Hertzian contact analysis describes the deformation and pressure distribution when two elastic solids are pressed together. It assumes the contact surfaces are continuous and smooth, and the strains are small. The analysis provides equations to calculate the contact area, pressure distribution, and yield point for plastic deformation based on the materials' properties, surface textures, and applied load. Hertzian contact is applicable for static contact situations to determine the onset of plasticity in the softer material.
The document discusses contact stresses that occur between two surfaces pressed together, such as between a locomotive wheel and rail. It provides examples where contact stresses are significant, like in bearings and gears. When surfaces are pressed together, high stresses develop just below the surface at the point of contact. These stresses can cause failures like cracking or pitting. The document presents equations to calculate the principal stresses that develop from an elliptical stress distribution between the pressed surfaces. Factors like the curvature of the surfaces and angle of contact are considered. Charts are also included showing stress distribution parameters for different angles of contact.
The document summarizes Hertz contact stress theory, which was developed by Heinrich Hertz in 1882 to calculate contact stress and deformation between two elastic bodies in contact. The theory makes assumptions that the bodies are non-conforming, non-adhesive, elastic, and deformations are small. It is applied to calculate properties like Young's modulus and has been used to study agricultural products like pumpkin seeds and oranges. The theory works best for regular geometries but has limitations like not applying to rigid bodies or irregularly shaped objects that could cause inconsistent results.
1. There are five main theories of failure used to predict failure of machine components under multi-axial stresses: Rankine, Tresca, Saint Venant, Haigh, and Hencky-Von Mises.
2. Theories of failure are required because material strengths are determined from uni-axial tests, while actual components experience multi-axial stresses, and the theories relate uni-axial strengths to multi-axial stresses.
3. Rankine's theory applies to brittle materials and ductile materials under uniaxial or similar biaxial stresses, while Tresca's theory applies to ductile materials prone to shear failure.
Saint-Venant's principle states that the stresses and strains far away from the load application point are unaffected by the exact nature of the load or its application method, but only depend on the resultant load magnitude and application area. Stress concentrations occur where the cross-sectional area changes abruptly, like holes, notches, or threads, and cause local stress values much higher than the average stress. The stress concentration factor K is used to relate the maximum stress σmax to the average stress σave in a cross-section. Design engineers use stress concentration factors and allowable stress values to determine if a given load will exceed the material's strength at stress concentration locations.
The document discusses various types of surface defects that can occur in crystals, including external surfaces, grain boundaries, tilt boundaries, twist boundaries, twin boundaries, and stacking faults. External surfaces have unsatisfied atomic bonds and higher surface energy than bulk atoms. Grain boundaries are regions between two adjacent grains that are slightly disordered with low density and high mobility. Tilt boundaries appear as arrays of edge dislocations when grains are misaligned with a parallel rotation axis. Twist boundaries have a perpendicular rotation axis and form as arrays of screw dislocations for low angle grain boundaries. Twin boundaries are mirror images of atomic arrangements across the boundary formed by shear deformation. Stacking faults are imperfections in the stacking sequence of atomic planes in crystals.
This document summarizes the deformation behavior of single crystals and polycrystalline materials under tensile stress. It explains that in single crystals, plastic deformation occurs through slip along specific crystallographic planes and directions known as slip systems. Schmid's law describes the relationship between applied stress and critical resolved shear stress required for slip. In polycrystalline materials, deformation is more complex due to interactions between randomly oriented grains. Neighboring grains constrain each other's deformation, resulting in higher strength compared to single crystals.
- When two surfaces are brought into contact, contact only occurs at discrete contact spots or junctions due to surface roughness. The sum of the areas of these contact spots is the real area of contact, which is typically much smaller than the apparent area of contact.
- The real area of contact depends on surface texture, material properties, and loading conditions. It determines the degree of interaction between surfaces and thereby influences friction and wear.
- During loading, contact initially occurs at a few high asperities. With increasing load, more asperities contact each other and existing contacts grow. Deformation can be elastic, plastic, or viscoelastic depending on stresses.
Hertzian contact analysis describes the deformation and pressure distribution when two elastic solids are pressed together. It assumes the contact surfaces are continuous and smooth, and the strains are small. The analysis provides equations to calculate the contact area, pressure distribution, and yield point for plastic deformation based on the materials' properties, surface textures, and applied load. Hertzian contact is applicable for static contact situations to determine the onset of plasticity in the softer material.
The document discusses contact stresses that occur between two surfaces pressed together, such as between a locomotive wheel and rail. It provides examples where contact stresses are significant, like in bearings and gears. When surfaces are pressed together, high stresses develop just below the surface at the point of contact. These stresses can cause failures like cracking or pitting. The document presents equations to calculate the principal stresses that develop from an elliptical stress distribution between the pressed surfaces. Factors like the curvature of the surfaces and angle of contact are considered. Charts are also included showing stress distribution parameters for different angles of contact.
The document summarizes Hertz contact stress theory, which was developed by Heinrich Hertz in 1882 to calculate contact stress and deformation between two elastic bodies in contact. The theory makes assumptions that the bodies are non-conforming, non-adhesive, elastic, and deformations are small. It is applied to calculate properties like Young's modulus and has been used to study agricultural products like pumpkin seeds and oranges. The theory works best for regular geometries but has limitations like not applying to rigid bodies or irregularly shaped objects that could cause inconsistent results.
1. There are five main theories of failure used to predict failure of machine components under multi-axial stresses: Rankine, Tresca, Saint Venant, Haigh, and Hencky-Von Mises.
2. Theories of failure are required because material strengths are determined from uni-axial tests, while actual components experience multi-axial stresses, and the theories relate uni-axial strengths to multi-axial stresses.
3. Rankine's theory applies to brittle materials and ductile materials under uniaxial or similar biaxial stresses, while Tresca's theory applies to ductile materials prone to shear failure.
Saint-Venant's principle states that the stresses and strains far away from the load application point are unaffected by the exact nature of the load or its application method, but only depend on the resultant load magnitude and application area. Stress concentrations occur where the cross-sectional area changes abruptly, like holes, notches, or threads, and cause local stress values much higher than the average stress. The stress concentration factor K is used to relate the maximum stress σmax to the average stress σave in a cross-section. Design engineers use stress concentration factors and allowable stress values to determine if a given load will exceed the material's strength at stress concentration locations.
The document discusses various types of surface defects that can occur in crystals, including external surfaces, grain boundaries, tilt boundaries, twist boundaries, twin boundaries, and stacking faults. External surfaces have unsatisfied atomic bonds and higher surface energy than bulk atoms. Grain boundaries are regions between two adjacent grains that are slightly disordered with low density and high mobility. Tilt boundaries appear as arrays of edge dislocations when grains are misaligned with a parallel rotation axis. Twist boundaries have a perpendicular rotation axis and form as arrays of screw dislocations for low angle grain boundaries. Twin boundaries are mirror images of atomic arrangements across the boundary formed by shear deformation. Stacking faults are imperfections in the stacking sequence of atomic planes in crystals.
This document summarizes the deformation behavior of single crystals and polycrystalline materials under tensile stress. It explains that in single crystals, plastic deformation occurs through slip along specific crystallographic planes and directions known as slip systems. Schmid's law describes the relationship between applied stress and critical resolved shear stress required for slip. In polycrystalline materials, deformation is more complex due to interactions between randomly oriented grains. Neighboring grains constrain each other's deformation, resulting in higher strength compared to single crystals.
- When two surfaces are brought into contact, contact only occurs at discrete contact spots or junctions due to surface roughness. The sum of the areas of these contact spots is the real area of contact, which is typically much smaller than the apparent area of contact.
- The real area of contact depends on surface texture, material properties, and loading conditions. It determines the degree of interaction between surfaces and thereby influences friction and wear.
- During loading, contact initially occurs at a few high asperities. With increasing load, more asperities contact each other and existing contacts grow. Deformation can be elastic, plastic, or viscoelastic depending on stresses.
Theories of Failure- Design of Machine Elements-I (DME)DrMathewJohn1
1. The document discusses various theories of failure including maximum shear stress theory, maximum principal stress theory, maximum distortion energy theory, maximum strain theory, and maximum total strain energy theory.
2. It also covers topics like stress tensors, principal stresses, combined stresses, and design for strength under static loads.
3. Examples, equations, and references are provided to explain concepts related to stress analysis and failure theories.
A review of constitutive models for plastic deformationSamir More
Materials like mild steel have defined yield point hence it is easy to distinguish between the elastic region and plastic region of deformation. But for materials that do not have specified yield point, it is hard to distinguish between elastic and plastic deformation region. In that case may be plastic deformation starts from beginning of the application of the load. For elastic region, stress and strain are in linear relationship with each other hence Hook’s law valid true. But for plastic region, the relation between stress and strain is nonlinear and complicated. So need for continuum plasticity model arises. The main aim of continuum plasticity model is to formulate mathematical model based on experimental results that can predict the plastic deformation of material under varying loading conditions and at different elevated temperature.
This document provides an introduction to fracture mechanics from Ozen Engineering Inc. It discusses key fracture mechanics concepts like stress intensity factors, J-integrals, and cohesive zone modeling. It also outlines Ozen's fracture mechanics training sessions which will cover topics like linear elastic fracture mechanics analysis in ANSYS, extended finite element modeling, and fatigue crack propagation modeling.
This document discusses stress-strain relations during plastic flow. It presents the following key points:
1. Plastic flow occurs when stresses exceed the elastic limit and results in irreversible deformation. Stress-strain relations in plasticity relate differential strain increments rather than finite relations like in Hooke's law.
2. The Prandtl-Reuss equations and Saint Venant-von Mises equations describe the relationships between stress and plastic strain increments using assumptions about isotropic materials and proportionality between deviatoric stress and plastic strain.
3. For fully developed plastic deformation, the Saint Venant-von Mises equations simplify by ignoring elastic strains, relating plastic strain directly to deviatoric stress increments.
This document discusses fracture mechanics and provides background information on the topic. It introduces key concepts in fracture mechanics including stress intensity factor, linear elastic fracture mechanics (LEFM), ductile to brittle transition, and fracture toughness. Applications of fracture mechanics are described such as its use in analyzing cracking in pavement systems. The document also covers probabilistic fracture of brittle materials and how their strength is affected by the presence of flaws.
1. Electromagnetic forming is a high-energy rate forming technique that uses a pulsed magnetic field to rapidly deform electrically conductive materials like aluminum alloys. It offers benefits like improved formability, reduced wrinkling, and lower springback compared to conventional forming.
2. The process involves storing electrical energy in capacitors and discharging it through a coil to generate an intense magnetic field. This induces eddy currents in a conductive workpiece within the coil, creating repelling magnetic forces that deform the workpiece at velocities of 100 m/s or more.
3. Electromagnetic forming has applications in tube compression/expansion and sheet metal forming. It is commonly used for assembly operations and has advantages over conventional forming like
The document discusses various theories of failure that are used to determine the safe dimensions of components under combined loading conditions. It describes five theories: (1) Maximum principal stress theory, (2) Maximum principal strain theory, (3) Maximum strain energy theory, (4) Maximum distortion energy theory, and (5) Maximum shear stress theory. The maximum distortion energy theory provides the safest design for ductile materials as it results in the largest allowable stresses before failure compared to the other theories. The document also compares the various theories and discusses when each is best applied depending on the material type and stress conditions.
The document discusses various topics related to stress and strain including: principal stresses and strains, Mohr's stress circle theory of failure, 3D stress and strain, equilibrium equations, and impact loading. It provides examples of stresses acting in different planes including normal, shear, oblique, and principal planes. It also gives examples of calculating normal and tangential stresses on an oblique plane subjected to stresses in one, two, or multiple directions with and without shear stresses.
This document summarizes Griffith and Irwin fracture mechanics theories. [1] Griffith's theory explains brittle fracture and proposes that crack growth occurs when the potential energy released by fracturing exceeds the new surface energy. [2] Irwin modified Griffith's theory for ductile materials by including a term for the energy dissipated by plastic deformation near the crack tip. Irwin's theory partitions the energy into stored elastic energy driving fracture and dissipated energy resisting it. Crack growth occurs when the stored energy exceeds the dissipated energy.
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.
The document discusses different theories of material failure including maximum principal stress, maximum shear stress, maximum principal strain, maximum strain energy, and maximum distortion energy theories. It provides details on each theory, noting that maximum principal stress theory is suitable for brittle materials, maximum shear stress theory for ductile materials, and maximum distortion energy theory is highly recommended.
1. The document discusses four common failure theories used in engineering: maximum shear stress theory, maximum principal stress theory, maximum normal strain theory, and maximum shear strain theory.
2. It provides details on the maximum shear stress (Tresca) theory, which states that failure occurs when the maximum shear stress equals the yield point stress under simple tension.
3. An example problem is presented involving determining the required diameter of a circular shaft using the maximum shear stress theory with a safety factor of 3, given the material properties and loads on the shaft.
Finite element analysis (FEA) involves breaking a model down into small pieces called finite elements. FEA was first developed in 1943 and involved numerical analysis techniques. By the 1970s, FEA was used primarily by aerospace, automotive, and defense industries due to the high cost of computers. Modern FEA involves preprocessing like meshing a model, applying properties and boundary conditions, solving the model using software, and postprocessing to analyze results like stresses and displacements.
This document discusses various mechanical properties of materials including elastic deformation, engineering strain, tensile strength, toughness, yielding, modulus of elasticity, Poisson's ratio, ductility, malleability, hardness, and fatigue. It provides definitions and explanations of these key material properties and how they relate to a material's behavior under stress or loads over time.
There are several mechanisms that can strengthen materials by hindering the movement of dislocations:
1) Grain size reduction - Smaller grain sizes provide more barriers to dislocation movement at grain boundaries. According to the Hall-Petch relationship, smaller grain diameters yield higher yield strengths.
2) Solid solution strengthening - Impurity atoms distort the crystal lattice and generate stress fields that impede dislocation motion. The effectiveness depends on size difference and concentration of solute atoms.
3) Strain hardening - Plastic deformation increases dislocation density within a material, making further dislocation movement more difficult through interactions between dislocations. This causes strain hardened metals to strengthen with increasing plastic deformation.
The document discusses fatigue failure in materials. It defines fatigue as failure occurring from fluctuating stresses even if the stress is below the material's yield strength. Fatigue typically starts with crack initiation and propagation over many stress cycles. The document outlines various fatigue testing methods and factors that influence fatigue life such as surface finish, notches, corrosion and stress concentration. Fatigue is graphically represented using an S-N curve showing the relationship between cyclic stress and cycles to failure.
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 provides an overview of topics related to simple stresses and strains, including:
- Types of stresses and strains such as tensile, compressive, direct stress, and direct strain.
- Hooke's law and how stress is proportional to strain below the material's yield point.
- Stress-strain diagrams and key points such as the elastic region, yield point, and fracture point.
- Definitions of terms like working stress, factor of safety, Poisson's ratio, and elastic moduli.
- Examples of problems calculating stresses, strains, extensions, and deformations of simple structural members under various loads.
This document provides information about the Solid Mechanics course ME 302 taught by Dr. Nirmal Baran Hui at NIT Durgapur in West Bengal, India. It lists four required textbooks for the course and provides a detailed syllabus covering topics like stress, strain, elasticity, bending, deflection, columns, torsion, pressure vessels, combined loadings, springs, and failure theories. The document also includes examples of lecture content on stress analysis, stresses on oblique planes, and material subjected to pure shear.
Stress concentration occurs where there are irregularities or discontinuities in a material, like holes or grooves, and greatly increases stresses in these local areas, where fatigue failure often originates. Stress concentration factors quantify how much a discontinuity increases stresses but are not needed for ductile materials under static loads, as local yielding relieves these concentrations. Notch sensitivity values between 0 and 1 indicate a material's sensitivity to notches, with 1 being fully sensitive and 0 having no sensitivity. Geometric stress concentration factors estimate stress amplification near geometric features.
Hertz Contact Stress Analysis and Validation Using Finite Element AnalysisPrabhakar Purushothaman
In general machines are designed with a set of elements to reduce cost, ease of assembly and manufacturability
etc. One also needs to address stress issues at the contact regions between any two elements, stress is induced when a load is applied to two elastic solids in contact. If not considered and addressed adequately serious flaws can occur within the mechanical design and the end product may fail to qualify. Stresses formed by the contact of two radii can cause extremely high stresses, the application and evaluation of Hertzian contact stress equations can estimate maximum stresses produced
and ways to mitigate can be sought. Hertz developed a theory to calculate the contact area and pressure between the two
surfaces and predict the resulting compression and stress induced in the objects. The roller bearing assembly and spur gear pair assembly is an example were the assembly undergoes fatigue failure due to contact stresses. This paper discusses the hertz contact theory validation using finite element Analysis.
Rolling element bearings transmit loads through rolling contact and provide lower coefficients of friction than sliding contact bearings. They are composed of an inner race, outer race, rolling elements (balls or rollers), and a cage. Ball bearings are further classified as deep groove, angular contact, or filled notch types. Roller bearings use cylindrical or tapered rollers and have higher load capacity than ball bearings. Bearing life is rated based on the number of revolutions or hours it can operate before spalling or pitting failure occurs, with an L10 life rating meaning 10% of tested bearings will fail by that point.
Theories of Failure- Design of Machine Elements-I (DME)DrMathewJohn1
1. The document discusses various theories of failure including maximum shear stress theory, maximum principal stress theory, maximum distortion energy theory, maximum strain theory, and maximum total strain energy theory.
2. It also covers topics like stress tensors, principal stresses, combined stresses, and design for strength under static loads.
3. Examples, equations, and references are provided to explain concepts related to stress analysis and failure theories.
A review of constitutive models for plastic deformationSamir More
Materials like mild steel have defined yield point hence it is easy to distinguish between the elastic region and plastic region of deformation. But for materials that do not have specified yield point, it is hard to distinguish between elastic and plastic deformation region. In that case may be plastic deformation starts from beginning of the application of the load. For elastic region, stress and strain are in linear relationship with each other hence Hook’s law valid true. But for plastic region, the relation between stress and strain is nonlinear and complicated. So need for continuum plasticity model arises. The main aim of continuum plasticity model is to formulate mathematical model based on experimental results that can predict the plastic deformation of material under varying loading conditions and at different elevated temperature.
This document provides an introduction to fracture mechanics from Ozen Engineering Inc. It discusses key fracture mechanics concepts like stress intensity factors, J-integrals, and cohesive zone modeling. It also outlines Ozen's fracture mechanics training sessions which will cover topics like linear elastic fracture mechanics analysis in ANSYS, extended finite element modeling, and fatigue crack propagation modeling.
This document discusses stress-strain relations during plastic flow. It presents the following key points:
1. Plastic flow occurs when stresses exceed the elastic limit and results in irreversible deformation. Stress-strain relations in plasticity relate differential strain increments rather than finite relations like in Hooke's law.
2. The Prandtl-Reuss equations and Saint Venant-von Mises equations describe the relationships between stress and plastic strain increments using assumptions about isotropic materials and proportionality between deviatoric stress and plastic strain.
3. For fully developed plastic deformation, the Saint Venant-von Mises equations simplify by ignoring elastic strains, relating plastic strain directly to deviatoric stress increments.
This document discusses fracture mechanics and provides background information on the topic. It introduces key concepts in fracture mechanics including stress intensity factor, linear elastic fracture mechanics (LEFM), ductile to brittle transition, and fracture toughness. Applications of fracture mechanics are described such as its use in analyzing cracking in pavement systems. The document also covers probabilistic fracture of brittle materials and how their strength is affected by the presence of flaws.
1. Electromagnetic forming is a high-energy rate forming technique that uses a pulsed magnetic field to rapidly deform electrically conductive materials like aluminum alloys. It offers benefits like improved formability, reduced wrinkling, and lower springback compared to conventional forming.
2. The process involves storing electrical energy in capacitors and discharging it through a coil to generate an intense magnetic field. This induces eddy currents in a conductive workpiece within the coil, creating repelling magnetic forces that deform the workpiece at velocities of 100 m/s or more.
3. Electromagnetic forming has applications in tube compression/expansion and sheet metal forming. It is commonly used for assembly operations and has advantages over conventional forming like
The document discusses various theories of failure that are used to determine the safe dimensions of components under combined loading conditions. It describes five theories: (1) Maximum principal stress theory, (2) Maximum principal strain theory, (3) Maximum strain energy theory, (4) Maximum distortion energy theory, and (5) Maximum shear stress theory. The maximum distortion energy theory provides the safest design for ductile materials as it results in the largest allowable stresses before failure compared to the other theories. The document also compares the various theories and discusses when each is best applied depending on the material type and stress conditions.
The document discusses various topics related to stress and strain including: principal stresses and strains, Mohr's stress circle theory of failure, 3D stress and strain, equilibrium equations, and impact loading. It provides examples of stresses acting in different planes including normal, shear, oblique, and principal planes. It also gives examples of calculating normal and tangential stresses on an oblique plane subjected to stresses in one, two, or multiple directions with and without shear stresses.
This document summarizes Griffith and Irwin fracture mechanics theories. [1] Griffith's theory explains brittle fracture and proposes that crack growth occurs when the potential energy released by fracturing exceeds the new surface energy. [2] Irwin modified Griffith's theory for ductile materials by including a term for the energy dissipated by plastic deformation near the crack tip. Irwin's theory partitions the energy into stored elastic energy driving fracture and dissipated energy resisting it. Crack growth occurs when the stored energy exceeds the dissipated energy.
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.
The document discusses different theories of material failure including maximum principal stress, maximum shear stress, maximum principal strain, maximum strain energy, and maximum distortion energy theories. It provides details on each theory, noting that maximum principal stress theory is suitable for brittle materials, maximum shear stress theory for ductile materials, and maximum distortion energy theory is highly recommended.
1. The document discusses four common failure theories used in engineering: maximum shear stress theory, maximum principal stress theory, maximum normal strain theory, and maximum shear strain theory.
2. It provides details on the maximum shear stress (Tresca) theory, which states that failure occurs when the maximum shear stress equals the yield point stress under simple tension.
3. An example problem is presented involving determining the required diameter of a circular shaft using the maximum shear stress theory with a safety factor of 3, given the material properties and loads on the shaft.
Finite element analysis (FEA) involves breaking a model down into small pieces called finite elements. FEA was first developed in 1943 and involved numerical analysis techniques. By the 1970s, FEA was used primarily by aerospace, automotive, and defense industries due to the high cost of computers. Modern FEA involves preprocessing like meshing a model, applying properties and boundary conditions, solving the model using software, and postprocessing to analyze results like stresses and displacements.
This document discusses various mechanical properties of materials including elastic deformation, engineering strain, tensile strength, toughness, yielding, modulus of elasticity, Poisson's ratio, ductility, malleability, hardness, and fatigue. It provides definitions and explanations of these key material properties and how they relate to a material's behavior under stress or loads over time.
There are several mechanisms that can strengthen materials by hindering the movement of dislocations:
1) Grain size reduction - Smaller grain sizes provide more barriers to dislocation movement at grain boundaries. According to the Hall-Petch relationship, smaller grain diameters yield higher yield strengths.
2) Solid solution strengthening - Impurity atoms distort the crystal lattice and generate stress fields that impede dislocation motion. The effectiveness depends on size difference and concentration of solute atoms.
3) Strain hardening - Plastic deformation increases dislocation density within a material, making further dislocation movement more difficult through interactions between dislocations. This causes strain hardened metals to strengthen with increasing plastic deformation.
The document discusses fatigue failure in materials. It defines fatigue as failure occurring from fluctuating stresses even if the stress is below the material's yield strength. Fatigue typically starts with crack initiation and propagation over many stress cycles. The document outlines various fatigue testing methods and factors that influence fatigue life such as surface finish, notches, corrosion and stress concentration. Fatigue is graphically represented using an S-N curve showing the relationship between cyclic stress and cycles to failure.
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 provides an overview of topics related to simple stresses and strains, including:
- Types of stresses and strains such as tensile, compressive, direct stress, and direct strain.
- Hooke's law and how stress is proportional to strain below the material's yield point.
- Stress-strain diagrams and key points such as the elastic region, yield point, and fracture point.
- Definitions of terms like working stress, factor of safety, Poisson's ratio, and elastic moduli.
- Examples of problems calculating stresses, strains, extensions, and deformations of simple structural members under various loads.
This document provides information about the Solid Mechanics course ME 302 taught by Dr. Nirmal Baran Hui at NIT Durgapur in West Bengal, India. It lists four required textbooks for the course and provides a detailed syllabus covering topics like stress, strain, elasticity, bending, deflection, columns, torsion, pressure vessels, combined loadings, springs, and failure theories. The document also includes examples of lecture content on stress analysis, stresses on oblique planes, and material subjected to pure shear.
Stress concentration occurs where there are irregularities or discontinuities in a material, like holes or grooves, and greatly increases stresses in these local areas, where fatigue failure often originates. Stress concentration factors quantify how much a discontinuity increases stresses but are not needed for ductile materials under static loads, as local yielding relieves these concentrations. Notch sensitivity values between 0 and 1 indicate a material's sensitivity to notches, with 1 being fully sensitive and 0 having no sensitivity. Geometric stress concentration factors estimate stress amplification near geometric features.
Hertz Contact Stress Analysis and Validation Using Finite Element AnalysisPrabhakar Purushothaman
In general machines are designed with a set of elements to reduce cost, ease of assembly and manufacturability
etc. One also needs to address stress issues at the contact regions between any two elements, stress is induced when a load is applied to two elastic solids in contact. If not considered and addressed adequately serious flaws can occur within the mechanical design and the end product may fail to qualify. Stresses formed by the contact of two radii can cause extremely high stresses, the application and evaluation of Hertzian contact stress equations can estimate maximum stresses produced
and ways to mitigate can be sought. Hertz developed a theory to calculate the contact area and pressure between the two
surfaces and predict the resulting compression and stress induced in the objects. The roller bearing assembly and spur gear pair assembly is an example were the assembly undergoes fatigue failure due to contact stresses. This paper discusses the hertz contact theory validation using finite element Analysis.
Rolling element bearings transmit loads through rolling contact and provide lower coefficients of friction than sliding contact bearings. They are composed of an inner race, outer race, rolling elements (balls or rollers), and a cage. Ball bearings are further classified as deep groove, angular contact, or filled notch types. Roller bearings use cylindrical or tapered rollers and have higher load capacity than ball bearings. Bearing life is rated based on the number of revolutions or hours it can operate before spalling or pitting failure occurs, with an L10 life rating meaning 10% of tested bearings will fail by that point.
This document provides instructions for properly using chain-tongs, which are tools used to make up and break out tubulars. It describes chain-tongs have three main components: a chain, nut and bolt, and jaws. It outlines proper usage such as not applying side loads, not using as a lever, and not modifying the chain-tongs. It emphasizes the importance of inspecting chain-tongs for damage and wearing parts. Specific instructions are provided for making up and breaking out tubulars using chain-tongs as well as locking the chain, removing chain-tongs, and maintaining control of the chain. Hazards of improper use are highlighted.
The Nursery Rhymes powerpoint show is not dealing with the lyrics but just a few lines and then the photo or image. Accompanied with Strauss, Roses from the South. Enjoy!
James Dias, CEO, and Lucas Dailey, Senior User Experience Designer, will present a workshop, “Designing connected care solutions at the intersection of medicine and finance” on Saturday, September 6th from 2:20-3:50 PM PDT.
The workshop will explore how the business of performance-based healthcare requires a balance between giving patients the best possible quality outcomes and doing it in a cost effective manner. This emphasis on value-driven medicine is producing the opportunity for new technology solutions that address both care and costs. Designing effective solutions for “Connected Care” requires an interdisciplinary approach that brings together the disparate fields of healthcare economics, patient engagement, and digital technology.
This document discusses the beliefs and services of Jack In The Box Worldwide, a communications and content agency. It advocates that brand communications should focus on meaningful content rather than just product advertising. It also stresses the importance of defining a clear brand purpose and having a cohesive content strategy and newsroom to deliver consistent messaging across channels. The document provides information on Jack In The Box Worldwide's leadership, services which include strategy, content creation, and analytics, as well as some of their clients and case studies.
The official case study of the viral phenomenon called 'Kolaveri'. The viral marketing of this campaign was strategised and executed by Jack in the Box Worldwide.
A man was walking in the forest and heard a frightening noise. He saw a ferocious animal and ran until he came to a cliff. The man slipped over the cliff and held onto a strawberry plant, unable to climb up or down. Seeing that he would die, he picked a juicy strawberry and savored it. The story teaches us to savor every moment in life like it may be our last.
A how to video about creating the racks for the vertical grow aquaponics system.
Learn more about ZipGrow towers here: http://brightagrotech.com/zipgrow/
Milo targets "future champions" aged 3-13 and positions itself as encouraging an active lifestyle. It has the largest share of the PHP 6 billion powdered chocolate drink market at 84%. Milo is a chocolate-flavored drink that is 13% more expensive than competitors. It uses TV, radio, print, online and event marketing nationwide. Milo has a niche strategy of dominating the youth market by supporting sports and promoting excellence. The document recommends Milo continue its strong marketing campaign, consider expanding its flavor options, and keep utilizing events and social media.
The Health Benefits of Dogs. A presentation about the mental and physical health benefits owning a dog can bring you.
This is my special way of saying thank you to my lovely dog for all those 'walkies' we've had together.
Blackleg is a plant disease of potato caused by pectolytic bacteria that can result in stunting, wilting, chlorosis of leaves, necrosis of several tissues, a decline in yield, and at times the death of the potato plant.
This document provides guidance on proper telephone etiquette and skills. The objectives are to state the importance of professional telephone service, provide suitable greetings and farewells, use the phone effectively by transferring or placing calls on hold properly, and taking messages. Key tips include answering promptly, identifying yourself and department, offering assistance, asking permission to place on hold, explaining delays, informing callers of transfers, staying on the line until transfers are complete, taking detailed messages, and ending calls positively by thanking the caller.
Personal Branding To Stand Out & Differentiate YourselfMohamed Yasser
Learn how to stand out of the crowd and differentiate yourself by personal branding strategies, treat yourself as a brand that delivers a unique value in your career field, personal branding will help you stand out and differentiate yourself away of competitors.
Seaweed meal for poultry industry has diversified and versatile functional properties and is ideal for countries like Pakistan where poultry industry is facing challenges such as Bacterial resistance etc
This document provides an overview of time management concepts and techniques. It defines time management, discusses how time is a limited resource for both individuals and organizations, and identifies essential habits like prioritizing and scheduling. It also describes different types of time and challenges like overestimating or underestimating time for tasks. The document outlines principles of effective time management including using matrices to categorize how time is spent and prioritize activities.
24 Time Management Hacks to Develop for Increased ProductivityIulian Olariu
These are some ideas I talk about in my Time Management training sessions. Try to approach each of them and develop in a new habit, in order to increase your productivity and manage your time better. Don't forget to share if you find them useful!
Diseno en ingenieria mecanica de Shigley - 8th ---HDes
descarga el contenido completo de aqui http://paralafakyoumecanismos.blogspot.com.ar/2014/08/libro-para-mecanismos-y-elementos-de.html
SlideShare is a global platform for sharing presentations, infographics, videos and documents. It has over 18 million pieces of professional content uploaded by experts like Eric Schmidt and Guy Kawasaki. The document provides tips for setting up an account on SlideShare, uploading content, optimizing it for searchability, and sharing it on social media to build an audience and reputation as a subject matter expert.
Hertzian contact analysis describes the deformation and pressure distribution when two elastic solids are pressed together. It assumes the contact surfaces are continuous and smooth, and the strains are small. The analysis provides equations to calculate the contact area, pressure distribution, and yield point for plastic deformation based on the materials' properties, surface textures, and applied load. Hertzian contact is applicable for static contact situations to determine the onset of plasticity in the softer material.
The document discusses Hertz contact stresses that occur between two curved surfaces in contact. Some key points:
- The theoretical contact area between two spheres is a point, while for two cylinders it is a line, which would cause infinite pressure. In reality, a small contact area is created through elastic deformation to limit stresses.
- Equations for spheres and cylinders in contact also apply to spheres on flat plates and cylinders in cylindrical grooves.
- Maximum shear and Von Mises stresses occur below the contact area, causing pitting from material breaking out.
- Point contact of a sphere creates larger stresses, displacements and lower stiffness than line contact of a cylinder.
- Maximum contact pressure depends on type
This document summarizes Alessandro Rigazzi's PhD dissertation defense on his research into modeling the effects of surface roughness on contact area and friction using finite element modeling. His research investigated how surface roughness parameters like root mean square roughness and Hurst exponent affect the real contact area between surfaces and elastic friction forces. Through numerical experiments on self-affine rough surfaces, he found that increasing roughness decreases contact area and increases friction coefficient in a way that can be modeled with polynomials. He also validated the models by simulating tire-road contact and comparing to experimental data on wet roads.
Friction is the resistance to motion when one solid body moves over another in contact. There are two main types of friction: dry friction and fluid friction. Dry friction, also called Coulomb friction, occurs between two dry surfaces in contact. Fluid friction occurs between layers of a fluid moving at different velocities.
The document discusses the mechanisms and theories of friction. It explains that friction arises from interactions between surface asperities or roughness. The dominant mechanisms are adhesion between contact areas and plastic deformation. Adhesion contributes to friction through the force needed to overcome molecular bonds between contacting asperities. Deformation friction is the energy required for plastic plowing or deformation of asperities. The total friction force is the sum
Nanoindentation is a technique used to determine material properties such as hardness and elastic modulus at small length scales. It works by pressing an indenter with a very small tip into the material and measuring the resulting load and displacement. Factors like thermal drift, machine compliance, and real tip geometry must be accounted for when analyzing the load-displacement data to determine properties. Commercial nanoindentation machines use various methods like capacitive sensing or optical lever systems to precisely measure displacement during indentation testing.
The document discusses the ring compression test method for determining the coefficient of friction between a die and workpiece. It investigates the friction factors of aluminum rings under dry and lubricated conditions. The key findings are:
1) Lubrication reduces interface friction coefficients compared to dry conditions.
2) Friction coefficients decrease with reductions in ring height and outer radius but increase with increases in inner radius.
3) Molybdenum disulfide and zinc stearate provide the lowest friction, while dry conditions provide the highest, according to experimental, theoretical and analytical analyses.
Contact stresses occur where two solid bodies are pressed together over a limited contact area. They are important because failures often initiate at contact surfaces due to high cyclic stresses. Contact stresses are computed using elasticity equations that assume homogenous, isotropic materials and an elliptical contact patch shape. The maximum principal stress is largest in magnitude and occurs at the contact surface, while maximum shear stress occurs just below the surface. Orthogonal shear stresses on planes parallel to the contact are also significant for fatigue failure analysis. Line contact problems have different equations from point contact due to the contact geometry.
1 Field:
What is field ? How to add dynamic field ?
Work with fields.
2 Collision effect:
What is collision effect ?
Make collide.
Make particle collision events.
3 Examples:
Creating waterfalls.
Rain on car.
Module 4 flexural stresses- theory of bendingAkash Bharti
This document provides an overview of flexural stresses and the theory of simple bending. It discusses key concepts such as:
- Assumptions in the derivation of the bending equation relating bending moment (M) to curvature (1/R) and stress (f)
- Determining the neutral axis where bending stress is zero
- Calculating bending stresses in beams undergoing simple bending and pure bending
- Deriving Bernoulli's bending equation relating stress (f) to distance from the neutral axis (y) and bending moment (M)
- Using the bending equation to locate the neutral axis and design beam cross-sections based on permissible stresses
Worked examples are provided to illustrate calculating load capacity based on beam geometry and material properties
Detailed content on shear strength of soils, principles of effective stresses, tests conducted to determine the shear strength of soils and its applications, dilatancy, thixotropy and sensitivity.
This document discusses riveted connections and their design. It covers the different types of riveted joints like lap joints and butt joints. It provides specifications for riveted connections like the gross diameter of rivets, gauge, pitch and edge distance. It also discusses the types of failures in riveted connections and how to calculate the strength of riveted joints based on the strength of rivets in shear and bearing and the strength of plates in tension. The efficiency of riveted joints is defined. Examples of calculating rivet values are also provided.
This document provides a summary of key concepts in strength of materials for mechanical engineers. It defines terms like stress, strain, Hooke's law, moment of force, couple, center of gravity, moment of inertia, shear stress, Poisson's ratio, bulk modulus, principal plane and stress, Mohr's circle, resilience, malleability and ductility. It also discusses different types of beams, loading, shear force, bending moment, riveted joints, pitch and margin. The document aims to give a quick brush up on important topics in strength of materials through concise definitions and explanations of key terms and concepts.
The document describes the static bending test process. It discusses how a beam undergoes bending when subjected to transverse loads, inducing compressive and tensile stresses. The bending moment is expressed as the sum of the moments acting to one side of a beam section. Failure modes depend on the material's ductility - brittle materials rupture suddenly while ductile materials develop plastic hinges. Test variables like loading type, specimen dimensions, and test speed affect bending strength values. Cold bending and hot bending tests evaluate ductility.
This document discusses the contact stress analysis of spur gears using finite element analysis. It begins by introducing pitting and Hertzian contact stresses in gears. It then discusses modeling spur gears in SolidWorks and analyzing the contact stresses using ANSYS. The analytical and ANSYS results both show that contact pressure decreases with increasing gear module. The conclusions drawn are that a higher module gear is better for transmitting large power and has a higher safety factor. Future work could look at applying gear coatings to reduce contact stresses.
Bending Stresses are important in the design of beams from strength point of view. The present source gives an idea on theory and problems in bending stresses.
Pias Chakraborty presented on the topic of shear stress for their 4th year, 2nd semester Pre-stressed Concrete Lab course taught by Sabreena Nasrin Madam and Munshi Galib Muktadir Sir. Shear stress acts parallel to the selected plane and is determined by the formula tau = F/A, where tau is the shear stress, F is the applied force, and A is the cross-sectional area. Shear stress causes a material to deform into a parallelogram shape and is maximum at the neutral axis of a beam.
This document discusses various topics related to stresses and failure theories in machine elements. It defines notations used for stress analysis and provides formulas to calculate torsional shear stress, bending stress in straight and curved beams, principal stresses under bi-axial loading, and maximum stresses based on different failure theories. Examples are also presented on topics like torsion, shafts in series/parallel, bending stresses, and determination of principal stresses. Theories of failure under static load for ductile and brittle materials are described based on yield point and ultimate stresses from tension tests.
This document provides an overview of plate bending theory. It discusses how plate theory models bending in thin plates using Kirchhoff's plate theory and thick plates using Mindlin plate theory. Kirchhoff's plate theory assumes plates bend without shear deformation and strains are related to plate deflection. Mindlin plate theory allows for shear deformation and separates plate rotation and deflection. The document also discusses deriving plate stresses and forces, applying boundary conditions, and using triangular plate bending elements in finite element analysis.
Applications of artificial Intelligence in Mechanical Engineering.pdfAtif Razi
Historically, mechanical engineering has relied heavily on human expertise and empirical methods to solve complex problems. With the introduction of computer-aided design (CAD) and finite element analysis (FEA), the field took its first steps towards digitization. These tools allowed engineers to simulate and analyze mechanical systems with greater accuracy and efficiency. However, the sheer volume of data generated by modern engineering systems and the increasing complexity of these systems have necessitated more advanced analytical tools, paving the way for AI.
AI offers the capability to process vast amounts of data, identify patterns, and make predictions with a level of speed and accuracy unattainable by traditional methods. This has profound implications for mechanical engineering, enabling more efficient design processes, predictive maintenance strategies, and optimized manufacturing operations. AI-driven tools can learn from historical data, adapt to new information, and continuously improve their performance, making them invaluable in tackling the multifaceted challenges of modern mechanical engineering.
Rainfall intensity duration frequency curve statistical analysis and modeling...bijceesjournal
Using data from 41 years in Patna’ India’ the study’s goal is to analyze the trends of how often it rains on a weekly, seasonal, and annual basis (1981−2020). First, utilizing the intensity-duration-frequency (IDF) curve and the relationship by statistically analyzing rainfall’ the historical rainfall data set for Patna’ India’ during a 41 year period (1981−2020), was evaluated for its quality. Changes in the hydrologic cycle as a result of increased greenhouse gas emissions are expected to induce variations in the intensity, length, and frequency of precipitation events. One strategy to lessen vulnerability is to quantify probable changes and adapt to them. Techniques such as log-normal, normal, and Gumbel are used (EV-I). Distributions were created with durations of 1, 2, 3, 6, and 24 h and return times of 2, 5, 10, 25, and 100 years. There were also mathematical correlations discovered between rainfall and recurrence interval.
Findings: Based on findings, the Gumbel approach produced the highest intensity values, whereas the other approaches produced values that were close to each other. The data indicates that 461.9 mm of rain fell during the monsoon season’s 301st week. However, it was found that the 29th week had the greatest average rainfall, 92.6 mm. With 952.6 mm on average, the monsoon season saw the highest rainfall. Calculations revealed that the yearly rainfall averaged 1171.1 mm. Using Weibull’s method, the study was subsequently expanded to examine rainfall distribution at different recurrence intervals of 2, 5, 10, and 25 years. Rainfall and recurrence interval mathematical correlations were also developed. Further regression analysis revealed that short wave irrigation, wind direction, wind speed, pressure, relative humidity, and temperature all had a substantial influence on rainfall.
Originality and value: The results of the rainfall IDF curves can provide useful information to policymakers in making appropriate decisions in managing and minimizing floods in the study area.
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.
artificial intelligence and data science contents.pptxGauravCar
What is artificial intelligence? Artificial intelligence is the ability of a computer or computer-controlled robot to perform tasks that are commonly associated with the intellectual processes characteristic of humans, such as the ability to reason.
› ...
Artificial intelligence (AI) | Definitio
Embedded machine learning-based road conditions and driving behavior monitoringIJECEIAES
Car accident rates have increased in recent years, resulting in losses in human lives, properties, and other financial costs. An embedded machine learning-based system is developed to address this critical issue. The system can monitor road conditions, detect driving patterns, and identify aggressive driving behaviors. The system is based on neural networks trained on a comprehensive dataset of driving events, driving styles, and road conditions. The system effectively detects potential risks and helps mitigate the frequency and impact of accidents. The primary goal is to ensure the safety of drivers and vehicles. Collecting data involved gathering information on three key road events: normal street and normal drive, speed bumps, circular yellow speed bumps, and three aggressive driving actions: sudden start, sudden stop, and sudden entry. The gathered data is processed and analyzed using a machine learning system designed for limited power and memory devices. The developed system resulted in 91.9% accuracy, 93.6% precision, and 92% recall. The achieved inference time on an Arduino Nano 33 BLE Sense with a 32-bit CPU running at 64 MHz is 34 ms and requires 2.6 kB peak RAM and 139.9 kB program flash memory, making it suitable for resource-constrained embedded systems.
Discover the latest insights on Data Driven Maintenance with our comprehensive webinar presentation. Learn about traditional maintenance challenges, the right approach to utilizing data, and the benefits of adopting a Data Driven Maintenance strategy. Explore real-world examples, industry best practices, and innovative solutions like FMECA and the D3M model. This presentation, led by expert Jules Oudmans, is essential for asset owners looking to optimize their maintenance processes and leverage digital technologies for improved efficiency and performance. Download now to stay ahead in the evolving maintenance landscape.
Software Engineering and Project Management - Introduction, Modeling Concepts...Prakhyath Rai
Introduction, Modeling Concepts and Class Modeling: What is Object orientation? What is OO development? OO Themes; Evidence for usefulness of OO development; OO modeling history. Modeling
as Design technique: Modeling, abstraction, The Three models. Class Modeling: Object and Class Concept, Link and associations concepts, Generalization and Inheritance, A sample class model, Navigation of class models, and UML diagrams
Building the Analysis Models: Requirement Analysis, Analysis Model Approaches, Data modeling Concepts, Object Oriented Analysis, Scenario-Based Modeling, Flow-Oriented Modeling, class Based Modeling, Creating a Behavioral Model.
Batteries -Introduction – Types of Batteries – discharging and charging of battery - characteristics of battery –battery rating- various tests on battery- – Primary battery: silver button cell- Secondary battery :Ni-Cd battery-modern battery: lithium ion battery-maintenance of batteries-choices of batteries for electric vehicle applications.
Fuel Cells: Introduction- importance and classification of fuel cells - description, principle, components, applications of fuel cells: H2-O2 fuel cell, alkaline fuel cell, molten carbonate fuel cell and direct methanol fuel cells.
Redefining brain tumor segmentation: a cutting-edge convolutional neural netw...IJECEIAES
Medical image analysis has witnessed significant advancements with deep learning techniques. In the domain of brain tumor segmentation, the ability to
precisely delineate tumor boundaries from magnetic resonance imaging (MRI)
scans holds profound implications for diagnosis. This study presents an ensemble convolutional neural network (CNN) with transfer learning, integrating
the state-of-the-art Deeplabv3+ architecture with the ResNet18 backbone. The
model is rigorously trained and evaluated, exhibiting remarkable performance
metrics, including an impressive global accuracy of 99.286%, a high-class accuracy of 82.191%, a mean intersection over union (IoU) of 79.900%, a weighted
IoU of 98.620%, and a Boundary F1 (BF) score of 83.303%. Notably, a detailed comparative analysis with existing methods showcases the superiority of
our proposed model. These findings underscore the model’s competence in precise brain tumor localization, underscoring its potential to revolutionize medical
image analysis and enhance healthcare outcomes. This research paves the way
for future exploration and optimization of advanced CNN models in medical
imaging, emphasizing addressing false positives and resource efficiency.
2. Objects
1. Introduction.
2. Hertzian theory.
3. Hertzian theory assumptions.
4. Non Hertzian Contacts.
5. Common Engineering Contact Applications .
6. Real and Nominal Area of Contact Measurement.
7. Experimental Contact Stress Analysis.
2
3. 1. Introduction
• contact stress is a description of the stress
within mating parts.
• It causes serious problems if not take it into
account in some cases.
3
5. 2. Hertzian theory
• When two curved bodies are brought into contact they
initially contact at a single point or along a line.
• With the smallest application of load elastic
deformation occurs and contact is made over a finite
area.
• A method for determining the size of this region was
first described by Heinrich Hertz in 1881.
5
6. 3. Hertzian theory assumptions
• The strains are small and within the elastic limit.
• Each body can be considered as an elastic half space,
i.e., the area of contact is much smaller than the
characteristic radius of the body.
• The surfaces are continuous and non-conforming.
• The surfaces are frictionless.
• The gap (h) between the
undeformed surfaces can be
approximated by an expression of the
form
6
8. • Cylinders in Contact– VerticalStressDistribution
along Centerlineof ContactArea
• The maximum shear and Von Mises stress are reached
below the contact area.
• This causes pitting where little pieces of material break out
of the surface.
8
9. • Spheres in Contact– VerticalStressDistribution
at Centerof ContactArea
• The maximum shear and Von Mises stress are reached below the
contact area.
• This causes pitting where little pieces of material break out of the
surface.
9
10. 4. Non-Hertzian Contacts
1. Flat Rigid Planar Punch
• A flat-ended punch, of width 2b and of infinite length in the y-
direction, pressed onto an elastic half-space with a force per
unit length P .
• The surface of the punch is assumed frictionless .
• Contact occurs across the width of the punch, 2b.
• The pressure distribution is given by:
10
11. 4. Non-Hertzian Contacts
• the deflection can only be presented relative to some datum.
The normal deflection uz of the surface, outside the contact
region, is given by:
where δ is the normal deflection at an
arbitrary datum point.
11
12. 4. Non-Hertzian Contacts
2. Flat Rigid Axisymmetric Punch
• In this case the punch has a circular section of radius a.
• It is pressed onto an elastic half-space with a force P.
• The surface of the punch is assumed frictionless.
• Contact occurs across a circle of radius a and the resulting pressure
distribution is (Timoshenko and Goodier, 1951)
• The penetration ∆ of the punch is given by:
12
13. 4. Non-Hertzian Contacts
3. Indentation by an Angular Wedge
• If a two-dimensional wedge of semi-angle α is pressed onto a
frictionless elastic half-space with a force per unit length, P
then contact is made over a rectangular region of semi-width
b, such that
• This time the pressure distribution
has a singularity at the wedge apex
and is given by:
13
14. 5. Common Engineering Contact Applications
• Gears
• Meshing gear teeth are subjected to bending stresses and contact
stresses.
• The appropriate values of R1, R2and Pare then used in the Hertz
relations to determine the geometry of the contact and associated
stresses.
14
16. 5. Common Engineering Contact Applications
• Ball Bearings
• The rolling element is loaded against the conforming grooves in the
inner and outer raceways.
• For a radially loaded ball bearing the contact between the ball and
either the inner or outer raceway will be elliptical.
• The radii are readily obtained from the ball bearing geometry.
• For a bearing containing )z( balls carrying a radial load, F, the
maximum load on the ball, P(located diametrically opposite the
loading point) is approximated by :
16
17. 5. Common Engineering Contact Applications
• This load and the contact radii can then be used in the
expressions for elliptical point contact to determine the
contact area and stresses.
17
18. 6. Real and Nominal Area of Contact Measurement
• Electrical and Thermal Resistance
Measurement of the electrical resistance between contacting
surfaces can give information about the true area of contact
(Holm, 1967; Bowden and Tabor, 1939).
18
19. 6. Real and Nominal Area of Contact Measurement
• Ultrasonic Reflection
A wave of ultrasound incident at an interface between two
materials will transmit through regions of contact and be
reflected back at air gaps.
This phenomenon can be used to investigate the true area of
contact at an interface (Kendall and Tabor, 1971)
19
20. 7. Experimental Contact Stress Analysis
• Photoelasticity and Caustics
The contacting bodies are modeled in photoelastic material,
such as polycarbonate or epoxy resin. For two-dimensional
applications a planar model is fabricated and loaded in a
polariscope
20