Engineering Fracture Mechanics. Engineers try to have high-strength, high ductility, high crack resistance, and faultless structures. The most reliable approach is "No cracks - no problems,"
When all is not possible, there are different methods of prevention of catastrophic failure: increase crack resistance by ductile material, by local heating; decrease SIF by placing holes on the crack path, by patching, by stiffing elements or by using composite materials. "Leak-before-break" is an effective strategy to prevent catastrophic failure of pressure vessels. It is better to allow a semi-elliptical crack to grow through the wall and to detect it by leaking than to have the dynamic start and failure of the whole vessel. There are two characteristics of the material: crack resistance for semi-elliptical crack and crack resistance for through crack.
This PPT discusses Fatigue and Fracture mechanism, some history and problems. It has included on research paper. You can refer the literature review for further study of the topic.
This PPT discusses Fatigue and Fracture mechanism, some history and problems. It has included on research paper. You can refer the literature review for further study of the topic.
Structural Integrity Analysis features a collection of selected topics on structural design, safety, reliability, redundancy, strength, material science, mechanical properties of materials, composite materials, welds, finite element analysis, stress concentration, failure mechanisms and criteria. The engineering approaches focus on understanding and concept visualization rather than theoretical reasoning. The structural engineering profession plays a key role in the assurance of safety of technical systems such as metallic structures, buildings, machines, and transport. The chapter 9 explains the engineering fundamentals of composite materials and structures. Copyright 2013 Igor Kokcharov, Andrey Burov
Structural Integrity Analysis features a collection of selected topics on structural design, safety, reliability, redundancy, strength, material science, mechanical properties of materials, composite materials, welds, finite element analysis, stress concentration, failure mechanisms and criteria. The engineering approaches focus on understanding and concept visualization rather than theoretical reasoning. The structural engineering profession plays a key role in the assurance of safety of technical systems such as metallic structures, buildings, machines, and transport. The first chapter explains the engineering fundamentals of stress analysis.
Structural Integrity Analysis: Chapter 3 Mechanical Properties of MaterialsIgor Kokcharov
Structural Integrity Analysis features a collection of selected topics on structural design, safety, reliability, redundancy, strength, material science, mechanical properties of materials, composite materials, welds, finite element analysis, stress concentration, failure mechanisms and criteria. The engineering approaches focus on understanding and concept visualization rather than theoretical reasoning. The structural engineering profession plays a key role in the assurance of safety of technical systems such as metallic structures, buildings, machines, and transport. The third chapter explains the engineering tests and fundamentals of mechanical properties of materials.
Structural Integrity Analysis features a collection of selected topics on structural design, safety, reliability, redundancy, strength, material science, mechanical properties of materials, composite materials, welds, finite element analysis, stress concentration, failure mechanisms and criteria. The engineering approaches focus on understanding and concept visualization rather than theoretical reasoning. The structural engineering profession plays a key role in the assurance of safety of technical systems such as metallic structures, buildings, machines, and transport. The chapter 9 explains the engineering fundamentals of composite materials and structures. Copyright 2013 Igor Kokcharov, Andrey Burov
Structural Integrity Analysis features a collection of selected topics on structural design, safety, reliability, redundancy, strength, material science, mechanical properties of materials, composite materials, welds, finite element analysis, stress concentration, failure mechanisms and criteria. The engineering approaches focus on understanding and concept visualization rather than theoretical reasoning. The structural engineering profession plays a key role in the assurance of safety of technical systems such as metallic structures, buildings, machines, and transport. The first chapter explains the engineering fundamentals of stress analysis.
Structural Integrity Analysis: Chapter 3 Mechanical Properties of MaterialsIgor Kokcharov
Structural Integrity Analysis features a collection of selected topics on structural design, safety, reliability, redundancy, strength, material science, mechanical properties of materials, composite materials, welds, finite element analysis, stress concentration, failure mechanisms and criteria. The engineering approaches focus on understanding and concept visualization rather than theoretical reasoning. The structural engineering profession plays a key role in the assurance of safety of technical systems such as metallic structures, buildings, machines, and transport. The third chapter explains the engineering tests and fundamentals of mechanical properties of materials.
Stress concentrations produced by discontinuities in structures such as holes, notches, and fillets will be introduced in this section. The stress concentration factor will be defined. The concept of fracture toughness will also be introduced.
An overview of the major materials used in aeronautical and automotive structures will be given in this section. The mechanical and physical properties of the materials will be highlighted, with an emphasis placed on the stiffness versus density and strength versus density of various materials.
The section will cover the behaviour of materials by introducing the stress-strain curve. The concepts of elastic and plastic deformation will be covered. This will then lead to a discussion of the micro-structure of materials and a physical explanation of what is happening to a polycrystalline material as it is loaded to failure.
In this section the concept of stress will be introduced, and this will be applied to components that are in a state of tension, compression, and shear. Strain measurement methods will also be briefly discussed.
The module aims and objectives will be covered, together with the module outline and the methods of teaching and assessment. The module will then be introduced, and the important physical assumptions that will be applied throughout this module will be highlighted.
This section will introduce how to solve problems of axially loaded members such as stepped and tapered rods loaded in tension. The concept of strain energy will also be introduced.
The relationship between stress and deformation will be covered in this section, and some of the important elastic material properties such as Young’s modulus and the modulus of rigidity will be defined.
An introduction to the module is given, including forces, moments, and the important concepts of free-body diagrams and static equilibrium. These concepts will then be used to solve static framework (truss) problems using two methods: the method of joints and the method of sections.
Tractor-trailers are used all across America to transport cargo, but are not designed with fuel efficiency in mind. Therefor, there is an incentive for companies to invest in making their tractor-trailers more aerodynamic in order to save on fuel costs. I go into the testing and methodology of how my team and I decided to tackle the problem of reducing the coefficient of drag on tractor-trailers by implementing air channeling devices (ACDs). Then, I cover the results from our experiments and our ACD recommendation.
International Journal of Engineering and Science Invention (IJESI)inventionjournals
International Journal of Engineering and Science Invention (IJESI) is an international journal intended for professionals and researchers in all fields of computer science and electronics. IJESI publishes research articles and reviews within the whole field Engineering Science and Technology, new teaching methods, assessment, validation and the impact of new technologies and it will continue to provide information on the latest trends and developments in this ever-expanding subject. The publications of papers are selected through double peer reviewed to ensure originality, relevance, and readability. The articles published in our journal can be accessed online
fracture mechanics and damage tolerance .Why do high strain rate, low temperature and triaxial state of stress promote brittle fracture?Method of Crack/Crack Like Defect Analysis
Simulation of Critical Crack Length Propagation Using Fracture Mechanicsijceronline
The focus of this paper is to investigate and analyze the study on the plate of steel, Aluminum and Epoxy with a center crack. Linear elastic fracture mechanics principles have been used for calculating Stress Intensity Factor, Critical crack length, Increment in crack, Mean stress and strain Amplitude at critical fatigue load cycles. Above calculations will be done on the plate with centre crack of various materials (steel, aluminum and epoxy) to predict crack length to evaluate and to compare the results with theoretical calculations. .Conclusions/results obtained on the basis of analysis.
Review on the Effect of Shear Connectors on Composite Deck SlabsIJAEMSJORNAL
This paper presents a review on the effect of shear connectors on composite deck slabs. Composite deck slabs consist of profile deck sheet and concrete. Several researchers have been studying the behaviour of composite slab but due to its complex behaviour yet it is not completely understood. The behaviour of composite slab directly depends on the deformability and contact strength. Here, some important literature reviews regarding composite slab behavior incorporating different profiles were discussed.
Under repeated impact composite domes subjected 6 J energy, changes locally with
increasing drop height. The action of the dynamic load generates reactions at the
support and bending moments at points on the surface of the composite. The peak loads
were noted to increase and stabilise about some mean value; and the 150mm diameter
shell was more damage tolerant compared to the 200 mm diameter one.
INTERFACIAL STRESS ANALYSIS OF EXTERNALLY PLATED RC BEAMSIjripublishers Ijri
has become a popular retrofit method due to its rapid, simple and other advantages. However, debonding along the
Steel-RC beam interface can lead to premature failure of the structures. The interfacial stresses play a significant role
in understanding this premature debonding failure of such repaired structures. This paper presents a careful finite
element investigation into interfacial stresses in the adhesive layer bonding RC beam and soffit plate. Finite element
modelling issues like proper selection of contact between adherents and symmetry conditions are first
discussed, with particular attention on appropriate finite element meshes for the accurate determination of interfacial
stresses. The interfacial stress behaviour at plate end has been analysed for two cases of loading taken one by applying
uniformly distributed load and the other with a two point loading. Two special cases are considered in two point
loading – for the cases when the plate terminates with-in the constant moment region (CMR) and for the case when
plate is extended beyond constant moment region where bending moment is minimal. The interfacial stresses are
increasing with a reduction in adhesive layer thickness where as the stresses are increasing with the increase in soffit
plate thickness. Carbon fibre reinforced polymer (CFRP) has shown a significant reduction in interfacial stresses
when compared to steel plate. The interfacial stresses for the plate restricted within the constant moment region are very
high near the plate end leading to flexural debonding compared to the case where plate is extended beyond constant
moment region where bending moment is minimal. The concentration of stresses in the adhesive layer near the plate
end explained the significance in considering their influence in flexural debonding.
INTERFACIAL STRESS ANALYSIS OF EXTERNALLY PLATED RC BEAMSIjripublishers Ijri
Strengthening reinforced concrete (RC) beams by bonding steel or fibre reinforced polymer (FRP) on its tension face
has become a popular retrofit method due to its rapid, simple and other advantages. However, debonding along the
Steel-RC beam interface can lead to premature failure of the structures. The interfacial stresses play a significant role
in understanding this premature debonding failure of such repaired structures. This paper presents a careful finite
element investigation into interfacial stresses in the adhesive layer bonding RC beam and soffit plate. Finite element
modelling issues like proper selection of contact between adherents and symmetry conditions are first
discussed, with particular attention on appropriate finite element meshes for the accurate determination of interfacial
stresses. The interfacial stress behaviour at plate end has been analysed for two cases of loading taken one by applying
uniformly distributed load and the other with a two point loading. Two special cases are considered in two point
loading – for the cases when the plate terminates with-in the constant moment region (CMR) and for the case when
plate is extended beyond constant moment region where bending moment is minimal. The interfacial stresses are
increasing with a reduction in adhesive layer thickness where as the stresses are increasing with the increase in soffit
plate thickness. Carbon fibre reinforced polymer (CFRP) has shown a significant reduction in interfacial stresses
when compared to steel plate. The interfacial stresses for the plate restricted within the constant moment region are very
high near the plate end leading to flexural debonding compared to the case where plate is extended beyond constant
moment region where bending moment is minimal. The concentration of stresses in the adhesive layer near the plate
end explained the significance in considering their influence in flexural debonding.
Keywords-- Interfacial stresses, flexural debonding, constant moment region, soffit plate, finite element method.
Job Interview Puzzles 2022 from Aplusclick.org The brainteaser, logical questions, puzzles are used at job interviews in It companies for engineering and managerial positions. These are the most interesting and difficult logical questions with the links to the answers.
Project Portfolio Management is Managing several projects and coordinate them to achieve specific organizational objectives.
Examples show typical tasks of the Portfolio Managers, the key indicators, challenges, and tools they use to reach Strategic objectives. The samples from the project portfolio management simulation SimulTrain(R)+ explain how to manage complex portfolios and adapt to the changing environment.
GUESTIMATE methods are a combination of mathematics, statistics and common sense of getting meaningful results for decision making.
The most famous approach was suggested by Enrico Fermi. Mr. Fermi was convinced that an error of order of magnitude (up to ten times) can be accepted for certain problems.
There are many useful results can be obtained by using probability estimation.
Expected values are largely used in economics, business, finance, and opportunity choice.
Old fashion rule of thumb is a widely used approach among non-mathematicians.
Certain results can be obtained if we consider either limits or average values of variables.
Logical Puzzles for Geeks by Gerry Geek. The puzzles are a collection of funny questions, brainteasers and think-outside-the-box questions for curious mind. The full collection of the cards are at the website http://geek.aplusclick.com
Risk Management is the identification, assessment, and prioritization of risks to minimize, monitor, and control the probability and/or impact of unfortunate events or to maximize the realization of opportunities.
The same is explained by real example of managing project via project management simulator SimulTrain(R). Simultrain(R) prepares managers to confront risks in real projects. Major conclusion is showing how managers do it in real projects every day.
Similar to Maslow's Hierarchy of Needs (the Theory of Human Motivation), the Pyramid / Hierarchy of Skills is suggested. It includes 5 levels: Know, Play, Work, Solve, and Invent. Another classification includes roles: Student, Apprentice, Specialist, Expert, and Craftsman.
Hierarchy of competence is analysed for Unconscious / Conscious Competence / Incompetence.
"The craftsman represents the special human condition of being engaged." - Richard Sennett
The work is inspired by two books:
- Maslow A.H. A Theory of Human Motivation
- Sennett R. The Craftsman. 2008.
A+Click Short Math Situations STS includes 100 short math puzzles and problems.
SMS stands for Short Math Situation.
Don’t confuse with SMS (Short Message Service), which is used as an acronym for all types of short text messaging. The last one is the most widely used data application in the world with several billion active users.
If the length of the SMS text messages is limited to 140 characters, the Short Math Situation questions are limited to 64 characters. Everything should be made as short as possible, but no shorter.
Math Practical Problems we meet in real life. The slides are an extract from free ebook A+ Click Everyday Math that helps students become problem solvers. This e-book features a collection of 120 challenging math problems. Students aged 12 years and up with an itch for math will enjoy it as much as curious adults. The e-book presents the best practical problems from www.aplusclick.com adapted to the e-book format. The website offers over 3500 problems, starting from the very simple and moving toward the extremely difficult. Each problem must be solved within one minute and without using a calculator. The exercises focus on understanding, spatial reasoning, and problem solving rather than math rules and theorems.
Seven Sins, Seven Jokes, and Seven Riddles is a collection of the best phrases in the project management life. The riddles are taken from the book Math Puzzles for MBAs by Igor Kokcharov. The book features a collection of challenging math puzzles that people with masters of business administration degrees, project managers, and entrepreneurs encounter in real life. The book includes the following topics: Business (Scope), Money (Cost), Time (Scheduling), Risk, and People (Project Resources).
Welcome to WIPAC Monthly the magazine brought to you by the LinkedIn Group Water Industry Process Automation & Control.
In this month's edition, along with this month's industry news to celebrate the 13 years since the group was created we have articles including
A case study of the used of Advanced Process Control at the Wastewater Treatment works at Lleida in Spain
A look back on an article on smart wastewater networks in order to see how the industry has measured up in the interim around the adoption of Digital Transformation in the Water Industry.
COLLEGE BUS MANAGEMENT SYSTEM PROJECT REPORT.pdfKamal Acharya
The College Bus Management system is completely developed by Visual Basic .NET Version. The application is connect with most secured database language MS SQL Server. The application is develop by using best combination of front-end and back-end languages. The application is totally design like flat user interface. This flat user interface is more attractive user interface in 2017. The application is gives more important to the system functionality. The application is to manage the student’s details, driver’s details, bus details, bus route details, bus fees details and more. The application has only one unit for admin. The admin can manage the entire application. The admin can login into the application by using username and password of the admin. The application is develop for big and small colleges. It is more user friendly for non-computer person. Even they can easily learn how to manage the application within hours. The application is more secure by the admin. The system will give an effective output for the VB.Net and SQL Server given as input to the system. The compiled java program given as input to the system, after scanning the program will generate different reports. The application generates the report for users. The admin can view and download the report of the data. The application deliver the excel format reports. Because, excel formatted reports is very easy to understand the income and expense of the college bus. This application is mainly develop for windows operating system users. In 2017, 73% of people enterprises are using windows operating system. So the application will easily install for all the windows operating system users. The application-developed size is very low. The application consumes very low space in disk. Therefore, the user can allocate very minimum local disk space for this application.
Explore the innovative world of trenchless pipe repair with our comprehensive guide, "The Benefits and Techniques of Trenchless Pipe Repair." This document delves into the modern methods of repairing underground pipes without the need for extensive excavation, highlighting the numerous advantages and the latest techniques used in the industry.
Learn about the cost savings, reduced environmental impact, and minimal disruption associated with trenchless technology. Discover detailed explanations of popular techniques such as pipe bursting, cured-in-place pipe (CIPP) lining, and directional drilling. Understand how these methods can be applied to various types of infrastructure, from residential plumbing to large-scale municipal systems.
Ideal for homeowners, contractors, engineers, and anyone interested in modern plumbing solutions, this guide provides valuable insights into why trenchless pipe repair is becoming the preferred choice for pipe rehabilitation. Stay informed about the latest advancements and best practices in the field.
TECHNICAL TRAINING MANUAL GENERAL FAMILIARIZATION COURSEDuvanRamosGarzon1
AIRCRAFT GENERAL
The Single Aisle is the most advanced family aircraft in service today, with fly-by-wire flight controls.
The A318, A319, A320 and A321 are twin-engine subsonic medium range aircraft.
The family offers a choice of engines
Sachpazis:Terzaghi Bearing Capacity Estimation in simple terms with Calculati...Dr.Costas Sachpazis
Terzaghi's soil bearing capacity theory, developed by Karl Terzaghi, is a fundamental principle in geotechnical engineering used to determine the bearing capacity of shallow foundations. This theory provides a method to calculate the ultimate bearing capacity of soil, which is the maximum load per unit area that the soil can support without undergoing shear failure. The Calculation HTML Code included.
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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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.
Quality defects in TMT Bars, Possible causes and Potential Solutions.PrashantGoswami42
Maintaining high-quality standards in the production of TMT bars is crucial for ensuring structural integrity in construction. Addressing common defects through careful monitoring, standardized processes, and advanced technology can significantly improve the quality of TMT bars. Continuous training and adherence to quality control measures will also play a pivotal role in minimizing these defects.
Vaccine management system project report documentation..pdfKamal Acharya
The Division of Vaccine and Immunization is facing increasing difficulty monitoring vaccines and other commodities distribution once they have been distributed from the national stores. With the introduction of new vaccines, more challenges have been anticipated with this additions posing serious threat to the already over strained vaccine supply chain system in Kenya.
About
Indigenized remote control interface card suitable for MAFI system CCR equipment. Compatible for IDM8000 CCR. Backplane mounted serial and TCP/Ethernet communication module for CCR remote access. IDM 8000 CCR remote control on serial and TCP protocol.
• Remote control: Parallel or serial interface.
• Compatible with MAFI CCR system.
• Compatible with IDM8000 CCR.
• Compatible with Backplane mount serial communication.
• Compatible with commercial and Defence aviation CCR system.
• Remote control system for accessing CCR and allied system over serial or TCP.
• Indigenized local Support/presence in India.
• Easy in configuration using DIP switches.
Technical Specifications
Indigenized remote control interface card suitable for MAFI system CCR equipment. Compatible for IDM8000 CCR. Backplane mounted serial and TCP/Ethernet communication module for CCR remote access. IDM 8000 CCR remote control on serial and TCP protocol.
Key Features
Indigenized remote control interface card suitable for MAFI system CCR equipment. Compatible for IDM8000 CCR. Backplane mounted serial and TCP/Ethernet communication module for CCR remote access. IDM 8000 CCR remote control on serial and TCP protocol.
• Remote control: Parallel or serial interface
• Compatible with MAFI CCR system
• Copatiable with IDM8000 CCR
• Compatible with Backplane mount serial communication.
• Compatible with commercial and Defence aviation CCR system.
• Remote control system for accessing CCR and allied system over serial or TCP.
• Indigenized local Support/presence in India.
Application
• Remote control: Parallel or serial interface.
• Compatible with MAFI CCR system.
• Compatible with IDM8000 CCR.
• Compatible with Backplane mount serial communication.
• Compatible with commercial and Defence aviation CCR system.
• Remote control system for accessing CCR and allied system over serial or TCP.
• Indigenized local Support/presence in India.
• Easy in configuration using DIP switches.
Final project report on grocery store management system..pdfKamal Acharya
In today’s fast-changing business environment, it’s extremely important to be able to respond to client needs in the most effective and timely manner. If your customers wish to see your business online and have instant access to your products or services.
Online Grocery Store is an e-commerce website, which retails various grocery products. This project allows viewing various products available enables registered users to purchase desired products instantly using Paytm, UPI payment processor (Instant Pay) and also can place order by using Cash on Delivery (Pay Later) option. This project provides an easy access to Administrators and Managers to view orders placed using Pay Later and Instant Pay options.
In order to develop an e-commerce website, a number of Technologies must be studied and understood. These include multi-tiered architecture, server and client-side scripting techniques, implementation technologies, programming language (such as PHP, HTML, CSS, JavaScript) and MySQL relational databases. This is a project with the objective to develop a basic website where a consumer is provided with a shopping cart website and also to know about the technologies used to develop such a website.
This document will discuss each of the underlying technologies to create and implement an e- commerce website.
2. Structural Integrity Analysis 2. Fracture Mechanics
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2. FRACTURE MECHANICS
Igor Kokcharov
2.1 DEFECTS
Structural materials have inner defects such as cracks, which are extreme stress
concentrators.
There are technological defects shown in diagrams A and B below, which are cracks that grew
under exploitation into fatigue cracks, shown as diagrams C, D, F, corrosion attack (E), or
thermal impact cracking. Improper exploitation such as scratching produces such defects.
Leaking occurs through the cracks, allowing detection of defects before catastrophic failure
occurs in pressure vessels.
3. Structural Integrity Analysis 2. Fracture Mechanics
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The most dangerous defects are perpendicular to tensile stress in the material.
It is possible to approximate the curved front of the defect by an ellipse or circle. A three-dimensional
singular defect can be replaced by projecting onto a surface perpendicular to the
tensile stress. A surface defect is more dangerous than an inner defect of the same size. It is
easier to inspect surface defects than inner pores by nondestructive control.
4. Structural Integrity Analysis 2. Fracture Mechanics
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2.2 STRESS IN THE CRACK TIP
A crack is an obstacle in the path of force lines. A concentration of force lines affects the
stress pattern in the cross section. According to the solution of the theory of elasticity for an
extreme concentrator such as a crack, the maximum stress tends towards infinity. The
solutions were obtained for ideal elastic material. Fortunately, the structural materials are not
ideally elastic, as there are plastic deformations and microstructural changes in the crack tip.
In Section 2.4 (Plasticity) we discuss the real value of stress. The other figure shows force
line distribution and stress patterns for specimens with a crack under pure bending.
The figure below shows the original and deformed state (displacements are magnified) of a
plate with a central crack. According to the theory, a sharp crack will transform into an
elliptical hole with a shorter length and very small height.
There is a three-component stress field in the crack tip. The plot shows the stress distribution
in the center of the specimen with a central crack, only the right part is shown.
In the crack tip there is a small zone where the formula for stress can be simplified. The
magnitude rs is the size of the singular zone. Expression 2 is a singular solution. The
expression is valid for all types of crack in tension with different geometries. The curve lies
higher for larger nominal stress or for a larger crack length, but its form is the same. The size
of singular zone is different for different schemes. In many cases, it is about 0.1 of crack
length.
5. Structural Integrity Analysis 2. Fracture Mechanics
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2.3 STRESS INTENSITY FACTOR
The solution to the theory of elasticity shows that two plates with different stresses and crack
lengths can have the same stress distribution in the crack tips (in the singular zones). There
are other combinations (for example «nominal stress-crack length») that also give the same
stress distribution and the same stress intensity in the crack tip.
6. Structural Integrity Analysis 2. Fracture Mechanics
Stress intensity factor (SIF) is a measure of stress intensity in the crack tip. A higher SIF
means larger stress pattern at the line of crack continuation (axis X). Expression 3 is valid for
a wide plate with a central crack.
For a plate where the crack size and width have the same order there is an additional
coefficient F for equation 3.
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For small side cracks the correction factor is F = 1.12.
For small semi-elliptical cracks the maximum value of stress intensity is in point A and the
correction factor is approximately equal to 1.12 for wide defects. The correction factor
decreases with the larger ratio a/B and the lower value of 2c/B.
7. Structural Integrity Analysis 2. Fracture Mechanics
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The correction functions for other loading schemes can be found in the SIF handbooks.
The value of KI allows us to determine the stress values at a distance r in the crack tip.
SIF KI is measured in MPa m1/2 or in ksi in1/2
1 ksi in1/2 is approximately equal to 1.1 MPa m1/2.
SIF KI is the magnitude of the ideal crack tip stress field.
8. Structural Integrity Analysis 2. Fracture Mechanics
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2.4 PLASTICITY
Plastic deformation is unrecovered shear in zones of high stress concentration. The figure
shows examples of plastic shear in the crack tip.
The stress in the crack tip of elastic-plastic models is finite. The maximum value is not as
important as the magnitude of SIF.
9. Structural Integrity Analysis 2. Fracture Mechanics
For thick plates, the size of the plastic zone at the surface is bigger than in the center due to
a three-dimensional state of stress in the central part of the plate. Despite this, stress
intensity is higher in the center of a thick plate with a crack. There are different models of
plastic zone in the crack tip that allow substitution of the plastic crack with a larger pure
elastic crack. The size ry is determined by yield strength sYS.
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2.5 FRACTURE TOUGHNESS
If stress is increased in a structure with cracks, crack initiation and fast growth will occur. The
magnitude of the SIF KI at the time of crack extension is the maximum acceptable (critical)
value for the material - KIC. As nominal stress increases, the SIFs in the crack tips A, B, and
C increase proportionally. KI(A) reaches its critical value KIC first. The structure fails at point
A. Fracture toughness is a measure of resistance to the extension of a crack. KIC crack
extension resistance has units of SIF [MPa m1/2] or [ksi in1/2].
Expression 8 above shows a condition of safe exploitation of a structure with cracks. The
figure below shows that there are combinations of «nominal stress and crack size» that end
in failure over the curve. There are combinations that do not end in failure. The nominal
10. Structural Integrity Analysis 2. Fracture Mechanics
stress cannot be larger than ultimate tensile strength, since this is a simplified correction for
short cracks. Some plastic materials demonstrate slow crack extension before catastrophic
failure. The safety margin in the presence of cracks is equal to the ratio of KIC to the
maximum SIF.
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The value of crack extension resistance is obtained by conducting a special fracture
toughness test on standard fatigue pre-cracked specimens.
2.6 TEMPERATURE AND DEFORMATION RATE
There are mainly two kinds of fracture: brittle cleavage and ductile fracture. They
demonstrate different values of the crack resistance. A material can have both types if the
11. Structural Integrity Analysis 2. Fracture Mechanics
test temperature varies widely. A decrease in temperature causes dramatic decrease of crack
resistance at the transition temperature.
A crack progressing at high speed has no time to realize ductile fracture mode. An initiated
crack will release stored energy of deformation and accelerate itself. If the speed reaches 1.5
km/sec, 4 seconds is enough to destroy 5 km of gas pipeline. Dynamic crack resistance KID is
lower than the static equivalent KIC.
Corrosion cracking tests are conducted on double beam specimens with a wedging bolt.
Corrosion causes the material in the crack tip to be brittle. As the crack begins and grows, the
force and SIF decreases with increased flexibility of the beams.
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The curve KIC constantly corresponds to the beginning of slow crack growth. When the
release energy is enough to accelerate the crack, the dynamic crack extension begins.
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2.7 SCALE EFFECT
An increase in sheet thickness is reflected in the size of the plastic zone and fracture mode.
Thin plate usually fractures by shear, while the cleavage is typical for thick plates. The
minimum value KIC is considered characteristic of the material.
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Crack resistance also decreases if the size of the specimen increases.
Usually materials with smaller grain size demonstrate better mechanical characteristics.
The maximum stress in a plate with a crack cannot exceed the ultimate tensile strength,
there is a correction function FU for the SIF that accounts for this. The middle of the diagram
is controlled by SIF without the correction functions.
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2.8 MIXED MODE LOADING
There are three basic modes of crack (surface) displacement:
I - opening mode;
II - plane shear;
III - anti-plane shear;
There is also the combination of the three basic modes, known as mixed mode.
There are a few modes of failure, for example by cleavage A or by shear B. There are
practical cases when the fracture mode is cleavage under pure torsion or plastic shear under
nominal tensile stress. The crack extension A is perpendicular to maximal tangential stress.
15. Structural Integrity Analysis 2. Fracture Mechanics
The initial direction of crack extension depends on the loading scheme and type of the
material. Brittle materials usually fracture by cleavage (A). Plastic shear is typical for ductile
materials and specimens with a narrow cross section.
Cracks perpendicular to the maximum tensile stress have larger stress intensity. Crack A,
inclined to the stress is equivalent to crack B if they have the same projection. They start at
the same stress.
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Shear stress distribution is similar to the normal stress pattern.
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2.9 FAILURE PREVENTION
The most reliable approach is "No cracks - no problems," but it is not easy to accomplish.
Engineers try to have high-strength, high ductility, high crack resistance, and faultless
structures.
When all is not possible, there are some methods of prevention of catastrophic failure, as
shown below: increase crack resistance by ductile material (A - C), by local heating (D);
decrease SIF by placing holes on the crack path (E, F), by patching (G), by stiffing elements
(H) or by using composite materials (I).
"Leak-before-break" is an effective strategy to prevent catastrophic failure of pressure
vessels (J).
It is better to allow a semi-elliptical crack to grow through the wall (J) and to detect it by
leaking than to have the dynamic start and failure of the whole vessel. There are two
characteristics of the material: crack resistance for semi-elliptical crack KICT and crack
resistance for through crack KIC.
Patching accepts inner loads from the cracked plate and decreases SIF. If the connection is
strong enough the SIF does not exceed a certain value.
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Stringers on the crack path change the critical combination of "stress - crack size." The
reinforced structure has a larger crack size at the same stress.
2.10 Failure analysis
Brittle and ductile fractures have different views of the broken surfaces. It is possible to
reveal defects at the broken surfaces. Defects in the zones of tensile stress are usually the
main source of fatigue cracks.
Crack resistance depends on crack orientation and is usually bigger for cracks perpendicular
to the rolling direction (L-T).
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Fracture toughness and ultimate tensile strength are used for short cracks in pressure
vessels.
Fatigue crack rate depends on SIF. The larger the SIF, the faster the crack growth rate. The
figure below shows a typical diagram of the "fatigue crack size - number of cycles."
Short cracks starting from a hole are in the zone of stress concentration (stress concentration
factor is 3). Relatively long cracks passing through a hole are considered cracks augmented
by the diameter of the hole.
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REFERENCES
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Baker R.D. Peter B.F. Why Metals Fail, Gordon and Breach Science Publishers, 1971.
Barsom J.M., Stanley T.R. Fracture and Fatigue Control in Structures, Prentice-Hall, Inc.,
1987.
Broek D. Elementary Engineering Fracture Mechanics, Kluwer, 1987.
Broek D. Practical Use of Fracture Mechanics, Kluwer, 1988.
Cherepanov G.P. Mechanics of Brittle Fracture, McGraw-Hill, 1979.
Fatigue Design Handbook , Ed. by R.C.Rice, Society of Automative Engineers, Inc., 1988.
Fisher J.W. Fatigue and Fracture in Steel Bridges - Case Studies, John Willey & Sons, 1984.
Freund .B. Dynamic Fracture Mechanics, Cambridge Univ. Press, Cambridge, 1990.
Gordon J.E. Structures, or Why Things Don't Fall Down. Penguin Books, Harmondsworth,
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Hellan K. Introduction to Fracture Mechanics, McGraw-Hill, New York, 1984.
Hertzberg R. Deformation And Fracture Mechanics Of Engineering Materials, John Wiley &
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Hutchinson J.W. Micro-mechanics of Damage in Deformation and Fracture, Lyngby: Technical
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Kanninen M.F., Popelar C.H. Advanced Fracture Mechanics, Oxford University Press, 1985.
Knott J.F. Fundamentals of Fracture Mechanics, Butterworth, London, 1973.
Miller K.J. Creep and Fracture, North Holland Publishing Company, 1982.
Nishida, Shin-ichi Failure Analysis in Engineering Applications, Butterworth-Heineman,
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Parker A.P. Mechanics of Fracture and Fatigue, An Introduction, E. and F.N. Spin, London,
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Sih G.C. Handbook of Stress Intensity Factors for Researchers and Engineers, Bethlehem, Pa:
Lehigh University, (vol.1-1973, vol.2 - 1974).
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