Fracture Toughness Of Ferritic Steels Research Articles

Statistical characterization of specimen size and temperature dependence of cleavage fracture toughness of ferritic steels

AbstractBased on the numerical results on the non‐linear correlation between volume of plastic zone and global loading level represented by stress intensity factor, the dependence of cleavage fracture toughness of ferritic steels on specimen size and temperature is evaluated based on an empirical statistical model. The statistical correlation is supported by two sets of toughness data measured from different sized compact tension specimens at different temperatures. To further improve the accuracy of the statistical model, future work is identified to quantify the variation of volume of plastic deformation zone with loading level and measure the average volume for each microcrack at different temperature.

Fundamental insights on ductile to brittle transition phenomenon in ferritic steel

Ductile to brittle transition (DBT) is a well-known phenomenon responsible for deteriorating the low temperature fracture toughness of ferritic steels. It is unambiguous to state that the transition phenomenon is a direct consequence of the strong temperature and strain rate sensitivity of flow stress, which in turn is regulated by the thermally activated motion of screw dislocation at the atomic scale. Due to very high Peierls stress, screw dislocation motion is accompanied by the nucleation and propagation of kink-pairs along the dislocation line. Thus, the activation energy required for kink-pair nucleation is an essential ingredient for correctly predicting the flow stress sensitivity and hence the ductile to brittle transition temperature (DBTT) of ferritic steel. However, experimental determination of kink-pair activation energy is rather tedious and there exists a strong discrepancy between atomistic simulation results (using Density Functional Theory and empirical potentials). Therefore, the present review is aimed at understanding the mechanism of screw dislocation motion in BCC Fe lattice and comparing the results obtained for kink-pair activation energy through experiments and simulations. The effect of different alloying elements on the overall flow stress sensitivity of Fe is also discussed with reference to the interaction of screw dislocation with solute atoms or clusters. Finally, the importance of screw dislocation on predicting the DBTT is explored to identify the present knowledge gaps and the future research directions.

Weibull Modulus of Cleavage Fracture Toughness of Ferritic Steels

The ordinary Weibull distribution function has been commonly accepted for empirical characterization of cleavage fracture toughness of nuclear reactor and containment pressure vessel steels. However, this method lacks a fundamental basis. This work adopts the standardized Weibull distribution function to analyze cleavage fracture toughness of ferritic steels measured from different sized fracture mechanics specimens at different temperatures to estimate the Weibull modulus. The toughness data of five different nuclear reactor and containment vessel steels are analyzed. The estimations obtained the Weibull modulus (m) in the range of 1.83 to 2.55 and strong temperature dependence of the threshold cleavage fracture toughness Kmin, as opposed to the constant values of mK = 4 and Kmin = 20 MPam1/2 given in ASTM E1921-19. The goodness of fit test by the one-sample Kolmogorov–Smirnov (K–S) test validated Weibull distribution function for describing the toughness distribution.

Some thoughts about the application of the Master Curve methodology to ferritic steels containing notches

The Master Curve (MC) is an engineering tool that allows the fracture toughness of ferritic steels operating within their ductile-to-brittle transition zone to be estimated. It is based on statistical considerations, related to the distribution of cleavage-promoting particles around the crack tip, and assumes that: a) fracture is controlled by weakest link statistics; b) it follows a three parameter Weibull distribution. The authors have previously provided two different approaches for applying the MC in notched conditions. The first one consists of determining the reference temperature (T0) in cracked conditions and applying a subsequent notch correction to estimate the fracture toughness at a given temperature; the second one proposes obtaining directly a notch reference temperature (T0N) for a given notch radius by testing notched specimens. This second approach assumes that both the Weibull parameters (Kmin=20 MPam1/2 and b=4) and the censoring criteria used in cracked conditions are applicable in notched conditions. This paper provides some thoughts about these assumptions with the aim of analysing the applicability of the MC in ferritic steels containing notches, and includes specific validation on steels S460M and S690Q.

Finite element simulation of fracture toughness testing of 20MnMoNi55 steel and the effect of loading rate on reference temperature

Fracture toughness of ferritic steel in the ductile-to-brittle transition zone is scattered and probabilistic owing to embrittlement. Use of master curve along with the reference temperature ( T0) adopted in ASTM E-1921 is widely accepted for characterization of this embrittlement. Reference temperature is a measure of embrittlement in the temperature scale. Factors affecting fracture toughness like geometry and loading rate are expected to influence the reference temperature. In the present study, the role of the loading rate on the reference temperature for 20MnMoNi55 steel is assessed experimentally using compact tension C(T) and three-point bend (TPB) specimens. Finite element simulation of tests at different loading rates and cryogenic temperature are carried out using a suitable viscoplastic material model that incorporates flow characteristics of the material for varying displacement rates and cryogenic temperatures. Results from simulation studies are compared with experimental ones.

A method to determine minimum design metal temperature of pressure vessels made from ferritic steel by Master Curve approach

The four impact exemption curves in ASME are convenient to estimate the minimum design metal temperature (MDMT) of ferritic steel. However they can’t distinguish low temperature fracture toughness of ferritic steel well. Materials with similar fracture toughness, divided into different impact exemption curves will have different MDMT and conservative degree. And the MDMT of ferritic steel are estimated by the steel grade. There are differences in toughness for steel with same steel grade from different factories and different heats and batches of the same factory. In this paper, the seven MDMT curves, identified with labels I, II, III, IV, V, VI and VII are proposed based on assumed yield strength and seven reference temperatures, (T0MC = 20 °C, 0 °C, −20 °C, −40 °C, −60 °C, −80 °C and −100 °C) which can cover the temperature range for commonly used pressure vessels made from ferritic steel. The MDMT for a ferritic steel can be determined once the reference temperature and yield strength are measured. SA508-3 and Q345R, as a representative of ferritic steel are used to illustrate the applicability of the MDMT curves.

Study on fracture toughness evaluation method of SA738Gr.B steel heat affected zone in ductile-brittle transition region

ABSTRACT The Master Curve (MC) method is widely used to evaluate the fracture toughness of ferritic steels for reactor pressure vessels in the ductile-brittle transition zone, but this method is only applicable to macroscopically uniform ferritic steels. Based on the measured fracture toughness data of China-produced SA738Gr.B steel Heat-Affected Zone (HAZ) in the as-welded and heat-treated state, the problems of the standard MC method for characterizing the fracture toughness of the HAZ are discussed. Then the Bi-modal master curve method (BMC), SINTAP method, and Single point estimation method (SPE) were used to characterize the fracture toughness of the HAZ of SA738Gr.B steel in the ductile-to-brittle transition zone. The comparative analysis found that the BMC method is better in terms of the accuracy of the estimation and the over-dispersion envelope was caused by the heterogeneity. The estimation results of the SINTAP and SPE models are conservative but can be used for the safety evaluation of the actual structure. The study provided technical support for SA738Gr.B steel to exempt post-weld heat treatment issue.

A Statistical Model of Cleavage Fracture Toughness of Ferritic Steel DIN 22NiMoCr37 at Different Temperatures

It is a conventional practice to adopt Weibull statistics with a modulus of 4 for characterizing the statistical distribution of cleavage fracture toughness of ferritic steels, albeit based on a rather weak physical justification. In this study, a statistical model for cleavage fracture toughness of ferritic steels is proposed according to a new local approach model. The model suggests that there exists a unique correlation of the cumulative failure probability, fracture toughness and yield strength. This correlation is validated by the Euro fracture toughness dataset for 1CT specimens at four different temperatures, which deviates from the Weibull statistical model with a modulus of four.

Investigation of cleavage fracture under dynamic loading conditions: Part I fractographic analysis

The fracture toughness of ferritic steels under dynamic loading conditions on the one hand shows decreasing values with elevated loading rates but on the other hand the shape of the temperature dependent fracture toughness curve has turned out to be different from the static Master Curve according to ASTM E 1921. This difference is often explained by adiabatic heating in the crack tip region, yet it is not clear if there are other additional mechanisms under dynamic loading conditions that contribute to these changes. This work is dedicated to systematically identifying and quantifying additional mechanisms regarding cleavage fracture under dynamic loading conditions. In part I of this study an extensive fractographic analysis of the fracture surfaces was conducted for various crack tip loading rates and testing temperatures. The primary fracture-inducing mechanism was found to be identical to the dominant one under quasi-static conditions (carbide cracking). Yet, the dynamic loading conditions appear to change the origin of fracture, promote local crack arrest, and cause multiple fracture initiation sites that lead to global failure. These results also question the reliability of current local approach concepts if used to assess fracture probability at elevated loading rates. The fractographic results are used in, and complemented by, part II of this study which deals with the numerical analysis of other additional mechanisms such as inertia.

Influence of carbide particles on crack initiation and propagation with competing ductile-brittle transition in ferritic steel

Carbide particles play an important role for the fracture toughness of ferritic steels in the ductile-brittle transition (DBT) region as cracks mainly originate from a broken or debonded carbide. It is well-known that size, volume fraction, strength and distribution of carbides are relevant for the competition of ductile and brittle mechanisms of failure. In the present study, the influence of the carbide strength and carbide-ferrite interaction on the fracture toughness of ferritic steels is investigated in the DBT regime by a micromechanical, deterministic FEM model. The carbide particles are resolved discretely in the fracture process zone at the crack tip. Cleavage of ferrite, of carbides and debonding of the carbide-ferrite interface are modeled by cohesive zones. The simulated fracture toughness in the DBT region do compare well with experimental data from literature. Thus, the capability of the model is demonstrated to capture the competition of the various microscopic mechanism.

Analysis of specimen size conversion in the ductile to brittle transition region of ferritic steels

The ASTM E 1921-15 standard covers the determination of the Master Curve, a function used to characterize the fracture toughness of ferritic steels that experience onset of cleavage fracture in the transition region. In the standard, the specimen size effect on fracture toughness at cleavage (KJc) in the transition range is explained by the weakest-link theory, using a three-parameter Weibull distribution with shape (b) and threshold (Kmin) parameters fixed. When specimens from different sizes are tested, a KJc conversion is necessary. The effect of size conversion using either the equation given by the standard and a three parameter Weibull distribution with the parameters estimated from data sets are compared in this work. It was found that the distributions obtained from results converted to one-inch size did not adjust the data in the way the weakest link model would predict, meaning that the statistical effect due to the difference in the crack front volume would not be the only responsible for the difference in results for different specimen sizes. This was found using both the ASTM E1921 method and the three parameter Weibull distribution.

A study on the ASTM E1921 standard in determining the fracture toughness of ferritic steels

ABSTRACTOne of the most important aims of the fracture mechanics is to determine the fracture toughness of a material. Various methods were developed for this purpose and have been still used nowadays. In the J‐integral method that is one of them, providing of a dominant linear elastic condition on the specimen is not required. However, in ferritic steels, the fracture toughness values (KJC) obtained by the J‐integral method show some inconsistencies. Therefore, the ASTM E1921 standard was developed on ferritic steels, which are instabilities in the values of elastic or elastoplastic fracture toughness. In this study, a new method was used to determine the fracture toughness (KIC) of ferritic steels, and it was compared with the standard. Three steels with different mechanical properties and average grain size were investigated in this study.

Fracture Toughness of Ferritic Steels: Lower Bounds and their Implications on Testing and Application

For physical reasons fracture toughness KJc of ferritic steels in the brittle-to-ductile transition regime is affected by a pronounced scatter, which requires statistical methods to be applied for evaluation of test results as well as for application in safety analysis of structures. For this purposes the probabilistic Master-Curve-approach according to ASTM E1921 is often used. However, for engineering purposes like a screening safety analysis of a defect-containing component it is usually preferable to use a deterministic lower bound. However, within the framework of ASTM-standards there is no possibility to determine KIc experimentally. So KIc needs to be determined indirectly from the reference temperature T0. In the present paper it is shown how lower bounds of fracture toughness – either plane strain KIc for large components or thickness-dependent KJc for smaller ones - can be derived from T0, and how the latter can be determine with sufficient accuracy from one or a few KJc values.

Influence of Grain Size on the Ductile Fracture Toughness of Ferritic Steel

Influence of Grain Size on the Ductile Fracture Toughness of Ferritic Steel

Rational Determination of Lower-Bound Fracture Toughness Curves Using Master Curve Approach

The Master Curve gives the relation between the median of fracture toughness of ferritic steels and the temperature in the ductile–brittle transition temperature region. The procedure used to determine the Master Curve is provided in the current American Society for Testing and Materials (ASTM) E1921 standard. By considering the substitution of the alternative lower-bound curves based on the Master Curve approach for the KIc curves based on reference data sets in the present codes such as ASME Code Cases N-629 and N-631, the statistical characteristic should be well incorporated in the determination of the lower-bound curves. Appendix X4 in the ASTM standard describes the procedure used to derive the lower-bound curves; however, it appears to be addressed without sufficient consideration of the statistical reliability. In this study, we propose a rational determination method of lower-bound fracture toughness curves using the Master Curve approach. The method considers the effect of sample size in the determination of the tolerance-bound curve. The adequacy of the proposed method was verified by comparing the tolerance-bound curve with the fracture toughness database for national reactor pressure vessel (RPV) steels including plate and forging obtained from 4 T to 0.4 T C(T) specimens and 0.4 T SE(B) specimens. The method allows the application of the Master Curve using fewer specimens, which can coexist with the present surveillance program.

A new method for determining the fracture toughness of main pipeline steels

ABSTRACTOne of the fundamental aims of fracture mechanics is to define fracture toughness KIC of a material. Hence, the ASTM E399 standard was developed. However according to the standard, large‐sized specimens are required to determine the fracture toughness of low alloy carbon steels. ASTM E1921 standard was developed on the fracture toughness of ferritic steels. In this study, a new method was proposed to determine the fracture toughness of ferritic steels. The purpose of the present paper is to compare the results of the method with the experimental results. Two steels that are used in gas and oil main pipelines were investigated in this study.

RELATIONSHIP BETWEEN RADIATION INDUCTED YIELD STRENGTH INCREMENT AND CHARPY TRANSITION TEMPERATURE SHIFT IN REACTOR PRESSURE VESSEL STEELS OF KOREAN NUCLEAR POWER PLANTS

The decrease in the fracture toughness of ferritic steels in a reactor pressure vessel is an important factor in determining the lifetime of a nuclear power plant. A surveillance program has been in place in Korea since 1979 to assess the structural integrity of RPV steels. In this work, the surveillance data were collected and analyzed statistically in order to derive the empirical relationship between the embrittlement and strengthening of irradiated reactor pressure vessel steels. There was a linear relationship between the yield strength change and the transition temperature shift change at 41 J due to irradiation. The proportional coefficient was about 0.5℃/MPa in the base metals (plate/forgings). The upper shelf energy decrease ratio was non-linearly proportional to the yield strength change, and most of the data lay along the trend curve of the US results. The transition regime temperature interval, ΔTT, was less than the US data. The overall change from irradiation was very similar to the US results. It is expected that the results of this study will be applied to basic research on the multiscale modeling of the irradiation embrittlement of RPV materials in Korea.

Comparison of 3P-Weibull parameters based on JC and KJC values

The characterization of fracture toughness of ferritic steels in the ductile-to-brittle transition is problematic due to the scatter of test results. Several proposals using Weibull statistics have been made, some of them in terms of J and others in terms of K; some authors employ a two parameters Weibull function (2P-W), while others use a three parameters function (3P-W), although ASTM E1921 uses 3P-W in terms of K with two fixed parameters to determine the Reference Temperature To. An analysis about the relationship between Weibull distributions expressed in terms of J and K is presented in this paper. It is shown that if the J C results follow a 3P-W, their equivalent K JC values do not exactly fit a 3P-W function obtained by means of a simple transformation of the three parameters. Nevertheless, an approximated 3P-W function in K terms is proposed in this work. It fits very well with the transformed values and their parameters are related to the ones expressed in J terms. In case the experimental results follow a 3P-W in K JC , a similar analysis can be performed. For the particular situation of a 2P-W, there is an exact equivalence between the distributions in terms of J and K, being the Weibull slope in terms of K twice the slope in terms of J.

Fracture characterisation of a nuclear vessel steel under dynamic conditions in the transition region

The Master Curve (MC) methodology, originally proposed by Kim Wallin, is a standardised engineering tool for analysing the fracture toughness of ferritic steels in the ductile to brittle transition (DBT) region by means of the reference temperature T 0 . This temperature is normally estimated from quasi-static fracture toughness tests, nevertheless, it has been recently extended to the determination of dynamic fracture toughness. The aim of the present contribution is to characterise the fracture resistance in the DBT region under high strain rate conditions by applying the MC methodology to the steel of the Santa María de Garoña Spanish nuclear power plant (NPP). In this sense, 15 Charpy instrumented tests were performed on pre-cracked specimens from the surveillance program of the plant. The dynamic reference temperature, T 0,dyn , was obtained and compared with the quasi-static reference temperature, T 0,sta . The reliability of a semi-empirical formula proposed by Wallin to obtain T 0,dyn from T 0,sta has been analysed for this material.

Influence of crack deflection into the carbide/ferrite interface on cleavage fracture initiation in ferritic steels

In this and a companion study (Kroon, M., Faleskog, J., 2005. Micromechanics of cleavage fracture initiation in ferritic steels by carbide cracking. J. Mech. Phys. Solids 53, 171–196), the initiation of cleavage fracture in ferritic steels is studied. The initiation is modelled explicitly in the form of a microcrack, which nucleates in a brittle carbide and propagates into the surrounding ferrite. The carbide is modelled as an elastic cylinder and the ferrite as an elastic viscoplastic material. The crack growth is modelled using a cohesive surface, in which the tractions are governed by a modified exponential cohesive law. The advancing microcrack, which has nucleated in the carbide, may either continue into the ferrite or deflect into the interface between the carbide and the ferrite. Special attention is given to the influence of the mode mixity factor β , which is defined as the ratio between the shear and tensile strength of the interface between the carbide and the ferrite. Crack growth in the interface occurs in shear mode and is driven by a fibre loading mechanism. For mode mixity values β ⩽ 0.2 , the crack deflects into the interface. The results indicate that crack growth in the interface can have a profound influence on the macroscopic fracture toughness of ferritic steels.