1. Fatigue crack growth relies on sufficient energy absorption at the crack tip to drive the growth process. For crack growth to occur, the stress intensity factor range (ΔK) must exceed a minimum threshold (ΔKmin).
2. If ΔK is equal to ΔKmin, the smallest possible non-zero crack growth per cycle (da/dN) would correspond to the advancement of the crack tip by one atomic spacing.
3. The atomic spacing can be estimated as twice the atomic radius, which is on the order of 100-250 picometers for most metals. This provides a theoretical basis for deriving ΔKmin values from fundamental material properties.
Static Aeroelasticity Analysis of Spinning Rocket for Divergence Speed -- Zeu...Abhishek Jain
Above Research Paper can be downloaded from www.zeusnumerix.com
The research paper aims to develop a method to model the spin effects of rocket for Aeroelastic analysis. As the speed of the rocket increases, the structural integrity of the fins becomes more dependent on aeroelastic loads. Methods exist to analyze aeroelasticity of fins for non-spinning missiles. Most software use panel methods for calculation of load distribution. The current research replaces the panel methods to RANS CFD and introduces source terms in equations to model spin. The results of new formulation are validated w.r.t. published data on non-spinning projectile and then the method is used to simulate current projectile. Mode shapes up to 6th mode are delivered as result. Authors - Sanjay Kumar and Prof GR Shevare (Zeus Numerix), Subhash Mukane and PT Rojatkar (ARDE, DRDO)
Boiling and Condensation heat transfer -- EES Functions and Procedurestmuliya
This file contains notes on Engineering Equation Solver (EES) Functions and Procedures for Boiling and Condensation heat transfer. Some problems are also included.
These notes were prepared while teaching Heat Transfer course to the M.Tech. students in Mechanical Engineering Dept. of St. Joseph Engineering College, Vamanjoor, Mangalore, India.
Contents: Summary of formulas used -
EES Functions/Procedures for boiling: Nucleate boiling heat flux for any geometry - critical heat flux for large horizontal surface, horizontal cylinder and sphere - Film boiling for horizontal cylinder, sphere and horizontal surface – Problems.
EES Functions/Procedures for condensation of: steam on vertical surface – any fluid on a vertical surface – steam on vertical cylinder – any fluid on vertical cylinder – steam on horizontal cylinder – any fluid on horizontal cylinder – steam on a horizontal tube bank – any fluid on horizontal tube bank – any fluid on a sphere – any fluid inside a horizontal cylinder - Problems.
It is hoped that these notes will be useful to teachers, students, researchers and professionals working in this field.
Impact of Electrification on Asset Life Degradation and Mitigation with DERPower System Operation
Distribution networks are currently faced with a plethora of changes in resources, equipment technology, structure, and loading. First, Distributed Energy Resources (DERs) have been increasingly penetrating distribution grids worldwide. DERs have been recognized as a Non-Wires Alternative (NWA) in certain use cases including peak shaving, renewable integration etc). The second imminent change in distribution networks is the electrification of loads, especially in the transportation and space heating sectors, driven at least in part by clean-air and sustainability goals. Electrification is expected to result in higher peak load levels as well as flatter daily and annual load shapes, due to the fact that it is primarily composed of off-peak and by storage-like loads like those of EVs, storage, and electric heating. Their valley-filling behavior results in distribution network apparatus being consistently loaded to high utilization levels.
As a result of these changes in load curve shape, distribution equipment may be subjected to increased operational stress compared to what it endured in the past, even if not loaded to higher net peak loads. For example, in the United States, the majority of distribution substation transformers typically warm up during the morning and afternoon as they approach demand peaks and then cool down afterwards as loading falls. Cumulative loss of life from this repetitive daily cycle is slow, so that expected service life of a typical unit is on the order of fifty years or more, even allowing for periods of intense overload during very rare contingencies. This has been the norm for the US electric utility industry in the last seventy years, but may no longer be the case in environments where electrification is more prevalent.
Static Aeroelasticity Analysis of Spinning Rocket for Divergence Speed -- Zeu...Abhishek Jain
Above Research Paper can be downloaded from www.zeusnumerix.com
The research paper aims to develop a method to model the spin effects of rocket for Aeroelastic analysis. As the speed of the rocket increases, the structural integrity of the fins becomes more dependent on aeroelastic loads. Methods exist to analyze aeroelasticity of fins for non-spinning missiles. Most software use panel methods for calculation of load distribution. The current research replaces the panel methods to RANS CFD and introduces source terms in equations to model spin. The results of new formulation are validated w.r.t. published data on non-spinning projectile and then the method is used to simulate current projectile. Mode shapes up to 6th mode are delivered as result. Authors - Sanjay Kumar and Prof GR Shevare (Zeus Numerix), Subhash Mukane and PT Rojatkar (ARDE, DRDO)
Boiling and Condensation heat transfer -- EES Functions and Procedurestmuliya
This file contains notes on Engineering Equation Solver (EES) Functions and Procedures for Boiling and Condensation heat transfer. Some problems are also included.
These notes were prepared while teaching Heat Transfer course to the M.Tech. students in Mechanical Engineering Dept. of St. Joseph Engineering College, Vamanjoor, Mangalore, India.
Contents: Summary of formulas used -
EES Functions/Procedures for boiling: Nucleate boiling heat flux for any geometry - critical heat flux for large horizontal surface, horizontal cylinder and sphere - Film boiling for horizontal cylinder, sphere and horizontal surface – Problems.
EES Functions/Procedures for condensation of: steam on vertical surface – any fluid on a vertical surface – steam on vertical cylinder – any fluid on vertical cylinder – steam on horizontal cylinder – any fluid on horizontal cylinder – steam on a horizontal tube bank – any fluid on horizontal tube bank – any fluid on a sphere – any fluid inside a horizontal cylinder - Problems.
It is hoped that these notes will be useful to teachers, students, researchers and professionals working in this field.
Impact of Electrification on Asset Life Degradation and Mitigation with DERPower System Operation
Distribution networks are currently faced with a plethora of changes in resources, equipment technology, structure, and loading. First, Distributed Energy Resources (DERs) have been increasingly penetrating distribution grids worldwide. DERs have been recognized as a Non-Wires Alternative (NWA) in certain use cases including peak shaving, renewable integration etc). The second imminent change in distribution networks is the electrification of loads, especially in the transportation and space heating sectors, driven at least in part by clean-air and sustainability goals. Electrification is expected to result in higher peak load levels as well as flatter daily and annual load shapes, due to the fact that it is primarily composed of off-peak and by storage-like loads like those of EVs, storage, and electric heating. Their valley-filling behavior results in distribution network apparatus being consistently loaded to high utilization levels.
As a result of these changes in load curve shape, distribution equipment may be subjected to increased operational stress compared to what it endured in the past, even if not loaded to higher net peak loads. For example, in the United States, the majority of distribution substation transformers typically warm up during the morning and afternoon as they approach demand peaks and then cool down afterwards as loading falls. Cumulative loss of life from this repetitive daily cycle is slow, so that expected service life of a typical unit is on the order of fifty years or more, even allowing for periods of intense overload during very rare contingencies. This has been the norm for the US electric utility industry in the last seventy years, but may no longer be the case in environments where electrification is more prevalent.
International Refereed Journal of Engineering and Science (IRJES)irjes
International Refereed Journal of Engineering and Science (IRJES) is a leading international journal for publication of new ideas, the state of the art research results and fundamental advances in all aspects of Engineering and Science. IRJES is a open access, peer reviewed international journal with a primary objective to provide the academic community and industry for the submission of half of original research and applications
Understanding and Predicting CO2 Properties for CCS Transport, Richard Graham, University of Nottingham. Presented at CO2 Properties and EoS for Pipeline Engineering, 11th November 2014
SPLIT SECOND ANALYSIS COVERING HIGH PRESSURE GAS FLOW DYNAMICS AT PIPE OUTLET...AEIJjournal2
A detailed investigation covering piped gas flow characteristics in high pressure flow conditions. Such flow analysis can be resolved using established mathematical equations known as the Fanno condition, which usually cover steady state, or final flow conditions. However, in real life, such flow conditions are
transient, varying with time. This paper uses CFD analysis providing a split second “snapshot” at what happens at the pipe outlet, and therefore, a closer understanding at what happens at the pipe’s outlet in high pressure gas flow condition
EES Functions and Procedures for Natural convection heat transfertmuliya
This file contains notes on Engineering Equation Solver (EES) Functions and Procedures for Natural (or, free) convection heat transfer calculations. Some problems are also included.
These notes were prepared while teaching Heat Transfer course to the M.Tech. students in Mechanical Engineering Dept. of St. Joseph Engineering College, Vamanjoor, Mangalore, India.
It is hoped that these notes will be useful to teachers, students, researchers and professionals working in this field.
Contents:
• Natural convection formulas - Tables
• Natural convection from Vertical plates & cylinders, horizontal plates, cylinders and spheres, from enclosed spaces, rotating disks and spheres, and from finned surfaces
• Combined Natural and forced convection
A New Under-Frequency Load Shedding Method Using the Voltage Electrical Dista...IJAEMSJORNAL
This paper proposes a method for determining location to shed the load in order to recover the frequency back to the allowable range. Prioritize distribution of the load shedding at load bus positions based on the voltage electrical distance between the outage generator and the loads. The nearer the load bus from the outage generator is, the sooner the load bus will shed and vice versa. Finally, by selecting the rate of change of generation active power, rate of change of active power of load, rate of change of frequency, rate of change of branches active power and rate of change of voltage in the system as the input to an Artificial Neural Network, the generators outage, the load shedding bus are determined in a short period of time to maintain the stability of the system. With this technique, a large amount of load shedding could be avoided, hence, saved from economic losses. The effectiveness of the proposed method tested on the IEEE 39 Bus New England has demonstrated the effectiveness of this method.
International Refereed Journal of Engineering and Science (IRJES)irjes
International Refereed Journal of Engineering and Science (IRJES) is a leading international journal for publication of new ideas, the state of the art research results and fundamental advances in all aspects of Engineering and Science. IRJES is a open access, peer reviewed international journal with a primary objective to provide the academic community and industry for the submission of half of original research and applications
Understanding and Predicting CO2 Properties for CCS Transport, Richard Graham, University of Nottingham. Presented at CO2 Properties and EoS for Pipeline Engineering, 11th November 2014
SPLIT SECOND ANALYSIS COVERING HIGH PRESSURE GAS FLOW DYNAMICS AT PIPE OUTLET...AEIJjournal2
A detailed investigation covering piped gas flow characteristics in high pressure flow conditions. Such flow analysis can be resolved using established mathematical equations known as the Fanno condition, which usually cover steady state, or final flow conditions. However, in real life, such flow conditions are
transient, varying with time. This paper uses CFD analysis providing a split second “snapshot” at what happens at the pipe outlet, and therefore, a closer understanding at what happens at the pipe’s outlet in high pressure gas flow condition
EES Functions and Procedures for Natural convection heat transfertmuliya
This file contains notes on Engineering Equation Solver (EES) Functions and Procedures for Natural (or, free) convection heat transfer calculations. Some problems are also included.
These notes were prepared while teaching Heat Transfer course to the M.Tech. students in Mechanical Engineering Dept. of St. Joseph Engineering College, Vamanjoor, Mangalore, India.
It is hoped that these notes will be useful to teachers, students, researchers and professionals working in this field.
Contents:
• Natural convection formulas - Tables
• Natural convection from Vertical plates & cylinders, horizontal plates, cylinders and spheres, from enclosed spaces, rotating disks and spheres, and from finned surfaces
• Combined Natural and forced convection
A New Under-Frequency Load Shedding Method Using the Voltage Electrical Dista...IJAEMSJORNAL
This paper proposes a method for determining location to shed the load in order to recover the frequency back to the allowable range. Prioritize distribution of the load shedding at load bus positions based on the voltage electrical distance between the outage generator and the loads. The nearer the load bus from the outage generator is, the sooner the load bus will shed and vice versa. Finally, by selecting the rate of change of generation active power, rate of change of active power of load, rate of change of frequency, rate of change of branches active power and rate of change of voltage in the system as the input to an Artificial Neural Network, the generators outage, the load shedding bus are determined in a short period of time to maintain the stability of the system. With this technique, a large amount of load shedding could be avoided, hence, saved from economic losses. The effectiveness of the proposed method tested on the IEEE 39 Bus New England has demonstrated the effectiveness of this method.
Probabilistic Q-margin Calculations Considering Dependency of Uncertain Load ...IJAPEJOURNAL
This paper presents a novel probabilistic approach for computation of the reactive power margin (or Q-margin) of a power system with large-scale uncertain wind generation. Conventionally, Q-margin has been used as an index for indicating the system voltage stability level on system operation and planning. The conventional Q-margin method needs to be modified to fully accommodate uncertainties due to wind generation. This paper proposes a new Q-margin computation method using Q-matrix and the expected Q-margin (EQM). Q-matrix is a generic uncertainty matrix representing a discrete joint distribution of load and wind generation and the EQM, calculated from the Q-matrix, is a specific probabilistic variable that supersedes the conventional Q-margin. The proposed method is verified with the IEEE 39-bus test system including wind generation.
Numerical modeling of the welding defect influence on fatigue life of the wel...inventy
Research Inventy : International Journal of Engineering and Science is published by the group of young academic and industrial researchers with 12 Issues per year. It is an online as well as print version open access journal that provides rapid publication (monthly) of articles in all areas of the subject such as: civil, mechanical, chemical, electronic and computer engineering as well as production and information technology. The Journal welcomes the submission of manuscripts that meet the general criteria of significance and scientific excellence. Papers will be published by rapid process within 20 days after acceptance and peer review process takes only 7 days. All articles published in Research Inventy will be peer-reviewed.
Analysis of Reactivity Accident for Control Rods Withdrawal at the Thermal Re...ijrap
In the present work, the point kinetics equations are solved numerically using the stiffness confinement
method (SCM). The solution is applied to the kinetics equations in the presence of different types of
reactivities, and is compared with other methods. This method is, also used to analyze reactivity accidents
in thermal reactor at start-up, and full power conditions for control rods withdrawal. Thermal reactor
(HTR-M) is fuelled by uranium-235. This analysis presents the effect of negative temperature feedback, and
the positive reactivity of control rods withdrawal. Power, temperature pulse, and reactivity following the
reactivity accidents are calculated using programming language (FORTRAN), and (MATLAB) Codes. The
results are compared with previous works and satisfactory agreement is found.
Analysis of Reactivity Accident for Control Rods Withdrawal at the Thermal Re...ijrap
In the present work, the point kinetics equations are solved numerically using the stiffness confinement
method (SCM). The solution is applied to the kinetics equations in the presence of different types of
reactivities, and is compared with other methods. This method is, also used to analyze reactivity accidents
in thermal reactor at start-up, and full power conditions for control rods withdrawal. Thermal reactor
(HTR-M) is fuelled by uranium-235. This analysis presents the effect of negative temperature feedback, and
the positive reactivity of control rods withdrawal. Power, temperature pulse, and reactivity following the
reactivity accidents are calculated using programming language (FORTRAN), and (MATLAB) Codes. The
results are compared with previous works and satisfactory agreement is found.
EFFECTS OF TRANSIENT LOAD ONGASTURBINE BLADE STRESS AND FATIGUE LIFE CHARACTE...Barhm Mohamad
The turbine blade is the most important component in the jet engine gas turbine. The common fatigue
failures of the blade include the thermo-mechanical fatigue. Firstly, the finite element simulation of
the blade is carried out in the working condition including the centrifugal load and mechanical load.
The aim of this work was to develop and implement methods for the resource calculation of the jet
turbine blade in which fatigue zone were detected during the load. The approach is based on a directstep
simulation of the load point based on the finite-element method (FEM).According to the
simulation results of the thermos-mechanical load, the stress distribution of the blade body is
reasonable in the working condition load; the stress level on the blade suction surface is higher than
the pressure surface; in the blade body, the maximum Von Mises stress is 126 MPa, and the location
of the minimum fatigue life is close to the blade shroud. Above simulation results is very useful for
the structural design and fatigue experiment. Secondly, the stress and thermo-mechanical fatigue life
characteristic are both analyzed with ANSYS software. Through the transient structure stress analysis,
the stress-time history in the blade body is obtained; through the thermo-mechanical fatigue analysis,
the fatigue zone of the blade first appears in the middle of the blade exhaust side. Based on these
virtual results. These results are significant for the blade fatigue failure in the future.
Quantification of operating reserves with high penetration of wind power cons...IJECEIAES
The high integration of wind energy in power systems requires operating reserves to ensure the reliability and security in the operation. The intermittency and volatility in wind power sets a challenge for day-ahead dispatching in order to schedule generation resources. Therefore, the quantification of operating reserves is addressed in this paper using extreme values through Monte-Carlo simulations. The uncertainty in wind power forecasting is captured by a generalized extreme value distribution to generate scenarios. The day-ahead dispatching model is formulated as a mixed-integer linear quadratic problem including ramping constraints. This approach is tested in the IEEE-118 bus test system including integration of wind power in the system. The results represent the range of values for operating reserves in day-ahead dispatching.
Compilation and Verification of FatigueLoad Spectrum ofHighSpeed Maglev Vehic...IJRES Journal
The purpose of this study was to construct the fatigue test load spectrum for use in the high speed
maglev vehicleswing rod.Based on the measured load spectrum of the high speed maglev vehicle running
gear,the relatively poor condition and location of the swing rod was determined, according to the statistics and
analysis the load data of swing rod. With the rain-flow cycle quantile extrapolation, a high degree confidence
load spectrum was obtained in view of the differential damage among the different tests. The eight level
one-dimensional load spectrum after mean equivalent processing was established, by applying the Goodman to
correct mean stress effect on the fatigue strength and life; The stresses under the loadswere calculated using the
ANSYSsimulation.The fatigue life obtained from the programmed load spectrum is compared with that
calculated from measured load data using Miner theory,and the accuracy and validation of the programmed
load spectrum for thehigh speed maglev vehicleswing rodwere verified.
International Journal of Computational Engineering Research (IJCER) is dedicated to protecting personal information and will make every reasonable effort to handle collected information appropriately. All information collected, as well as related requests, will be handled as carefully and efficiently as possible in accordance with IJCER standards for integrity and objectivity.
Industrial Training at Shahjalal Fertilizer Company Limited (SFCL)MdTanvirMahtab2
This presentation is about the working procedure of Shahjalal Fertilizer Company Limited (SFCL). A Govt. owned Company of Bangladesh Chemical Industries Corporation under Ministry of Industries.
NUMERICAL SIMULATIONS OF HEAT AND MASS TRANSFER IN CONDENSING HEAT EXCHANGERS...ssuser7dcef0
Power plants release a large amount of water vapor into the
atmosphere through the stack. The flue gas can be a potential
source for obtaining much needed cooling water for a power
plant. If a power plant could recover and reuse a portion of this
moisture, it could reduce its total cooling water intake
requirement. One of the most practical way to recover water
from flue gas is to use a condensing heat exchanger. The power
plant could also recover latent heat due to condensation as well
as sensible heat due to lowering the flue gas exit temperature.
Additionally, harmful acids released from the stack can be
reduced in a condensing heat exchanger by acid condensation. reduced in a condensing heat exchanger by acid condensation.
Condensation of vapors in flue gas is a complicated
phenomenon since heat and mass transfer of water vapor and
various acids simultaneously occur in the presence of noncondensable
gases such as nitrogen and oxygen. Design of a
condenser depends on the knowledge and understanding of the
heat and mass transfer processes. A computer program for
numerical simulations of water (H2O) and sulfuric acid (H2SO4)
condensation in a flue gas condensing heat exchanger was
developed using MATLAB. Governing equations based on
mass and energy balances for the system were derived to
predict variables such as flue gas exit temperature, cooling
water outlet temperature, mole fraction and condensation rates
of water and sulfuric acid vapors. The equations were solved
using an iterative solution technique with calculations of heat
and mass transfer coefficients and physical properties.
Water billing management system project report.pdfKamal Acharya
Our project entitled “Water Billing Management System” aims is to generate Water bill with all the charges and penalty. Manual system that is employed is extremely laborious and quite inadequate. It only makes the process more difficult and hard.
The aim of our project is to develop a system that is meant to partially computerize the work performed in the Water Board like generating monthly Water bill, record of consuming unit of water, store record of the customer and previous unpaid record.
We used HTML/PHP as front end and MYSQL as back end for developing our project. HTML is primarily a visual design environment. We can create a android application by designing the form and that make up the user interface. Adding android application code to the form and the objects such as buttons and text boxes on them and adding any required support code in additional modular.
MySQL is free open source database that facilitates the effective management of the databases by connecting them to the software. It is a stable ,reliable and the powerful solution with the advanced features and advantages which are as follows: Data Security.MySQL is free open source database that facilitates the effective management of the databases by connecting them to the software.
Using recycled concrete aggregates (RCA) for pavements is crucial to achieving sustainability. Implementing RCA for new pavement can minimize carbon footprint, conserve natural resources, reduce harmful emissions, and lower life cycle costs. Compared to natural aggregate (NA), RCA pavement has fewer comprehensive studies and sustainability assessments.
Forklift Classes Overview by Intella PartsIntella Parts
Discover the different forklift classes and their specific applications. Learn how to choose the right forklift for your needs to ensure safety, efficiency, and compliance in your operations.
For more technical information, visit our website https://intellaparts.com
Understanding Inductive Bias in Machine LearningSUTEJAS
This presentation explores the concept of inductive bias in machine learning. It explains how algorithms come with built-in assumptions and preferences that guide the learning process. You'll learn about the different types of inductive bias and how they can impact the performance and generalizability of machine learning models.
The presentation also covers the positive and negative aspects of inductive bias, along with strategies for mitigating potential drawbacks. We'll explore examples of how bias manifests in algorithms like neural networks and decision trees.
By understanding inductive bias, you can gain valuable insights into how machine learning models work and make informed decisions when building and deploying them.
NO1 Uk best vashikaran specialist in delhi vashikaran baba near me online vas...Amil Baba Dawood bangali
Contact with Dawood Bhai Just call on +92322-6382012 and we'll help you. We'll solve all your problems within 12 to 24 hours and with 101% guarantee and with astrology systematic. If you want to take any personal or professional advice then also you can call us on +92322-6382012 , ONLINE LOVE PROBLEM & Other all types of Daily Life Problem's.Then CALL or WHATSAPP us on +92322-6382012 and Get all these problems solutions here by Amil Baba DAWOOD BANGALI
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Saudi Arabia stands as a titan in the global energy landscape, renowned for its abundant oil and gas resources. It's the largest exporter of petroleum and holds some of the world's most significant reserves. Let's delve into the top 10 oil and gas projects shaping Saudi Arabia's energy future in 2024.
The Internet of Things (IoT) is a revolutionary concept that connects everyday objects and devices to the internet, enabling them to communicate, collect, and exchange data. Imagine a world where your refrigerator notifies you when you’re running low on groceries, or streetlights adjust their brightness based on traffic patterns – that’s the power of IoT. In essence, IoT transforms ordinary objects into smart, interconnected devices, creating a network of endless possibilities.
Here is a blog on the role of electrical and electronics engineers in IOT. Let's dig in!!!!
For more such content visit: https://nttftrg.com/
Hybrid optimization of pumped hydro system and solar- Engr. Abdul-Azeez.pdffxintegritypublishin
Advancements in technology unveil a myriad of electrical and electronic breakthroughs geared towards efficiently harnessing limited resources to meet human energy demands. The optimization of hybrid solar PV panels and pumped hydro energy supply systems plays a pivotal role in utilizing natural resources effectively. This initiative not only benefits humanity but also fosters environmental sustainability. The study investigated the design optimization of these hybrid systems, focusing on understanding solar radiation patterns, identifying geographical influences on solar radiation, formulating a mathematical model for system optimization, and determining the optimal configuration of PV panels and pumped hydro storage. Through a comparative analysis approach and eight weeks of data collection, the study addressed key research questions related to solar radiation patterns and optimal system design. The findings highlighted regions with heightened solar radiation levels, showcasing substantial potential for power generation and emphasizing the system's efficiency. Optimizing system design significantly boosted power generation, promoted renewable energy utilization, and enhanced energy storage capacity. The study underscored the benefits of optimizing hybrid solar PV panels and pumped hydro energy supply systems for sustainable energy usage. Optimizing the design of solar PV panels and pumped hydro energy supply systems as examined across diverse climatic conditions in a developing country, not only enhances power generation but also improves the integration of renewable energy sources and boosts energy storage capacities, particularly beneficial for less economically prosperous regions. Additionally, the study provides valuable insights for advancing energy research in economically viable areas. Recommendations included conducting site-specific assessments, utilizing advanced modeling tools, implementing regular maintenance protocols, and enhancing communication among system components.
HEAP SORT ILLUSTRATED WITH HEAPIFY, BUILD HEAP FOR DYNAMIC ARRAYS.
Heap sort is a comparison-based sorting technique based on Binary Heap data structure. It is similar to the selection sort where we first find the minimum element and place the minimum element at the beginning. Repeat the same process for the remaining elements.
Student information management system project report ii.pdfKamal Acharya
Our project explains about the student management. This project mainly explains the various actions related to student details. This project shows some ease in adding, editing and deleting the student details. It also provides a less time consuming process for viewing, adding, editing and deleting the marks of the students.
Pile Foundation by Venkatesh Taduvai (Sub Geotechnical Engineering II)-conver...
The Lower Bound Threshold for Fatigue Crack Growth
1. The Lower Bound Threshold for Fatigue Crack Growth
“A processby which a crackcan formand then grow underfluctuating loading,in which the resulting
failure can be sudden and catastrophic”
Fatigue damage accumulationisone of several degradationmechanismsconsideredinthe designof
nuclearpowerplantcomponents.Ingeneral,the severityof fatigue damage isevaluatedby
computinga cumulative usage factor(CUF), derivedfromalineardamage rule (Miner’sRule); witha
designfatigue curve,derivedfromthe resultsof uniaxial,strain-controlledfatigue tests.Suchtests
are usuallyperformedundercontrolledlaboratoryconditions(roomtemperature,air,low-humidity)
on smooth,un-notched specimens.The general ideaisthatfatigue testdataderivedfromspecimen
testsremainvalidwhenusedforengineeringsizedcomponentssubjectedtoplantrepresentative
pressure-temperature transients. Fatigue damage assessmentmethodshave beencodifiedin
several designstandards(ASMEIII/VIII,RCC-M,EN13445 toname a few),withrelativelylittle
divergence betweenthe general proceduresapplied.Code prescribedmethodshave aproven
historyof successful implementation,withsufficientconservativism(albeittoomuchinsome cases)
to ensure componentstructural integrityoverincreasinglylongeroperatinglifetimes [1].Inthe
contextof the civil nuclearpowergeneration,operatinglicenserenewal islikelytoextendthe
operatinglifetimeof existingplantsto60 years,providedthe necessarychecksagainst
environmentallyassisteddegradationare satisfied [2].Withincreasingcomponentoperatinglives,
furtherjustificationof protectionagainstfatigue failureiswarranted;asfatigue damage assessment
isheavilydatadependent,thiswill undoubtedlyrequire agreaternumberof fatigue teststobe
carriedout infuture,includingplantrepresentative componenttesting;simulationof severe plant-
representative transients–non-isothermal,out-of-phase,thermal-mechanical loadingeventswith
significantstraingradienteffects –will alsoneedtobe investigatedfurther .
Now,itis clearthat the increasingdemandforenergycombinedwithadrive towardsgreaterenergy
efficiencywillinevitablyforce industriestoadopta more sustainable long-life approachto
componentdesignwithinreason. Withthisobjective,itbaresrememberingwhythisisactually
possible inthe firstplace!Asengineers,more oftenthannot, amacroscopicapproach isall that is
necessarytomodel a givenproblem.Withthisapproachinmind,we treatengineeringmaterialsas
an isotropic,homogenouscontinuum,andfocusourattentiononthe mechanical propertiesof the
material,andthe prescribedloadingconditions.Inthisframework,fatiguedamage canonlyoccur
underthree conditions,all of whichmustbe satisfiedconcurrently.
1. Tensile stressesmustexist.
2. Repeatedloading
3. Plasticity
The 3rd
requirementisnottrivial andwarrantsfurtherconsideration.Fatigue damage relieson
energydeposition (irreversible absorption) whichcanonlyoccur if plasticityispresent;inother
words,there mustbe a developedhysteresiscycle.We oftenonlyconsidersuchconditionsto prevail
at the tipsof visible notchesorflaws,butthe real flaw (pardonthe pun) liesinonlyconsideringthe
macroscopicpropertiesof the material.Inreality,microscopicflawswillexhibitplasticity,evenin
caseswhere the macroscopicbehaviourof the material remainselastic.Iam no metallurgist,butI
wouldhazardan informedguessthatthisphenomenonissimplyascaled-downmacroscopic
analogue;thatis,damage occurs due to plasticenergydepositionatthe tipsof microscopicflaws.
2. Figure 1 illustratesthe crackgrowthprocess;sufficientenergyabsorptionisrequiredtotranslate the
crack-tipplasticzone to a newposition.Because plasticityisirreversible, regionswithsignificant
plasticstrainwill be leftbehindthe crack-tipfieldascrack growthprogresses.
Well,thisbegsthe question,if plasticityreallyisprevalentonamicroscopicscale,thenwhy doesthis
not alwaystranslate tomore damage on a macroscopicscale whenthe three above conditionsare
satisfied?Lookingbackat the openingdefinition,we know fatiguefailure canonlyoccurwhena
crack growsto a critical length,leadingtosuddenfailure byfracture.Butformicroscopicplasticityto
exist,amicroscopiccrack mustalreadybe present.Therefore,itiscrack growthwe are concerned
withhere. Since crackgrowth ultimatelyreliesonasupplyof energytothe crack tipregion(the zone
of cyclicplasticity) todrive the fatigue damage mechanism, the processcanonlyprogressif each
cycle of loadprovidesincreasinglymore energytothe region.Thus,anenergythreshold mustbe
overcome forcrack growthto occur [3].
It isuseful toconsiderhowmuchplasticenergyisdepositedpercycle of load.The fatigue crack
growthper cycle can be relatedtothe stressintensityfactorrange, ∆𝐾,underthe assumptionof
LinearElasticFracture Mechanics(LEFM),or the J-Integral range, ∆𝐽,forPost-YieldFracture
Mechanics (PYFM), where plasticityisgenerallynotconfinedtothe crack-tipregion.This empirical
relationship,knownasThe ParisLaw,isexpressedasfollows [4].
𝑑𝑎
𝑑𝑁
∝ ∆𝐾 𝑚 ⇛
𝑑𝑎
𝑑𝑁
= 𝐶∆𝐾 𝑚 (1)
If we considerthe assumptionof LEFMconditions –where the plasticzone issmall incomparisonto
the total section where LEFMfieldsprevail –we can confine ourattentiontothe crack-tipresponse
underloading. Considerthe followingscenarioassumingaconstantloadamplitude: Onfirstload,
the crack-tipplasticzone exceedsthe materialyieldstrength,but doesnotexceedtwice yieldwhen
calculatedonan elasticbasis.Hence,whenloadisremoved,the crack-tipplasticzone will unload
elastically andplasticitywill be containeddue tothe “elasticcore”behaviourof the section.
Subsequentloadcycleswill thuscycle elasticallybetweenamaximumof +𝑦𝑖𝑒𝑙𝑑 (𝑡𝑒𝑛𝑠𝑖𝑙𝑒)and
−𝑦𝑖𝑒𝑙𝑑 (𝑐𝑜𝑚𝑝𝑟𝑒𝑠𝑠𝑖𝑣𝑒), or throughthe range twice-yield;thisprocessiscalled Shakedown. Because
the crack-tipzone cycleselasticallyin thisinstance,itcannotbe responsible forabsorbingenergyto
drive fatigue crackgrowth.Onlya regionof cyclicplasticity –where the alternatingstressintensity
range exceedstwice-yield–can be responsibleforfatigue damage. Therefore,if we consideracrack
loadedinMode I, and assumingthe limitingcase of ∆𝜎 = 2𝜎 𝑦,we can derive anexpressionforthe
size of the plasticzone [5].
2𝜎 𝑦 =
∆𝐾
√2𝜋𝑟
⇛ 𝑟 =
∆𝐾2
8𝜎 𝑦
2 𝜋
(2)
θ
PlasticZone ∆𝒂
Crack Growth
𝑟
Figure 1. Illustration of Crack Growth Under Cyclic Loading
3. Definingthe strainatyieldas 𝜀 𝑦, andassumingonlymechanical loading, the strainenergycanbe
expressedasfollows
𝑊 =
1
2
𝐶𝑖𝑗𝑘𝑙 𝜀𝑖, 𝑗 𝜀 𝑘,𝑙 (3)
Where 𝐶 is the fourth-orderelasticitytensor,the componentsof whichrepresentthe elasticmoduli
of the material,and 𝜀 isthe infinitesimal straintensor.The stress-strainrelation,ignoringthe effects
of temperature,canbe expressedbydifferentiatingeqn.(3) withrespecttothe infinitesimalstrain
𝜎 =
𝑑𝑊
𝑑𝜀
( 𝜀) = 𝐶𝜀 𝑜𝑟 𝜎𝑖𝑗 = 𝐶𝑖𝑗𝑘𝑙 𝜀 𝑘𝑙 𝑖𝑛 𝑖𝑛𝑑𝑖𝑐𝑖𝑎𝑙 𝑛𝑜𝑡𝑎𝑡𝑖𝑜𝑛 (4)
The energydeposited perunitvolume istherefore 2𝜎𝜀,or2𝜎 𝑦 𝜀 𝑦 inour example.
The plasticzone infront of the crack-tipis usuallyelliptical.Forsimplicity,we canassume acircular
plasticzone (like thatinFigure 1) withitscentre coincident withthe tipof the crack. Thus,the
volume of concernis 𝜋𝑟2 𝑡, where 𝑡 representsthe lengthalongthe crackfront.We can now further
expandeqn.(2) byconsideringthe energydepositedperunitvolume andrearrangingfor 𝑟.
2𝜎 𝑦 𝜀 𝑦 =
𝑊
𝜋𝑟2 𝑡
⇛ 𝑟 = √
𝑊
2𝜎 𝑦 𝜀 𝑦 𝜋𝑡
(5)
Substitute eqn.(5) intoeqn.(2) andon rearrangingwe obtainanexpressionforthe energy
depositedforeachcycle of load
√
𝑊
2𝜎 𝑦 𝜀 𝑦 𝜋𝑡
=
∆𝐾2
8𝜎 𝑦
2 𝜋
⇛ 𝑊 =
𝜀 𝑦 𝑡∆𝐾4
32𝜋𝜎 𝑦
3
(6)
Consideringeqn.(6) representsthe thresholdenergypercycle,we cansimplifythisexample further
by assumingthere existsafixedamountof strainenergy providedbythe externalloads,
correspondingtoa unitincrease incrack area – i.e.the derivativeof energywithrespecttocrack
area.We introduce the energyreleaserate, 𝐺,andfurthersimplifyeqn.(6).
𝐺 =
𝑑𝑊
𝑑𝑎
⇛
𝑑𝑎
𝑑𝑁
=
𝑑𝑊
𝐺
=
𝜀 𝑦∆𝐾4
32𝜋𝜎 𝑦
3 𝐺
(7)
The resultisthe ParisLaw with 𝐶 =
𝜀 𝑦
32𝜋𝜎 𝑦
3 𝐺
and 𝑚 = 4 whichconformswith empirical dataformost
structural steels. Obviously,we have made some fairlyonerousassumptionshere,butanimportant
observationabouteqn.(7) deservesattention:If there existsaminimum, non-zero(andfixed)
amountof energyrequiredtodrive crackgrowth,thenthismustalsocorrespondtoa minimum,
non-zero,stressintensityfactorrange, ∆𝐾 𝑚𝑖𝑛; when∆𝐾 < ∆𝐾 𝑚𝑖𝑛,there isinsufficientenergy
depositiontodrive the crackgrowthmechanism.
𝐹𝑜𝑟 ∆𝐾 < ∆𝐾 𝑚𝑖𝑛,
𝑑𝑎
𝑑𝑁
= 0
Now,forthe interestingpart!Whathappensif ∆𝐾 isexactlyequal to ∆𝐾 𝑚𝑖𝑛?
𝐹𝑜𝑟 ∆𝐾 = ∆𝐾 𝑚𝑖𝑛,
𝑑𝑎
𝑑𝑁
= ?
4. We knowunderthese conditionsthat
𝑑𝑎
𝑑𝑁
≠ 0, sowhat isthe smallest,non-zerovalue that 𝑑𝑎 can
take?A somewhatmeaningfulanswerpresentsitselfwhenwe considerthe behaviourof
engineeringmaterialsinthe quantumrealm.
For polycrystallinematerials(mostmetalsandceramics),atomsare arrangedina repeatingor
periodicarrayoverlarge atomic distances.Differentatomsandionscan be modelledassolid
spheresof fixedsize,arrangedinthe smallestpossible repeatinggroups;these groupsare knownas
Unit Cells andare illustratedin Figure 2. The grosscrystal structure of any polycrystalline material is
therefore dependentonthe configurationof atomswithinthe unitcell [6].
Figure 2. Unit Cell within a Polycrystalline Lattice Structure
Four simple crystallinestructuresaccountformostmetallicmaterials:
1. Simple Cubic(SCC)
2. Body-CentredCubic(BCC)
3. Face-CentredCubic(FCC)
4. Hexagonal Close-Packed(HCP)
Withoutdelvinginto muchdepth,the commonfeature of anyconfiguration isthatthe unitcell
correspondstothe lowestpossiblepotential energystate achievable foragivencrystal structure.If
atomsare to form a stable metallicstructure,the meanenergyof the free electronswithinthe
lattice mustbe lessthanthe energyof the electron energy level thatwouldprevailif the atom
existedfreely.The equilibriumseparationdistance of the atomsof atomswithinthe lattice isthat
for whichanyfurtherclosure wouldresultinanincrease inthe repulsive force whichexceedsthe
attendantdecrease inmeanelectronenergy [7].Thisphenomenonisdepicted inFigure 3.
UnitCell
The smallestrepeatingarrangementof
atoms
Usuallyprismsorparallelepipeds
Three setsof parallel faces
5. Figure 3. Variation in Atomic Energy Levels with Inter-Atomic Closure
The inter-atomicdistance betweenatomsisdeterminedbythe inter-atomicbondlength. Asarough
approximation,the bondlengthbetweentwodifferentatomsisequal tothe sumof the individual
covalentradii,andcan be measuredusingelectrondiffraction.
Table 1 belowshowssome importantcharacteristicsof well-knownelements.
Element Symbol
Atomic
Weight
(amu)
Density
(g/cm^3)
Crystal
Structure
Atomic
Radius (pm)
Aluminium Al 26.98 2.71 FCC 143
Argon Ar 39.95
Barium Ba 137.33 3.5 BCC 217
Beryllium Be 9.012 1.85 HCP 114
Boron B 10.81 2.34 Rhombohedral
Bromine Br 79.9
Cadmium Cd 112.41 8.65 HCP 149
Calcium Ca 40.08 1.55 FCC 197
Carbon C 12.011 2.25 Hexagonal 71
Caesium Cs 132.91 1.87 BCC 265
Chlorine Cl 35.45
Chromium Cr 52 7.19 BCC 125
Cobalt Co 58.93 8.9 HCP 125
Copper Cu 63.55 8.94 FCC 128
Fluorine F 19
Gallium Ga 69.72 5.9 Orthorhombic 122
Germanium Ge 72.59 5.32
Diamond
Cubic 122
Gold Au 196.97 19.32 FCC 144
Helium He 4.003
Hydrogen H 1.008
Table 1. Selected Element Properties
6. At firstglance,we can see thatthe atomic radii donot differdrasticallybetweendifferent metals;
mostatomic radii lie inthe range of 100 − 250𝑝𝑚, withthe inter-atomicspacingcorrespondingto
twice the atomicradius. Thisanswersourquestion,atleast ina theoretical sense –the smallest
possible non-zerocrack lengthincrement, d𝒂, correspondsto one atomic spacing. Fromthis
observation,valuesof ∆𝐾 𝑚𝑖𝑛 have beenderivedformany structural materials.Of course,the
accuracy of these valuesispredicatedonthe assumptionthatthe ParisLaw still holds atthe lower
boundcrack growth limit of one atomicspacing.
Finally,asanaside,itisworth consideringthe engineeringconsequences thatwould arise –inthe
contextof very-highcycle fatigue(VHCF)–if the thresholdSIFrange, ∆𝐾 𝑚𝑖𝑛,didnotexist.VHCF
range correspondsroughlytoover 108 cyclesto failure.Componentsoperatinginthisregime
include internal combustionengine cylinderheads,gasturbine disks,andball bearings [8].
Conventionalfatiguetestingisusuallylimitedto100Hz, correspondingtoaround 107cyclesperday,
or 3 × 109 cyclesper year.Thisof course isimpractical andcostlydue to time constraints,hence
mostVHCF testingisdone using ultrasonicfatiguetestingrangesof 15 to 30 kHz, corresponding
roughlyto107 cyclesperminute or1.6 × 109 cyclesperday!
Let usconsiderboththe conventional andultrasonictestingscenarios,underthe assumptionof no
fatigue crack growththreshold,withthe smallestpossible crackgrowthincrementof asingle atomic
displacement.Forsimplicity,we willassume anaverage inter-atomicspacingof 200𝑝𝑚 (or
2 𝐴𝑛𝑔𝑠𝑡𝑟𝑜𝑚𝑠, 𝐴̇).Afterone day, the resultingcrackgrowthisas follows:
𝑎 𝑐𝑜𝑛𝑣𝑒𝑛𝑡𝑖𝑜𝑛𝑎𝑙 = 107 × 2𝑒−10 = 2 𝑚𝑚
𝑎 𝑢𝑙𝑡 𝑟𝑎𝑠𝑜𝑛𝑖𝑐 = 1.6𝑒9 × 2𝑒−10 = 320 𝑚𝑚
“Failure”– or the terminationpoint –of most fatigue testsisusuallyestablishedusingthe 25% load-
drop criterion;thiscorrespondstothe initiationandpropagationof afatigue crackto “engineering
size”,orroughly 3 𝑚𝑚. The worryingconclusionisclearfromthese results:
In absenceof a fatiguethreshold belowwhich zero crackgrowth occurs,mostengineering structures
would incur fatiguefailurewithin a matter of weeks at most.
Alas, we can be thankful thatrealityisat leasta little more forgiving!
7. References
[1] ASME, “ASME III,Division1,SubsectionNB,”in ASMEBoiler & PressureVesselCode,2015.
[2] NuclearRegulatoryCommision,“RegulatoryGuide1.207: GUIDELINES FOR EVALUATING
FATIGUE ANALYSESINCORPORATINGTHELIFE REDUCTION OF METAL COMPONENTSDUE TO
THE EFFECTS OFTHE LIGHT-WATER REACTOR ENVIRONMENTFORNEW REACTORS,”no.
March, pp.1–7, 2007.
[3] R. Bradford,“The Effectsof PlasticIrreversibilityonLow Temperature Fracture,”2015.
[4] P. C.Paris,M. P.Gomez,and W. E. Anderson,“A Rational AnalyticTheoryof Fatigue,” Trend
Eng.,no.13, pp. 9–14, 1961.
[5] R. J. Roark,W. C. Young,and R. Plunkett, Formulas forStressand Strain,vol.43,no.3. 1976.
[6] J. Datsko, MaterialsSelection forDesign and Manufacturing,3rded.AnnArbor,Michigan:
MichiganUniversityPress,1997.
[7] R. E. SmallmanandR. J. BiShop,“ModernPhysical MetallurgyandMaterialsEngineering,”
Mod.Phys.Metall.Mater.Eng.,pp.320–350, 1999.
[8] V.Kazymyrovych, Very high cycle fatigueof engineering materials - A literature review.2009.