scholarly journals The Definition Method and Optimization of Atomic Strain Tensors for Nuclear Power Engineering Materials

2016 ◽  
Vol 2016 ◽  
pp. 1-9
Author(s):  
Xiangguo Zeng ◽  
Ying Sheng ◽  
Huayan Chen ◽  
Tixin Han
Keyword(s):  
Weight Function ◽  
Optimization Model ◽  
Nuclear Power ◽  
Weighted Least Squares ◽  
Deformation Gradient ◽  
Local Deformation ◽  
Parameters Identification ◽  
Atomic Scale ◽  
Overall Analysis Method ◽  
Strain Tensors

A common measure of deformation between atomic scale simulations and the continuum framework is provided and the strain tensors for multiscale simulations are defined in this paper. In order to compute the deformation gradient of any atomm, the weight function is proposed to eliminate the different contributions within the neighbor atoms which have different distances to atomm, and the weighted least squares error optimization model is established to seek the optimal coefficients of the weight function and the optimal local deformation gradient of each atom. The optimization model involves more than 9 parameters. To guarantee the reliability of subsequent parameters identification result and lighten the calculation workload of parameters identification, an overall analysis method of parameter sensitivity and an advanced genetic algorithm are also developed.

Strain Tensors at the Atomic Scale

1999 ◽  
Vol 578 ◽  
Author(s):  
M.F. Horstemeyer ◽  
M.I. Baskes
Keyword(s):  
Weighting Function ◽  
Scalar Potential ◽  
Deformation Gradient ◽  
Local Strain ◽  
Small Strain ◽  
Lattice Parameter ◽  
Atomic Scale ◽  
Inhomogeneous Deformation ◽  
Green Strain ◽  
Strain Tensors

AbstractAlmansi and Green strain tensors are developed for use in large deformation molecular dynamics/statics simulations that employ Embedded Atom Method (EAM) potentials for metals. The strain tensors are formulated with respect to the deformation gradient. A scalar potential function is used with a weighting function that is dependent upon a cutoff radius for the deformation gradient. For a homogeneous or inhomogeneous deformation, a cutoff distance of one lattice parameter can be used to approximate local strain level. Inhomogeneous deformation reveals different results for Almansi and Green strain tensors indicating that the small strain assumption cannot be used to determine large atomic strains.

The KNOO Research Consortium: Work Package 3—An Integrated Approach to Waste Immobilisation and Management

2009 ◽  
Author(s):  
Simon Biggs ◽  
Michael Fairweather ◽  
James Young ◽  
Robin W. Grimes ◽  
Neil Milestone ◽  
...  
Keyword(s):  
Nuclear Power ◽  
Integrated Approach ◽  
Imperial College ◽  
Nuclear Industry ◽  
Atomic Scale ◽  
Engineering Properties ◽  
Work Package ◽  
Process Scale ◽  
Research Consortium ◽  
The Uk

The Keeping the Nuclear Option Open (KNOO) research consortium is a four-year research council funded initiative addressing the challenges related to increasing the safety, reliability and sustainability of nuclear power in the UK. Through collaboration between key industrial and governmental stakeholders, and with international partners, KNOO was established to maintain and develop skills relevant to nuclear power generation. Funded by a research grant of £6.1M from the “Towards a Sustainable Energy Economy Programme” of the UK Research Councils, it represents the single largest university-based nuclear research programme in the UK for more than 30 years. The programme is led by Imperial College London, in collaboration with the universities of Manchester, Sheffield, Leeds, Bristol, Cardiff and the Open University. These universities are working with the UK nuclear industry, who contributed a further £0.4M in funding. The industry/government stakeholders include AWE, British Energy, the Department for Environment, Food and Rural Affairs, the Environment Agency, the Health and Safety Executive, Doosan Babcock, the Ministry of Defence, Nirex, AMEC NNC, Rolls-Royce PLC and the UK Atomic Energy Authority. Work Package 3 of this consortium, led by the University of Leeds, concerns “An Integrated Approach to Waste Immobilisation and Management”, and involves Imperial College London, and the Universities of Manchester and Sheffield. The aims of this work package are: to study the re-mobilisation, transport, solid-liquid separation and immobilisation of particulate wastes; to develop predictive models for particle behaviour based on atomic scale, thermodynamic and process scale simulations; to develop a fundamental understanding of selective adsorption of nuclides onto filter systems and their immobilisation; and to consider mechanisms of nuclide leaving and transport. The paper describes highlights from this work in the key areas of multi-scale modeling (using atomic scale, thermodynamic and process scale models), the engineering properties of waste (linking microscopic and macroscopic behaviour, and transport and rheology), and waste reactivity (considering waste hosts and wasteforms, generation IV wastes, and waste interactions).

scholarly journals An Enhanced Preventive Maintenance Optimization Model Based on a Three-Stage Failure Process

2015 ◽  
Vol 2015 ◽  
pp. 1-13 ◽  
Author(s):  
Ruifeng Yang ◽  
Jianshe Kang ◽  
Zhenya Quan
Keyword(s):  
Optimization Model ◽  
Preventive Maintenance ◽  
Nuclear Power ◽  
Power Plants ◽  
Nuclear Power Plants ◽  
Failure Process ◽  
Maintenance Optimization ◽  
Maintenance Policy ◽  
Model Based ◽  
Inspection Interval

Nuclear power plants are highly complex systems and the issues related to their safety are of primary importance. Probabilistic safety assessment is regarded as the most widespread methodology for studying the safety of nuclear power plants. As maintenance is one of the most important factors for affecting the reliability and safety, an enhanced preventive maintenance optimization model based on a three-stage failure process is proposed. Preventive maintenance is still a dominant maintenance policy due to its easy implementation. In order to correspond to the three-color scheme commonly used in practice, the lifetime of system before failure is divided into three stages, namely, normal, minor defective, and severe defective stages. When the minor defective stage is identified, two measures are considered for comparison: one is that halving the inspection interval only when the minor defective stage is identified at the first time; the other one is that if only identifying the minor defective stage, the subsequent inspection interval is halved. Maintenance is implemented immediately once the severe defective stage is identified. Minimizing the expected cost per unit time is our objective function to optimize the inspection interval. Finally, a numerical example is presented to illustrate the effectiveness of the proposed models.

scholarly journals Understanding the deformation gradient in Abaqus and key guidelines for anisotropic hyperelastic user material subroutines (UMATs)

2019 ◽  
Author(s):  
David Nolan ◽  
Caitriona Lally ◽  
Patrick McGarry
Keyword(s):  
Local Coordinate System ◽  
Deformation Gradient ◽  
Worked Examples ◽  
Local Deformation ◽  
Cauchy Stress ◽  
Precise Understanding ◽  
Key Issues ◽  
Key Steps ◽  
Orientation Systems ◽  
Global And Local

This tutorial paper provides a step-by-step guide to developing a comprehensive understanding of the different forms of the deformation gradient used in Abaqus, and outlines a number of key issues that must be considered when developing an Abaqus user defined material subroutine (UMAT) in which the Cauchy stress is computed from the deformation gradient. Firstly, we examine the "classical" forms of global and local deformation gradients. We then show that Abaqus/Standard does not use the classical form of the local deformation gradient when continuum elements are used, and we highlight the important implications for UMAT development. We outline the key steps that must be implemented in developing an anisotropic fibre-reinforced hyperelastic UMAT for use with continuum elements and local orientation systems. We also demonstrate that a classical local deformation gradient is provided by Abaqus/Standard if structural (shell and membrane) elements are used, and by Abaqus/Explicit for all element types. We emphasise, however, that the majority of biomechanical simulations rely on the use of continuum elements with a local coordinate system in Abaqus/Standard, and therefore the development of a hyperelastic UMAT requires an in-depth and precise understanding of the form of the non-classical deformation gradient provided as input by Abaqus. Several worked examples and case studies are provided for each section, so that the details and implications of the form of the deformation gradient can be fully understood. For each worked example in this tutorial paper the source files and code (Abaqus input files, UMATs, and Matlab script files) are provided, allowing the reader to efficiently explore the implications of the form of the deformation gradient in the development of a UMAT.

A method to reconstruct myocardial sarcomere lengths and orientations at transmural sites in beating canine hearts

1992 ◽  
Vol 263 (1) ◽  
pp. H293-H306 ◽  
Author(s):  
E. K. Rodriguez ◽  
W. C. Hunter ◽  
M. J. Royce ◽  
M. K. Leppo ◽  
A. S. Douglas ◽  
...  
Keyword(s):  
Sarcomere Length ◽  
Deformation Gradient ◽  
Local Deformation ◽  
Left Ventricular ◽  
Reference State ◽  
Cellular Processes ◽  
Chamber Volume ◽  
Length Changes ◽  
Whole Heart ◽  
Cyclic Changes

The ability to measure cyclic changes in myocardial sarcomere lengths and orientations during cardiac ejection and filling would improve our understanding of how the cellular processes of contraction relate to the pumping of the whole heart. Previously, only postmortem sarcomere measurements were possible after arresting the heart in one state and fixing it for histology. By combining such histological measurements with direct observations of the deformation experienced by the same myocardial region while the heart was beating, we have developed a method to reconstruct sarcomere lengths and orientations throughout the cardiac cycle and at several transmural layers. A set of small (1 mm) radiopaque beads was implanted in approximately 1 cm3 of the left ventricular free wall. Using biplane cineradiography, we tracked the motion of these markers through various cardiac cycles. To quantify local myocardial deformation (as revealed by the relative motion of the markers), we calculated the local deformation gradient tensors. As the heart deforms, these describe how any short vectorial line segment alters its length and orientation relative to a reference state. Specifically, by choosing the reference state to be the arrested and fixed heart and by measuring the sarcomere vector in that state, we could then use the deformation gradient tensors to reconstruct the sarcomere vector that would exist in the beating heart. As ventricular chamber volume varied over its normal range of operation, the range of reconstructed sarcomere lengths (approximately 1.7-2.4 microns) was comparable to other histological studies and to measurements of sarcomere length in excised papillary muscles or trabeculae. The pattern of sarcomere length changes was markedly different, however, during ejection vs. filling.

Characterization of Point Defect Generation, Migration and Coalescence in Irradiated SiC by Atomistic Simulation

2007 ◽  
Vol 1043 ◽  
Author(s):  
David Farrell ◽  
Noam Bernstein ◽  
Wing Kam Liu
Keyword(s):  
Point Defect ◽  
Nuclear Power ◽  
Large Scale ◽  
The United States ◽  
Ceramic Composites ◽  
Atomic Scale ◽  
Empirical Potential ◽  
Defect Clusters ◽  
Point Defect Clusters

AbstractRenewed interest in nuclear power in the United States has prompted investigations into new reactor designs, resulting in a need to gain a greater understanding of the properties of the materials which are proposed for use in next generation nuclear reactors. This presentation will focus on preliminary results of large-scale empirical potential atomistic studies into the generation of point defect clusters in 3C SiC by particle irradiation and the evolution from point defect clusters to ‘voids’ on the atomic scale. Our working definition of ‘void’ will be explained in the context of small length-scale simulations. The determination of interstitial and vacancy diffusivities for the empirical potential employed and its impact on defect coalescence will be discussed. The characterization of initial damage states for given irradiation conditions will be presented and compared to previous work on ceramics and ceramic-composites.

scholarly journals Atomistic Analysis Of Radiation-Induced Segregation In Ion-Irradiated Stainless Steel 316

2015 ◽  
Vol 60 (2) ◽  
pp. 1179-1184 ◽  
Author(s):  
G.-G. Lee ◽  
H.-H. Jin ◽  
K. Chang ◽  
B.H. Lee ◽  
J. Kwon
Keyword(s):  
Stainless Steel ◽  
Nuclear Power ◽  
Power Plants ◽  
Potential Problem ◽  
Atom Probe ◽  
Atomic Scale ◽  
Dislocation Loops ◽  
Radiation Induced ◽  
Solute Atoms ◽  
Stainless Steel 316

Abstract Stainless steel (SS) is a well-known material for the internal parts of nuclear power plants. It is known that these alloys exhibit radiation-induced segregation (RIS) at point defect sinks at moderate temperature, while in service. The RIS behavior of SS can be a potential problem by increasing the susceptibility to irradiation-assisted stress corrosion cracking. In this work, the RIS behavior of solute atoms at sinks in SS 316 irradiated with Fe4+ ions were characterized by atom probe tomography (APT). There were torus-shaped defects along with a depletion of Cr and enrichment of Ni and Si. These clusters are believed to be dislocation loops resulting from irradiation. The segregation of solutes was also observed for various defect shapes. These observations are consistent with other APT results from the literature. The composition of the clusters was analyzed quantitatively almost at the atomic scale. Despite the limitations of the experiments, the APT analysis was well suited for discovering the structure of irradiation defects and performing a quantitative analysis of RIS in irradiated specimens.

Closed-Form Relations for Stress Intensity Factor Influence Coefficients for Axial ID Surface Flaws in Cylinders for Appendix A of ASME Section XI

2014 ◽  
Author(s):  
Steven X. Xu ◽  
Darrell R. Lee ◽  
Douglas A. Scarth ◽  
Russell C. Cipolla
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Weight Function ◽  
Closed Form ◽  
Nuclear Power ◽  
Cubic Equation ◽  
Evaluation Procedures ◽  
Influence Coefficients ◽  
Surface Flaws

Analytical evaluation procedures for determining the acceptability of flaws detected during in-service inspection of nuclear power plant components are provided in Section XI of the ASME Boiler and Pressure Vessel Code. Linear elastic fracture mechanics based evaluation procedures in ASME Section XI require calculation of the stress intensity factor. In Article A-3000 of Appendix A of the 2013 Edition of ASME Section XI, the calculation of stress intensity factor for a surface crack is based on characterization of stress field with a cubic equation and use of stress intensity factor influence coefficients. The influence coefficients are only provided for a flat plate geometry. The ASME Section XI Working Group on Flaw Evaluation is in the process of rewriting Article A-3000 of Appendix A. Major updates include the implementation of an alternate method for calculation of the stress intensity factor for a surface flaw that makes explicit use of the Universal Weight Function Method and does not require a polynomial fit to the actual stress distribution, and the inclusion of stress intensity factor influence coefficients for the cylinder geometry. Tabular data of influence coefficients for the cylinder geometry are available in API 579-1/ASME FFS-1 2007. Effort has been made to develop closed-form relations for the stress intensity factor influence coefficients for the cylinder geometry based on API data. With the inclusion of the explicit weight function approach and the closed-form relations for influence coefficients, the procedures of Appendix A for the calculation of stress intensity factors can be used more efficiently. The development of closed-form relations for stress intensity factor influence coefficients for axial ID surface flaws in cylinders is described in this paper.

Estimating weights when fitting linear regression models for tree volume

1993 ◽  
Vol 23 (8) ◽  
pp. 1725-1731 ◽  
Author(s):  
Michael S. Williams ◽  
Timothy G. Gregoire
Keyword(s):  
Linear Regression ◽  
Weight Function ◽  
Loblolly Pine ◽  
Weighted Least Squares ◽  
Data Sets ◽  
Regression Equations ◽  
Linear Regression Models ◽  
White Oak ◽  
Data Set ◽  
Error Structure

The method of weighted least squares can be used to achieve homogeneity of variance with linear regression that has a heterogeneous error structure. A weight function commonly used when constructing regression equations to predict tree volume is [Formula: see text], where k1 ≈ 1.0–2.1. This paper examines the weight function [Formula: see text] for modelling the error structure in two loblolly pine (Pinustaeda L.) data sets and one white oak (Quercusalba L.) data set. The weight function [Formula: see text] is recommended for all three data sets, for which the k1 values ranged from 1.80 to 2.07.

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