Cleavage Fracture Toughness Research Articles

A probabilistic model to predict specimen geometry effects on fracture toughness in ferritic–pearlitic steels

This work describes a probabilistic framework for cleavage fracture of ferritic–pearlitic steels incorporating experimental measurements of microcrack distribution associated with the cracking of the pearlitic microstructure. A central objective of this study is to explore and further extend application of a probabilistic framework incorporating the statistics of microcracks to predict specimen geometry effects on the fracture toughness distribution for a typical ferritic–pearlitic structural steel. Fracture toughness values for an ASTM A572 Grade 50 structural steel derived from fracture tests using conventional SE(B) specimens with varying thickness and a/W-ratios provide the cleavage fracture resistance data needed to assess specimen geometry effects on the probability distribution of Jc-values. The present exploratory study successfully predicts the measured statistical distribution of cleavage fracture toughness in shallow crack specimens and provides further support of the proposed probabilistic model as a more advanced and effective engineering-level procedure in fracture assessment methodologies.

Investigation of Residual Stress Effect on Cleavage Fracture Toughness in the Transition Temperature Region by Considering the Crack-Tip Constraint

Investigation of Residual Stress Effect on Cleavage Fracture Toughness in the Transition Temperature Region by Considering the Crack-Tip Constraint

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.

Novel framework for predicting constraint effects on fracture toughness using an elastic–plastic phase field model and modified boundary layer formulations

Fracture toughness is dependent on geometry according to a phenomenon known as the constraint effect on fracture toughness. In this paper, we propose a framework to predict constraint effects on fracture toughness using an elastic–plastic phase field model and modified boundary layer formulations. An elastic–plastic material was adopted because constraint effects are typically related to plastic deformation at the crack tip. Modified boundary layer formulations were used as loading methods to control phase field evolution at the crack tip. Numerical results indicate that fracture toughness increases with negative T-stress. The effects of yield stress and the linear hardening coefficient on constraint effects were also investigated. The results revealed that the variation in fracture toughness was greater in materials with low-strain hardening and yield stress compared to that in materials with high-strain hardening and yield stress. Finally, the variation in cleavage fracture toughness as predicted by our framework with a limited set of available experimental data was evaluated. The trend of the predicted results is consistent with that of the experimental results.

A constraint-based approach for notch cleavage fracture toughness estimations

A stress-based approach is used to evaluate the role of notch sharpness on effective toughness of S355J2 + N steel samples. A notch corrected constraint method based on a J-Q approach is proposed for the first time. The approach is calibrated using experimental fracture data of pre-cracked and notched SEN(B) samples and validated using notched C(T) data from open literature for the same material. A two-parameter Weibull model is used to describe the probability of failure to incorporate confidence levels into the analysis. The methodology shows to be a promising method for assessment of non-sharp defects where benefit may be taken from resolving non-sharp defects acuity.

Temperature Dependence of Cleavage Fracture Toughness for an Ultrahigh Strength Martensitic Steel

Abstract This work conducts an exploratory evaluation of the brittle fracture behavior for an ultrahigh strength martensitic steel using conventional three-point bend SE(B) and precracked Charpy V-notch (PCVN) specimens. A primary purpose of this study is to verify the effectiveness of the Master Curve methodology in providing a reliable estimate of the reference temperature (T0) derived from fracture toughness data sets measured in the ductile-to-brittle transition (DBT) region of an ultrahigh strength, low alloy martensitic steel. Fracture toughness testing conducted on three-point bend SE(B) specimens and PCVN configurations at different test temperatures in the DBT region provides the cleavage fracture resistance data in terms of the J-integral at cleavage instability, Jc, and its corresponding KJc-values for the tested material. Although this class of ultrahigh strength steel having a martensitic microstructure is currently beyond the reach of ASTM E1921, Standard Test Method for Determination of Reference Temperature, T0, for Ferritic Steels in the Transition Range, the analyses described here show that the predicted normalized curves of median fracture toughness versus temperature are in good agreement with the experimental measurements.

Grain refinement by rapid cyclic heating and its effect on cleavage fracture behaviour of an S690 high strength steel

The simultaneous improvement of strength and toughness with grain refinement is widely known. However, the literature lacks studies on the grain refinement effect on cleavage fracture toughness in multiphase steels containing detrimental brittle inclusions. Understanding whether the grain refinement can effectively improve fracture toughness of such steels will allow for the improvement of their design. Therefore, a quenched and tempered S690QL high strength steel with Nb-rich and oxide inclusions was subjected to a rapid cyclic heating (RCH) treatment aimed at grain refinement, followed by quenching and tempering to produce a microstructure equivalent to the as-received steel. The microstructure was investigated via scanning electron microscopy (SEM), energy-dispersive X-ray spectroscopy (EDS), and electron backscatter diffraction (EBSD). The cleavage fracture toughness was measured via three-point bending tests at −100 °C. The RCH effectively reduced the prior austenite grain size by 55%. However, other microstructural changes occurred. The elongated, parallel-aligned block sub-structure of martensitic/bainitic grains changed to rounded, randomly distributed blocks. Also, the ferritic content increased and martensite and cementite clusters were formed. The concurrent effects of microstructural modifications and grain refinement explain the very minor improvements in hardness and tensile properties. The grain refinement, theoretically responsible for decreasing the ductile-to-brittle transition temperature, improved the fracture toughness up to a factor of 2.5 and 8.6 when Nb-rich and oxide inclusions trigger fracture, respectively. The microstructural changes have minor effects on fracture toughness. Therefore, the proposed RCH treatment is effective in reducing the grain size and improving cleavage fracture toughness in steels containing brittle inclusions.

Effects of microstructure and specimen size on the fracture toughness of EH47 shipbuilding steel at low temperature

This study investigated the effects of microstructure and specimen size on the fracture behavior of EH47 shipbuilding steel at low temperature. The fracture toughness (characterized by the Crack Tip Opening Displacement, i.e., CTOD) was evaluated using compact tensile specimens with various microstructures and sizes at − 60 °C. The results revealed that due to inhomogeneous microstructure along the steel plate thickness direction, fracture toughness decreased as the sampling location shifted from the surface to the center of the steel plate. Furthermore, the fracture toughness values of 19, 25, and 38 mm-thick specimens taken from the center of an 80 mm-thick steel plate remained almost constant. Based on the analysis of fracture surfaces, metallography and the characteristics of cleavage initiation site, it was found that grain size had significant effect on the cleavage fracture toughness. When the microstructure was strongly inhomogeneous distributed along the thickness direction and tested at the properly low temperature range, the influence of the microstructure on the fracture toughness was more significant than that of the specimen size. In this condition, small specimens taken from the central location of steel plate can be used to estimate the fracture toughness of specimens with full thickness.

A probabilistic approach for cleavage fracture including the statistics of microcracks: Application to a reactor pressure vessel steel

This work describes a probabilistic framework for cleavage fracture incorporating the measured statistics of microcracks to characterize the cleavage fracture toughness distribution in structural ferritic steels. Fracture toughness testing conducted on standard compact tension C(T) specimens for a 22NiMoCr37 pressure vessel steel, known as the EURO steel A, for varying test temperatures provides the cleavage fracture resistance data needed to determine the experimentally measured Jc-distribution. Metallographic examination of etched surfaces for the EURO 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 the probabilistic model incorporating the statistics of microcracks holds significant promise as an engineering-level procedure to predict the fracture behavior in structural components with diverse range of temperature and possibly crack-tip constraint.

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

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

Relating matrix stress to local stress on a hard microstructural inclusion for understanding cleavage fracture in high strength steel

Macroscale cleavage fracture toughness of high strength steels is strongly related to the fracture of hard microstructural inclusions. Therefore, an accurate determination of the local stress on these inclusions based on the matrix stress is necessary for the statistical modelling of macroscale cleavage fracture. This paper presents analytical equations to quantitatively estimate the stress of the microstructural inclusions from the far-field stress of the matrix. The analytical equations account for the inclusion shape, the inclusion orientation, the far-field stress state and matrix material properties. Finite element modelling of a representative volume element containing a hard inclusion shows that the equations provide an accurate representation of the local stress state. The equations are implemented into a multi-barrier model and compared with CTOD experiments with two different levels of constraint.

Micromechanics driven design of ferritic–austenitic duplex stainless steel microstructures for improved cleavage fracture toughness

Ferritic–austenitic duplex stainless steels are known to offer favorable combinations of good mechanical properties and corrosion resistance to be used for structural purposes. Lean duplex grades have already been introduced for consideration to replace standard 18–8 austenitic stainless steels in various industrial applications. Ferrite and austenite represent different deformation behaviors and contribute to the resulting fracture toughness characteristics. Micromechanical crystal plasticity based assessment of this cleavage fracture behavior is the subject area of current work. The objective is to bridge cleavage fracture models to full field crystal plasticity imaging based modeling of microstructures of ferritic–austenitic duplex stainless steels. The goal is to introduce means to computationally assess the effects of different multi-phase microstructural morphologies to cleavage fracture toughness and develop both the respective constitutive and cleavage fracture modeling capabilities. Such means can be used as an aid to develop better cleavage resistant, while in the current context lean, steel grades. Three different steels are investigated with differing austenite phase morphologies, and their behavior with respect to fracture mechanical response evaluated by micromechanical modeling. The effect of austenite fraction and morphology in terms of improving fracture toughness, a critical parameter concerning these steel grades and improvement of their cleavage fracture properties, is investigated. Deleterious features such as large ferrite grain size and microstructural property mismatching are identified and their implications to fracture toughness and development of applicable modeling capabilities for ferritic–austenitic duplex steels discussed. Simple design task of varying the austenite phase fraction is performed using synthetic microstructural modeling and the results evaluated with respect to their influence on the fracture toughness ductile-to-brittle transition.

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.

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.

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.

A simplified estimation procedure for the Weibull stress parameter, m, and applications to predict the specimen geometry dependence of cleavage fracture toughness

This study describes a simplified procedure to estimate the Weibull stress parameter, m, using cleavage fracture toughness values measured from testing high constraint fracture specimens. The estimation procedure builds upon the conventional toughness scaling methodology (TSM) based on the Weibull stress coupled with the weakest link model to correct measured toughness distributions for high constraint fracture specimens with identical in-plane dimensions but varying thickness. The approach thus requires a correspondence between predictions based upon the Weibull stress methodology and the weakest link model for measured toughness values under high constraint conditions. Applications of the proposed procedure to analyze specimen geometry effects on fracture toughness values in a typical structural steel provide predictions that agree remarkably well with experimental data for shallow crack bend specimens with different thickness. These exploratory studies demonstrate the potential capability of the proposed estimation procedure which can greatly simplify engineering integrity assessments based upon the Weibull stress model.

Modelling of Fracture Toughness of X80 Pipeline Steels in DTB Transition Region Involving the Effect of Temperature and Crack Growth

This work presents an investigation of the effects of temperature and crack growth on cleavage fracture toughness for weld thermal simulated X80 pipeline steels in the ductile-to-brittle transition (DBT) regime. A great bulk of fracture toughness (crack tip opening displacement—CTOD) tests and numerical simulations are carried out by deep-cracked single-edge-notched bending (SENB) and shallow-cracked single-edge-notched tension (SENT) specimens at various temperatures (−90 °C, −60 °C, −30 °C, and 0 °C). Three-dimensional (3D) finite element (FE) models of tested specimens have been employed to obtain computational data. The results show that temperature exerts only a slight effect on the material hardening behavior, which indicates the crack tip constraint (as denoted by Q-parameter) is less dependent on the temperature. The measured CTOD-values give considerable scatter but confirm well-established trends of increasing toughness with increasing temperature and reducing constraint. Crack growth and 3D effect exhibited significant influences on CTOD-CMOD relations at higher temperatures, −30 °C and 0 °C for the SENT specimen.

A modified local approach including plastic strain effects to predict cleavage fracture toughness from subsize precracked Charpy specimens

This work addresses a probabilistic, micromechanics-based methodology incorporating plastic strain effects on cleavage fracture and its dependence on the microcrack distribution. The present model extends current developments of a local approach to fracture (LAF) adopting a plastic-strain based form of the Weibull stress (σ̃w) to assess changes in cleavage fracture toughness for a reactor pressure vessel (RPV) steel due to constraint loss effects in subsize precracked Charpy (PCVN) specimens. Cleavage fracture toughness data obtained by Rathbun et al. (2006) for an A533 Gr B reactor pressure vessel steel are employed to demonstrate the capability of the modified LAF in predicting the strong influence of specimen geometry on fracture toughness. By combining detailed non-linear, 3-D finite element analyses for the side-grooved C(T) and PCVN specimens with varying geometries, the plastic-strain based form of the Weibull stress is shown to effectively remove the dependence of Jc-values on specimen geometry thereby generating more accurate assessments of cleavage fracture behavior in larger crack configurations from small specimens.

Use of local approaches to calculate changes in cleavage fracture toughness due to pre-straining and constraint effects

Presented are experimental data and analyses of fracture toughness tests across three different crack tip constraint conditions and two different material conditions – as-received and pre-strained to 5% plastic strain. Analyses are performed using a local approach, based on a plasticity-modified Weibull stress interpreted as a crack driving force for cleavage fracture. Local approach parameters are calibrated using experimental data from the highest and lowest constraint geometries of as-received material. Results suggest one point of practical importance for testing reduction: use of large constraint difference for calibration yields good predictions for cleavage fracture toughness at intermediate constraints; use of small constraint difference for calibration cannot guarantee good predictions for constraints outside the calibration interval. Further, the calibrated local approach is used to predict the fracture toughness of pre-strained material. Pre-straining is found to reduce both the elastic modulus and the proportionality stress of the material, which at the micro-structural scale could be attributed to increased dislocation mobility after unpinning, and in addition to possible damage around second phase particles. Resulting characteristic toughness values are 2–2.5 times smaller than those of as-received material for corresponding constraint conditions, with pronounced diminishing constraint benefit. The degradation of deformation properties changes the initial conditions for Weibull stress calculation. A simple scaling method is proposed, based on flow stress changes, to account for changes in initial conditions. Predictions based on the proposed Weibull stress scaling are shown to be in good agreement with experimental data. This suggests a second point of practical importance for testing reduction: changes in fracture toughness due to load history could be predicted using only tensile test data of aged material and tensile and fracture toughness data from original material at two significantly different constraint conditions. Further experimental evidence is required to support this suggestion.

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.