A new method is developed for determining material hardness from depth sensing indentation tests. Both loading and unloading data are used to calculate Meyer hardness values, which agree well with conventional optical measurements. While the new method characterizes hardness even for elastic materials, the conventional mean contact pressure definition differs significantly from hardness for elastic materials. A relationship is found between work during loading and unloading that allows hardness to be calculated using only load-depth data.
2D and 3D Density Block Models Creation Based on Isostasy Usageatsidaev
This document describes methods for creating 2D and 3D density block models based on the concept of isostasy from gravity survey data. Gravity surveys measure variations in the gravitational field, which are influenced by subsurface density distributions. The authors use lithostatic pressure anomalies calculated from fitted density models to select coherent density blocks within the lithosphere. In 2D, blocks are selected along seismic profiles where lithostatic pressure anomalies approach zero. In 3D, lithostatic pressure is calculated for different depth levels from a gridded density model, allowing blocks to be traced at various depths. Comparisons between the 3D lithostatic model and density model show blocks correspond to boundaries of tectonic structures mapped at the surface. This
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
International Journal of Engineering Inventions (IJEI) provides a multidisciplinary passage for researchers, managers, professionals, practitioners and students around the globe to publish high quality, peer-reviewed articles on all theoretical and empirical aspects of Engineering and Science.
International Journal of Computational Engineering Research(IJCER)ijceronline
International Journal of Computational Engineering Research (IJCER) is dedicated to protecting personal information and will make every reasonable effort to handle collected information appropriately. All information collected, as well as related requests, will be handled as carefully and efficiently as possible in accordance with IJCER standards for integrity and objectivity.
Simulation and Experimental Studies on Composite BeamsIJERA Editor
This document summarizes the analytical and experimental investigation of composite beams made of glass and epoxy. Composite beams were manufactured using hand layup and tested under bending loads. Analytical expressions were derived to determine stresses in the beams and validated using experimental results. MATLAB codes were generated to calculate beam deflection and stresses based on the analytical equations.
This document discusses plastic instability in uniaxial tension testing of materials. It defines true stress and strain, which account for changes in cross-sectional area during tension, and explains how they relate to engineering stress and strain. The condition for plastic instability is derived as the maximum in the true stress-strain curve where the rate of true stress increase with respect to true strain is equal to the true stress. This occurs at a uniform true strain value called the instability strain. Examples of true stress-strain curves and determinations of the strain hardening exponent are also provided.
Predictive model of moment of resistance for rectangular reinforced concrete ...Alexander Decker
This document presents a predictive model for calculating the moment of resistance (MR) for rectangular reinforced concrete sections. The model is developed based on stress-strain analysis of a singly reinforced concrete beam. The governing equation relates MR to the concrete compressive strength (fcu), breadth (b), and effective depth (d). Simulation results show that MR increases with larger b and d values. MR also increases at a higher rate with greater d due to its quadratic relationship in the equation, whereas the increase is linear with b. The model allows accurate selection of section dimensions for structural design based on required resistance.
Acta Mater 57 (2009) 559 Investigation Of The Indentation Size EffectDierk Raabe
Investigation of the indentation size effect through the measurement of the geometrically necessary dislocations beneath small indents of different depths using EBSD tomography
2D and 3D Density Block Models Creation Based on Isostasy Usageatsidaev
This document describes methods for creating 2D and 3D density block models based on the concept of isostasy from gravity survey data. Gravity surveys measure variations in the gravitational field, which are influenced by subsurface density distributions. The authors use lithostatic pressure anomalies calculated from fitted density models to select coherent density blocks within the lithosphere. In 2D, blocks are selected along seismic profiles where lithostatic pressure anomalies approach zero. In 3D, lithostatic pressure is calculated for different depth levels from a gridded density model, allowing blocks to be traced at various depths. Comparisons between the 3D lithostatic model and density model show blocks correspond to boundaries of tectonic structures mapped at the surface. This
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
International Journal of Engineering Inventions (IJEI) provides a multidisciplinary passage for researchers, managers, professionals, practitioners and students around the globe to publish high quality, peer-reviewed articles on all theoretical and empirical aspects of Engineering and Science.
International Journal of Computational Engineering Research(IJCER)ijceronline
International Journal of Computational Engineering Research (IJCER) is dedicated to protecting personal information and will make every reasonable effort to handle collected information appropriately. All information collected, as well as related requests, will be handled as carefully and efficiently as possible in accordance with IJCER standards for integrity and objectivity.
Simulation and Experimental Studies on Composite BeamsIJERA Editor
This document summarizes the analytical and experimental investigation of composite beams made of glass and epoxy. Composite beams were manufactured using hand layup and tested under bending loads. Analytical expressions were derived to determine stresses in the beams and validated using experimental results. MATLAB codes were generated to calculate beam deflection and stresses based on the analytical equations.
This document discusses plastic instability in uniaxial tension testing of materials. It defines true stress and strain, which account for changes in cross-sectional area during tension, and explains how they relate to engineering stress and strain. The condition for plastic instability is derived as the maximum in the true stress-strain curve where the rate of true stress increase with respect to true strain is equal to the true stress. This occurs at a uniform true strain value called the instability strain. Examples of true stress-strain curves and determinations of the strain hardening exponent are also provided.
Predictive model of moment of resistance for rectangular reinforced concrete ...Alexander Decker
This document presents a predictive model for calculating the moment of resistance (MR) for rectangular reinforced concrete sections. The model is developed based on stress-strain analysis of a singly reinforced concrete beam. The governing equation relates MR to the concrete compressive strength (fcu), breadth (b), and effective depth (d). Simulation results show that MR increases with larger b and d values. MR also increases at a higher rate with greater d due to its quadratic relationship in the equation, whereas the increase is linear with b. The model allows accurate selection of section dimensions for structural design based on required resistance.
Acta Mater 57 (2009) 559 Investigation Of The Indentation Size EffectDierk Raabe
Investigation of the indentation size effect through the measurement of the geometrically necessary dislocations beneath small indents of different depths using EBSD tomography
Surface roughness effect on the performance of a magnetic fluid based porous ...Alexander Decker
This document summarizes a study analyzing the performance of a porous rough secant shaped slider bearing using a magnetic fluid lubricant. The authors develop stochastic equations to model the pressure distribution and account for the random surface roughness. They present dimensionless equations for the load carrying capacity and friction. Graphs show that the magnetic fluid increases load capacity and decreases friction compared to conventional lubricants. However, increased porosity and surface roughness negatively impact performance. The positive effects of magnetization can reduce these negative impacts, especially for negatively skewed roughness and negative variance. The study concludes magnetic fluids improve bearing performance and can support loads even without fluid flow.
Research on Contact Characteristics between Bump End Effector and WaferIJRES Journal
In the IC industry, commonly used methods are wafer clamping friction transmission type and vacuum suction. Combining science and theological contact theory,the contact friction transmission characteristics when using the bump and transmission actuator wafer, the wafer and the end actuators. Starting from the material properties of the wafer by ANSYS simulation analysis in contact with the wafer bump deformation due to its own gravity, and verify that it meets the requirements of small deformation wafer transfer. Compute and solve the friction contact with the wafer bump bristles between.
Peculiarities of irrecoverable straining in stress-drop testIJERA Editor
The paper concerns with analytical description of the phenomena observed in stress drop tests, namely, negative increment in plastic and creep deformation due to the sudden decrease in the acting stresses while the net stress remains positive. The model is developed in terms of the synthetic theory of irrecoverable deformation which has been generalized by introducing interplay between the deformation properties of material in the direction of acting load and opposite to it.
The document summarizes an investigation comparing experimental and computational modeling results of grain deformation in a cast nickel superalloy. Digital image correlation was used to experimentally measure strain distributions across a tensile sample, finding heterogeneous strain localized in certain grains. A crystal plasticity finite element model was developed to simulate the deformation using orientations from EBSD maps. The model showed improved agreement with experimental strain distributions at lower values of the strain rate sensitivity parameter m, but still some disagreement on strain localization. Including subsurface grains in the model further improved agreement, showing the importance of full 3D microstructure representation.
This document describes Standard Test Method E 384 for determining microindentation hardness of materials. The standard covers using Knoop and Vickers indenters to make indentations between 1-1000 gf force. Hardness is calculated based on indentation size and geometry. Key points:
- Hardness is determined by dividing force by projected area or surface area of indentation for Knoop or Vickers respectively.
- Equipment must precisely control low forces and indentation size must be measured via microscope.
- Specimens must be flat and polished to accurately measure indentation diagonals and calculate hardness.
- Multiple sources of error exist and can affect accuracy of results, including force variation, indenter geometry, and measurement errors. Standard aims
The document discusses rock mass properties and the Hoek-Brown failure criterion for estimating the strength of jointed rock masses. It presents the generalized Hoek-Brown criterion equation and describes how to determine the intact rock properties of uniaxial compressive strength (σci) and the Hoek-Brown constant (mi) from triaxial test data or estimates. It also discusses estimating the Geological Strength Index (GSI) of the rock mass.
Prediction of joint strength and effect of the surface treatment on the singl...Filipe Giesteira
This document presents four analytical methods for predicting the strength of single overlap adhesive joints: Volkersen's shear lag analysis, Goland and Reissner's theory, the generalized failure criterion, and the adherend failure criterion. It also examines the effect of surface treatment on joint strength. Experimental testing showed that untreated joint surfaces were four times weaker than treated surfaces. Two of the analytical methods - Volkersen's analysis and the adherend failure criterion - achieved reasonably accurate predictions of failure load.
EFFECT OF SURFACE ROUGHNESS ON CHARACTERISTICS OF SQUEEZE FILM BETWEEN POROUS...IAEME Publication
In investigation aims to analyse the effect of transverse surface roughness on the squeeze film performance between porous rectangular plates. The associated differential equation is stochastically averaged making use of stochastic averaging method of Christensen and Tonder for transverse surface roughness. The equation is solved with appropriate boundary conditions to obtain the pressure and consequentlythe load bearing. The graphical results suggest that the bearing suffers because of transverse surface roughness. However the situation is slightly better in the case of
negatively skew roughness. Further variance (-ve) makes the situation furtherimproved even if moderate values of porosity are involved
This document discusses applying the NCHRP-1-28 resilient modulus model to characterize blended unbound granular materials in Sudan. An experimental testing program measured the resilient modulus of blended samples using dynamic triaxial tests. The NCHRP-1-28 model was used to predict resilient modulus values, which showed good agreement with measured values, being 8-10% lower, providing conservative estimates. The materials tested included natural gravels blended with sand and crushed stone to meet gradation specifications for base materials. Measured properties like density, CBR and gradation are reported for the blended samples.
This document presents a simple phenomenological approach to modeling nanoindentation creep using conventional spring and dashpot elements. It describes how creep, which is the time-dependent increase in depth under a held load, can be modeled for a variety of materials using Maxwell and Voigt models. Equations are presented that relate the depth increase over time to the elastic modulus and viscosity of the material being tested. A method is described for fitting experimental nanoindentation data, including holding periods, to these equations to determine material properties while accounting for creep. The approach aims to provide an accessible way to analyze creep in nanoindentation that can be incorporated into computer programs.
A composite material can be defined as a combination of two or more materials that
gives better properties than those of the individual components used alone. In contrast to
metallic alloys, each material retains its separate chemical, physical, and mechanical
properties. The two constituents are reinforcement and a matrix. The main advantages of
composite materials are their high strength and stiffness combined with low density when
compared to classical materials. Micromechanical approach is found to be more suitable for
the analysis of composite materials because it studies the volume proportions of the
constituents for the desired lamina stiffness and strength.
Interrelation of Friction-Wear and Mechanism of Energy Dissipation for MEMS A...ijceronline
Adhesion is a predominating force in Micro electro mechanical System (MEMS) due to high surface to volume ratio. In the present study of MEMS surfaces contact, adhesional friction force and adhesive wear volume have been computed numerically and new interrelation in between the wear and friction is developed after, finding their ratio. Also, mechanism of energy dissipation has been summarized on the basis of Arrhenius theory of mechanochemical reaction under working condition of MEMS devices.
This document presents revisions to the Hoek-Brown failure criterion for rock masses. It resolves uncertainties in applying the criterion and incorporating it into numerical models. The revised criterion sets out a recommended calculation sequence and defines equations to determine rock mass strength parameters like cohesive strength and friction angle from the Geological Strength Index rating of rock mass quality. It also distinguishes between undisturbed and disturbed rock masses using a new disturbance factor.
Cohesive forces prevent the rotational breakup of rubble-pile asteroid (29075...Carlos Bella
1) The asteroid (29075) 1950 DA is rotating faster than would be allowed without cohesive forces, with a rotation period of just over 2 hours.
2) Thermal infrared observations and measurements of its orbital drift were used to determine it has a low bulk density of 1.7 g/cm3, indicating it is a rubble pile asteroid made of smaller pieces held together weakly.
3) For it to retain its fine-grained surface and resist breaking up from centrifugal forces at its rate of rotation, cohesive van der Waals forces between the grains comparable to lunar regolith are required, with a minimum cohesive strength of 64 Pa.
Three dimensional static analysis of two dimensional functionally graded platesijmech
In this paper, static analysis of two dimensional functionally graded plates based on three dimensional theory of elasticity is investigated. Graded finite element method has been used to solve the problem. The effects of power law exponents on static behavior of a fully clamped 2D-FGM plate have been investigated. The model has been compared with result of a 1D-FGM plate for different boundary conditions, and it shows very good agreement.
Three dimensional static analysis of two dimensional functionally graded platesrtme
In this paper, static analysis of two dimensional functionally graded plates based on three dimensional
theory of elasticity is investigated. Graded finite element method has been used to solve the problem. The
effects of power law exponents on static behavior of a fully clamped 2D-FGM plate have been investigated.
The model has been compared with result of a 1D-FGM plate for different boundary conditions, and it
shows very good agreement
This document compares the linear buckling analysis of flat plates with different thicknesses. Two flat plates with thicknesses of 1mm and 5mm were modeled and analyzed using LUSAS finite element software. The results showed that thicker plates had higher buckling loads, with the 5mm plate's buckling load being over 10 times greater than the 1mm plate's load. In conclusion, a plate's thickness directly influences its buckling value, with thicker plates exhibiting higher buckling strengths.
Dynamic Relaxation (DR) method is presented for the analysis of geometrically linear laterally loaded, rectangular laminated plates. The analysis uses the Mindlin plate theory which accounts for transverse shear deformations. A computer program has been compiled. The convergence and accuracy of the DR solutions of isotropic, orthotropic, and laminated plates for elastic small deflection response are established by comparison with different exact and approximate solutions. The present Dynamic Relaxation (DR) method shows a good agreement with other analytical and numerical methods used in the verification scheme. It was found that: The convergence and accuracy of the DR solution were dependent on several factors which include boundary conditions, mesh size and type, fictitious densities, damping coefficients, time increment and applied load. Also, the DR small deflection program using uniform meshes can be employed in the analysis of different thicknesses for isotropic, orthotropic or laminated plates under uniform loads in a fairly good accuracy.
This document discusses theories of composite plates and numerical methods used for bending and buckling analysis of laminated plates. It summarizes different plate theories including classical laminate theory (CLPT), first-order shear deformation theory (FSDT), and higher-order shear deformation theory (HSDT). Numerical methods covered include finite difference method (FDM), dynamic relaxation (DR), and finite element method (FEM). The document concludes that FEM can provide acceptable accuracy for modeling composite plates and is applicable to complex geometries.
This document presents a new model for describing the pressure dependence of elastic properties in uncemented sedimentary rocks. The model incorporates effects of sedimentary compaction and critical porosity on how porosity and density change with increasing pressure. It fits laboratory data on various rock samples well over a wide range of pressures. The new model provides an improved way to predict pressure-dependent rock properties and interpret seismic data compared to previous theoretical models.
This document summarizes a numerical study of indentation-induced cracking in brittle coatings on ductile substrates. Finite element modeling was used to simulate indentation with a spherical indenter. The coating was modeled as linear elastic, the substrate as elastic-perfectly plastic, and cracks in the coating were modeled using cohesive surfaces. Circumferential cracks were found to initiate at the coating surface near the contact edge due to high tensile radial stresses. The first crack caused a kink in the load-displacement curve. The spacing between cracks was on the order of the coating thickness. The effects of material properties and cohesive parameters on crack initiation and spacing were also investigated.
1) A finite element method was used to simulate the indentation of a ductile substrate coated with a thin elastic film using a rigid spherical indenter.
2) During loading, delamination was found to initiate tangentially at a distance of two to three times the contact radius.
3) During unloading, a circular part of the coating directly under the contact area was lifted off from the substrate, indicating normal delamination. Normal delamination was seen as a hump on the load-displacement curve.
4) There was a critical interfacial strength above which delamination could be prevented for a given indentation depth and material system. The effects of residual stress in the film and interface waviness
Surface roughness effect on the performance of a magnetic fluid based porous ...Alexander Decker
This document summarizes a study analyzing the performance of a porous rough secant shaped slider bearing using a magnetic fluid lubricant. The authors develop stochastic equations to model the pressure distribution and account for the random surface roughness. They present dimensionless equations for the load carrying capacity and friction. Graphs show that the magnetic fluid increases load capacity and decreases friction compared to conventional lubricants. However, increased porosity and surface roughness negatively impact performance. The positive effects of magnetization can reduce these negative impacts, especially for negatively skewed roughness and negative variance. The study concludes magnetic fluids improve bearing performance and can support loads even without fluid flow.
Research on Contact Characteristics between Bump End Effector and WaferIJRES Journal
In the IC industry, commonly used methods are wafer clamping friction transmission type and vacuum suction. Combining science and theological contact theory,the contact friction transmission characteristics when using the bump and transmission actuator wafer, the wafer and the end actuators. Starting from the material properties of the wafer by ANSYS simulation analysis in contact with the wafer bump deformation due to its own gravity, and verify that it meets the requirements of small deformation wafer transfer. Compute and solve the friction contact with the wafer bump bristles between.
Peculiarities of irrecoverable straining in stress-drop testIJERA Editor
The paper concerns with analytical description of the phenomena observed in stress drop tests, namely, negative increment in plastic and creep deformation due to the sudden decrease in the acting stresses while the net stress remains positive. The model is developed in terms of the synthetic theory of irrecoverable deformation which has been generalized by introducing interplay between the deformation properties of material in the direction of acting load and opposite to it.
The document summarizes an investigation comparing experimental and computational modeling results of grain deformation in a cast nickel superalloy. Digital image correlation was used to experimentally measure strain distributions across a tensile sample, finding heterogeneous strain localized in certain grains. A crystal plasticity finite element model was developed to simulate the deformation using orientations from EBSD maps. The model showed improved agreement with experimental strain distributions at lower values of the strain rate sensitivity parameter m, but still some disagreement on strain localization. Including subsurface grains in the model further improved agreement, showing the importance of full 3D microstructure representation.
This document describes Standard Test Method E 384 for determining microindentation hardness of materials. The standard covers using Knoop and Vickers indenters to make indentations between 1-1000 gf force. Hardness is calculated based on indentation size and geometry. Key points:
- Hardness is determined by dividing force by projected area or surface area of indentation for Knoop or Vickers respectively.
- Equipment must precisely control low forces and indentation size must be measured via microscope.
- Specimens must be flat and polished to accurately measure indentation diagonals and calculate hardness.
- Multiple sources of error exist and can affect accuracy of results, including force variation, indenter geometry, and measurement errors. Standard aims
The document discusses rock mass properties and the Hoek-Brown failure criterion for estimating the strength of jointed rock masses. It presents the generalized Hoek-Brown criterion equation and describes how to determine the intact rock properties of uniaxial compressive strength (σci) and the Hoek-Brown constant (mi) from triaxial test data or estimates. It also discusses estimating the Geological Strength Index (GSI) of the rock mass.
Prediction of joint strength and effect of the surface treatment on the singl...Filipe Giesteira
This document presents four analytical methods for predicting the strength of single overlap adhesive joints: Volkersen's shear lag analysis, Goland and Reissner's theory, the generalized failure criterion, and the adherend failure criterion. It also examines the effect of surface treatment on joint strength. Experimental testing showed that untreated joint surfaces were four times weaker than treated surfaces. Two of the analytical methods - Volkersen's analysis and the adherend failure criterion - achieved reasonably accurate predictions of failure load.
EFFECT OF SURFACE ROUGHNESS ON CHARACTERISTICS OF SQUEEZE FILM BETWEEN POROUS...IAEME Publication
In investigation aims to analyse the effect of transverse surface roughness on the squeeze film performance between porous rectangular plates. The associated differential equation is stochastically averaged making use of stochastic averaging method of Christensen and Tonder for transverse surface roughness. The equation is solved with appropriate boundary conditions to obtain the pressure and consequentlythe load bearing. The graphical results suggest that the bearing suffers because of transverse surface roughness. However the situation is slightly better in the case of
negatively skew roughness. Further variance (-ve) makes the situation furtherimproved even if moderate values of porosity are involved
This document discusses applying the NCHRP-1-28 resilient modulus model to characterize blended unbound granular materials in Sudan. An experimental testing program measured the resilient modulus of blended samples using dynamic triaxial tests. The NCHRP-1-28 model was used to predict resilient modulus values, which showed good agreement with measured values, being 8-10% lower, providing conservative estimates. The materials tested included natural gravels blended with sand and crushed stone to meet gradation specifications for base materials. Measured properties like density, CBR and gradation are reported for the blended samples.
This document presents a simple phenomenological approach to modeling nanoindentation creep using conventional spring and dashpot elements. It describes how creep, which is the time-dependent increase in depth under a held load, can be modeled for a variety of materials using Maxwell and Voigt models. Equations are presented that relate the depth increase over time to the elastic modulus and viscosity of the material being tested. A method is described for fitting experimental nanoindentation data, including holding periods, to these equations to determine material properties while accounting for creep. The approach aims to provide an accessible way to analyze creep in nanoindentation that can be incorporated into computer programs.
A composite material can be defined as a combination of two or more materials that
gives better properties than those of the individual components used alone. In contrast to
metallic alloys, each material retains its separate chemical, physical, and mechanical
properties. The two constituents are reinforcement and a matrix. The main advantages of
composite materials are their high strength and stiffness combined with low density when
compared to classical materials. Micromechanical approach is found to be more suitable for
the analysis of composite materials because it studies the volume proportions of the
constituents for the desired lamina stiffness and strength.
Interrelation of Friction-Wear and Mechanism of Energy Dissipation for MEMS A...ijceronline
Adhesion is a predominating force in Micro electro mechanical System (MEMS) due to high surface to volume ratio. In the present study of MEMS surfaces contact, adhesional friction force and adhesive wear volume have been computed numerically and new interrelation in between the wear and friction is developed after, finding their ratio. Also, mechanism of energy dissipation has been summarized on the basis of Arrhenius theory of mechanochemical reaction under working condition of MEMS devices.
This document presents revisions to the Hoek-Brown failure criterion for rock masses. It resolves uncertainties in applying the criterion and incorporating it into numerical models. The revised criterion sets out a recommended calculation sequence and defines equations to determine rock mass strength parameters like cohesive strength and friction angle from the Geological Strength Index rating of rock mass quality. It also distinguishes between undisturbed and disturbed rock masses using a new disturbance factor.
Cohesive forces prevent the rotational breakup of rubble-pile asteroid (29075...Carlos Bella
1) The asteroid (29075) 1950 DA is rotating faster than would be allowed without cohesive forces, with a rotation period of just over 2 hours.
2) Thermal infrared observations and measurements of its orbital drift were used to determine it has a low bulk density of 1.7 g/cm3, indicating it is a rubble pile asteroid made of smaller pieces held together weakly.
3) For it to retain its fine-grained surface and resist breaking up from centrifugal forces at its rate of rotation, cohesive van der Waals forces between the grains comparable to lunar regolith are required, with a minimum cohesive strength of 64 Pa.
Three dimensional static analysis of two dimensional functionally graded platesijmech
In this paper, static analysis of two dimensional functionally graded plates based on three dimensional theory of elasticity is investigated. Graded finite element method has been used to solve the problem. The effects of power law exponents on static behavior of a fully clamped 2D-FGM plate have been investigated. The model has been compared with result of a 1D-FGM plate for different boundary conditions, and it shows very good agreement.
Three dimensional static analysis of two dimensional functionally graded platesrtme
In this paper, static analysis of two dimensional functionally graded plates based on three dimensional
theory of elasticity is investigated. Graded finite element method has been used to solve the problem. The
effects of power law exponents on static behavior of a fully clamped 2D-FGM plate have been investigated.
The model has been compared with result of a 1D-FGM plate for different boundary conditions, and it
shows very good agreement
This document compares the linear buckling analysis of flat plates with different thicknesses. Two flat plates with thicknesses of 1mm and 5mm were modeled and analyzed using LUSAS finite element software. The results showed that thicker plates had higher buckling loads, with the 5mm plate's buckling load being over 10 times greater than the 1mm plate's load. In conclusion, a plate's thickness directly influences its buckling value, with thicker plates exhibiting higher buckling strengths.
Dynamic Relaxation (DR) method is presented for the analysis of geometrically linear laterally loaded, rectangular laminated plates. The analysis uses the Mindlin plate theory which accounts for transverse shear deformations. A computer program has been compiled. The convergence and accuracy of the DR solutions of isotropic, orthotropic, and laminated plates for elastic small deflection response are established by comparison with different exact and approximate solutions. The present Dynamic Relaxation (DR) method shows a good agreement with other analytical and numerical methods used in the verification scheme. It was found that: The convergence and accuracy of the DR solution were dependent on several factors which include boundary conditions, mesh size and type, fictitious densities, damping coefficients, time increment and applied load. Also, the DR small deflection program using uniform meshes can be employed in the analysis of different thicknesses for isotropic, orthotropic or laminated plates under uniform loads in a fairly good accuracy.
This document discusses theories of composite plates and numerical methods used for bending and buckling analysis of laminated plates. It summarizes different plate theories including classical laminate theory (CLPT), first-order shear deformation theory (FSDT), and higher-order shear deformation theory (HSDT). Numerical methods covered include finite difference method (FDM), dynamic relaxation (DR), and finite element method (FEM). The document concludes that FEM can provide acceptable accuracy for modeling composite plates and is applicable to complex geometries.
This document presents a new model for describing the pressure dependence of elastic properties in uncemented sedimentary rocks. The model incorporates effects of sedimentary compaction and critical porosity on how porosity and density change with increasing pressure. It fits laboratory data on various rock samples well over a wide range of pressures. The new model provides an improved way to predict pressure-dependent rock properties and interpret seismic data compared to previous theoretical models.
This document summarizes a numerical study of indentation-induced cracking in brittle coatings on ductile substrates. Finite element modeling was used to simulate indentation with a spherical indenter. The coating was modeled as linear elastic, the substrate as elastic-perfectly plastic, and cracks in the coating were modeled using cohesive surfaces. Circumferential cracks were found to initiate at the coating surface near the contact edge due to high tensile radial stresses. The first crack caused a kink in the load-displacement curve. The spacing between cracks was on the order of the coating thickness. The effects of material properties and cohesive parameters on crack initiation and spacing were also investigated.
1) A finite element method was used to simulate the indentation of a ductile substrate coated with a thin elastic film using a rigid spherical indenter.
2) During loading, delamination was found to initiate tangentially at a distance of two to three times the contact radius.
3) During unloading, a circular part of the coating directly under the contact area was lifted off from the substrate, indicating normal delamination. Normal delamination was seen as a hump on the load-displacement curve.
4) There was a critical interfacial strength above which delamination could be prevented for a given indentation depth and material system. The effects of residual stress in the film and interface waviness
The document summarizes different hardness testing methods. It describes macrohardness tests like Rockwell, Brinell and Vickers which use indenters with loads over 1kg. Microhardness tests like Knoop and Vickers use loads under 1kg for small parts. The Rockwell test measures depth changes from minor and major loads. Brinell uses a steel ball under load and measures indentation diameter. Vickers uses a pyramidal indenter and calculates hardness from diagonal lengths. Hardness is related to properties like tensile strength and can estimate them for materials like steel. Experiments will test and calculate hardness values for various materials using these methods.
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.
Annals of Materials Science & Engineering is a scholarly open access, peer reviewed journal dedicated to publish articles in all areas of Material Science such as aerospace engineering, mechanical engineering, metallurgical engineering, electrical/electronic engineering, civil engineering, fluid mechanics and instrumentation.
The aim of this journal is for scientists and academicians all over the world to support, share, and discuss various new issues and developments in different areas of Material Science & Engineering.
Annals of Materials Science & Engineering accepts original research articles, review articles, case reports, commentaries, clinical images and rapid communication on all the aspects of Material science and engineering.
This document summarizes a study on plastic zone size and effective distance under mixed mode fracture using a volumetric approach. U-notched circular ring specimens made of 45CDS6 steel were subjected to compression loading with notch radii ranging from 0.15-2mm and angles from 0-33 degrees. Finite element analysis was conducted to determine stress distributions. Two methods were used to evaluate plastic zone size - the volumetric method relating it to effective stress and notch stress intensity factor, and the von Mises yield criterion. The plastic zone sizes determined from both methods showed good agreement. A new model was proposed to evaluate plastic zone size under mixed mode fracture conditions.
We study the link between the indentation size effect and the density of geometrically necessary dislocations (GNDs) through the following
approach: four indents of different depth and hardness were placed in a Cu single crystal using a conical indenter with a spherical tip. The
deformation-induced lattice rotations below the indents were monitored via a three-dimensional electron backscattering diffraction method
with a step size of 50 nm. From these data we calculated the first-order gradients of strain and the GND densities below the indents. This
approach allowed us to quantify both the mechanical parameters (depth, hardness) and the lattice defects (GNDs) that are believed to be
responsible for the indentation size effect.Wefind that theGNDdensity does not increase with decreasing indentation depth but rather drops
instead.
While the computed transported turbulence dissipation rate, , works well as part of a differential
equation-based turbulence model in predicting turbulent flows, it doesn’t seem to work well when used to
determine the Kolmogorov length-scale (ℓ퐾표푙) which, like the other Kolmogorov scales, exists within the viscous
sublayer portion of the inner turbulent boundary layer zone. Using may lead to an increase in ℓ퐾표푙 as roughness
increases, the opposite of what should happen. It is proposed here to replace the computed (and its level at the
1
st point off the wall as dictated by wall functions) with the one resulting from basic law-of-the-wall sublayer
relationships which includes the Prandtl-Schlichting (P-S) roughness effect. This approach enables physically
correct prediction of ℓ퐾표푙, particularly a reliable decrease thereof with increasing roughness level.
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The present study deals with the assessment of
higher order theory of laminated beams under static
mechanical loads. The theory has been presented for general
lay-up of the laminate. The displacement field is expressed in
terms of only three primary displacement variables by
satisfying exactly the conditions of zero transverse shear stress
at the top and bottom and its continuity at layer interfaces.
The governing equations of motion and boundary conditions
are derived using virtual work. The number of primary
displacement unknowns is three, which is independent of the
number of layers and equal in number to the ones used in the
first order shear deformation theory. Higher order theory thus
preserves the computational advantage of an equivalent single
layer theory. The Third order theory and First order shear
deformation theory are assessed by comparison with the exact
two-dimensional elasticity solution of the simply-supported
beam. A theory is good only if it yields accurate results for all
kinds of loads and for any lay-up of the beam. For this purpose,
parametric studies for composite laminates and sandwich
beams are conducted.
Application of CAD and SLA Method in Dental ProsthesisIDES Editor
Placement of dental implants requires precise
planning that accounts for anatomic limitations and
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planning to the surgical field is limited. Precise implant
placement no longer relies upon so called mental-navigation
but rather can be computer guided, based on a three
dimensional prosthetically directed plan. Recently, novel CAD/
CAM techniques such as stereolithographic rapid prototyping
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improve precision of implant placement. The purpose of this
paper is to discuss the use of scanning equipments to transfer
clinically relevant prosthetic information which can be used
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surgical guides. The proposed method provides solid evidence
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1989 optical measurement of the refractive index, layer thickness, and volume...pmloscholte
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This summary provides an overview of Jimmy Pan's summer research project at Vanderbilt University's Multiscale Computational Mechanics Laboratory:
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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 Birefringent Property of an Optical Resinfor the Study of a Stress Field ...ijceronline
International Journal of Computational Engineering Research(IJCER) is an intentional online Journal in English monthly publishing journal. This Journal publish original research work that contributes significantly to further the scientific knowledge in engineering and Technology.
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.
Numerical modeling of the welding defect influence on fatigue life of the wel...inventy
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2. Communications
the entire loading-unloading period (Fig. 1):
Wd Wt 2 We . (4)
The work performed during loading (Wt ) and that re-
gained during unloading (We ) can be calculated by the
integration of Eqs. (2) and (3), respectively.
It was found that in spite of the linear terms appear-
ing in Eqs. (2) and (3) for a broad variety of materials
and in a wide load range, the following relationship is
with good accuracy valid (see Fig. 2):
r
We c3
. (5)
Wt c3
The parameter c3 characterizes the resistance of the
material against the elastic-plastic deformation.11 In the
case of ideally plastic materials, the load-depth function
FIG. 1. Schematic picture of an indentation cycle.
is purely quadratic: P c3 h2 ,1,12 and in this case there
is no elastic relaxation, the d 7 ? hm equation between
TABLE I. Compositions and densities of Si3 N4 ceramic samples. the diagonal d and the maximum indentation depth hm
90 wt. %, Si3 N4 , 4 wt. % 90.9 wt. %, Si3 N4 , 3 wt. % which is the consequence of the geometry of the Vickers
Al2 O3 , 6 wt. % Y2 O3 Al2 O3 , 6.1 wt. % Y2 O3 pyramid is exactly satisfied [Fig. 3(a)]. Consequently the
Meyer hardness of ideally plastic materials can be given
Sample Density (g cm3 ) Sample Density (g cm3 )
in the following form:
1 2.03 6 2.697
2 2.11 7 2.823 P P
H 2 a1 ? c3 (6)
3 2.34 8 2.935 d2 2
24.5hm
4 2.54 9 2.954
5 2.70 10 3.032 with a1 0.0408 for the Vickers geometry.
11 3.115 If the material is not ideally plastic then with in-
12 3.161 creasing elastic contribution, the elastic deflection under
the indenter is increasing [Fig. 3(b)]. Consequently 7hm
becomes increasingly larger than d, and as a result of
(sy E is large) then a significant portion of the contact this a1 ? c3 will be less than H. This can be taken into
area at maximum depth is due to elastic deformation. account introducing a relationship between H and a1 ? c3
Consequently, the residual projected area is smaller than of the form:
the projected contact area at maximum penetration, and
Wt
the conventional Meyer hardness is larger than the mean H a1 ? c3 ? . (7)
contact pressure. Wd
The load-penetration depth function can be de-
scribed with quadratic polinoms (Fig. 1):
P c2 h 1 c3 h2 , (2)
P c2 h 2 h0 1 c3 h 2 h0 2 , (3)
both in the loading and in the unloading periods, respec-
tively, where P is the load, h is the penetration depth,
and h0 is the residual indentation depth after removing
the punch; c2 , c3 , c2 , and c3 are fitting parameters.
The total indentation work, Wt , is the integral of the
load versus the indentation depth, i.e., the area under
the load-penetration depth curve during the unloading
period. Upon unloading a part of this work, We , can be
regained; it equals to the area under the load-indentation
depth curve for this latter period. The difference of these FIG. 2. The ratio of the elastic and total work versus the parameters
two quantities, Wd , gives the net work expended during of the indentation curves.
J. Mater. Res., Vol. 11, No. 12, Dec 1996 2965
3. Communications
Sneddon’s elastic theory13 and empirical results of Oliver
and Pharr,3 the contact depth can be given as:
Pm
hc hm 2 e , (9)
S
where S is the slope of the initial part of the unloading
curve (Fig. 1) and e 0.75 for the case of Vickers
indenters.
To compare the new hardness formula (7) with the
mean contact pressure as expressed in Eqs. (8) and (9),
Pm and hc are expressed with the c3 and c3 parameters
and the indentation works. If only the quadratic terms
existed in Eqs. (2) and (3), Pm and hc could be expressed
easily with the parameters c3 and c3 . Because of the
existence of the linear terms, some approximations are
FIG. 3. Schematic picture showing the behavior of various materials used in the considerations.
(a –c) during Vickers indentation. According to Eq. (3) S can be given as
dP Å
It is obvious that this new definition of H gives back S c2 1 2c3 hm 2 h0 . (10)
Eq. (6) for ideally plastic materials and it increases dh hm
with increasing elasticity, and in the limiting case of The second term in Eq. (10) may be expressed as a
an ideally elastic material it becomes infinite, because in fraction of S:
this case there is no residual deformation after unloading
[Fig. 3(c)]. Figure 4 shows that the H values determined kS 2c3 hm 2 h0 (11)
from DSI measurements according to Eq. (7) agree well
within the experimental errors with the conventionally and similarly the quadratic term of the load-depth func-
determined hardness. tion of the unloading curve as a fraction of the maximum
The most frequently used hardness determination load:
method from DSI measurements introduced by Oliver
k Pm c3 hm 2 h0 2 . (12)
and Pharr3 is based on the mean contact pressure at
the maximum indentation depth with the following With Eqs. (11) and (12) Pm S can be given as
expression:
Pm Pm Pm Pm k k hm 2 h0
Hm a1 , (8) . (13)
A 2
24.5hc 2
hc S k k 2
From Eqs. (3) and (10) –(13), hc can be given in the
where A is the projected contact area and hc is the
following form:
contact depth at the maximum load [Fig. 3(b)]. Using
2 e
hc hm 2 h m 2 h0 . (14)
11k 2
Expressing the quadratic term in Eq. (2) as a fraction of
the maximum load:
2
kPm c3 hm , (15)
the Hm mean contact pressure in Eq. (8) can be written
as follows:
1
Hm a 1 c3 ≥ p p q ¥.
2 k e c3
(16)
k2 11k 2 c3
According to our measurements for the different
materials investigated with different loads, k and k vary
p
FIG. 4. The conventionally determined hardness number versus the between 0.64 and 1. If k > 0.64 then 2 k 11
quantity calculated on the basis of Eq. (7). k > 0.98; therefore, this quantity can be taken as 1.
2966 J. Mater. Res., Vol. 11, No. 12, Dec 1996
4. Communications
Using Eq. (5) the following relationship is obtained for A new formula is proposed for the characterization
Hm : of the hardness of materials from DSI tests. The val-
1 ues of the hardness calculated by this equation agree
Hm a 1 c3 ≥ p ¥ . (17) well with those measured by the conventional method
e We 2
k2 2 Wt for a broad variety of materials. Comparing the new
hardness formula with that based on the mean contact
This can be compared with the new hardness formula pressure, the former correctly describes the behavior of
Eq. (7), which using Eq. (4) can be written as: the conventional hardness both in the ideally plastic and
1 ideally elastic limiting cases, while the latter deviates
H a 1 c3 We . (18) from the conventional hardness number in the ideally
12 Wt
elastic limit. At the same time in the range where optical
The difference between H and Hm can be seen in measurements can also be applied (0 < We Wt < 0.7),
Fig. 5 in which the two hardness numbers divided by the difference between the two DSI evaluation methods
a1 c3 are shown as a function of We Wt . For Hm a1 c3
p is within the experimental error. A technical advantage
three curves are shown as k equal to 0.8 or 0.9 or of the new evaluation method is that the parameters used
1 (k 0.64 or 0.81 or 1). We Wt equals zero for the in the hardness formula can be determined at a high
ideally plastic limiting case; it increases with increasing accuracy from the registered indentation curves. Further
elastic deformation in the indentation, and it is 1 for the measurements are planned on materials and for loading
ideally elastic material. By the new hardness formula conditions falling in the region where the new hardness
[Eqs. (7) or (18)], the behavior of the conventional hard- number is rapidly increasing (0.8 < We Wt < 1). This
ness number (and consequently the plastic properties of regime, however, is not easy to obtain experimentally.
materials) is better characterized than by the mean con-
tact pressure, because while the former tends to infinity
ACKNOWLEDGMENTS
the latter gives a finite value in the ideally elastic limiting
case. As it can be seen in Fig. 5 in the region 0 < The authors are grateful to P. Arat´ for providing
o
We Wt < 0.7, there is no significant difference between the Si3 N4 ceramic samples. This work was supported
the two hardness numbers. The We Wt values for the ma- by the Hungarian National Scientific Fund in Contract
terials investigated here are in this region; consequently Nos. T-017637 and T-017639.
the hardness numbers obtained by both methods agree
well with the values of the Meyer hardness obtained by REFERENCES
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