The document discusses failure of engineering materials. It describes that failure is undesirable as it puts lives and economics at risk. While causes of failure are known, prevention is difficult. Common causes are improper material selection, processing, or design flaws. The document then goes on to describe different types of failure like brittle and ductile fracture as well as fatigue failure. It provides details on how these failures occur and how they can be tested and characterized.
Brittle Ductile Behaviour For ( STEEL - RIENFORCED CONCRETE - CONCRETE )Ahmed Abdullah
- Steel exhibits ductile behavior by allowing large strains before rupturing or failing. It can stretch substantially under tension.
- Concrete and cast iron exhibit brittle behavior, failing abruptly with little warning once their strength limits are exceeded. Their stress-strain curves are steep with little plastic deformation.
- Reinforced concrete can show ductile behavior if designed properly with sufficient confinement and ductile reinforcement to allow inelastic deformations without collapse.
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 document discusses toughness and fracture toughness testing. It defines toughness as the energy absorbed by a material until fracture. Common toughness tests include the Charpy and Izod impact tests, which measure the energy absorbed during a high-velocity impact. However, these tests do not provide data needed for designing with cracks and flaws. Fracture toughness is a better property for design, as it indicates the stress required to propagate a preexisting flaw. The document outlines fracture toughness testing methods like compact tension and single edge notch bending specimens. It also discusses factors that influence fracture toughness values like material thickness, grain orientation, and plane strain versus plane stress conditions.
A fracture mechanics based method for prediction ofSAJITH GEORGE
The document presents a fracture mechanics-based method for predicting cracking in circular and elliptical concrete rings undergoing restrained shrinkage. It describes an experimental program using different ring geometries and material tests to determine properties. A numerical model is developed using ANSYS to model the restrained shrinkage process and calculate stress intensity factors. The model uses a fictitious temperature field to simulate shrinkage and determines cracking age by comparing driving and resistance curves. It finds cracking occurs earlier in elliptical rings and the method accurately predicts experimental cracking ages.
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.
Griffith proposed that brittle materials contain fine cracks that concentrate stress below the theoretical strength, causing fracture. When a crack propagates, the new surface area requires energy from the released elastic strain energy of the material. Griffith established that a crack will propagate when the decrease in elastic strain energy is equal to or greater than the energy required to create the new surface. The stress intensity factor describes the stress near a crack tip and is used to predict crack propagation. Fracture toughness is the material property describing a material's resistance to crack propagation.
This document provides an overview of failure analysis in materials science. It discusses why failure is studied, different failure modes like fracture, fatigue and creep. It covers ductile and brittle fracture in detail. The principles of fracture mechanics are explained, including stress concentration factors, fracture toughness and different modes of crack propagation. Methods of fracture toughness testing like impact testing and ductile to brittle transition are outlined. Finally, it discusses fatigue failure, different cyclic stress modes, parameters used to characterize fatigue and S-N curves. The document aims to help understand failure mechanisms and principles to prevent in-service failures through appropriate design.
Brittle Ductile Behaviour For ( STEEL - RIENFORCED CONCRETE - CONCRETE )Ahmed Abdullah
- Steel exhibits ductile behavior by allowing large strains before rupturing or failing. It can stretch substantially under tension.
- Concrete and cast iron exhibit brittle behavior, failing abruptly with little warning once their strength limits are exceeded. Their stress-strain curves are steep with little plastic deformation.
- Reinforced concrete can show ductile behavior if designed properly with sufficient confinement and ductile reinforcement to allow inelastic deformations without collapse.
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 document discusses toughness and fracture toughness testing. It defines toughness as the energy absorbed by a material until fracture. Common toughness tests include the Charpy and Izod impact tests, which measure the energy absorbed during a high-velocity impact. However, these tests do not provide data needed for designing with cracks and flaws. Fracture toughness is a better property for design, as it indicates the stress required to propagate a preexisting flaw. The document outlines fracture toughness testing methods like compact tension and single edge notch bending specimens. It also discusses factors that influence fracture toughness values like material thickness, grain orientation, and plane strain versus plane stress conditions.
A fracture mechanics based method for prediction ofSAJITH GEORGE
The document presents a fracture mechanics-based method for predicting cracking in circular and elliptical concrete rings undergoing restrained shrinkage. It describes an experimental program using different ring geometries and material tests to determine properties. A numerical model is developed using ANSYS to model the restrained shrinkage process and calculate stress intensity factors. The model uses a fictitious temperature field to simulate shrinkage and determines cracking age by comparing driving and resistance curves. It finds cracking occurs earlier in elliptical rings and the method accurately predicts experimental cracking ages.
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.
Griffith proposed that brittle materials contain fine cracks that concentrate stress below the theoretical strength, causing fracture. When a crack propagates, the new surface area requires energy from the released elastic strain energy of the material. Griffith established that a crack will propagate when the decrease in elastic strain energy is equal to or greater than the energy required to create the new surface. The stress intensity factor describes the stress near a crack tip and is used to predict crack propagation. Fracture toughness is the material property describing a material's resistance to crack propagation.
This document provides an overview of failure analysis in materials science. It discusses why failure is studied, different failure modes like fracture, fatigue and creep. It covers ductile and brittle fracture in detail. The principles of fracture mechanics are explained, including stress concentration factors, fracture toughness and different modes of crack propagation. Methods of fracture toughness testing like impact testing and ductile to brittle transition are outlined. Finally, it discusses fatigue failure, different cyclic stress modes, parameters used to characterize fatigue and S-N curves. The document aims to help understand failure mechanisms and principles to prevent in-service failures through appropriate design.
FRACTURE BEHAVIOUR OF NANOCOMPOSITES -FATIGUEArjun K Gopi
This document discusses the fracture and fatigue behavior of polymer nanocomposites. It notes that nanoparticles have higher specific surface areas than microparticles, which can improve stress transfer and that nanoparticles can be added at lower loadings while retaining properties of the neat polymer matrix. The document covers different types of fractures like brittle and ductile, and describes how the addition of nanoparticles up to 5 wt% can improve the fatigue resistance of polyamide nanocomposites by inhibiting crack propagation, but higher loadings may embrittle the material. TEM images show the differences in clay dispersion with varying nanoparticle content.
The document discusses the failure of a rolled slab due to improper cooling. Specifically:
1) A crack was found in the middle slab after air cooling, but not in the top or bottom slabs.
2) Analysis showed the middle slab cooled more slowly due to being sandwiched, allowing embrittling Ni4Mo phases to precipitate.
3) This embrittlement, combined with tensile stresses from the slab weight, caused the crack to form intergranularly in the middle slab. Proper cooling of each slab individually is the recommended solution.
CROSS-CORRELATION OF STRESSES IN THE TRAN REINFORCEMENT UNDER SHEAR LOAD AND ...IAEME Publication
The main aim of the present study is to give an answer to the question whether the transverse reinforcement, which is required for the shear resistance of columns, must be added to the one required for the cross section confinement, or it is possible for one to substitute the other. The superposition of these reinforcements is defended by the fact that the shear reinforcement results from the shear action, while the transverse reinforcement, required by the confinement, results from the axial compression of the section. The present study is experimental and uses strain gauges, in order to check the stresses of the transverse reinforcement. Useful conclusions are drawn.
Two 7075 aluminum samples were prepared and tested to determine their fracture toughness properties. A compact tension sample reached a maximum load of 4435 lbs before fracturing, yielding a KQ value of 89.1 ksi in1/2. However, this value was determined to be invalid for being KIC due to the ratio of maximum to critical load exceeding 1.1. A single edge notch bend sample fractured at 4295 lbs but its final crack length was too small to measure, and its KQ value of 33.1 ksi in1/2 was also found to not represent KIC. In summary, neither sample provided a valid measurement of plane strain fracture toughness KIC for the 7075 aluminum material
This document summarizes key parameters that can be determined from a true stress-true strain curve obtained from tensile testing of a material sample. These parameters include:
- True stress and true strain at maximum load, which represent the material's ultimate tensile strength and strain at necking.
- True fracture stress and true fracture strain, which represent the stress and strain at fracture after significant necking has occurred.
- True uniform strain, representing the strain up to maximum load before necking.
- True local necking strain, representing the additional strain from maximum load to fracture during necking.
- Strain hardening exponent and strength coefficient, materials constants that describe work hardening behavior and
Modified maximum tangential stress criterion for fracture behavior of zirconi...dentalid
The veneering porcelain sintered on zirconia is widely used in dental prostheses, but
repeated mechanical loadings may cause a fracture such as edge chipping or delamination.
In order to predict the crack initiation angle and fracture toughness of zirconia/veneer bilayered
components subjected to mixed mode loadings, the accuracy of a new and
traditional fracture criteria are investigated. A modified maximum tangential stress
criterion considering the effect of T-stress and critical distance theory is introduced, and
compared to three traditional fracture criteria. Comparisons to the recently published
fracture test data show that the traditional fracture criteria are not able to properly predict
the fracture initiation conditions in zirconia/veneer bi-material joints. The modified
maximum tangential stress criterion provides more accurate predictions of the experimental
results than the traditional fracture criteria
This document discusses fractography, which is the analysis of fracture surfaces. It begins by defining fractography and distinguishing between macrofractography and microfractography. Macrofractography examines fracture surfaces with the naked eye or low-power magnification and can reveal features like the fracture type, origin, and secondary cracks. Microfractography uses higher magnification microscopy to study details like dimple shapes that indicate the fracture mode. Examples are given of using scanning electron microscopes to analyze ductile and brittle fracture surfaces at the microscopic level.
This document summarizes key concepts regarding fatigue crack propagation. It discusses three stages of crack growth: (1) crack initiation, where microcracks form due to cyclic stresses; (2) crack propagation, where cracks grow according to Paris' law and form fatigue striations; and (3) final failure, where cracks rapidly grow unstable until catastrophic fracture. Critical factors like stress levels, number of cycles, and material properties are outlined. Paris' law and sigmoidal crack growth curves are also summarized.
Mumbai University.
Mechanical Engineering
SEM III
Material Technology
MOdule 2.1
Fracture:
Definition and types of facture, Brittle fracture: Griffith’s theory of fracture, Orowan’s modification, Dislocation theory of fracture, Critical stress and crack propagation velocity for brittle fracture, Ductile fracture: Notch effect on fracture, Fracture toughness, Ductility transition, Definition and significance
The Crack Pattern Of R.C Beams Under LoadingAhmed Abdullah
1. A reinforced concrete beam was tested under static two-point concentrated loading to study the effect of different web reinforcement arrangements on ultimate shear strength.
2. It was observed that diagonal cracks developed first in deeper beams while flexural cracks developed first in shallower beams with sufficient reinforcement.
3. The crack pattern and failure mode were similar across all test beams despite variations in web reinforcement, with diagonal cracks forming first in deeper beams.
The document discusses creep and stress rupture behavior of materials at high temperatures. It provides an introduction to creep and stress rupture tests, describing the three stages of creep curves and how applied stress and temperature affect creep behavior. Different deformation mechanisms at high temperatures are discussed, including dislocation glide/creep, diffusion creep, and grain boundary sliding. The document also covers topics such as structural changes during creep, superplasticity, and fracture modes at elevated temperatures.
Fatigue is the weakening of a material caused by repeatedly applied loads. It leads to premature failure under cyclic stresses or strains, similar to how humans experience fatigue from repetitive tasks. There are three stages of fatigue failure: crack initiation, crack propagation, and fracture. Many factors influence fatigue life, including surface condition, size, load type, temperature, and manufacturing variables. Empirical models incorporate factors like surface finish, size, load type, and temperature to adjust the expected fatigue life of a component based on these influential characteristics.
"Fracture Toughness I" is the first half of a 2-hour presentation on Fracture Mechanics by metallurgical expert Carl Ziegler of Stork Testing and Metallurgical Consulting , Houston, Texas. In this webinar, Mr. Ziegler will cover many aspects of Fracture Toughness, including theory, applications, specifications, testing methods, and the effects of various stresses, strains and environmental conditions on your materials.
Griffith proposed that brittle materials contain small cracks and flaws that concentrate stress enough to reach the theoretical strength at nominal stresses below theoretical values. For a crack to propagate, the decrease in elastic strain energy from crack growth must be equal to or greater than the increase in surface energy. Griffith established a criterion where the stress required for crack propagation is inversely proportional to the square root of the crack length. This theory provides an equation to calculate the maximum crack length possible without fracture given a material's surface energy, modulus of elasticity, and applied stress.
Brittle fracture occurs without plastic deformation through rapid crack propagation perpendicular to the applied tensile stress. Dislocation theories state that brittle fracture involves three stages: 1) plastic deformation from dislocation pile-up, 2) nucleation of micro-cracks from shear stress, and 3) micro-crack growth driven by stored elastic energy. Brittle fracture surfaces exhibit distinctive patterns without signs of plastic deformation, such as chevron markings in steel or fanlike ridges radiating from the crack origin. Crack propagation in brittle crystalline materials corresponds to successive breaking of atomic bonds along crystallographic planes, known as cleavage.
This document discusses the use of cohesive zone modeling to simulate fatigue crack growth and retardation. Cohesive zone models define cohesive stresses around a crack tip that are related to crack opening width. Crack propagation occurs when cohesive stresses reach a failure value. The models can account for material properties through a cohesive law. Finite element implementations use cohesive elements located at crack fronts. The models can simulate crack closure effects, wedge effects, and predict crack growth under various loading conditions like overloads through an unloading-reloading hysteresis. Cohesive theory provides a unified way to model long cracks under constant loading as well as short cracks and overloads.
Fracture mechanics CTOD Crack Tip Opening DisplacementDavalsab M.L
Fracture Mechanics .Whilst the Crack Tip Opening Displacement (CTOD) test was developed for the characterisation of metals it has also been used to determine the toughness of non-metallics such as weldable plastics.
The CTOD test is one such fracture toughness test that is used when some plastic deformation can occur prior to failure - this allows the tip of a crack to stretch and open, hence 'tip opening displacement
This document summarizes a master's thesis presentation on modeling deep girders supporting shear walls. The presentation introduces various analysis techniques for deep beams, including the strut-and-tie method, finite element analysis using VecTor2, and two parameter kinematic theory. Seven test beams with varying sizes, loading eccentricities are described to compare the predictions of failure load between VecTor2 and the other methods. The results show that VecTor2 predictions match well but the other methods are unconservative. Adjusting parameters in the two parameter kinematic theory improves predictions. Size effects are demonstrated through a scaled model analysis.
Welcome to International Journal of Engineering Research and Development (IJERD)IJERD Editor
call for paper 2012, hard copy of journal, research paper publishing, where to publish research paper,
journal publishing, how to publish research paper, Call For research paper, international journal, publishing a paper, IJERD, journal of science and technology, how to get a research paper published, publishing a paper, publishing of journal, publishing of research paper, reserach and review articles, IJERD Journal, How to publish your research paper, publish research paper, open access engineering journal, Engineering journal, Mathemetics journal, Physics journal, Chemistry journal, Computer Engineering, Computer Science journal, how to submit your paper, peer reviw journal, indexed journal, reserach and review articles, engineering journal, www.ijerd.com, research journals,
yahoo journals, bing journals, International Journal of Engineering Research and Development, google journals, hard copy of journal
This document discusses stress-strain curves and various material testing methods. It contains the following key points:
1. Creep testing involves applying a constant load to a material sample at high temperature and measuring deformation over time to evaluate materials performance. Fatigue testing subjects samples to repeated stresses to determine fatigue strength.
2. Stress-strain curves relate the stress and strain experienced by materials. They contain useful data like proportional limit, elastic limit, yield point, ultimate strength, and ductile vs. brittle fracture behavior.
3. True stress-strain diagrams account for changes in cross-sectional area during testing, while engineering stress-strain curves do not. Both are commonly used in design as long as strains remain
FRACTURE BEHAVIOUR OF NANOCOMPOSITES -FATIGUEArjun K Gopi
This document discusses the fracture and fatigue behavior of polymer nanocomposites. It notes that nanoparticles have higher specific surface areas than microparticles, which can improve stress transfer and that nanoparticles can be added at lower loadings while retaining properties of the neat polymer matrix. The document covers different types of fractures like brittle and ductile, and describes how the addition of nanoparticles up to 5 wt% can improve the fatigue resistance of polyamide nanocomposites by inhibiting crack propagation, but higher loadings may embrittle the material. TEM images show the differences in clay dispersion with varying nanoparticle content.
The document discusses the failure of a rolled slab due to improper cooling. Specifically:
1) A crack was found in the middle slab after air cooling, but not in the top or bottom slabs.
2) Analysis showed the middle slab cooled more slowly due to being sandwiched, allowing embrittling Ni4Mo phases to precipitate.
3) This embrittlement, combined with tensile stresses from the slab weight, caused the crack to form intergranularly in the middle slab. Proper cooling of each slab individually is the recommended solution.
CROSS-CORRELATION OF STRESSES IN THE TRAN REINFORCEMENT UNDER SHEAR LOAD AND ...IAEME Publication
The main aim of the present study is to give an answer to the question whether the transverse reinforcement, which is required for the shear resistance of columns, must be added to the one required for the cross section confinement, or it is possible for one to substitute the other. The superposition of these reinforcements is defended by the fact that the shear reinforcement results from the shear action, while the transverse reinforcement, required by the confinement, results from the axial compression of the section. The present study is experimental and uses strain gauges, in order to check the stresses of the transverse reinforcement. Useful conclusions are drawn.
Two 7075 aluminum samples were prepared and tested to determine their fracture toughness properties. A compact tension sample reached a maximum load of 4435 lbs before fracturing, yielding a KQ value of 89.1 ksi in1/2. However, this value was determined to be invalid for being KIC due to the ratio of maximum to critical load exceeding 1.1. A single edge notch bend sample fractured at 4295 lbs but its final crack length was too small to measure, and its KQ value of 33.1 ksi in1/2 was also found to not represent KIC. In summary, neither sample provided a valid measurement of plane strain fracture toughness KIC for the 7075 aluminum material
This document summarizes key parameters that can be determined from a true stress-true strain curve obtained from tensile testing of a material sample. These parameters include:
- True stress and true strain at maximum load, which represent the material's ultimate tensile strength and strain at necking.
- True fracture stress and true fracture strain, which represent the stress and strain at fracture after significant necking has occurred.
- True uniform strain, representing the strain up to maximum load before necking.
- True local necking strain, representing the additional strain from maximum load to fracture during necking.
- Strain hardening exponent and strength coefficient, materials constants that describe work hardening behavior and
Modified maximum tangential stress criterion for fracture behavior of zirconi...dentalid
The veneering porcelain sintered on zirconia is widely used in dental prostheses, but
repeated mechanical loadings may cause a fracture such as edge chipping or delamination.
In order to predict the crack initiation angle and fracture toughness of zirconia/veneer bilayered
components subjected to mixed mode loadings, the accuracy of a new and
traditional fracture criteria are investigated. A modified maximum tangential stress
criterion considering the effect of T-stress and critical distance theory is introduced, and
compared to three traditional fracture criteria. Comparisons to the recently published
fracture test data show that the traditional fracture criteria are not able to properly predict
the fracture initiation conditions in zirconia/veneer bi-material joints. The modified
maximum tangential stress criterion provides more accurate predictions of the experimental
results than the traditional fracture criteria
This document discusses fractography, which is the analysis of fracture surfaces. It begins by defining fractography and distinguishing between macrofractography and microfractography. Macrofractography examines fracture surfaces with the naked eye or low-power magnification and can reveal features like the fracture type, origin, and secondary cracks. Microfractography uses higher magnification microscopy to study details like dimple shapes that indicate the fracture mode. Examples are given of using scanning electron microscopes to analyze ductile and brittle fracture surfaces at the microscopic level.
This document summarizes key concepts regarding fatigue crack propagation. It discusses three stages of crack growth: (1) crack initiation, where microcracks form due to cyclic stresses; (2) crack propagation, where cracks grow according to Paris' law and form fatigue striations; and (3) final failure, where cracks rapidly grow unstable until catastrophic fracture. Critical factors like stress levels, number of cycles, and material properties are outlined. Paris' law and sigmoidal crack growth curves are also summarized.
Mumbai University.
Mechanical Engineering
SEM III
Material Technology
MOdule 2.1
Fracture:
Definition and types of facture, Brittle fracture: Griffith’s theory of fracture, Orowan’s modification, Dislocation theory of fracture, Critical stress and crack propagation velocity for brittle fracture, Ductile fracture: Notch effect on fracture, Fracture toughness, Ductility transition, Definition and significance
The Crack Pattern Of R.C Beams Under LoadingAhmed Abdullah
1. A reinforced concrete beam was tested under static two-point concentrated loading to study the effect of different web reinforcement arrangements on ultimate shear strength.
2. It was observed that diagonal cracks developed first in deeper beams while flexural cracks developed first in shallower beams with sufficient reinforcement.
3. The crack pattern and failure mode were similar across all test beams despite variations in web reinforcement, with diagonal cracks forming first in deeper beams.
The document discusses creep and stress rupture behavior of materials at high temperatures. It provides an introduction to creep and stress rupture tests, describing the three stages of creep curves and how applied stress and temperature affect creep behavior. Different deformation mechanisms at high temperatures are discussed, including dislocation glide/creep, diffusion creep, and grain boundary sliding. The document also covers topics such as structural changes during creep, superplasticity, and fracture modes at elevated temperatures.
Fatigue is the weakening of a material caused by repeatedly applied loads. It leads to premature failure under cyclic stresses or strains, similar to how humans experience fatigue from repetitive tasks. There are three stages of fatigue failure: crack initiation, crack propagation, and fracture. Many factors influence fatigue life, including surface condition, size, load type, temperature, and manufacturing variables. Empirical models incorporate factors like surface finish, size, load type, and temperature to adjust the expected fatigue life of a component based on these influential characteristics.
"Fracture Toughness I" is the first half of a 2-hour presentation on Fracture Mechanics by metallurgical expert Carl Ziegler of Stork Testing and Metallurgical Consulting , Houston, Texas. In this webinar, Mr. Ziegler will cover many aspects of Fracture Toughness, including theory, applications, specifications, testing methods, and the effects of various stresses, strains and environmental conditions on your materials.
Griffith proposed that brittle materials contain small cracks and flaws that concentrate stress enough to reach the theoretical strength at nominal stresses below theoretical values. For a crack to propagate, the decrease in elastic strain energy from crack growth must be equal to or greater than the increase in surface energy. Griffith established a criterion where the stress required for crack propagation is inversely proportional to the square root of the crack length. This theory provides an equation to calculate the maximum crack length possible without fracture given a material's surface energy, modulus of elasticity, and applied stress.
Brittle fracture occurs without plastic deformation through rapid crack propagation perpendicular to the applied tensile stress. Dislocation theories state that brittle fracture involves three stages: 1) plastic deformation from dislocation pile-up, 2) nucleation of micro-cracks from shear stress, and 3) micro-crack growth driven by stored elastic energy. Brittle fracture surfaces exhibit distinctive patterns without signs of plastic deformation, such as chevron markings in steel or fanlike ridges radiating from the crack origin. Crack propagation in brittle crystalline materials corresponds to successive breaking of atomic bonds along crystallographic planes, known as cleavage.
This document discusses the use of cohesive zone modeling to simulate fatigue crack growth and retardation. Cohesive zone models define cohesive stresses around a crack tip that are related to crack opening width. Crack propagation occurs when cohesive stresses reach a failure value. The models can account for material properties through a cohesive law. Finite element implementations use cohesive elements located at crack fronts. The models can simulate crack closure effects, wedge effects, and predict crack growth under various loading conditions like overloads through an unloading-reloading hysteresis. Cohesive theory provides a unified way to model long cracks under constant loading as well as short cracks and overloads.
Fracture mechanics CTOD Crack Tip Opening DisplacementDavalsab M.L
Fracture Mechanics .Whilst the Crack Tip Opening Displacement (CTOD) test was developed for the characterisation of metals it has also been used to determine the toughness of non-metallics such as weldable plastics.
The CTOD test is one such fracture toughness test that is used when some plastic deformation can occur prior to failure - this allows the tip of a crack to stretch and open, hence 'tip opening displacement
This document summarizes a master's thesis presentation on modeling deep girders supporting shear walls. The presentation introduces various analysis techniques for deep beams, including the strut-and-tie method, finite element analysis using VecTor2, and two parameter kinematic theory. Seven test beams with varying sizes, loading eccentricities are described to compare the predictions of failure load between VecTor2 and the other methods. The results show that VecTor2 predictions match well but the other methods are unconservative. Adjusting parameters in the two parameter kinematic theory improves predictions. Size effects are demonstrated through a scaled model analysis.
Welcome to International Journal of Engineering Research and Development (IJERD)IJERD Editor
call for paper 2012, hard copy of journal, research paper publishing, where to publish research paper,
journal publishing, how to publish research paper, Call For research paper, international journal, publishing a paper, IJERD, journal of science and technology, how to get a research paper published, publishing a paper, publishing of journal, publishing of research paper, reserach and review articles, IJERD Journal, How to publish your research paper, publish research paper, open access engineering journal, Engineering journal, Mathemetics journal, Physics journal, Chemistry journal, Computer Engineering, Computer Science journal, how to submit your paper, peer reviw journal, indexed journal, reserach and review articles, engineering journal, www.ijerd.com, research journals,
yahoo journals, bing journals, International Journal of Engineering Research and Development, google journals, hard copy of journal
This document discusses stress-strain curves and various material testing methods. It contains the following key points:
1. Creep testing involves applying a constant load to a material sample at high temperature and measuring deformation over time to evaluate materials performance. Fatigue testing subjects samples to repeated stresses to determine fatigue strength.
2. Stress-strain curves relate the stress and strain experienced by materials. They contain useful data like proportional limit, elastic limit, yield point, ultimate strength, and ductile vs. brittle fracture behavior.
3. True stress-strain diagrams account for changes in cross-sectional area during testing, while engineering stress-strain curves do not. Both are commonly used in design as long as strains remain
This document discusses stress-strain curves and various material testing methods. It contains the following key points:
1. Creep testing involves applying a constant load to a material sample at high temperature and measuring deformation over time to evaluate materials performance. Fatigue testing subjects samples to repeated stresses to determine fatigue strength.
2. Stress-strain curves relate the stress and strain experienced by materials. They contain useful data like proportional limit, elastic limit, yield point, ultimate strength, and ductile vs. brittle fracture behavior.
3. True stress-strain curves account for changes in cross-sectional area during testing, providing a more accurate representation of material behavior, though engineering stress-strain curves are sufficient for most design
This document summarizes key concepts related to mechanical failure of materials. It discusses how cracks form and propagate, leading to brittle or ductile failure. Factors like stress concentration, loading rate, temperature and microstructure affect failure behavior. The main failure modes covered are fracture, fatigue and creep. Fracture toughness and impact testing help quantify a material's resistance to failure when cracks are present. The ductile to brittle transition temperature is also explained.
This document discusses various failure modes in materials including cracks, fracture, fatigue, and the ductile to brittle transition. It addresses how cracks form and propagate, how fracture resistance is quantified, and factors that influence failure such as loading rate, temperature, and stress concentration. Ductile fracture involves plastic deformation while brittle fracture does not. Fatigue failure can occur at stresses lower than the material strength from cyclic loading. The ductile to brittle transition temperature depends on the material. Fracture toughness measures resistance to crack propagation.
This document discusses various mechanical properties that are important for selecting materials for structural components. It describes different types of mechanical tests like tension, compression, torsion, bending, impact and fatigue tests that are conducted on metal specimens to determine properties like strength, ductility and toughness. Specifically, it outlines the process for a uniaxial tension test including the equipment used, steps to conduct the test, and how to analyze the stress-strain diagram produced. It also discusses factors that influence mechanical properties like temperature, notches, grain size and hardness tests.
This document discusses various topics related to mechanical design including types of loads and stresses, theories of failure, stress concentration, fatigue, creep, and design of cotter joints. It defines stress and strain, describes different types of loading and the resulting stresses. It discusses various theories of failure for predicting failure under different stress conditions. It also covers stress concentration, factors affecting it, and methods to reduce it. Fatigue behavior is described using S-N curves and endurance limits. Creep behavior and different creep stages are outlined. Design of cotter joints is explained focusing on its components and advantages.
The document discusses two main mechanisms of plastic deformation: slip and twinning. Slip occurs when one part of a crystal moves over another along specific crystallographic planes and directions. Twinning results when a portion of a crystal takes on a symmetrical orientation to the rest of the crystal, dividing it into two mirrored regions. Factors like external loads, crystal structure, and orientation influence whether slip or twinning occurs. The document also covers different types of material failure like ductile fracture, brittle fracture, creep, and fatigue.
This document summarizes material failure and fracture. It discusses the different ways components can fail, including excessive deformation, fracture, corrosion, and degradation of properties. It describes the three main ways structural elements and machine elements can fail: excessive elastic deformation, plastic deformation/yielding, and fracture. Ductile and brittle fracture are also summarized. Ductile fracture involves plastic deformation and leaves a cup-and-cone shaped surface, while brittle fracture involves little deformation and leaves a smooth, bright surface. Microscopic examination of fracture surfaces can provide details about the fracture mechanism.
Module 1 Behaviour of RC beams in Shear and TorsionVVIETCIVIL
This document summarizes key concepts related to shear and torsion behavior in reinforced concrete beams. It discusses modes of cracking in shear, shear failure modes, critical sections for shear design, the influence of axial forces and longitudinal reinforcement on shear strength, and shear transfer mechanisms. The key points covered include web shear cracking, flexure-shear cracking, diagonal tension failure, shear-compression and shear-tension failures, and the four mechanisms that contribute to shear transfer: aggregate interlock, dowel action, stirrups, and the interaction between axial compression and shear strength.
The document discusses plastic deformation in crystalline materials. It describes how plastic deformation occurs primarily through slip mediated by dislocation motion. Other mechanisms like twinning and creep can also contribute to plastic deformation under certain conditions. The uniaxial tension test is discussed as a common experimental technique to evaluate plastic deformation behavior. True stress-strain curves are preferred over engineering stress-strain curves for quantitative analysis since they account for changes in cross-sectional area during deformation. Key regions of the stress-strain curve are also outlined, including the elastic portion, yield point, strain hardening region, and necking/fracture points.
The document discusses plastic deformation in crystalline materials. It describes how plastic deformation occurs primarily through slip mediated by dislocation motion. Other mechanisms like twinning and creep can also contribute to plastic deformation under certain conditions. The uniaxial tension test is discussed as a common experimental technique to evaluate plastic deformation behavior. True stress-strain curves are preferred over engineering stress-strain as they account for changes in cross-sectional area during deformation. Key regions of the stress-strain curve are described including the elastic portion, yield point, strain hardening region, necking onset, and fracture.
Fatigue is a type of failure that occurs in structures subjected to repeatedly applied loads, such as bridges and aircraft components. It can cause failure at stress levels lower than the material's static strength. Fatigue is responsible for approximately 90% of all metallic failures and occurs suddenly without warning. Fatigue failure is brittle-like and involves crack initiation and propagation. The fatigue behavior of materials is characterized by S-N curves, which relate the cyclic stress amplitude to the number of cycles to failure. Some materials exhibit a fatigue limit below which failure will not occur, while others do not have a fatigue limit. Surface treatments like shot peening can improve fatigue resistance by inducing compressive stresses near the surface.
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
The document discusses stress-strain curves, which plot the stress and strain of a material sample under load. It describes the typical stress-strain behavior of ductile materials like steel and brittle materials like concrete. For ductile materials, the curve shows an elastic region, yield point, strain hardening region, and ultimate strength before failure. The yield point marks the transition between elastic and plastic deformation. The document also discusses factors that influence a material's yield stress, such as temperature and strain rate, and implications for structural engineering like reduced buckling strength after yielding.
1. The document discusses fatigue life estimation and fatigue crack initiation. It covers how fatigue occurs through repeated loading and unloading causing microscopic cracks.
2. Fatigue life is estimated using S-N curves which plot stress versus cycles to failure. The main steps in fatigue life estimation using S-N curves are also outlined.
3. Fatigue crack initiation involves two stages - micro cracks forming and growing (Stage I) and mechanically small cracks propagating (Stage II). The mechanism and factors influencing fatigue crack initiation are described.
- Fracture is the separation of an object into pieces due to stress. There are two main types: ductile fracture and brittle fracture.
- Ductile fracture involves plastic deformation and occurs through processes like necking and the formation and coalescence of microvoids. It results in a cup-and-cone pattern. Brittle fracture occurs suddenly without plastic deformation.
- Fracture mechanics studies how cracks propagate in materials. The Griffith theory and models like the Mohr-Coulomb criterion describe how stresses lead to fracture based on factors like crack size and material properties.
Experimental Evaluation of the Effect of Thread Angle on the Fatigue Life of ...IOSR Journals
Abstract : The present work is concerned with fatigue strength, obtained by plotting the S-N Curves for
determining the fatigue life of various thread geometries of bolts under cyclic loading. The stress equations
obtained from Majzoobi are being used for calculations of core stress produced due to cyclic loading,
which is being carried usually by the first thread of the bolt. The higher stress concentration occurs in the root
of first threads.The experimental work has been carried out for five different thread profiles of varying flank
angles, having six samples of each profile. The fatigue testing on each profile has been performed under cyclic
loading, in order to obtain the number of cycles to failure of a particular specimen. The results obtained
experimentally have been compared with the work of Gane . Finally the work is used to obtain the failure life of
bolts, which means which thread profile has higher fatigue life or simply higher strength to failure. As strength
is of direct use to the designer regarding the safety of structures.
This technical article discusses fatigue striations and the practice of counting striations to obtain information about fatigue failures. It begins by providing background on fatigue and explaining that counting striations can provide insights into loading conditions, time to failure, and failure events. The article then discusses the challenges and accuracy of striation counting. It describes different types of loading conditions and how they impact striation patterns. Specifically, it explains that constant amplitude loading produces evenly spaced striations while variable loading produces randomly spaced striations. The article concludes by noting that striation counting remains the best way to confirm fatigue but has limitations in accuracy.
This document discusses the mechanical properties of materials. It defines mechanical properties as how materials behave when subjected to stresses and strains from applied forces. It explains different types of loading like tension, compression, and shear that materials can experience. It also defines concepts like stress, strain, elastic deformation, plastic deformation, and viscous deformation. Different material behaviors are described like elastic, plastic, elastoplastic, and viscoelastic. The document also discusses properties such as modulus of elasticity, Poisson's ratio, yield strength, ductility, toughness, resilience, hardness, and factors of safety in material design. Testing methods for mechanical properties and examples of stress-strain curves are provided.
The document discusses atomic structure and bonding. It covers the following key points in 3 sentences:
Atomic structure consists of electrons, protons, and neutrons, with electrons orbiting the nucleus. Elements are made of one type of atom, and molecules form when two or more atoms bond together through ionic, covalent, or metallic bonding. Ionic bonding occurs through electron transfer between atoms, covalent bonding involves electron sharing, and metallic bonding results from delocalized electrons interacting with positive ion cores.
The document discusses the history of materials used by human civilization and the development of materials science and engineering. It describes how early civilizations progressed from the Stone Age to the Bronze Age to the Iron Age based on their ability to produce and use increasingly advanced materials. More recently, the development of advanced materials like ceramics, polymers, composites, and semiconductors has driven technological progress. The core components of materials science are described as structure, properties, processing, and performance, and how they interrelate.
The document discusses the preparation of biodiesel from animal fat through transesterification. Specific objectives include processing and characterizing the animal fat and biodiesel. Biodiesel is prepared using a base catalyst method with KOH and methanol or an acid catalyst method with H2SO4 and methanol. The biodiesel is then characterized by testing properties such as viscosity, moisture content, ash content, boiling point, and cetane number. Comparing biodiesel properties to pure diesel and testing blends is also discussed. The methodology outlines animal fat processing, biodiesel preparation methods, and characterizing both the animal fat and resulting biodiesel.
This document provides an overview of technical drawing, including:
1. It defines technical drawing as a communication method that uses lines, symbols, dimensions, and notations to accurately describe objects.
2. It distinguishes technical drawing from artistic drawing, noting that technical drawing is used to convey precise design information while artistic drawing expresses ideas.
3. It discusses the different types of technical drawings like instrument drawings, computer-aided drawings, sketches, details drawings, assembly drawings, and pictorial drawings.
Coupling refers to the process of connecting two shafts together to transmit power or motion. There are different types of couplings used depending on the application and needs, including rigid couplings that have zero clearance between connected parts and flexible couplings that can accommodate some misalignment. Proper selection and installation of the correct coupling is important to ensure efficient and reliable power transmission without damage to equipment.
The document discusses sectional views in engineering drawings. Sectional views reveal the internal features of an object by imagining a cutting plane passes through it. There are different types of section views such as full section, half section, and broken-out section views. Section lines are used to indicate the cut surfaces and come in standard patterns for different materials. Dimensioning rules are similar to normal views but use one-sided dimension lines for half sections. Aligned sections rotate features about an axis so internal geometry is clearer.
The document discusses auxiliary views in technical drawings. It begins by defining auxiliary views as orthographic projections of angled surfaces that appear foreshortened in standard multi-view drawings. It then explains that auxiliary views are used to show the true size and shape of angled surfaces. The document provides steps for creating auxiliary views, including determining the dimension to show, drawing construction lines, and projecting points perpendicular from the reference view. It distinguishes between primary, secondary, partial, and half auxiliary views.
The document discusses various types of technical drawings including axonometric projections, oblique projections, and isometric drawings. It explains the differences between axonometric, oblique, and isometric projections. The key steps for creating isometric sketches from actual objects and multi-view drawings are outlined, including positioning the object, defining axes, adding details, and darkening visible lines. Guidelines for orienting complex objects in isometric sketches are also provided.
Orthographic projection is a technique used to create multi-view drawings. It involves projecting lines perpendicular from an object to projection planes to create two-dimensional views. A multi-view drawing shows two or more views of a three-dimensional object. Standard views include the top, front, and side views. Additional views are included as needed to fully describe the object's shape and dimensions.
This document discusses different types of projections used in engineering graphics to represent 3D objects in 2D. It describes projection as mapping a 3D space onto a 2D plane. There are two main types of projections: parallel projections and perspective projections. Parallel projections preserve relationships between features, while perspective projections provide a view similar to human vision but can distort sizes and shapes. Common parallel projections discussed are multi-view, oblique, and axonometric projections, while perspective projections are classified as one-point, two-point, or three-point based on the viewpoint.
The document provides an overview of engineering drawings and graphic communication. It defines graphic communication and discusses different types of drawings including freehand sketches, instrument drawings, and computer-aided drawings. It explains the key differences between artistic and technical drawings. Technical drawings are used to clearly convey design information to allow objects to be manufactured. The document also outlines various drawing elements, standards, scales, lines types, and common drawing tools used to create precise technical drawings.
ACEP Magazine edition 4th launched on 05.06.2024Rahul
This document provides information about the third edition of the magazine "Sthapatya" published by the Association of Civil Engineers (Practicing) Aurangabad. It includes messages from current and past presidents of ACEP, memories and photos from past ACEP events, information on life time achievement awards given by ACEP, and a technical article on concrete maintenance, repairs and strengthening. The document highlights activities of ACEP and provides a technical educational article for members.
A review on techniques and modelling methodologies used for checking electrom...nooriasukmaningtyas
The proper function of the integrated circuit (IC) in an inhibiting electromagnetic environment has always been a serious concern throughout the decades of revolution in the world of electronics, from disjunct devices to today’s integrated circuit technology, where billions of transistors are combined on a single chip. The automotive industry and smart vehicles in particular, are confronting design issues such as being prone to electromagnetic interference (EMI). Electronic control devices calculate incorrect outputs because of EMI and sensors give misleading values which can prove fatal in case of automotives. In this paper, the authors have non exhaustively tried to review research work concerned with the investigation of EMI in ICs and prediction of this EMI using various modelling methodologies and measurement setups.
KuberTENes Birthday Bash Guadalajara - K8sGPT first impressionsVictor Morales
K8sGPT is a tool that analyzes and diagnoses Kubernetes clusters. This presentation was used to share the requirements and dependencies to deploy K8sGPT in a local environment.
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.
Electric vehicle and photovoltaic advanced roles in enhancing the financial p...IJECEIAES
Climate change's impact on the planet forced the United Nations and governments to promote green energies and electric transportation. The deployments of photovoltaic (PV) and electric vehicle (EV) systems gained stronger momentum due to their numerous advantages over fossil fuel types. The advantages go beyond sustainability to reach financial support and stability. The work in this paper introduces the hybrid system between PV and EV to support industrial and commercial plants. This paper covers the theoretical framework of the proposed hybrid system including the required equation to complete the cost analysis when PV and EV are present. In addition, the proposed design diagram which sets the priorities and requirements of the system is presented. The proposed approach allows setup to advance their power stability, especially during power outages. The presented information supports researchers and plant owners to complete the necessary analysis while promoting the deployment of clean energy. The result of a case study that represents a dairy milk farmer supports the theoretical works and highlights its advanced benefits to existing plants. The short return on investment of the proposed approach supports the paper's novelty approach for the sustainable electrical system. In addition, the proposed system allows for an isolated power setup without the need for a transmission line which enhances the safety of the electrical network
CHINA’S GEO-ECONOMIC OUTREACH IN CENTRAL ASIAN COUNTRIES AND FUTURE PROSPECTjpsjournal1
The rivalry between prominent international actors for dominance over Central Asia's hydrocarbon
reserves and the ancient silk trade route, along with China's diplomatic endeavours in the area, has been
referred to as the "New Great Game." This research centres on the power struggle, considering
geopolitical, geostrategic, and geoeconomic variables. Topics including trade, political hegemony, oil
politics, and conventional and nontraditional security are all explored and explained by the researcher.
Using Mackinder's Heartland, Spykman Rimland, and Hegemonic Stability theories, examines China's role
in Central Asia. This study adheres to the empirical epistemological method and has taken care of
objectivity. This study analyze primary and secondary research documents critically to elaborate role of
china’s geo economic outreach in central Asian countries and its future prospect. China is thriving in trade,
pipeline politics, and winning states, according to this study, thanks to important instruments like the
Shanghai Cooperation Organisation and the Belt and Road Economic Initiative. According to this study,
China is seeing significant success in commerce, pipeline politics, and gaining influence on other
governments. This success may be attributed to the effective utilisation of key tools such as the Shanghai
Cooperation Organisation and the Belt and Road Economic Initiative.
Advanced control scheme of doubly fed induction generator for wind turbine us...IJECEIAES
This paper describes a speed control device for generating electrical energy on an electricity network based on the doubly fed induction generator (DFIG) used for wind power conversion systems. At first, a double-fed induction generator model was constructed. A control law is formulated to govern the flow of energy between the stator of a DFIG and the energy network using three types of controllers: proportional integral (PI), sliding mode controller (SMC) and second order sliding mode controller (SOSMC). Their different results in terms of power reference tracking, reaction to unexpected speed fluctuations, sensitivity to perturbations, and resilience against machine parameter alterations are compared. MATLAB/Simulink was used to conduct the simulations for the preceding study. Multiple simulations have shown very satisfying results, and the investigations demonstrate the efficacy and power-enhancing capabilities of the suggested control system.
Comparative analysis between traditional aquaponics and reconstructed aquapon...bijceesjournal
The aquaponic system of planting is a method that does not require soil usage. It is a method that only needs water, fish, lava rocks (a substitute for soil), and plants. Aquaponic systems are sustainable and environmentally friendly. Its use not only helps to plant in small spaces but also helps reduce artificial chemical use and minimizes excess water use, as aquaponics consumes 90% less water than soil-based gardening. The study applied a descriptive and experimental design to assess and compare conventional and reconstructed aquaponic methods for reproducing tomatoes. The researchers created an observation checklist to determine the significant factors of the study. The study aims to determine the significant difference between traditional aquaponics and reconstructed aquaponics systems propagating tomatoes in terms of height, weight, girth, and number of fruits. The reconstructed aquaponics system’s higher growth yield results in a much more nourished crop than the traditional aquaponics system. It is superior in its number of fruits, height, weight, and girth measurement. Moreover, the reconstructed aquaponics system is proven to eliminate all the hindrances present in the traditional aquaponics system, which are overcrowding of fish, algae growth, pest problems, contaminated water, and dead fish.
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.
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DEEP LEARNING FOR SMART GRID INTRUSION DETECTION: A HYBRID CNN-LSTM-BASED MODELgerogepatton
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solve this issue, this paper develops a hybrid Deep Learning (DL) model specifically designed for intrusion
detection in smart grids. The proposed approach is a combination of the Convolutional Neural Network
(CNN) and the Long-Short-Term Memory algorithms (LSTM). We employed a recent intrusion detection
dataset (DNP3), which focuses on unauthorized commands and Denial of Service (DoS) cyberattacks, to
train and test our model. The results of our experiments show that our CNN-LSTM method is much better
at finding smart grid intrusions than other deep learning algorithms used for classification. In addition,
our proposed approach improves accuracy, precision, recall, and F1 score, achieving a high detection
accuracy rate of 99.50%.
2. The failure of engineering materials is almost always an undesirable
event for several reasons; these include human lives that are put in
jeopardy, economic losses, and the interference with the availability
of products and services.
Even though the causes of failure and the behavior of materials may
be known, prevention of failures is difficult to guarantee
The usual causes are improper materials selection and processing and
inadequate design of the component or its misuse.
3. Simple fracture is the separation of a body into two or more pieces in
response to an imposed stress that is static (i.e., constant or slowly
changing with time) and at temperatures that are low relative to the
melting temperature of the material.
The applied stress may be tensile, compressive, shear, or torsional
Any fracture process involves two steps—crack formation and
propagation—in response to an imposed stress.
The mode of fracture is highly dependent on the mechanism of crack
propagation.
Ductile fracture is characterized by extensive plastic deformation in
the vicinity of an advancing crack.
4. Ductile fracture surfaces will have their own distinctive
features on both macroscopic and microscopic levels.
Figure 8.1 shows schematic representations for two
characteristic macroscopic fracture profiles.
The configuration shown in Figure 8.1a is found for
extremely soft metals, such as pure gold and lead at room
temperature, and other metals, polymers, and inorganic
glasses at elevated temperatures.
These highly ductile materials neck down to a point fracture,
showing virtually 100% reduction in area.
5. Brittle fracture takes place without any appreciable deformation, and
by rapid crack propagation.
The direction of crack motion is very nearly perpendicular to the
direction of the applied tensile stress and yields a relatively flat
fracture surface, as indicated in Figure 8.1c.
Fracture surfaces of materials that failed in a brittle manner will have
their own distinctive patterns; any signs of gross plastic deformation
will be absent.
For example, in some steel pieces, a series of V-shaped “chevron”
markings may form near the center of the fracture cross section that
point back toward the crack initiation site (Figure 8.5a).
Other brittle fracture surfaces contain lines or ridges that radiate from
the origin of the crack in a fanlike pattern (Figure 8.5b).
6. For most brittle crystalline materials, crack
propagation corresponds to the successive and
repeated breaking of atomic bonds along
specific crystallographic planes (Figure 8.6a);
such a process is termed cleavage.
This type of fracture is said to be
transgranular (or transcrystalline), because
the fracture cracks pass through the grains.
Figure 8.6 (a) Schematic cross-section
profile showing crack propagation
through the interior of grains for
transgranular fracture.
(b) Scanning electron fractograph of
ductile cast iron showing a transgranular
fracture surface. Magnification unknown.
7. STRESS CONCENTRATION
1. The measured fracture strengths for most brittle materials are
significantly lower than those predicted by theoretical calculations
based on atomic bonding energies.
2. This discrepancy is explained by the presence of very small,
microscopic flaws or cracks that always exist under normal conditions
at the surface and within the interior of a body of material.
3. These flaws are a detriment to the fracture strength because an
applied stress may be amplified or concentrated at the tip, the
magnitude of this amplification depending on crack orientation and
geometry.
4. This phenomenon is demonstrated in Figure 8.8, a stress profile across
a cross section containing an internal crack.
8. As indicated by this profile, the magnitude of this localized stress
diminishes with distance away from the crack tip.
At positions far removed, the stress is just the nominal stress or the
applied load divided by the specimen cross-sectional area
(perpendicular to this load).
Due to their ability to amplify an applied stress in their locale, these
flaws are sometimes called stress raisers.
If it is assumed that a crack is similar to an elliptical hole through a
plate, and is oriented perpendicular to the applied stress, the
maximum stress,
the radius of curvature of the crack tip
a represents the length of a surface crack
9. For a relatively long microcrack that has a small tip
radius of curvature, the factormaybeverylarge
10. All brittle materials contain a population of small cracks and flaws that have a
variety of sizes, geometries, and orientations.
When the magnitude of a tensile stress at the tip of one of these flaws exceeds
the value of this critical stress, a crack forms and then propagates, which
results in fracture.
11.
12. Furthermore, using fracture mechanical principles, an
expression has been developed that relates this critical stress
for crack propogation бc and crack length (a) as
In this expression Kc is the fracture toughness, a property that is a measure
of a material’s resistance to brittle fracture when a crack is present.
Y is a dimensionless parameter or function that depends on both crack and
specimen sizes and geometries, as well as the manner of load application
13. Relative to this Y parameter, for planar specimens containing cracks
that are much shorter than the specimen width, Y has a value of
approximately unity.
For example, for a plate of infinite width having a through-thickness
crack (Figure 8.9a) Y= 1.0 , whereas for a plate of semi-infinite width
containing an edge crack of length a (Figure 8.9b), Y is approx. equal
to 1.1.
Mathematical expressions for Y have been determined for a variety of
crack-specimen geometries; these expressions are often relatively
complex.
For relatively thin specimens, the value of will depend on specimen
thickness.
However, when specimen thickness is much greater than the crack
dimensions,Kc becomes independent of thickness; under these
conditions a condition of PLANE STRAIN exists.
14. By plane strain we mean that when a load operates on a
crack in the manner represented in Figure 8.9a, there is no
strain component perpendicular to the front and back faces.
The Kc value for this thick specimen situation is known as the
PLANE STRAIN Fracture toughness KIC
15. Prior to the advent of fracture mechanics as a scientific discipline,
impact testing techniques were established so as to ascertain the
fracture characteristics of materials.
It was realized that the results of laboratory tensile tests could not be
extrapolated to predict fracture behavior;
For example, under some circumstances normally ductile metals
fracture abruptly and with very little plastic deformation.
Impact test conditions were chosen to represent those most severe
relative to the potential for fracture—namely, (1) deformation at a
relatively low temperature, (2) a high strain rate (i.e., rate of
deformation), and (3) a triaxial stress state (which may be introduced
by the presence of a notch).
17. For both Charpy and Izod, the specimen is in the shape of a bar of square cross
section, into which a V-notch is machined (Figure 8.12a).
The apparatus for making V-notch impact tests is illustrated schematically in
Figure 8.12b.
The load is applied as an impact blow from a weighted pendulum hammer that
is released from a cocked position at a fixed height h.
The specimen is positioned at the base as shown.
Upon release, a knife edge mounted on the pendulum strikes and fractures the
specimen at the notch, which acts as a point of stress concentration for this
high-velocity impact blow.
The pendulum continues its swing, rising to a maximum height which is lower
than h. The energy absorption, computed from the difference between h and
h’ is a measure of the impact energy.
18. One of the primary functions of Charpy and Izod tests is to determine
whether or not a material experiences a ductile to brittle transition with
decreasing temperature and, if so, the range of temperatures over which it
occurs.
The ductile-to-brittle transition is related to the temperature dependence
of the measured impact energy absorption.
This transition is represented for a steel by curve A in figure shown
At higher temperatures the CVN energy is relatively large, in correlation
with a ductile mode of fracture.
As the temperature is lowered, the impact energy drops suddenly over a
relatively narrow temperature range, below which the energy has a
constant but small value; that is, the mode of fracture is brittle.
19. Fatigue is a form of failure that occurs in structures subjected to
dynamic and fluctuating stresses (e.g., bridges, aircraft, and machine
components).
Under these circumstances it is possible for failure to occur at a stress
level considerably lower than the tensile or yield strength for a static
load.
The term “fatigue” is used because this type of failure normally occurs
after a lengthy period of repeated stress or strain cycling.
Fatigue is important inasmuch as it is the single largest cause of failure
in metals, estimated to comprise approximately 90% of all metallic
failures; polymers and ceramics (except for glasses) are also
susceptible to this type of failure.
20. Furthermore, fatigue is catastrophic and insidious, occurring very suddenly and
without warning.
Fatigue failure is brittle like in nature even in normally ductile metals, in that
there is very little, if any, gross plastic deformation associated with failure.
The process occurs by the initiation and propagation of cracks, and ordinarily
the fracture surface is perpendicular to the direction of an applied tensile
stress.
21. The applied stress may be axial (tension-compression), flexural
(bending), or torsional (twisting) in nature.
In general, three different fluctuating stress–time modes are possible.
One is represented schematically by a regular and sinusoidal time
dependence in Figure 8.17a, wherein the amplitude is symmetrical
about a mean zero stress level,
22.
23.
24. As with other mechanical characteristics, the fatigue properties of
materials can be determined from laboratory simulation tests.
A test apparatus should be designed to duplicate as nearly as possible
the service stress conditions (stress level, time frequency, stress
pattern, etc.).
A schematic diagram of a rotating-bending test apparatus, commonly
used for fatigue testing, is shown in Figure 8.18; the compression and
tensile stresses are imposed on the specimen as it is simultaneously
bent and rotated.
Tests are also frequently conducted using an alternating uniaxial
tension-compression stress cycle.
25. A series of tests are commenced by subjecting a specimen to the stress cycling
at a relatively large maximum stress amplitude (бmax), usually on the order of
two thirds of the static tensile strength; the number of cycles to failure is
counted.
This procedure is repeated on other specimens at progressively decreasing
maximum stress amplitudes
Data are plotted as stress S versus the logarithm of the number N of cycles to
failure for each of the specimens.
26.
27. Two distinct types of S–N behavior are observed, which are
represented schematically in Figure 8.19.
As these plots indicate, the higher the magnitude of the stress, the
smaller the number of cycles the material is capable of sustaining
before failure.
For some ferrous (iron base) and titanium alloys, the S–N curve (Figure
8.19a) becomes horizontal at higher N values; or there is a limiting
stress level, called the fatigue limit (also sometimes the endurance
limit), below which fatigue failure will not occur.
28. Most nonferrous alloys (e.g., aluminum, copper, magnesium) do not
have a fatigue limit, in that the S–N curve continues its downward
trend at increasingly greater N values (Figure 8.19b).
Thus, fatigue will ultimately occur regardless of the magnitude of
the stress.
For these materials, the fatigue response is specified as fatigue
strength, which is defined as the stress level at which failure will
occur for some specified number of cycles (e.g., cycles).
Another important parameter that characterizes a material’s fatigue
behavior is fatigue life Nf
It is the number of cycles to cause failure at a specified stress level, as
taken from the S–N plot (Figure 8.19b).
31. The process of fatigue failure is characterized by three distinct steps:
(1) crack initiation, wherein a small crack forms at some point of high
stress concentration;
(2) crack propagation, during which this crack advances incrementally
with each stress cycle; and
(3) final failure, which occurs very rapidly once the advancing crack
has reached a critical size.
Cracks associated with fatigue failure almost always initiate (or
nucleate) on the surface of a component at some point of stress
concentration.
Crack nucleation sites include surface scratches, sharp fillets,
keyways, threads, dents, and the like.
32. In addition, cyclic loading can produce microscopic surface
discontinuities resulting from dislocation slip steps that may also act
as stress raisers, and therefore as crack initiation sites.
The region of a fracture surface that formed during the crack
propagation step may be characterized by two types of markings
termed beachmarks and striations.
Beachmarks (sometimes also called “clamshell marks”) are of
macroscopic dimensions (Figure 8.21), and may be observed with the
unaided eye
Fatigue striations are microscopic in size and subject to observation
with the electron microscope (either TEM or SEM)
33. Mean stress level,
Geometrical design,
Surface effects,
Metallurgical variables, as well as the environment
34. Thermal fatigue is normally induced at elevated temperatures by
fluctuating thermal stresses; mechanical stresses from an external
source need not be present.
The origin of these thermal stresses is the restraint to the dimensional
expansion and/or contraction that would normally occur in a structural
member with variations in temperature.
The magnitude of a thermal stress developed by a temperature change
is dependent on the coefficient of thermal expansion and the modulus
of elasticity E according to
Failure that occurs by the simultaneous action of a cyclic stress and chemical attack is
termed corrosion fatigue.
35. Materials are often placed in service at elevated temperatures and
exposed to static mechanical stresses (e.g., turbine rotors in jet
engines and steam generators that experience centrifugal stresses, and
high-pressure steam lines). Deformation under such circumstances is
termed creep.
It is observed in all materials types; for metals it becomes important
only for temperatures greater than about 0.4Tm
Where Tm – Absolute Melting Temperature
36. A typical creep test consists of subjecting a specimen to a constant
load or stress while maintaining the temperature constant;
deformation or strain is measured and plotted as a function of elapsed
time.
Most tests are the constant load type, which yield information of an
engineering nature; constant stress tests are employed toprovide a
better understanding of the mechanisms of creep.
Figure 8.28 is a schematic representation of the typical constant load
creep behavior of metals.
Upon application of the load there is an instantaneous deformation, as
indicated in the figure, which is mostly elastic.
37. The resulting creep curve consists of three regions,
each of which has its own distinctive strain–time
feature.
Primary or transient creep occurs first, typified by a
continuously decreasing creep rate
38. For metallic materials most creep tests are conducted in uniaxial
tension using a specimen having the same geometry as for tensile tests
(Figure 6.2).
On the other hand, uniaxial compression tests are more appropriate
for brittle materials; these provide a better measure of the intrinsic
creep properties inasmuch as there is no stress amplification and crack
propagation, as with tensile loads.
Compressive test specimens are usually right cylinders or
parallelepipeds having length-to-diameter ratios ranging from about 2
to 4.
For most materials creep properties are virtually independent of
loading direction.