The Weibull Stress Model for Predicting Cleavage Fracture in the Ductile-to-Brittle Transition Region

2008 ◽  
Author(s):  
Xiaosheng Gao ◽  
Jason P. Petti ◽  
Robert H. Dodds
Keyword(s):  
Fracture Toughness ◽  
Transition Region ◽  
Cleavage Fracture ◽  
Model Parameters ◽  
Ferritic Steels ◽  
Stress Model ◽  
Brittle Transition ◽  
Ductile To Brittle Transition ◽  
Constraint Effects ◽  
Weibull Stress

Transgranular cleavage fracture in the ductile-to-brittle transition region of ferritic steels often leads to spectacular and catastrophic failures of engineering structures. Due to the strongly stochastic effects of metallurgical scale inhomogenieties together with the nonlinear mechanical response from plastic deformation, the measured fracture toughness data exhibit a large degree of scatter and a strong dependence on constraint. This has stimulated an increasing amount of research over the past two decades, among which the Weibull stress model originally proposed by the Beremin group has gained much popularity. This model is based on weakest link statistics and provides a framework to quantify the relationship between macro and microscale driving forces for cleavage fracture. It has been successfully applied to predict constraint effects on cleavage fracture and on the scatter of macroscopic fracture toughness values. This paper provides a brief review of the research conducted by the authors in recent years to extend the engineering applicability of the Weibull stress model to predict cleavage fracture in ferritic steels. These recent efforts have introduced a threshold value in the Weibull stress model, introduced more robust calibration methods for determination of model parameters, predicted experimentally observed constraint effects, demonstrated temperature and loading rate effects on the model parameters, and expanded the original Beremin model to include the effects of microcrack nucleation.

Prediction of SENB Fracture Toughness From Charpy Data Using the Beremin Model in the Lower Transition Region

2013 ◽  
Author(s):  
Robin J. Smith ◽  
Andrew H. Sherry ◽  
Adam C. Bannister ◽  
Anthony J. Horn
Keyword(s):  
Fracture Toughness ◽  
Transition Region ◽  
Cleavage Fracture ◽  
Ferritic Steel ◽  
Transition Curve ◽  
Charpy Specimen ◽  
Absorbed Energy ◽  
Brittle Transition ◽  
Lower Transition ◽  
Ductile To Brittle Transition

This work focuses on the application of a mechanistic local approach model to describe the statistical distribution of experimental Charpy (CVN) impact test data obtained at several temperatures in the ductile to brittle transition temperature range. The current objective is to develop a correlation in the lower transition regime between quasi-static CVN absorbed energy (CVE) and the J-integral fracture toughness (Jc) obtained from deeply pre-cracked Charpy (PCCVN) specimens tested quasi-statically to laboratory test standards. The Beremin model for cleavage fracture has been applied to a ferritic steel which has been comprehensively tested using standard CVN, shallow U-notched and PCCVN specimen types in the lower ductile to brittle transition. This has enabled a prediction to be made of the absorbed CVE at cleavage fracture initiation for a Charpy specimen tested quasi-statically in the lower part of the CVN transition curve. By applying the Beremin model to PCCVN single edge notch bend specimens at quasi-static rates it was possible to use the Weibull stress, to achieve a reliable correlation between CVE and Jc in the lower ductile to brittle transition region. The results from this work indicate that the Beremin model can provide a theoretically based correlation for CVE to Jc fracture toughness for a ferritic steel under quasi-static loading conditions. The overall objective of the project remains to predict dynamic CVN absorbed energy using micromechanical modelling and which is valid for all ferritic steels.

scholarly journals Incorporation of Obstacle Hardening into Local Approach to Cleavage Fracture to Predict Temperature Effects in the Ductile to Brittle Transition Regime

Materials ◽  
2021 ◽  
Vol 14 (5) ◽  
pp. 1224
Author(s):  
Maria S. Yankova ◽  
Andrey P. Jivkov ◽  
Rajesh Patel
Keyword(s):  
Fracture Toughness ◽  
Cleavage Fracture ◽  
Cleavage Crack ◽  
Pressure Vessel Steel ◽  
Transition Regime ◽  
Vessel Steel ◽  
Integrity Assessment ◽  
Brittle Transition ◽  
Ductile To Brittle Transition ◽  
Weibull Stress

Ductile-to-brittle-transition refers to observable change in fracture mode with decreasing temperature—from slow ductile crack growth to rapid cleavage. It is exhibited by body-centred cubic metals and presents a challenge for integrity assessment of structural components made of such metals. Local approaches to cleavage fracture, based on Weibull stress as a cleavage crack-driving force, have been shown to predict fracture toughness at very low temperatures. However, they are ineffective in the transition regime without the recalibration of Weibull stress parameters, which requires further testing and thus diminishes their predictive capability. We propose new Weibull stress formulation with thinning function based on obstacle hardening model, which modifies the number of cleavage-initiating features with temperature. Our model is implemented as a post-processor of finite element analysis results. It is applied to analyses of standard compact tension specimens of typical reactor pressure vessel steel, for which deformation and fracture toughness properties in the transition regime are available. It is shown that the new Weibull stress is independent of temperature, and of Weibull shape parameter, within the experimental error. It accurately predicts the fracture toughness at any temperature in the transition regime without relying upon empirical fits for the first time.

A Monte Carlo Implementation of the James-Ford-Jivkov Micro-Structurally Informed Local Approach Applied to Predict Fracture Toughness Including Low Constraint Conditions

2015 ◽  
Author(s):  
Michael Ford ◽  
Peter James
Keyword(s):  
Fracture Toughness ◽  
Monte Carlo ◽  
Transition Region ◽  
Crack Size ◽  
Model Parameters ◽  
Local Approach ◽  
Rpv Steel ◽  
Low Constraint ◽  
Constraint Effects ◽  
Monte Carlo Implementation

The need to predict changes in fracture toughness for materials where the tensile properties change through life, such as with irradiation, whilst accounting for geometric constraint effects, such as crack size, are clearly important. Currently one of the most likely approaches by which to develop such ability are through application of local approach models. These approaches appear to be sufficient in predicting lower shelf toughness under high constraint conditions, but may fail when attempting to predict toughness in the transition region or for low constraint geometries when using the same parameters, making predictions impossible. Cleavage toughness predictions in the transition regime that are then extended to low constraint conditions are here made with a stochastic, Monte Carlo implementation of the recently proposed James-Ford-Jivkov model. This implementation is based around the creation of individual initiators following the experimentally observed distribution for specific RPV steel, and determining if these initiators form voids or cause cleavage failure using the model’s improved criterion for particle failure. The model has shown to predict experimentally measured locations of cleavage initiators. Further, initial results from the Monte Carlo implementation of the model predicts the fracture toughness in a large part of the transition region, demonstrates an ability to predict the constraint shift and shows a level of scatter similar to that observed experimentally. All results presented, for a given material, are obtained without changes in the model parameters. This suggests that the model can be used predicatively for assessing toughness changes due to constraint- and temperature-driven plasticity changes.

On the Use of the Notch Master Curve for Apparent Fracture Toughness Predictions of Notched Ferritic Steels Operating Within the Ductile-to-Brittle Transition Zone

2015 ◽  
Author(s):  
Sergio Cicero ◽  
Tiberio Garcia ◽  
Virginia Madrazo
Keyword(s):  
Fracture Toughness ◽  
Transition Zone ◽  
Fracture Resistance ◽  
Master Curve ◽  
Ferritic Steels ◽  
Brittle Transition ◽  
Apparent Fracture Toughness ◽  
Different Temperatures ◽  
Fracture Tests ◽  
Ductile To Brittle Transition

This paper presents the Notch-Master Curve as a model for the prediction of the apparent fracture toughness of ferritic steels in notched conditions and operating at temperatures corresponding to their ductile-to-brittle transition zone. The Notch-Master Curve combines the Master Curve of the material in cracked conditions and the notch corrections provided by the Theory of Critical Distances. In order to validate the model, the fracture resistance results obtained in fracture tests performed on notched CT and SENB specimens are presented. The results gathered here cover four ferritic steels (S275JR, S355J2, S460M and S690Q), three different notch radii (0.25 mm, 0.50 mm and 2.0 mm) and three different temperatures within the corresponding ductile-to-brittle transition zone. The results demonstrate that the Notch Master Curve provides good predictions of the fracture resistance in notched conditions for the four materials analyzed.

Additional Data Concerning French PWR RPV Steel to Evaluate the Relevance of a Size Effect Correction on Toughness in the Ductile-to-Brittle Transition

2014 ◽  
Author(s):  
C. Jacquemoud ◽  
I. Delvallée-Nunio ◽  
M. Nédélec ◽  
F. Balestreri
Keyword(s):  
Fracture Toughness ◽  
Size Effect ◽  
Crack Length ◽  
Compact Tension ◽  
Ferritic Steels ◽  
Transition Range ◽  
Brittle Transition ◽  
Reference Length ◽  
Rpv Steel ◽  
Ductile To Brittle Transition

In the ductile-to-brittle transition range of ferritic steels, fracture toughness exhibits a size effect. Up to now, in the safety demonstration of the French Reactor Pressure Vessel (RPV) integrity, a size effect correction has been considered by the operator to take into account fracture toughness variation of ferritic steels with crack length. The correction consists in increasing the toughness estimated on the RCC-M curve by a factor which depends on a reference length and on the crack length considered. IRSN has already examined the relevance of this correction through statistical analysis of toughness results coming from two ferritic steel databases. To complete its evaluation on French RPV steel, IRSN has supported a large experimental campaign on 16MND5 steel at different temperatures in the ductile-to-brittle transition (from −150°C to −50°C), including tests on various Compact Tension (CT) specimen geometries. Specimens with semi-elliptical crack have been also considered. The results confirm the observations made in its previous study: a size effect exists on mean or median toughness, for the latter more or less in accordance with Beremin theory. Nevertheless, the minimum toughness appears to be independent of the specimen geometry. This indicates that the use of a size effect correction on minimum toughness is not relevant.

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