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.

A Monte Carlo Implementation of the James-Ford-Jivkov Microstructurally Informed Local Approach Applied to Predict Fracture Toughness Across Irradiation Conditions

2016 ◽  
Author(s):  
Michael Ford ◽  
Peter James
Keyword(s):  
Fracture Toughness ◽  
Monte Carlo ◽  
Transition Region ◽  
Crack Size ◽  
Model Parameters ◽  
Pressure Vessel Steel ◽  
Local Approach ◽  
Vessel Steel ◽  
Reactor Pressure Vessel Steel ◽  
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, for low constraint geometries or for different irradiation states, when using the same parameters, making reliable predictions impossible. Cleavage toughness predictions in the transition regime 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 reactor pressure vessel steel, and determining if these initiators form voids or cause cleavage failure using the model’s improved criterion for particle failure. This implementation has been presented previously in PVP2015-45905, where it was successfully applied across different constraint conditions; in the work presented here it is applied across different irradiation conditions for a second type of steel. The model predicts the fracture toughness in a large part of the transition region, demonstrates an ability to predict the irradiation 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-, irradiation- and temperature-driven plasticity changes.

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.

Engineering Assessment of Constraint Effects on Cleavage Fracture

2004 ◽  
Author(s):  
Andrew Sherry ◽  
Dennis Hooton ◽  
David Lidbury
Keyword(s):  
Fracture Toughness ◽  
Cleavage Fracture ◽  
Stress Triaxiality ◽  
Crack Size ◽  
Structural Defects ◽  
Loading Mode ◽  
Safety Margins ◽  
Low Constraint ◽  
Specific Material ◽  
Constraint Effects

It is well known that material fracture toughness is influenced by factors including loading mode and crack size that influence the level of stress triaxiality ahead of the crack tip. This so-called “constraint effect” has been demonstrated both experimentally and analytically, with low constraint (low stress triaxiality) conditions leading to enhanced fracture toughness. Two-parameter fracture mechanics has been developed to provide a framework within which to assess the influence of constraint on safety margins for shallow structural defects. However, this requires the availability of a significant amount of plant-specific material with which to measure the materials’ constraint sensitivity experimentally. This paper presents a case study where constraint effects on cleavage fracture toughness of a shallow-cracked biaxially loaded bend specimen are assessed through a combination of modelling and miniaturised testing. The assessment is performed using the Failure Assessment Diagram approach of R6. It is concluded that the approach provides a practical engineering method for assessing the likely magnitude of constraint effects for low constraint configurations.

Application of a Weibull Stress Model to Predict the Failure of Surface and Embedded Cracks in Large Scale Beams Made of Clad and Unclad RPV Steel

2004 ◽  
Author(s):  
Shengjun Yin ◽  
Richard Bass ◽  
Paul Williams ◽  
Michael Ludwig ◽  
Elisabeth Keim
Keyword(s):  
Crack Front ◽  
Large Scale ◽  
Local Approach ◽  
Rpv Steel ◽  
Failure Scenario ◽  
Constraint Effects ◽  
The One ◽  
Stress Models ◽  
Large Scale Tests ◽  
Weibull Stress

Within the European Network NESC, the project NESC IV deals with constraint effects of cracks in large scale beam specimens, loaded by uni- or biaxial bending moments and containing surface or embedded cracks. The specimens are fabricated from original US RPV material, being cladded or cladding is removed. All large scale tests have been conducted at ORNL outside the NESC IV project. The outcome and the analyses of these uncladded and cladded beams containing the surface or embedded cracks are shown. By means of the finite element method, local approach methods and the Weibull stress models the specimens are analysed at the test temperatures and the probability of failure is calculated, taking into account constraint effects. For the case of the embedded cracks it turned out that the failure moment of the uncladded beam is 5% lower than the one of the cladded beam. Both crack fronts of the embedded crack are supposed to fail at the same failure moment. The results of the analysis of the cladded beam showed that the upper crack front nearer to the surface fails prior to the lower crack front, which is located deeper in the specimen (the failure moment is 5% lower). The numerical results agree very well with the experiments. The experimental failure moments could be well predicted and the failure scenario (which crack front fails first) could be determined. A theoretical shift in the transition temperature T0 due to constraint effects could be defined for both crack fronts.

scholarly journals Assessment of Local Approach Methods for Predicting End-of-Life Toughness of RPV Steels

2011 ◽  
Author(s):  
Andrey P. Jivkov ◽  
David P. G. Lidbury ◽  
Peter James
Keyword(s):  
Fracture Toughness ◽  
End Of Life ◽  
Cleavage Fracture ◽  
Failure Probability ◽  
Sufficient Accuracy ◽  
Model Parameters ◽  
Local Approach ◽  
Component Failure ◽  
Weakest Link ◽  
Future Work

Local approach methods are becoming increasingly popular as practical tools for cleavage fracture toughness prediction. Their application involves two distinct elements: calculation of ‘individual’ probabilities of failure, dictated by the local mechanical fields; and summation of these failure probabilities to predict the probability of component failure. In this work, we demonstrate that development of the local approach methods to date has been essentially focused on improving the criterion for predicting local failure as a function of the local mechanical fields. Yet, the existing methods fail to predict with sufficient accuracy the effects of irradiation and defect geometry on fracture toughness when the calculations are based on a common set of model parameters. A possible reason for this, common to all methods, is found in the calculation of the cumulative failure probability, which is based on the weakest-link argument. We discuss the implications of the weakest-link assumption, identify those situations where it needs to be reconsidered, and propose future work that will increase our understanding for improving the calculation of global failure probability.

Constraint Effect on Fracture Mechanics Evaluation for an Under-Clad Crack in a Reactor Pressure Vessel Steel

2020 ◽  
Author(s):  
Masaki Shimodaira ◽  
Tohru Tobita ◽  
Hisashi Takamizawa ◽  
Jinya Katsuyama ◽  
Satoshi Hanawa
Keyword(s):  
Fracture Toughness ◽  
Surface Crack ◽  
Pressure Vessel ◽  
Crack Tip ◽  
Reactor Pressure Vessel ◽  
Pressure Vessel Steel ◽  
Constraint Effect ◽  
Rpv Steel ◽  
Low Constraint ◽  
Reactor Pressure

Abstract For structural integrity assessment of the reactor pressure vessel (RPV) in JEAC 4206-2016, it is required that the fracture toughness (KJc) be higher than the stress intensity factor at the crack tip of a postulated under-clad crack (UCC) near the inner surface of RPV steel under the pressurized thermal shock event. Previous analytical studies showed a low constraint effect at the crack tip of an UCC, compared with that of a normal surface crack. Such a low constraint effect may increase the apparent KJc. In this study, we performed three-point bending (3PB) fracture toughness tests and finite element analysis (FEA) for RPV steel containing an UCC or a surface crack to quantitatively investigate the effect of cladding on the KJc. The FEAs considering the anisotropic property of the cladding successfully reproduced the load vs. load-line displacement curves obtained from the tests. We found that the apparent KJc for the UCC was considerably higher than that for the surface crack. FEA also showed that the constraint effect for the 3PB test specimen with the UCC was lower than that for the specimen with the surface crack owing to the cladding. Thus, a low constraint effect from an UCC may increase the apparent KJc.

Application of Local Approach Concept of Cleavage Fracture to VVER Materials

2002 ◽  
Author(s):  
B. Z. Margolin ◽  
G. P. Karzov ◽  
V. A. Shvetsova ◽  
E. Keim ◽  
R. Chaouadi
Keyword(s):  
Cleavage Fracture ◽  
Master Curve ◽  
Future Application ◽  
Surveillance Program ◽  
Model Parameters ◽  
Local Approach ◽  
Initial State ◽  
Master Curve Method ◽  
Rpv Steel ◽  
Curve Method

The Prometey local approach of cleavage fracture has been applied within the TACIS R2.06/96 project: “Surveillance Program for VVER 1000 Reactors”, sponsored by the European Commission. The main tasks are: • perform special experiments on smooth cylindrical and pre-cracked Charpy (PCC) specimens for VVER 1000 RPV material in initial, embrittled and irradiated state; • perform fracture toughness tests on 2T-CT specimens for RPV steel in initial and embrittled state; • predict the KJC(T) curves by this model; • compare the calculated and experimental results with the Master Curve results. The local approach of cleavage fracture is applied to predict KJC(T) curves in the transition regime of RPV materials in the initial state, embrittled by thermal heat treatment and irradiated, samples in the latter cases taken from surveillance capsules of a VVER 1000 NPP. The test data of large fracture mechanics specimens (2T-CT) could be well described over a wide temperature range for the initial state and the embrittled material, when the test results of PCC specimens at one temperature are used for the calibration of the model parameters. It is recommended for future application cases to use PCC specimens for the calibration of the parameters. A comparison of the Prometey local approach with the Master Curve approach lead to a good agreement for all investigated materials apart from the thermally embrittled material which has a very high embrittlement level (DBTT shift). The KJC(T) curves of VVER1000 RPV steels with low and moderate embrittlement level could be well predicted by both methods. Because the Master Curve method is already accepted as an international standard, it might be easier to apply in more routine cases. The Prometey probabilistic model may be also used for the prediction of KJC(T) curves of RPV steels with a high embrittlement level.

A novel model of Z-pin insertion in prepreg based on fracture mechanics

2021 ◽  
pp. 095440542110144
Author(s):  
Guobiao Ji ◽  
Liang Cheng ◽  
Shaohua Fei ◽  
Jiangxiong Li ◽  
Yinglin Ke
Keyword(s):  
Fracture Toughness ◽  
Fracture Mechanics ◽  
Analytical Model ◽  
Model Parameters ◽  
Force Model ◽  
Fe Model ◽  
Cohesive Elements ◽  
Fe Method ◽  
Insertion Force ◽  
Mechanics Model

Through-thickness reinforcement is a promising solution to the problem of delamination susceptibility in laminated composites. Modeling Z-pin–prepreg interaction is essential for accurate robotics-assisted Z-pin insertion. In this paper, a novel Z-pin insertion force model combining the classical cohesive finite element (FE) method with a dynamic analytical fracture mechanics model is proposed. The velocity-dependent cohesive elements, in which the fracture toughness is provided by the analytical model, are implemented in Z-pin insertion FE model to predict the crack initiation and propagation. Then Z-pin insertion experiments are performed on prepreg sample with metallic Z-pins at different velocities to identify the analytical model parameters and validate the simulation predictions offered by the model. Dynamics of Z-pin interaction with inhomogeneous prepreg is described and the effects of insertion velocity on prepreg contact force are studied. Results show that the force model agrees well with experiments and the fracture toughness rises with the increasing Z-pin insertion velocity.

scholarly journals Statistical Analysis of Tritium Breeding Ratio Deviations in the DEMO Due to Nuclear Data Uncertainties

2021 ◽  
Vol 11 (11) ◽  
pp. 5234
Author(s):  
Jin Hun Park ◽  
Pavel Pereslavtsev ◽  
Alexandre Konobeev ◽  
Christian Wegmann
Keyword(s):  
Monte Carlo ◽  
Fusion Reactor ◽  
Nuclear Data ◽  
Data File ◽  
Nuclear Model ◽  
Model Parameters ◽  
Tritium Breeding ◽  
Tritium Breeding Ratio ◽  
Nuclear Data Library ◽  
Breeding Ratio

For the stable and self-sufficient functioning of the DEMO fusion reactor, one of the most important parameters that must be demonstrated is the Tritium Breeding Ratio (TBR). The reliable assessment of the TBR with safety margins is a matter of fusion reactor viability. The uncertainty of the TBR in the neutronic simulations includes many different aspects such as the uncertainty due to the simplification of the geometry models used, the uncertainty of the reactor layout and the uncertainty introduced due to neutronic calculations. The last one can be reduced by applying high fidelity Monte Carlo simulations for TBR estimations. Nevertheless, these calculations have inherent statistical errors controlled by the number of neutron histories, straightforward for a quantity such as that of TBR underlying errors due to nuclear data uncertainties. In fact, every evaluated nuclear data file involved in the MCNP calculations can be replaced with the set of the random data files representing the particular deviation of the nuclear model parameters, each of them being correct and valid for applications. To account for the uncertainty of the nuclear model parameters introduced in the evaluated data file, a total Monte Carlo (TMC) method can be used to analyze the uncertainty of TBR owing to the nuclear data used for calculations. To this end, two 3D fully heterogeneous geometry models of the helium cooled pebble bed (HCPB) and water cooled lithium lead (WCLL) European DEMOs were utilized for the calculations of the TBR. The TMC calculations were performed, making use of the TENDL-2017 nuclear data library random files with high enough statistics providing a well-resolved Gaussian distribution of the TBR value. The assessment was done for the estimation of the TBR uncertainty due to the nuclear data for entire material compositions and for separate materials: structural, breeder and neutron multipliers. The overall TBR uncertainty for the nuclear data was estimated to be 3~4% for the HCPB and WCLL DEMOs, respectively.

scholarly journals Parameter stability and consistency in an alongshore-current model determined with Markov chain Monte Carlo

2008 ◽  
Vol 10 (2) ◽  
pp. 153-162 ◽  
Author(s):  
B. G. Ruessink
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Parameter Estimates ◽  
Model Parameters ◽  
Parameter Stability ◽  
Small Uncertainty ◽  
Best Fit ◽  
Stability And Consistency

When a numerical model is to be used as a practical tool, its parameters should preferably be stable and consistent, that is, possess a small uncertainty and be time-invariant. Using data and predictions of alongshore mean currents flowing on a beach as a case study, this paper illustrates how parameter stability and consistency can be assessed using Markov chain Monte Carlo. Within a single calibration run, Markov chain Monte Carlo estimates the parameter posterior probability density function, its mode being the best-fit parameter set. Parameter stability is investigated by stepwise adding new data to a calibration run, while consistency is examined by calibrating the model on different datasets of equal length. The results for the present case study indicate that various tidal cycles with strong (say, >0.5 m/s) currents are required to obtain stable parameter estimates, and that the best-fit model parameters and the underlying posterior distribution are strongly time-varying. This inconsistent parameter behavior may reflect unresolved variability of the processes represented by the parameters, or may represent compensational behavior for temporal violations in specific model assumptions.

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