Scatter Of Fracture Toughness Research Articles

The Scatter in Fracture Toughness of Two Different Pearlitic Railway Wheels

The Scatter in Fracture Toughness of Two Different Pearlitic Railway Wheels

Prediction of Fracture Toughness Scatter Based on Weibull Stress Using Crystal Plasticity Finite Element Method

A multi-scale prediction method was proposed to investigate the scatter of fracture toughness by combining the local approach (LA) to cleavage fracture and the crystal plasticity finite element method (CPFEM). The parameters in the crystal plasticity constitutive model were firstly determined by comparing the simulated stress-strain curves with tested curves for SA508-III steel. Then CT samples were modeled using the CPFEM to calculate Weibull stress. Using the calibration process of local approach, the relevant parameters of the Beremin model were obtained with m = 30 and σu = 2590 MPa. The fracture toughness was analyzed including the scatter for a given temperature, the master curve in a temperature range. The distribution of predicted fracture toughness shows good agreement with the test results. All of the tested fracture toughness value are fall in the range of 5% to 95% that precited using the proposed combined approach.

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.

Study of effect of loading rate on fracture toughness of SA516Gr.70 steel for nuclear pressure vessel and piping in DBTT regime and evaluation of shift in reference transition temperature

The objective of this work is to quantify the effect of loading rate on scatter as well as temperature-dependence of cleavage fracture toughness data of SA516 Gr.70 steel in the ductile-to-brittle transition temperature (DBTT) regime. This steel is a relatively high strength grade carbon steel and it is used for fabrication of nuclear pressure vessels, transportation casks and pipings etc. For integrity analysis in radioactive environment, the concept of master curve according to ASTM E1921 is used and the reference temperature T0 is evaluated from experimental data. The purpose of this work is to evaluate the change in T0 due to increase in loading rate when fracture specimens are tested in a modified split Hopkinson pressure bar (SHPB) test setup. In this work, a specially designed SHPB type test setup has been used to carry out the fracture tests using sub-sized single-edged notched bend specimens at a loading rate 700 m/min. The data from SHPB tests have been compared with those obtained from a lower loading rate of 0.5 m/min. From the results of the tests, it was observed that the median value as well as the scatter in fracture toughness increases with temperature in the DBTT regime for both the loading rates. For higher loading rate, the median values of fracture toughness increases slowly with temperature. The value of T0 was found to increase from −100 °C at 0.5 m/min to −10 °C at 700 m/min loading rate, signifying a positive shift in reference temperature with increase in loading rate. The reason for the observations regarding the variation of experimental data with loading rate has been explained from the point of view of micro-mechanism of the fracture process.

Microstructure-informed modelling of the fracture toughness of alloys representing macro-segregated zones in heavy forgings

The macro-segregation of carbon and alloying elements in heavy forged nuclear components can lead to significant variations in mechanical properties, and especially in fracture toughness. In the current work, the prediction of fracture toughness was addressed for three model alloys chemically representative of the compositions encountered in macro-segregated zones. Characterisations of the microstructure and of the fracture toughness properties, measured by compact tension (CT) specimens, were performed. Tensile properties were measured around the reference temperature for each material for the calibration of elasto-plastic parameters. Carbide size distributions were determined thanks to scanning electron microscopy (SEM) image analysis. The microstructure-informed brittle fracture (MIBF) local approach model was applied here to predict the scatter of brittle fracture toughness. This model involves two sources of scatter: the stress distribution inside a representative volume of the bainitic microstructure and the size distribution of carbides, which are assumed to be the brittle facture initiators. The simulation results demonstrated the capabilities of the MIBF model for predicting the fracture toughness scatter and the shift towards higher temperature of the brittle-to-ductile transition with the increase of carbon and alloying elements. The only parameter of the MIBF model to be calibrated is the effective surface energy γf which was found very close to estimated values for ferrite. The observed variation of γf in these three model alloys also suggests a possible effect of microstructural evolution on fracture toughness, in addition to the constitutive law and carbide distributions.

Application of fracture mechanics to welds with crack origin at the weld toe: a review Part 1: Consequences of inhomogeneous microstructure for materials testing and failure assessment

This two-part paper provides an overview on the state-of-the-art in the application of engineering fracture mechanics to weldments. This, of course, cannot be exhaustive but is limited to butt and fillet welds with crack initiation at weld toes. In the present first part, the authors briefly focus on the susceptibility of welds to cracks and other defects. Following this, they discuss in more detail the consequences of material inhomogeneity across the weld for fracture mechanics. Inhomogeneity causes scatter in fracture toughness and strength mismatch effects both of which have to be considered in fracture toughness testing, crack driving force determination, and fracture assessment of welded components. Part 2 of the paper series will add a discussion on welding residual stresses and questions of applying fracture mechanics to residual as well as total lifetime estimation of welds under cyclic loading.

Prediction of fracture toughness in ductile-to-brittle transition region using combined CDM and Beremin models

Scatter of fracture toughness in the ductile-to-brittle transition (DTB) region for ferritic steels may show a dependence on the specimen geometry constraint. Consequently, this can be a source of uncertainty in transferring fracture data from one test geometry to other configurations. In this work, the modified Beremin model (MBM) for cleavage and the Bonora damage model (BDM) for ductile tearing, were combined to account for the two failure mechanisms competing in the DTB and to predict fracture toughness scatter band with temperature. The model was validated predicting the scatter in the fracture toughness data of A533B steel for SEB specimens with shallow and deep crack. Present model predictions were compared with master curve results. For the MBM, a more physical definition for the process zone was introduced and the temperature dependence of the reference stress σu was described by the sum of athermal and thermally activated stress contributions. Results indicate that ductile crack growth occurring before fracture, which is predicted by the ductile damage model, has a relevant effect on the computed probability of brittle fracture. The proposed combined model is able to accurately account for the loss of constraint occurring in different specimen geometries confirming the geometry transferability of model parameters.

Effect of micro-cracks in nonhomogeneous stress field on fracture instability in structural components

The paper analyses the effects of statistical distribution in sizes of micro-cracks on scatter of fracture toughness of steels under brittle conditions. The results are utilized for reliability assessment of selected functional parts. The reliability considered as a complementary probability of brittle fracture initiation is discussed in dependence on the character of statistical distribution of micro-crack sizes, mechanical properties of steel, mechanisms of energy dissipation during cracks propagation, variation of loading, stress state of functional part and its service life. This probability approach is compared with deterministic reliability access originating from computation of safety factor. Its rational evaluation as a function of acceptable probability of fracture instability provides high economical effects saving materials and energy.

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.

Prediction of fracture toughness scatter of composite materials

Fracture toughness of a composite material is not a deterministic property. This is primarily due to the stochastic nature of its microstructure as well as the activation of different fracture mechanisms during the crack-microstructure interactions. Although Weibull distribution has been widely used to determine the probability of material fracture, its role has been confined to fitting fracture toughness data rather than providing predictive insight of material fracture toughness and the magnitude of scatter. Besides, the Weibull parameters which are obtained through curve fitting carry little physical significance. In this paper, an analytical model is developed to predict fracture toughness in a statistical sense. The Weibull distribution parameters are correlated with the statistical measures of microstructure characteristics and the statistical characterization of the competition between crack deflection and crack penetration at matrix/reinforcement interfaces. Although the quantification is specific to Al2O3/TiB2 composites, the approach and model developed here can be applied to other materials. The established correlations will lead to more reliable material design.

The effect of fatigue pre‐cracking forces on fracture toughness

AbstractTesting procedures for the determination of the fracture toughness of a material by monotonic loading of fatigue pre‐cracked specimens are well established in standards such as BS 7448, BS EN ISO 15653, ISO 12135, ASTM E1820 and ASTM E1921. However, a review of these standards indicates a wide range of permitted fatigue pre‐cracking forces, whilst the underlying assumption in each standard is that the pre‐cracking conditions do not affect the fracture toughness determined. In order to establish the influence of different fatigue pre‐cracking forces on the fracture toughness, tests were carried out on specimens from an API 5L X70 pipeline steel. Single‐edge notch bend specimens of Bx2B geometry were notched through thickness and tested at temperatures of +20 °C, −80 °C and −140 °C to show the fracture behaviour in different regions of the fracture toughness ductile‐to‐brittle transition curve. Fatigue pre‐cracking was conducted on a high‐frequency resonance fatigue test machine over a range of pre‐cracking forces permissible within the various standards and beyond. The results showed that an excessively high pre‐cracking force can result in a significant overestimation of the value of fracture toughness for material exhibiting brittle behaviour, whilst very low fatigue pre‐cracking forces appeared to result in an increase in scatter of fracture toughness. A review of standards indicated that there was a possibility to misinterpret the intention of the ISO 12135 standard and potentially use excessively high pre‐cracking forces. Suggested clarifications to this standard have therefore been proposed to avoid the risk of overestimating fracture toughness.

最弱リンク説に基づいた不均一材破壊靭性試験の確率論的評価方法

最弱リンク説に基づいた不均一材破壊靭性試験の確率論的評価方法

Monte Carlo Simulations of the effects of warm pre-stress on the scatter in fracture toughness

Warm pre-stressing (WPS) is the process of subjecting a pre-cracked component to a load cycle at a temperature higher than subsequent operating temperatures. This process is widely acknowledged as being able to enhance the load to fracture, especially in ferritic steels which exhibit lower shelf cleavage fracture. A WPS model developed by Chell and co-workers is reformulated to create a method of undertaking Monte Carlo Simulations to study the effects of WPS on brittle fracture. This requires the development of solution domains that are governed by the relative sizes of plastic zones ahead of the crack tip during the load and temperature cycles. Using recent experimental data it is shown that accurate estimates of the toughness distributions, after WPS, can be obtained. The scatter observed in this data is also replicated using these simulations. However, the accuracy of WPS predictions may be limited by the sample size. This analysis shows that a sample size smaller than 7 reduces the reliability of the results significantly. The enhancement caused by WPS can also be influenced by the presence of an existing residual stress field. It is shown that tensile residual stresses enhance the WPS effect (caused by an increase in both the pre-load magnitude and the unloaded state load level), provided that they do not cause premature fracture during the pre-load phase.

Effect of Notch Orientation on Fracture Toughness of a Submerged Arc Weld

This paper reports the effect of notch orientation on the fracture toughness of a submerged arc weld as determined by performing standard fracture mechanics tests using single edge notched bend specimens having through-thickness and surface notches. The notch orientations used were NP (through-thickness notch at weld centerline running parallel to the weld direction), NQ (surface notch at weld centerline with the notch plane parallel to the weld but running perpendicular to the weld direction from the cap toward the root), and PQ (a surface notch where the notch plane is transverse to the weld and propagating from the cap toward the root). Testing was carried out over a range of temperatures. It was found that the NP notch orientation led to less scatter in fracture toughness, and the greatest amount of scatter was shown for NQ and PQ notch orientations. The test data for each notch orientation were used to determine the reference temperature T0 using ASTM E1921-13 and FITNET procedures. Values of T0 were subsequently used to define the temperature-versus-toughness transition curve (master curve) for each notch orientation. The fracture toughness predicted by the master curve analyses showed differences among the three notch orientations. As the FITNET procedure is more conservative for highly scattered data than the ASTM procedure, the predicted fracture toughness for the PQ and NQ notch orientations was significantly less than that for the NP notch orientation.

Prediction of Temperature Dependence and Scatter in Fracture Toughness of Pressure Vessel Steel using Nonlocal Damage Models

Abstract The pressure vessel and piping components may be subjected to operation in the ductile-to-brittle transition regime of the material due to increase in the transition temperature. This increase can be due to irradiation embrittlement, vario s other material aging and degradation mechanisms taking place in a nuclear reactor environment. From fracture mechanics point of view, fracture toughness of the material must be adequate to prevent the failure. However, there is considerable scatter observed in the fracture toughness data and the analyst must account for this in the safety analysis. Master curve approach according to ASTM E1921 standard is popularly employed for this purpose. However, it requires the data for transition temperature T0, which is dependent upon the specimen geometry and loading configurations employed in the laboratory tests. Its transferability to safety analysis of components is questionable. Towards this objective, the authors have recently developed a nonlocal formulation for the Rousselier's damage model and combined this with the Beremin's model to predict the variation of fracture toughness and its scatter in the DBTT regime for the standard compact tension specimens. In this work, application of this new procedure to different types of geometry and loading conditions has been explored.

Evaluation of Fracture Toughness by Master Curve Approach Using Miniature C(T) Specimens

The fracture toughness master curve shows the relationship between the median of fracture toughness and temperature in the ductile–brittle transition temperature region of ferritic steels such as reactor pressure vessel (RPV) steels. The master curve approach specified in the ASTM standard theoretically provides the confidence levels of fracture toughness in consideration with the inherent scatter of fracture toughness. The authors have conducted several fracture toughness tests for typical Japanese RPV steels with various specimen sizes and shapes and ascertained that the master curve can be accurately applied to the specimens with a thickness of 0.4-in. or larger. With respect to using the master curve method with the current surveillance program for operating RPVs, the utilization of miniature specimens is important. Miniature specimens, which can be taken from the broken halves of surveillance specimens, are necessary for the efficient determination of the master curve from the limited volume of the available materials. In this study, fracture toughness tests were conducted for typical Japanese RPV steels, particularly SFVQ1A forged and SQV2A plate materials, using the miniature C(T) specimens with a thickness of 4 mm, following the procedure in the ASTM standard. The results show that the differences in the test temperature, evaluation method, and specimen size did not affect the master curves, and the fracture toughness indexed by the reference temperature, To, obtained from miniature C(T) specimens were consistent with those obtained from the standard and larger C(T) specimens. It was also found that valid reference temperatures can be determined with a realistic number of miniature C(T) specimens, i.e., less than ten, if the test temperature was appropriately selected. Thus, the master curve method using miniature C(T) specimens could be a practical method to determine the fracture toughness of actual RPV steels.

Statistical evaluation of fracture toughness with stable crack extension

The scatter of fracture toughness in the ductile-brittle transition temperature region was experimentally examined on 500MPa class low carbon steel. The Weibull distribution of the fracture toughness K(Jc) at −60°C showed the single modal distribution with the shape parameter of around 4. The Weibull distributions of the K(Jc and Ju)s at −20°C and −10°C, however, showed the bilinear distributions with the elbow point. The Weibull slopes below the elbow points were closed to the value of 4, but the slopes showed the transition to be smaller above the elbow points. The bilinear Weibull distributions were discussed from the viewpoints of the constraint loss and the stable crack extension. However, the fracture surface observations revealed that the stable crack extension was the main factor that brought the bilinear Weibull distributions. The bilinear Weibull distributions could be qualitatively simulated by the analytical model with the consideration of the stable crack extension.

Statistical scatter of fracture toughness in the ductile–brittle transition of a structural steel

The statistical scatter of fracture toughness in the ductile–brittle transition temperature range was experimentally examined on a 500 MPa class low carbon steel. Fracture toughness tests were replicatedly performed at −60 °C, −20 °C and −10 °C. The tests at −60 °C resulted in a single modal Weibull distribution with a shape parameter of 4 for the critical stress intensity factor converted from J-integral, whereas the Weibull distributions of the critical stress intensity factor at −20 °C and −10 °C showed a bilinear pattern with an elbow point, which caused a wider scatter than that at −60 °C. Such scatter transition behavior was discussed with reference to stable crack initiation. A model of the statistical scatter transition has been proposed in this work and the model reasonably explains the experimental results.

Evaluation of fracture toughness and its scatter in the DBTT region of different types of pressure vessel steels

Safety analysis of critical components and the overall plant is a major and important task in the field of mechanical engineering. Therefore, it is essential to know the allowable loads and the corresponding failure behaviour (e.g., crack initiation, growth and instability) of the component. Most of the safety critical components, such as pressure vessels of nuclear reactors, are made of ferritic grade low-alloy steels. When these components operate in the ductile-to-brittle transition (DBTT) regime of the material (due to irradiation embrittlement and other material aging and degradation mechanisms taking place), the two mechanisms that compete with each other in the failure process are: ductile and cleavage fracture. From fracture mechanics point of view, fracture toughness of the material must be adequate to prevent the failure. However, there is considerable scatter observed in the fracture toughness data and the analyst must account for this in the safety analysis. Master curve approach according to ASTM E-1921 standard is popularly employed for this purpose. However, it requires the data for transition temperature T 0, which is dependent upon the specimen geometry and loading configurations employed in the laboratory tests. Its transferability to safety analysis of components is questionable. In this work, a combined model for ductile and cleavage fracture is used to predict the fracture toughness scatter and its variation with temperature in the DBTT range. It is demonstrated that the above data for fracture toughness can be predicted once we know the material stress–strain data at different temperatures and a single set of Weibull statistics parameters for cleavage fracture. Extensive experimental investigations have been carried out on two types of pressure vessel steels in the DBTT region using different kinds of specimens to validate the predictions of the model.

マスターカーブ法による国産原子炉圧力容器鋼の破壊靭性評価(保全・設備診断技術,<特集>第13回動力・エネルギー技術シンポジウム)

The fracture toughness Master Curve is a universal relationship between the median of fracture toughness and temperature in the ductile-brittle transition temperature region of ferritic steels. The Master Curve approach specified in the ASTM standard theoretically provides the confidence levels of fracture toughness in consideration of the inherent scatter of fracture toughness. In this study, fracture toughness tests for Japanese reactor pressure vessel steels, with various specimen sizes and shapes were conducted. The differences in test temperature, evaluation method, and specimen size and shape did not affect the Master Curves, ascertaining that the Master Curve approach could be well applied to these classs of steels. The adequacy of the lower bounds based on the ASTM standard was also verified by comparing with experimental fracture toughness data.