibrated and applied to predict the probability of cleavage fracture after WPS: it is shown that the predictions are in good agreement with the experimental results.

Application of the Reference Temperature to the Evaluation of Cleavage Fracture in HSLA-100 Steel

Abstract The purpose of this study was to evaluate the fracture behavior of HSLA-100 steel at a temperature of −40°C (−40°F). Tests were conducted on three different compositions and two orientations of HSLA-100. HY-100 was also tested to provide a baseline for comparison. Various fracture-related tests were conducted, including traditional test methods, such as the Charpy V-notch and the Dynamic Tear, and more recent methods, such as ductile crack growth initiation (JIc) and the reference temperature. Transition temperatures from the Charpy tests were all very similar, falling around −129°C (−200°F), although the upper shelf Charpy energy for the HY-100 was lower than the HSLA-100 steels. Dynamic tear energies at −40°C for the four steels ranged from 800 to 1800 J. The average reference temperature of all four steels, measured according to ASTM E 1921, was around −151°C (−240°F), with one composition of HSLA-100 coming in as low as −179°C (−290°F) and another as high as −123°C (−190°F). Fracture toughness tests were conducted according to E 1820 at temperatures of −40, −29, and −18°C. These temperatures were more than 83°C above the highest of the reference temperatures, so cleavage fracture was not expected to occur. The HY-100 specimens exhibited an average initiation toughness of 227 kJ/m2 (1296 lb/in.) and crack growth remained ductile throughout the tests. Even though the HSLA-100 exhibited initiation toughnesses more than twice as high as the HY-100, many of the tests terminated in cleavage fracture after amounts of ductile crack growth varying from 0 to 1.85 mm (0.073 in.). This was an unexpected result based on good Charpy and dynamic tear energies at −40°C, and low reference temperatures. The higher initiation toughness and tearing resistance of HSLA-100 allowed very high stresses to develop in the fracture process zone. As ductile crack growth occurred, the fracture process zone swept through an increasing volume of metal, which increased the probability of cleavage fracture. It is shown that the load required to reach these levels of crack driving force may be above gross section yielding of a typical structure. In this case failure by gross section yielding would occur before fracture. This is demonstrated with the aid of a failure assessment diagram.

Probability of cleavage fracture for a crack propagating by fatigue

Standard fracture toughness tests use fatigue pre-cracked specimens loaded monotonically from zero to failure. Scatter in toughness (cleavage) occurs because steel is metallurgically inhomogeneous, and because each specimen has its crack tip in a different local microstructure. A probability of fracture toughness distribution can be obtained by conducting multiple repeat tests on the same steel. This is often used to make probabilistic structural fracture predictions for combinations of crack length and applied load. However, it is likely the true structural situation involves gradual extension of a fatigue crack under a cyclic load. The question then arises as to how often the probability of fracture for the structure needs to be re-calculated. It could be argued that each fatigue load cycle moves the crack tip to a new position and gives a different instantaneous probability of fracture. But if this were the case, the predicted cumulative probability of fracture would quickly tend to unity. This paper describes cold temperature, wide plate fatigue tests designed to investigate this apparent contradiction. The steel is 15 mm thick, grade A, ship plate and the tests involve propagation of a fatigue crack from 300 mm to 650 mm length under a constant amplitude fatigue cycle of 10–100 MPa at −50 °C. The cold temperature fatigue tests do not show an obviously increased probability of fracture compared with the standard monotonic load tests. Nevertheless, in view of uncertainties surrounding the issue, a cumulative probability of fracture determined at 5 mm intervals through the steel is recommended for safe structural predictions.

Ductile tearing and discrete void effects on cleavage fracture under small-scale yielding conditions

Over the mid-to-upper region of the ductile-to-brittle transition region, transgranular cleavage and ductile tearing define two competing failure mechanisms in ferritic steel. At metallurgical scales (≲50 μm), formation and growth of the voids driving ductile crack extension likely alter the local stress fields acting on the smaller inclusions that trigger cleavage fracture. Here we study the effects of void growth on cleavage fracture by modeling discrete cylindrical voids lying on the crack plane ahead of the crack tip within a small-scale yielding (SSY) boundary layer model. These discrete voids have a spacing, D, within a highly refined crack-front region. This enables identification of both single void growth and multiple void growth mechanisms that depend primarily on the initial void porosity, f 0. The crack grows in this model by release of nodal reactions (enforcing zero displacement) along the ligament (symmetry plane) between the blunted crack tip and closest void when the void obtains a specified critical porosity. This process grows the crack in discrete increments of size equal to the length of an intervoid ligament. Continued external loading leads to subsequent void growth and crack extensions through additional node releases. The external loads at the point of each crack extension define the crack growth resistance ( J R ) curves. This enables comparison with conventional J R –Δ a curves obtained using computational cell (Gurson–Tvergaard) analyses. The Weibull stress model is then employed to quantify the stress concentration effects on the probability of cleavage fracture. We describe a non-dimensional function, h ( J ^ ) , to represent stress concentration effects on the Weibull stress in a convenient framework ( J ^ = J / D σ 0 denotes a non-dimensional loading for SSY analyses). These h-functions also reflect the increase in volume of material sampled as the crack grows from the original tip to the first void, the second void, etc. The h-functions vary with material flow properties, initial porosity ( f 0), critical porosity ( f c), Weibull modulus ( m), and T-stress ( T σ ) or constraint level.

Prediction of cleavage fracture in ferritic steels: a modified Weibull stress model

A modified three-parameter Weibull stress model is proposed in this paper, which considers the conjoint influences of plastic strain and stress triaxiality in the region of the crack tip. The model parameters are calibrated using two sets of fracture toughness data obtained from specimens exhibiting different constraint conditions at fracture, namely, deep-cracked compact tension specimens and shallow-cracked single-edge bending specimens. The master curve method is used to relate the fracture toughness data obtained at the different test temperatures. The calibrated Weibull stress model is then used to predict the cumulative failure probability of cleavage fracture for specimens containing surface cracks and loaded in varying combinations of tension and bending. The model predictions capture the measured toughness distributions for both bolt-loaded and pin-loaded specimens, while concurrently revealing a strong influence of the difference in crack tip constraint, due to different mode of loading, on probability of failure by cleavage. This effectively proves the applicability of the modified model for predicting cleavage-type fracture in ferritic steels.

Prediction of cleavage fracture for a low-alloy steel in the ductile-to-brittle transition temperature range

This paper attempts to predict the cleavage fracture probability for a low-alloy bainitic steel. Fractographic analysis of broken compact tension (CT) and Charpy V-notch (CVN) specimens was performed. An evolution of physical mechanisms of cleavage initiation was found: cracked-particle-induced cleavage was observed at low temperature, whereas a plasticity-induced mechanism was assumed as temperature increases. To take into account these observations, temperature-dependent Weibull parameters were used in the Beremin model. The introduction of a threshold cleavage stress was necessary to account for the skewness of the fracture probability distribution. With these parameters identified on the instrumented Charpy data set, the fracture toughness Jc was successfully predicted in the DBTT range.

The influence of ductile tearing on fracture energy in the ductile-to-brittle transition temperature range

The aim of this study is to examine the relationship between fracture energy and the ductile area measured on the fracture surface. Instrumented Charpy tests and fracture toughness tests are performed in the transition temperature range, as well as at lower temperatures. Quantitative fractographic analyses of Charpy specimens reveal a certain proportion of ductile fracture even if the Charpy test is conducted at low temperatures, below the transition temperature. The ductile fracture area situated next to the notch is correlated to fracture energy for all temperatures. In the transition temperature range, fracture energy and the ductile area have a large scatter. Since the limiting event in the development of the ductile area is the initiation of cleavage, the maximum principal stress has been computed in different specimens using the finite element method. It has been shown that the propagating ductile crack does not increase the stress level, but does increase the probability of cleavage fracture through an expansion of the plastic volume where weak points can be found.

Modelling of fracture toughness data in the ductile to brittle transition temperature region by statistical analysis

A fracture toughness database for a ferritic 22NiMoCr37 steel forging for 12.5, 25, 50 and 100 mm thick specimens tested at nine different temperatures has been analysed statistically. The method employed uses a statistical procedure based on competing risks to evaluate the fracture toughness and quantify the probability of cleavage fracture as a function of temperature, specimen thickness and ductile crack growth. This paper describes the application of the competing risks statistical methods to the fracture toughness database obtained from the joint European Project.

Analysis of ductile to cleavage transition in part‐through cracks using a cell model incorporating statistics

This paper describes an approach to study ductile/cleavage transition in ferritic steels using the methodology of a cell model for ductile tearing incorporating weakest link statistics. The model takes into account the constraint effects and puts no restriction on the extent of plastic deformation or amount of ductile tearing preceding cleavage failure. The parameters associated with the statistical model are calibrated using experimental cleavage fracture toughness data, and the effect of threshold stress on predicted cleavage fracture probability is investigated. The issue of two approaches to compute Weibull stress, the ‘history approach’ and the ‘current approach’, is also addressed. The numerical approach is finally applied to surface‐cracked thick plates subject to different histories of bending and tension, and a new parameter, ψ, is introduced to predict the location of cleavage initiation.

Mechanistic Prediction of Fracture Processes in Ferritic Steel Welds Within the Transition Temperature Regime

This work examines the fracture behavior of ferritic steel welds in the transition temperature regime, where failure can occur either by ductile tearing or cleavage fracture. A computational and probabilistic-based mechanistic approach to cleavage fracture and ductile crack growth is adopted to model the fracture processes. The softening effect of ductile damage close to the crack tip is described by a Gurson-type material model. A statistical approach linked to both the Weibull stress and the initial void volume fraction is employed to determine the probability of cleavage fracture and the coupling between both fracture mechanisms. Finite element results are relied upon to interpret experimental fracture toughness data for the welds and to examine the effects of near crack tip damage and crack growth on the cleavage failure probabilities and cleavage and ductile fracture toughness distributions. The scatter in the weld experimental fracture toughness data is well reproduced by the proposed cleavage and ductile tearing models.

How a stable crack extension changes the Weibull modulus of cleavage fracture probability

How a stable crack extension changes the Weibull modulus of cleavage fracture probability

A tensile stress criterion for cleavage in precracked, notched and smooth bars

Using a statistical model derived for cleavage induced by hard particles, an analysis has been carried out of a newly defined critical tensile stress for cleavage, i.e. the statistical mean stress with respect to cleavage fracture probability. The results of the analysis show that the critical tensile stress (cleavage stress) is highest for a precracked bar, intermediate for a notched bar and lowest for a smooth bar, owing to the fact that small particles are possible to trigger cleavage when stress distribution in a bar is uneven. The cleavage stress for the precracked bar is found to decrease rapidly with increasing temperature while those for the notched and smooth bars remain almost constant. The cleavage stresses for the precracked, notched and smooth bars can be correlated through a definite formula. For a pure-bending notched bar, the conventional cleavage stress (maximum stress in the bar) is found to be a good approximation of the new cleavage stress. The difference between the two will increase when stress gradient becomes steeper.

The effect of ductile tearing on cleavage fracture probability in fracture toughness testing

Fracture toughness testing in the transition region often causes ductile tearing to precede cleavage fracture. The effect of ductile tearing on the fracture probability has in recent years become a subject of great interest. Brückner and Munz have developed a Weibull statistics based model to describe this effect. In this paper a similar model, based on the WST-model, is derived. The model is applied to several different sets of brittle fracture data. The differences between the present model and the B & M model is discussed. Finally the effect of loss of constraint on the models is noted.

A probabilistic analysis on thickness effect in fracture toughness

Fracture toughness values are often influenced by specimen thickness and they indicate generally decreasing toughness with increasing thickness. In the present paper, a probabilistic analysis has been carried out by using various kinds of toughness data in order to clarify the applicability of the weakest link model to thickness effect in fracture toughness. Moreover, a new statistical method is proposed for determining fracture toughness distribution, which is necessary for the above analysis, with taking the temperature dependency of fracture toughness into account. Thickness effect in fracture toughness is brought about by its statistical nature and the weakest link model can be applied to evaluate the thickness effect for both steel plate and its welds with heterogeneity in toughness. This thickness effect is considerably affected by Weibull shape parameter and the probability of cleavage fracture for the material. The statistical method proposed newly in this paper is sufficiently applicable and superior to the conventional method. By using this new method, Weibull parameters at a temperature of interest can be determined with much the same reliability as in the conventional method, and also Weibull parameters at lower and higher temperatures can be obtained with a certain confidence depending on the number of specimens tested.