Cleavage Fracture Toughness Research Articles

Progress and challenges with local approaches to cleavage fracture

Local approaches (LA) to cleavage fracture incorporate microstructure information and failure mechanisms into mathematical models for calculation of component failure probability. They offer a promising mechanistic alternative to global approaches and have been successfully applied to predict cleavage fracture toughness (CFT) changes due to material degradation and geometry effects. Predicting the dependence of CFT on temperature, specifically in the ductile-to-brittle transition (DBT) regime, remains a challenge. This work offers one avenue for addressing the challenge by revisiting the mathematical basis of LA and demonstrating that changes in continuum mechanical fields due to changes of deformation properties with temperature are insufficient to deliver predictions in agreement with experimentally measured CFT dependence on temperature. This suggests that the process by which cleavage initiators are generated is dependent on temperature separately from the dependence of the deformation properties on temperature. The temperature dependence of the generation process is derived for the material studied in the work. A methodology is described for predicting CFT in the DBT regime, using deformation and fracture toughness properties at one temperature and deformation properties at any other temperature of interest.

A local approach incorporating the measured statistics of microcracks to assess the temperature dependence of cleavage fracture for a reactor pressure vessel steel

This work describes a local approach to cleavage fracture (LAF) incorporating the statistics of microcracks to characterize the cleavage fracture toughness distribution in structural steels. Fracture toughness testing conducted on standard compact tension C(T) specimens for a 22NiMoCr37 pressure vessel steel provides the cleavage fracture resistance data needed to determine the measured toughness distribution. Metallographic examination of etched surfaces for the tested steel also provides the distribution of carbides, which are assumed as the Griffith fracture-initiating particles, dispersed in the material from which the cleavage fracture toughness distribution is predicted. Overall, the analyses conducted in the present work show that LAFs incorporating the statistics of microcracks are a viable engineering procedure to describe the dependence of fracture toughness on temperature in the DBT region for ferritic steels.

Effects of increased span on fracture toughness using non-standard PCVN specimens and implications for the reference temperature, T0

This work addresses an experimental investigation on the effects of increased span on the cleavage fracture behavior for an ASTM A572 high strength, low alloy structural steel using non-standard PCVN configuration. Fracture toughness testing conducted on PCVN specimen configurations with varying specimen span provides the cleavage fracture toughness in terms of the J-integral at cleavage instability, Jc. The experimental results show a rather marked effect of increased span on Jc-values which can help to mitigate the effects of constraint loss commonly observed in PCVN specimens. An exploratory application to evaluate the reference temperature, T0, based on the Master Curve methodology also provides additional support for using non-standard PCVN specimens in routine procedures to assess fracture toughness behavior of ferritic materials.

Predicting the effect of constraint on cleavage and ductile fracture toughness using area contour toughness scaling

The influence of constraint on the fracture toughness properties of materials containing defects has long been recognised. To maintain conservative design and assessment principles, lower bound measurements of fracture properties are commonly used. These are measured using test pieces with a high crack tip constraint. With more accurate design processes and tools becoming more widespread, there is a move toward using more representative properties than these lower bound values. The work presented provides a method that can be used to predict the influence of constraint on the cleavage and ductile fracture toughness of a range of ferritic steels, and hence the associated benefit to the onset upper shelf temperature, defined here as the intersection between the fracture toughness loci associated with 5% cleavage fracture and a 50% ductile initiation probability.The Anderson and Dodds toughness scaling procedure, based on the maximum principal stress, has been used with a range of normalised material tensile properties to generate solutions that allow the constraint benefit to cleavage fracture toughness to be predicted for different ferritic steels. A comparison of predictions with published data shows that this results in conservative predictions, similar to those using the Beremin Weibull stress.For the purposes of predicting constraint benefits to ductile initiation toughness, defined at 0.2 mm stable tearing, the scaling method proposed by Anderson and Dodds was extended to the Rice and Tracey model as a way to provide solutions for the same matrix of tensile properties. This approach was validated against literature data for constraint effects on ductile initiation.Finally, a worked example is provided, showing how the influence of crack tip constraint on the onset upper shelf temperature can be predicted using the solutions provided.

Notch bluntness effects on fracture toughness of a modified S690 steel at 150 °C

This paper addresses the effect of blunt defects on the structural integrity assessment of steels. Smooth tensile, notched bar tensile and multi-specimen single edge notched bend tests with various notch acuities have been performed and show an increase in effective ductile fracture toughness with increasing notch radius. A ductile fracture model has been shown to be capable of predicting the specimen responses including the local variation of ductile crack extension through the thickness. An empirical fit developed to describe the effect of notch radius on cleavage fracture toughness has been examined and found to be also capable of describing the effect of notch radius on ductile fracture toughness.

On the statistical modeling of cleavage fracture toughness of structural steels

The prevailing statistical models of cleavage fracture of structural steels for probabilistic risk assessment all infer a two- or three- parameter Weibull distribution of fracture toughness with a modulus of 4 and a fixed-value threshold independent of temperature and plastic constraint. This work starts with a critical review of three major statistical models of cleavage fracture toughness, namely the Beremin model, the Master Curve approach and the Prometey Unified Curve model, with a focus on their theoretical foundations, followed by a brief introduction and further extension of a newly developed statistical cleavage fracture toughness model. Then the Euro fracture toughness dataset is employed to assess these four models. The basic formulations of all the three existing models are not normative and defy the assumption of plastic yielding as a prerequisite to cleavage fracture. The key points of the new model are validated by the Euro dataset that cleavage fracture toughness does not necessarily obey the Weibull statistics while the threshold fracture toughness varies with temperature and plastic constraint.

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.

Development of New Formulation and Likelihood Function on Probabilistic Fracture Initiation Model

The authors propose a new model on cleavage fracture toughness of steels. Fracture toughness of steels is controlled by the weakest link mechanism, so it has intrinsic scatter. Beremin proposed Weibull stress through probabilistic fracture initiation model based on the weakest link theory, and it has been widely used for describing fracture toughness scatter. In his model, only propagation of micro crack is considered. However, micro crack nucleation should also be incorporated in order to estimate fracture toughness distribution more accurately. Bordet introduced micro crack initiation to the Beremin model, in which probability of micro crack nucleation is assumed proportional to plastic strain. Some previous studies have shown, however, that micro crack nucleation probability increases non-linearly with plastic strain. Then, we developed a new probabilistic model by introducing micro crack nucleation probability as a non-linear function of plastic strain.Furthermore, the authors developed a new method for obtaining Weibull parameters, in which not only distribution of fracture toughness values but also location of fracture initiation sites are considered through a newly developed likelihood function. We conducted fracture toughness tests with different specimen configurations and carried out convergence calculation for determining Weibull parameters by applying the likelihood function mentioned above. As a result of the calculation, the authors confirmed that the present model can obtain the Weibull parameters less sensitive to the specimen configurations and simulate distribution of fracture toughness more accurately than the previous models.

Joint evaluation of fracture results from distinct test conditions, implying loading, specimen size and geometry

The reliability of the statistical assessment of test results is strong influenced by the reduced data size emanating from the low number of specimens included in each of the groups, characterized by test type, specimen geometry and size implied in the material sample being tested. Due to the traditional economical and time limitations, the available experimental results owned by a research group lack of parameter diversity so that they must be complemented by foreign results reported elsewhere in order to verify a model, a methodology or reinforced probabilistic conclusions. Generally, difficulties arise in assessing the parameters involved in the phenomenon due to the diversity of samples and test conditions supported by few data results. In this paper, a methodology based on a generalized local model, denoted GLM, is proposed to overcome this limitation allowing a joint evaluation diversified tests as those resulting from different loading conditions and specimen shape and size. It implies the primary failure cumulative distribution function, PFCDF, as the failure characteristic of the material to be derived from experimental results obtained from distinct test programs. In this work, the local methodology is applied for probabilistic assessment of cleavage fracture toughness data of steel A533B lent from an external experimental program carried out by Rathbun et al. (2006), aiming at analyzing the constraint influence on the cleavage fracture once the scale effect is recognized

Monte Carlo Simulation to Predict Fracture Initiation in Mild Steel

The brittle fracture occurs suddenly and can cause the fatal accident, so it needs to be prevented. The brittle fracture has been studied by a lot of researchers, but the quantitative relationship between fracture toughness and microstructure has not become clear. In this study, we developed the numerical model to predict cleavage fracture toughness of mild steel by integrating the formulation in previous studies. Besides, the proposed model was validated by comparing the predicted results with the experimental results. The three-point bending tests with notched specimen were conducted and the fracture initiation sites were observed by SEM in order to validate the proposed model. The predicted fracture toughness values showed good agreement with those of the experiments. The fracture initiation sites which the model predicted also show good agreement with them. It is found that the proposed model represents the quantitative relationship between fracture toughness and microstructure of mild steel and predicts fracture toughness with high accuracy.

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.

Effects of Heating Rate on Microstructure and Fracture Toughness of Railway Wheel Steel

The microstructure and fracture toughness KIC (or KQ) of railway wheel steel with 0.53 wt pct C were studied under various heating rates. The effects of the heating rate on the grain size and the relation between the grain size and the fracture toughness were discussed. The results show that rapid heating not only refines the grains but can also result in more homogeneous grains. The cleavage fracture toughness strongly relates to the grains with larger size. It can be observed that under different heating rates, the fracture toughness KQ increases with decreasing average diameter of the top 5 pct grains D5. KQ (MPa m1/2) = 194.3–29.8 ln(D5) when D5 is in the range of 30 to 73 μm. This result can be interpreted by the cleavage fracture critical event, which is grain-sized crack propagation controlled.

A cumulative failure probability model for cleavage fracture in ferritic steels

The fundamental physical assumption of plastic deformation as a prerequisite to the cleavage fracture event demands to rule out the contribution of elastic stress components to the occurrence of fracture from both the pure elastic zone and the elastoplastic zone. It also commands the threshold stress for cleavage fracture to be no less than the yielding stress. Based on this understanding, a model of the cumulative failure probability for cleavage fracture in ferritic steels is developed. Further, a self-consistent statistical model of cleavage fracture toughness is also derived. The Beremin model does not conform to the normality axiom of probability, as it defies the premise of plastic yielding before cleavage fracture by counting in the elastic stress components inside the plastic zone to calculate the cumulative probability. Examples are given in several homogeneous uniaxial and multiaxial loading conditions to highlight the differences between the Beremin model and the presented model in probability calculation, model calibration, and interpretation of the temperature and constraint dependence of microscopic cleavage fracture stress.

Unified correlation of in-plane and out-of-plane constraints with cleavage fracture toughness

Extensive three-dimensional finite element analyses have been conducted for a large amount of experimental specimens with a wide range of in-plane and out-of-plane constraints. The capability of the new constraint parameter Ap for establishing a unified correlation of in-plane and out-of-plane constraints with cleavage fracture toughness of a reactor vessel steel were comparatively investigated with the conventional constraint parameters Q and T-stress. The results show that the parameter Ap can characterize both in-plane and out-of-plane constraints and their interaction. Based on the parameter Ap, the unified correlation of a wide range of in-plane and out-of-plane constraints with cleavage fracture toughness of the steel has been obtained. In structural integrity analyses based on fracture mechanics incorporating constraint effects for improving accuracy, the unified correlation may be used to determine constraint-dependent or structurally relevant fracture toughness of specimens or cracked components with a wide range of in-plane and out-of-plane constraint levels.

Understanding and accounting for the effects of residual stresses on cleavage fracture toughness measurements in the transition temperature regime

Secondary self-balancing stresses exist in structural components due to manufacturing processes, e.g. welding. When a defect is present, such secondary stresses will influence both the local crack driving force and the level of crack-tip constraint. Fracture mechanics specimens machined from welded components can also retain significant residual stresses, and these can influence the measurement of fracture toughness. This paper describes the results of an experimental and numerical programme aimed as quantifying the effect of residual stresses on cleavage fracture toughness measured in deeply-cracked and shallow-cracked fracture mechanics specimens and with a view to correcting the resultant data. The results indicate that the influence of retained residual stresses on cleavage fracture toughness in such specimens can be characterised using two-parameter fracture mechanics.

フェライト・パーライト鋼のへき開破壊靱性予測モデルの構築

A numerical model to quantitatively predict cleavage fracture initiation in ferrite-pearlite steel is proposed. The model is based on microscopic fracture process of three stages; Stage-I: formation of fracture origin in pearlite colony, Stage-II: propagation of the pearlite crack into ferrite matrix, and Stage-III: propagation of the crack across ferrite grain boundary. In the proposed model, fracture conditions are formulated by the probability of pearlite cracking based on the experimental results on Stage-I and the concept of fracture stress of ferrite matrix on Stage-II and Stage-III. Ferrite grains and cementite particles are assigned based on their distributions into each volume element. Applied plastic strain and stress of each volume element are calculated by finite element analysis. Cleavage fracture is assumed to initiate at the time when the fracture conditions of the all stages are satisfied in any one of the volume elements. Cleavage fracture toughness of three point bend test is simulated by the proposed model. The numerical predicted results of fracture toughness show good agreement with experimental ones. The bottleneck process of cleavage fracture is then evaluated by the number of arrested micro-cracks until all of the fracture process is satisfied. Influence of ferrite and pearlite size on cleavage fracture toughness is evaluated. It is shown that steel with finer pearlite colony is tougher, and then the developed model can reproduce the size effect of cleavage fracture toughness. Based on the aforementioned results, the validation and the effectiveness of the proposed model are found out.

Unified Correlation of Wide Range of In-Plane and Out-of-Plane Constraints with Cleavage Fracture Toughness

There generally exists a compound change of both in-plane and out-of-plane constraint in structures, and a unified constraint parameter Ap for charactering both constraints has been proposed by authors. However, it has not been investigated whether or not the Ap is suitable to be as a unified constraint parameter for wide range of in-plane and out-of-plane constraints. In this work, extensive three-dimensional finite element analyses have been conducted for a large amount of experimental specimens with wide range of in-plane and out-of-plane constraints. The ability of unified constraint parameter Ap in charactering the in-plane and out-of-plane constraints have been evaluated.

Experimental Study on the Cleavage Fracture Behavior of an ASTM A285 Grade C Pressure Vessel Steel

This work addresses an experimental investigation on the cleavage fracture behavior of an ASTM A285 Grade C pressure vessel steel. One purpose of this study is to enlarge previously reported work on mechanical and fracture properties for this class of steel to provide a more definite database for use in structural and defect analyses of pressurized components, including pressure vessels and storage tanks. Another purpose is to determine the reference temperature, T0, derived from the Master curve methodology which defines the dependence of fracture toughness with temperature for the tested material. Fracture toughness testing conducted on single edge bend SE(B) specimens in three-point loading extracted from an A285 Grade C pressure vessel steel plate provides the cleavage fracture resistance data in terms of the J-integral and crack tip opening displacement (CTOD) at cleavage instability, Jc and δc. Additional tensile and conventional Charpy tests produce further experimental data which serve to characterize the mechanical behavior of the tested pressure vessel steel. The experimental results reveal a strong effect of specimen geometry on Jc and δc-values associated with large scatter in the measured values of cleavage fracture toughness. Overall, the present investigation, when taken together with previous studies, provides a fairly extensive body of experimental results which describe in detail the fracture behavior of an ASTM A285 Grade C pressure vessel steel.

Objective comparison of the Unified Curve and Master Curve methods

The Unified Curve and the Master Curve are two popular cleavage fracture toughness assessment engineering methods. The methods are very similar. They basically differ only in the assumed fracture toughness temperature dependence. The standard Master Curve approximates the temperature dependence as being fixed, whereas the Unified Curve assumes that the shape changes as a function of transition temperature. The shape difference becomes significant only for highly brittle steels. Previous comparisons of the two methods have applied a procedure that may cause a bias on the comparison when assessing censored data sets. Here, a fully objective comparison using the censored likelihood, have been made for 50 large data sets with transition temperatures in the range +8 °C … +179 °C. The standard Master Curve shows overall a trend of higher likelihood than the Unified Curve. It is also shown that, because of shortages connected to the use of the Prometey probabilistic cleavage fracture model, the Unified Curve cannot be considered universally applicable.

Applying the Master Curve approach to a JRQ A533B Cl.1 material as part of the surveillance program of two BWR Units

Experimental measurements of the cleavage fracture toughness (KJc) of specimens were used to apply the Master Curve (MC) approach to a reference RPV steel A533B Cl.1 provided by the International Atomic Energy Agency (IAEA) as part of the surveillance programs of two BWR Units. This investigation focused on four practical issues: the effect of specimen geometry, loading rate and irradiation on the MC and the comparison of the MC to the conventional approach using Charpy data. Experiments on pre-cracked Charpy V-notch (PCCv) specimens validated the use of the Weibull model allowing correcting for the loss of constraint effect. These experiments were also used to determine the “bias” value between PCCv and standard compact tension (1T-C(T)) specimens and the effect of the loading rate on the MC. The reference temperatures indexed to T0 (RTTo and ARTTo) were directly measured and compared to the RTNDT and ARTNDT values obtained using the conventional semi-empirical approach of the American Society of Mechanical Engineers (ASME) Code, demonstrating that the latter approach was more conservative.