In the present analytical and numerical study, the thermal mismatching stress induced under differential
temperature conditions of tri-layered assembly with bond is investigated. The thermal mismatching stresses are
one of the reasons for structural failures between two or more connected devices. Therefore it is very essential to
understand variation of these stresses and estimation in the interfaces play an important role in design and
reliability studies of microelectronic assemblies. In this paper, a physical model is proposed for the interfacial
shearing and peeling stresses occurring at the interfaces of tri-layered dissimilar materials with the effect of
bonding subjected to differential uniform temperature in the layer. It observed from both analytical and
numerical study that the shearing stress reduced in the range of 60% to 70% at interface (1-2) and 35% to 40%
at (2-3) interface. Peeling stress are continuously reduced in the range of 10% - 20% at (1-2) interface and 13%
- 35% at (2-3) interface due to the influence of bond layer. Thus, it indicates that, the bond layer consideration
may influence significantly on interfacial stress. It is found that the both interfacial shearing stresses and peeling
stresses decreased considerably at the interface with the increase of bond layer thickness.
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.
Numerical Analysis of Hygrothermal Effect on Laminated Composite PlatesIRJET Journal
This document presents a numerical analysis of the hygrothermal effects on laminated composite plates. It summarizes previous research on modeling the behavior of composite laminates under temperature and moisture gradients. The analysis uses the finite element tool ABAQUS to model simply supported cross-ply laminates and compare the displacement and stress results to analytical solutions. The numerical model considers shear deformation and transverse thermal strains and predicts the hygrothermal response of symmetric and antisymmetric angle-ply plates with different layer orientations and material properties.
The document discusses theoretical models for predicting how material properties of GaN nanocrystals vary with size and shape. It presents a model based on cohesive energy that can describe size and shape dependencies of band gap, dielectric constant, Young's modulus, and melting temperature. The model predictions for melting temperature of GaN nanotubes agree well with molecular dynamics simulations. The model is then applied to derive an expression for how the band gap of GaN nanocrystals depends on size.
Numerical modeling of uneven thermoplastic polymers behaviour using experimen...Marcos Bianchi (Msc_Mba)
This document discusses numerical modeling of the behavior of uneven thermoplastic polymers using experimental stress-strain data and pressure dependent yield criteria to improve design practices. It presents the following:
1) Four polymers (PA-66, PA-6, PP, HDPE) were tested under tension and compression to determine their unevenness levels. PA-6 and PP showed significant unevenness, with compressive yield strengths 25-70% higher than tensile strengths.
2) Pressure dependent yield criteria that account for unevenness, such as conical and parabolic modified von Mises models, were reviewed. These criteria incorporate the effect of hydrostatic pressure on yield strength.
3) Experimental stress-strain data was
Higher Order Normal Shear Deformation Theory for Static FG Rectangular PlatesIRJET Journal
The document discusses static analysis of functionally graded rectangular plates using higher order normal shear deformation theory (HONST). Functionally graded materials have properties that vary continuously through the thickness, modeled by a power law relationship. HONST is used to derive governing equations for the functionally graded plate based on equilibrium and strain-displacement relationships. Material properties are calculated according to the power law and volume fractions. Numerical results are obtained for plates under different loads and boundary conditions and compared to validate the model.
This document summarizes different stress-strain curve models and their corresponding rheological models. It describes elastic-perfectly plastic, elastic-linear hardening, elastic-power hardening, and Ramberg-Osgood stress-strain relationships. The elastic-perfectly plastic model is flat beyond yielding. Elastic-linear hardening approximates curves that rise after yielding. Elastic-power hardening fits curves using a power law relationship for stress and strain beyond yielding. Ramberg-Osgood uses separate equations for elastic and plastic strains summed together in one continuous curve.
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.
Numerical Analysis of Hygrothermal Effect on Laminated Composite PlatesIRJET Journal
This document presents a numerical analysis of the hygrothermal effects on laminated composite plates. It summarizes previous research on modeling the behavior of composite laminates under temperature and moisture gradients. The analysis uses the finite element tool ABAQUS to model simply supported cross-ply laminates and compare the displacement and stress results to analytical solutions. The numerical model considers shear deformation and transverse thermal strains and predicts the hygrothermal response of symmetric and antisymmetric angle-ply plates with different layer orientations and material properties.
The document discusses theoretical models for predicting how material properties of GaN nanocrystals vary with size and shape. It presents a model based on cohesive energy that can describe size and shape dependencies of band gap, dielectric constant, Young's modulus, and melting temperature. The model predictions for melting temperature of GaN nanotubes agree well with molecular dynamics simulations. The model is then applied to derive an expression for how the band gap of GaN nanocrystals depends on size.
Numerical modeling of uneven thermoplastic polymers behaviour using experimen...Marcos Bianchi (Msc_Mba)
This document discusses numerical modeling of the behavior of uneven thermoplastic polymers using experimental stress-strain data and pressure dependent yield criteria to improve design practices. It presents the following:
1) Four polymers (PA-66, PA-6, PP, HDPE) were tested under tension and compression to determine their unevenness levels. PA-6 and PP showed significant unevenness, with compressive yield strengths 25-70% higher than tensile strengths.
2) Pressure dependent yield criteria that account for unevenness, such as conical and parabolic modified von Mises models, were reviewed. These criteria incorporate the effect of hydrostatic pressure on yield strength.
3) Experimental stress-strain data was
Higher Order Normal Shear Deformation Theory for Static FG Rectangular PlatesIRJET Journal
The document discusses static analysis of functionally graded rectangular plates using higher order normal shear deformation theory (HONST). Functionally graded materials have properties that vary continuously through the thickness, modeled by a power law relationship. HONST is used to derive governing equations for the functionally graded plate based on equilibrium and strain-displacement relationships. Material properties are calculated according to the power law and volume fractions. Numerical results are obtained for plates under different loads and boundary conditions and compared to validate the model.
This document summarizes different stress-strain curve models and their corresponding rheological models. It describes elastic-perfectly plastic, elastic-linear hardening, elastic-power hardening, and Ramberg-Osgood stress-strain relationships. The elastic-perfectly plastic model is flat beyond yielding. Elastic-linear hardening approximates curves that rise after yielding. Elastic-power hardening fits curves using a power law relationship for stress and strain beyond yielding. Ramberg-Osgood uses separate equations for elastic and plastic strains summed together in one continuous curve.
This document describes a Meshless Local Petrov-Galerkin (MLPG) Mixed Collocation Method for solving Cauchy inverse heat transfer problems. The method independently interpolates temperature and heat flux fields using the same meshless basis functions. Balance and compatibility equations are enforced through collocation at nodes. Numerical examples demonstrate the accuracy, convergence, and stability of the method for inverse heat transfer problems where both temperature and heat flux are prescribed on part of the boundary.
The document summarizes a study of test data on the compressive strength of masonry walls made of hollow clay units. It finds that the geometrical properties of the units, such as the ratio of bearing area to gross area (b), have an important effect on wall strength beyond just the compressive strength of the units. For end-constructed walls, the study derived an empirical equation (Equation 4) that expresses wall strength M as a function of the mortar strength m, unit strength u, and the b ratio. This simple equation was found to reasonably fit the available test data.
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
The document presents a mathematical analysis of the transient temperature distribution and thermal stresses in a solid sphere with internal heat generation. The heat conduction equation is solved using integral transforms to obtain the temperature as a trigonometric series involving the heat sources, initial temperature, and boundary conditions. Displacement and stresses are then derived from the temperature distribution. Key results include expressions for temperature, displacement, and stresses as functions of time and position within the sphere for different types of internal heat sources like point, volume, and spherical sources. Comparisons of the effects of varying heat sources on temperature profile and stresses are presented.
This document analyzes the electro-thermal stress and strain in a functionally graded metal (FGM) line under a direct current field. The FGM line is composed of copper and aluminum with properties varying linearly along the length. A finite difference method is used to numerically solve the coupled electrical, thermal, and mechanical equations. The results show that thermal stress and strain in the FGM line are between those of pure copper and aluminum lines. Maximum stress and strain occur slightly offset from the midpoint in the FGM line. Buried lines experience higher stress and strain than bare lines due to lack of convective cooling at the surface.
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.
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.
Effect of Process Parameters on the Total Heat Damaged Zone (HDZ) during Micr...IJAMSE Journal
In micro electrical discharge machining, three subsurface layersare formed on the workpiece, they are; recast zone, heat affected zone and converted zone, primarily due to heating-quenching cycles. The HDZ in micro-EDM is characterized by cracks and weakness in the grain boundary and thermal residual stresses. This paper presents the effect of process parameters on the HDZ in micro-EDM of plastic mold steel 1.2738. As the energy of the sparks increases, the thickness of the HDZ increases and the average coefficient of correlation between energy and HDZ considering three different sections of the zone is 0.8099. Therefore, the effect of process parameters governing the discharge energy are analyzed; they are: average current (Ia), peak current (Ip) and pulse ‘on-time’ (Ton). An overall increase in heat-damaged zone thickness by 105% is observed with an increase in pulse on time.
This document provides instructions for a mechanical engineering exam. It specifies that the exam contains 65 multiple choice questions worth 100 marks. Questions 1-25 are worth 1 mark each, questions 26-55 are worth 2 marks each, and questions 56-65 in the general aptitude section are worth 1 or 2 marks depending on the question. The document provides details on how to fill out the answer sheet, how marks will be awarded and deducted, and exam policies regarding calculators, rough work, and start time.
Establishing empirical relations to predict grain size and hardness of pulsed...drboon
SS 304L, an austenitic Chromium-Nickel stainless steel offering the optimum combination of corrosion resistance, strength and ductility, is favorable for many mechanical components. The low carbon content reduces susceptibility to carbide precipitation during welding. In case of single pass welding of thinner section of this alloy, pulsed current micro plasma arc welding was found beneficial due to its advantages over the conventional continuous current process. The paper focuses on developing mathematical models to predict grain size and hardness of pulsed current micro plasma arc welded SS304L joints. Four factors, five level, central composite rotatable design matrix is used to optimize the number of experiments. The mathematical models have been developed by response surface method. The adequacy of the models is checked by ANOVA technique. By using the developed mathematical models, grain size and hardness of the joints can be predicted with 99% confidence level. Contour plots are drawn to study the interaction effect of pulsed current micro plasma arc welding parameters on fusion zone grain size and hardness of SS304L steel.
Heat and mass transfer on mhd flow through a porous mediumAlexander Decker
This document summarizes a study on heat and mass transfer of an electrically conducting fluid flowing over a stretching surface through a porous medium. The study considers the effects of a magnetic field, heat source, and viscous dissipation. An exact solution is derived for the velocity field using similarity transformations. The coupled non-linear heat equation is solved using Kummer's function, with the non-homogeneity contributed by viscous dissipation. The skin friction and temperature profiles are obtained, with the temperature solution involving confluent hypergeometric functions.
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
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.
A Displacement-Potential Scheme to Stress Analysis of a Cracked Stiffened Pan...inventionjournals
This paper deals with an efficient analytical scheme for the analysis of stress and displacement fields of boundary-value problemsof plane elasticity with mixed boundary conditions and material discontinuity. More specifically, the mechanical behavior of a stiffened panel with an edge crack is analyzed under the influence of axial loading, using a new analytical scheme. Earlier mathematical models of elasticity were very deficient in handling the practical stress problems of solid mechanics. Analytical methods of solution have not gained that much popularity in the field of stress analysis, mainly because of the inability of dealing with mixed boundary conditions, irregular boundary shapes, and material discontinuity
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
This document provides a review of size effect models and fracture mechanics as they relate to small scale structural modeling. It discusses the history of studying size effects dating back to Leonardo da Vinci and Galileo. More recent contributions include Griffith's work founding fracture mechanics in 1921 and Weibull completing the statistical size effect theory. The review explores deterministic size effect models based on fracture energy and nonlinear fracture mechanics that can better predict behavior of quasibrittle materials like concrete compared to linear elastic fracture mechanics. It presents Bazant's size effect law relating nominal stress to characteristic structure size and discusses its application and limitations for notched and unnotched specimens.
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.
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.
O documento descreve um projeto sobre cultura afro desenvolvido com alunos. O projeto incluiu pesquisas sobre a África, sua cultura e população, além de atividades como rodas de conversa, leituras e vídeos para ensinar sobre o respeito à herança e cultura afro-descendente.
Grid-Connected Pv-Fc Hybrid System Power Control Using Mppt And Boost ConverterIJERA Editor
This paper proposes a method for operating a grid connected hybrid system. This system composed of a Photovoltaic (PV) array and a Proton exchange membrane fuel cell (PEMFC) is considered. As the variations occur in temperature and irradiation during power delivery to load, Photo voltaic (PV) system becomes uncontrollable. In coordination with PEMFC, the hybrid system output power becomes controllable. Two operation modes are the unit-power control (UPC) mode and the feeder-flow control (FFC) mode, can be applied to the hybrid system. All MPPT methods follow the same goal that is maximizing the PV system output power by tracking the maximum power on every operating condition. Maximum power point tracking technique (Incremental conductance) for photovoltaic systems was introduced to maximize the produced energy. The coordination of two control modes, coordination of the PV array and the PEMFC in the hybrid system, and determination of reference parameters are presented. The proposed operating strategy systems with a flexible operation mode change always operate the PV array at maximum output power and the PEMFC in its high efficiency performance band. Also thus improving the performance of system operation, enhancing system stability, and reducing the number of operating mode changes.
This document appears to be an email in Spanish from someone named Camille Automatico, but the content is unclear as it only contains their name and email address with no other text.
O documento lista locais noturnos em vários países asiáticos, começando pela entrada na Ásia pelo Bósforo, e incluindo Dubai, Índia, Singapura, Malásia, Hong Kong, China, Taiwan, Japão. As principais atrações incluem o Burj al Arab em Dubai, o Taj Mahal na Índia, as Torres Petronas na Malásia, a Grande Muralha da China e locais em Hong Kong, Xangai e Tóquio.
This document describes a Meshless Local Petrov-Galerkin (MLPG) Mixed Collocation Method for solving Cauchy inverse heat transfer problems. The method independently interpolates temperature and heat flux fields using the same meshless basis functions. Balance and compatibility equations are enforced through collocation at nodes. Numerical examples demonstrate the accuracy, convergence, and stability of the method for inverse heat transfer problems where both temperature and heat flux are prescribed on part of the boundary.
The document summarizes a study of test data on the compressive strength of masonry walls made of hollow clay units. It finds that the geometrical properties of the units, such as the ratio of bearing area to gross area (b), have an important effect on wall strength beyond just the compressive strength of the units. For end-constructed walls, the study derived an empirical equation (Equation 4) that expresses wall strength M as a function of the mortar strength m, unit strength u, and the b ratio. This simple equation was found to reasonably fit the available test data.
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
The document presents a mathematical analysis of the transient temperature distribution and thermal stresses in a solid sphere with internal heat generation. The heat conduction equation is solved using integral transforms to obtain the temperature as a trigonometric series involving the heat sources, initial temperature, and boundary conditions. Displacement and stresses are then derived from the temperature distribution. Key results include expressions for temperature, displacement, and stresses as functions of time and position within the sphere for different types of internal heat sources like point, volume, and spherical sources. Comparisons of the effects of varying heat sources on temperature profile and stresses are presented.
This document analyzes the electro-thermal stress and strain in a functionally graded metal (FGM) line under a direct current field. The FGM line is composed of copper and aluminum with properties varying linearly along the length. A finite difference method is used to numerically solve the coupled electrical, thermal, and mechanical equations. The results show that thermal stress and strain in the FGM line are between those of pure copper and aluminum lines. Maximum stress and strain occur slightly offset from the midpoint in the FGM line. Buried lines experience higher stress and strain than bare lines due to lack of convective cooling at the surface.
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.
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.
Effect of Process Parameters on the Total Heat Damaged Zone (HDZ) during Micr...IJAMSE Journal
In micro electrical discharge machining, three subsurface layersare formed on the workpiece, they are; recast zone, heat affected zone and converted zone, primarily due to heating-quenching cycles. The HDZ in micro-EDM is characterized by cracks and weakness in the grain boundary and thermal residual stresses. This paper presents the effect of process parameters on the HDZ in micro-EDM of plastic mold steel 1.2738. As the energy of the sparks increases, the thickness of the HDZ increases and the average coefficient of correlation between energy and HDZ considering three different sections of the zone is 0.8099. Therefore, the effect of process parameters governing the discharge energy are analyzed; they are: average current (Ia), peak current (Ip) and pulse ‘on-time’ (Ton). An overall increase in heat-damaged zone thickness by 105% is observed with an increase in pulse on time.
This document provides instructions for a mechanical engineering exam. It specifies that the exam contains 65 multiple choice questions worth 100 marks. Questions 1-25 are worth 1 mark each, questions 26-55 are worth 2 marks each, and questions 56-65 in the general aptitude section are worth 1 or 2 marks depending on the question. The document provides details on how to fill out the answer sheet, how marks will be awarded and deducted, and exam policies regarding calculators, rough work, and start time.
Establishing empirical relations to predict grain size and hardness of pulsed...drboon
SS 304L, an austenitic Chromium-Nickel stainless steel offering the optimum combination of corrosion resistance, strength and ductility, is favorable for many mechanical components. The low carbon content reduces susceptibility to carbide precipitation during welding. In case of single pass welding of thinner section of this alloy, pulsed current micro plasma arc welding was found beneficial due to its advantages over the conventional continuous current process. The paper focuses on developing mathematical models to predict grain size and hardness of pulsed current micro plasma arc welded SS304L joints. Four factors, five level, central composite rotatable design matrix is used to optimize the number of experiments. The mathematical models have been developed by response surface method. The adequacy of the models is checked by ANOVA technique. By using the developed mathematical models, grain size and hardness of the joints can be predicted with 99% confidence level. Contour plots are drawn to study the interaction effect of pulsed current micro plasma arc welding parameters on fusion zone grain size and hardness of SS304L steel.
Heat and mass transfer on mhd flow through a porous mediumAlexander Decker
This document summarizes a study on heat and mass transfer of an electrically conducting fluid flowing over a stretching surface through a porous medium. The study considers the effects of a magnetic field, heat source, and viscous dissipation. An exact solution is derived for the velocity field using similarity transformations. The coupled non-linear heat equation is solved using Kummer's function, with the non-homogeneity contributed by viscous dissipation. The skin friction and temperature profiles are obtained, with the temperature solution involving confluent hypergeometric functions.
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
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.
A Displacement-Potential Scheme to Stress Analysis of a Cracked Stiffened Pan...inventionjournals
This paper deals with an efficient analytical scheme for the analysis of stress and displacement fields of boundary-value problemsof plane elasticity with mixed boundary conditions and material discontinuity. More specifically, the mechanical behavior of a stiffened panel with an edge crack is analyzed under the influence of axial loading, using a new analytical scheme. Earlier mathematical models of elasticity were very deficient in handling the practical stress problems of solid mechanics. Analytical methods of solution have not gained that much popularity in the field of stress analysis, mainly because of the inability of dealing with mixed boundary conditions, irregular boundary shapes, and material discontinuity
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
This document provides a review of size effect models and fracture mechanics as they relate to small scale structural modeling. It discusses the history of studying size effects dating back to Leonardo da Vinci and Galileo. More recent contributions include Griffith's work founding fracture mechanics in 1921 and Weibull completing the statistical size effect theory. The review explores deterministic size effect models based on fracture energy and nonlinear fracture mechanics that can better predict behavior of quasibrittle materials like concrete compared to linear elastic fracture mechanics. It presents Bazant's size effect law relating nominal stress to characteristic structure size and discusses its application and limitations for notched and unnotched specimens.
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.
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.
O documento descreve um projeto sobre cultura afro desenvolvido com alunos. O projeto incluiu pesquisas sobre a África, sua cultura e população, além de atividades como rodas de conversa, leituras e vídeos para ensinar sobre o respeito à herança e cultura afro-descendente.
Grid-Connected Pv-Fc Hybrid System Power Control Using Mppt And Boost ConverterIJERA Editor
This paper proposes a method for operating a grid connected hybrid system. This system composed of a Photovoltaic (PV) array and a Proton exchange membrane fuel cell (PEMFC) is considered. As the variations occur in temperature and irradiation during power delivery to load, Photo voltaic (PV) system becomes uncontrollable. In coordination with PEMFC, the hybrid system output power becomes controllable. Two operation modes are the unit-power control (UPC) mode and the feeder-flow control (FFC) mode, can be applied to the hybrid system. All MPPT methods follow the same goal that is maximizing the PV system output power by tracking the maximum power on every operating condition. Maximum power point tracking technique (Incremental conductance) for photovoltaic systems was introduced to maximize the produced energy. The coordination of two control modes, coordination of the PV array and the PEMFC in the hybrid system, and determination of reference parameters are presented. The proposed operating strategy systems with a flexible operation mode change always operate the PV array at maximum output power and the PEMFC in its high efficiency performance band. Also thus improving the performance of system operation, enhancing system stability, and reducing the number of operating mode changes.
This document appears to be an email in Spanish from someone named Camille Automatico, but the content is unclear as it only contains their name and email address with no other text.
O documento lista locais noturnos em vários países asiáticos, começando pela entrada na Ásia pelo Bósforo, e incluindo Dubai, Índia, Singapura, Malásia, Hong Kong, China, Taiwan, Japão. As principais atrações incluem o Burj al Arab em Dubai, o Taj Mahal na Índia, as Torres Petronas na Malásia, a Grande Muralha da China e locais em Hong Kong, Xangai e Tóquio.
The document discusses the benefits of exercise for mental health. Regular physical activity can help reduce anxiety and depression and improve mood and cognitive functioning. Exercise causes chemical changes in the brain that may help protect against mental illness and improve symptoms.
Este documento describe un viaje a Burgos que incluye fotos de Frías desde el castillo, calles de Frías durante las fiestas, Orbaneja del Castillo y una cascada, así como las almenas del castillo de Orbaneja del Castillo.
El documento critica la hipocresía de Europa al tratar de evitar la llegada de inmigrantes africanos, cuando Europa se enriqueció a costa del saqueo y la explotación de África durante siglos de colonialismo. Compara a Europa con el príncipe en "La máscara de la muerte roja" de Poe, que intentó encerrarse de la peste pero la muerte entró de todos modos. Afirma que los africanos tienen derecho a compartir la riqueza que Europa se llevó de África, y que Europa debería
Este documento discute diferentes pedagogías centradas en la investigación. 1) Propone usar la investigación para dinamizar procesos escolares y generar alternativas metodológicas que desarrollen un espíritu científico en los estudiantes. 2) Describe varios modelos pedagógicos basados en la investigación que enfatizan procesos como la formulación de preguntas, la indagación colaborativa y la comunicación de resultados. 3) Explica el enfoque de "La mano en la masa" que busca reproducir pro
Effect Of Cuo-Distilled Water Based Nanofluids On Heat Transfer Characteristi...IJERA Editor
In this paper, the heat transfer and pressure drop characteristics of the distilled water and the copper oxide-distilled water based nanofluid flowing in a horizontal circular pipe under constant heat flux condition are studied. Copper oxide nanoparticles of 40nm size are dispersed in distilled water using sodium dodecyl sulphate as surfactant and sonicated the nanofluid for three hour. Both surfactant and sonication increases the stability of the nanofluid. The nanofluids are made in three different concentration i.e. 0.1 Vol. %, 0.25 Vol. % and 0.50 Vol. %. The thermal conductivity is measured by KD2 PRO, density with pycnometer, viscosity with Brookfield LVDV-III rheometer. The results show that the thermal conductivity increases with both temperature and concentration. The viscosity and density increases with concentration but decreases with temperature. The specific heat is calculated by model and it decreases with concentration. The experimental local Nusselt number of distilled water is compared with local Nusselt number obtained by the well known shah equation for laminar flow under constant heat flux condition for validation of the experimental set up. The relative error is 4.48 % for the Reynolds number 750.9. The heat transfer coefficient increases with increase in both flow rate and concentration. It increases from 14.33 % to 46.1 % when the concentration is increased from 0.1 Vol. % to 0.5 Vol. % at 20 LPH flow rate. Friction factor decreases with increase in flow rate. It decreases 66.54 % when the flow rate increases from 10 LPH to 30 LPH for 0.1 Vol. %.
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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.
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Null Bangalore | Pentesters Approach to AWS IAMDivyanshu
#Abstract:
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# Scenario Covered:
- Basics of IAM in AWS
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- Exploiting IAM PassRole Misconfiguration
-Allows a user to pass a specific IAM role to an AWS service (ec2), typically used for service access delegation. Then exploit PassRole Misconfiguration granting unauthorized access to sensitive resources.
- Objective: Demonstrate how a PassRole misconfiguration can grant unauthorized access.
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- Objective: Show how overly permissive IAM roles can lead to privilege escalation.
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- Perform administrative actions.
- Differentiation between PassRole vs AssumeRole
Try at [killercoda.com](https://killercoda.com/cloudsecurity-scenario/)
Effect of Bond Layer on Tri-Layered Assembly Subjected To Differential Uniform Temperature Change
1. C Nithin Shekar et al Int. Journal of Engineering Research and Applications www.ijera.com
ISSN : 2248-9622, Vol. 4, Issue 9( Version 5), September 2014, pp.185-192
www.ijera.com 185 | P a g e
Effect of Bond Layer on Tri-Layered Assembly Subjected To Differential Uniform Temperature Change C Nithin Shekar*, N G S Udupa*, Aswatha**, K N Seetharamu*** *(Department of Mechanical Engineering, Nagarjuna College of Engineering and Technology, Venkatagiri Kote Post, Devanahalli, Bangalore – 562 110, India) ** (Department of Mechanical Engineering, Bangalore Institute of Technology, Bangalore - 560 004, India) *** (Department of Mechanical Engineering, PES Institute of Technology, Bangalore - 560 085, India) ABSTRACT In the present analytical and numerical study, the thermal mismatching stress induced under differential temperature conditions of tri-layered assembly with bond is investigated. The thermal mismatching stresses are one of the reasons for structural failures between two or more connected devices. Therefore it is very essential to understand variation of these stresses and estimation in the interfaces play an important role in design and reliability studies of microelectronic assemblies. In this paper, a physical model is proposed for the interfacial shearing and peeling stresses occurring at the interfaces of tri-layered dissimilar materials with the effect of bonding subjected to differential uniform temperature in the layer. It observed from both analytical and numerical study that the shearing stress reduced in the range of 60% to 70% at interface (1-2) and 35% to 40% at (2-3) interface. Peeling stress are continuously reduced in the range of 10% - 20% at (1-2) interface and 13% - 35% at (2-3) interface due to the influence of bond layer. Thus, it indicates that, the bond layer consideration may influence significantly on interfacial stress. It is found that the both interfacial shearing stresses and peeling stresses decreased considerably at the interface with the increase of bond layer thickness.
Keywords – Tri-layered model, Shearing stress, Peeling stress, Different uniform temperature model, Electronic package
I. INTRODUCTION
Thermo mechanical mismatch induced interfacial stresses of the major concerned in the structural failure between two or more connected devices. The electronic assemblies are the heat generating source as they operated under high power conditions therefore thermal mismatching stresses are inevitably arises in the interfaces of bonded dissimilar metals, this is because of the differences in the co-efficient of thermal expansion. Timoshenko’s [1] proposed the fundamental solution to thermal stresses of biomaterial using a beam theory. The electronic signals may be incorrectly transferred and that may cause structural failure [2]. When two thin plates are bonded together, an extremely thin bond layer of third material is exists between them. Adhesively bonded and soldered bi-material assemblies are widely used in micro- and Opto- electronics [3-5]. Since from last two decades, the research on the thermal stresses on the structured layered is carried out. The effect of the bond layer is inspired by derivations of Chen and Nelson [6] and suhir considering the interfacial shearing and peeling stresses in to account. In the recent years many other researches Mirman [7], Matthys and Mey [8], Ru [9] and Moore and Jarvis [10-11] contributed on this aspect. An improved bi-material uniform temperature
model accounting for differential uniform temperature and thickness wise linear temperature gradient in the layers have been carried out by sujan et al. [12].
The model of tri-layered assembly subjected to uniform temperature was first proposed by Schmidt [13] in 1999 and suhir [14] in 2003. The mathematical model formed by these two authors is inconsistencies in consideration of the exponential parameter k in the interfacial shearing stress expression. This inconsistence is well addressed by sujan et al. [15] and proposed improved tri-material solution for both interfacial shearing and peeling stresses. It is found that the numerical solution suggested close agreement compare to earlier models. The bond layer acts as interfacial shear stress compliance between the two principal layers. Consequently, it will have some influence on the interfacial stresses in a Bi-material assembly. The value of interfacial shear stress compliance for the bond layer at the interface was proposed by Sujan [16] which is given as K0 as ho/Go. A Gold-Tin solder bond is introduced as the bond layer between silicon and diamond layers and they show that the effect of bond layer on the interfacial shearing and peeling stress. Recently, Sujan et al. [17] studied the tri- layered interfacial stress model with the effect of different temperatures in the layers only. The effect
RESEARCH ARTICLE OPEN ACCESS
2. C Nithin Shekar et al Int. Journal of Engineering Research and Applications www.ijera.com
ISSN : 2248-9622, Vol. 4, Issue 9( Version 5), September 2014, pp.185-192
www.ijera.com 186 | P a g e
of bond layer on interfacial shear and peeling stresses
is not considered. It is observed that the effect of
linear temperature gradient may influence interfacial
stresses considerably. Recently, Aswath et al. [18]
has been studied the effect of bond thickness on tri-layered
assembly subjected to uniform temperature
effect. It is found that the interfacial shearing and
peeling stresses are decreased considerably at the
interface with the increase of bond thickness.
However, to date no attempt as been made to
study the effect of the thermal mismatching
interfacial stresses and the tri-material assembly with
bond subjected to differentially uniform temperature
change. The thermo mechanical stresses as
significance to understanding of the nature of
interfacial stresses under different temperature
conditions is necessary to minimize or eliminate the
risk of structural failure.
The aim of the article is to present shear
compliance expressions to account for bond layer
effect. The effect of bond layer on interfacial
shearing and peeling stress models subjected to
differential uniform temperatures was presented.
II. MATHEMATICAL
FORMULATIONS
a. Analytical Method
Fig. 1 shows the physical model of full length
(2L) of the tri-layered assembly with the three layers
designated as 1, 2 and 3and a free body diagram for a
cut at some arbitrary x location. E, α, ν, and h
represent elastic modulus, thermal expansion
coefficient, Poisson’s, and thickness of i-th layer and
ΔT differential uniform temperature change in the
layers.
Fig. 1 Physical and materials properties of tri-layered
assembly with bond layer at the interface.
To develop the analytical model of shearing
stress Sujan [15] is referred until basic governing
equations. The forces F1 and F2 at any section of the
layers in Fig.1 are given by,
F dx
x
L
1 1 and F dx
x
L
2 2 (1)
Where, 1 and 2 represent shear stress between top-middle
and middle-bottom layers respectively.
Considering the bonding layer effect, the
compatibility condition at the interfaces are
expressed as,
x
K
x
K
T
X
B
X
T
X
B
X
(2) (3) 0
(1) (2) 0
(2)
Where, x(i) , i = 1, 2, 3 are axial strains given by
x
Ui
x i
( ) and i U represents the axial displacement
of the i-th layer and superscripts B and T denote
bottom and top surfaces.
Considering moment equilibrium about positive
Z-axis (perpendicular to the paper upward) at x and y
= 0 is given by,
0
2
1
2
1
1 2 3
2 3 0 2
1 2 0 1
h h h F
M M M h h h F
(3)
Since, Mi =
R
Di , the expression for radius of curvature
is
2
0
2 3
1
1 2 0
2 2
1
F
D
h h h
F
D
h h h
R
(4)
In equation (4) D= D1 +D2 +D3
Where, 2
3
1
121 i
i i E h
D
, i = 1, 2, 3
Axial strains at the interfaces of the uniformly
heated three layered structure take the form,
x
K
R
h
T F
x
K
R
h
T F F
x
K
R
h
T F F
x
K
R
h
T F
B
x
B
x
T
x
B
x
2
3
3
(3) 3 3 3 2
2
2
2
(2) 2 2 2 2 1
1
2
2
(2) 2 2 2 2 1
1
1
1
(1) 1 1 1 1
2
2
2
2
(5)
Where, axial compliance,
i i
i
E h
2
1 1
, coefficient
of interfacial compliance,
i
i
i G
h
K
3
. Substituting
(5) into (2), produces
x
K τ
x
τ
ΔT α α λ F λ F K
x
K τ
x
τ
ΔT α α λ F λ F K
2 0
2 2 3 23 2 20 1 23
1 0
1 1 2 12 1 20 2 12 (6)
Where, 0 0 K K K K ij i j ,
D
h h h h
4
1 2 2 3
20 2
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D
h h
ij i j
4
2
1 2
Shear compliance for bond layer, K0 = h0/ Go.
The solution for equation (6) is assumed to be of the
form:
sinh( ) sinh( ) 2
(2)
1
(1) A k x A k x i i i (7)
Where, (1)
i A and (2)
i A are arbitrary constants for i =
1, 2 and 1 k and 2 k are roots of certain characteristic
equation.
Where,
k K k k k L
T
A
k K k k k L
T
A
k K k k k L
T
A
k K k k k L
T
A
1
2
1
2
2 120 2
2 1 2 1 2 3
4
(2)
2
1
2
1
2
1 120 2
1 1 2 2 2 3
3
(1)
2
1
2
1
2
2 120 2
(2) 2 1 2 1 2 3
1
1
2
1
2
1 120 2
(1) 1 1 2 2 2 3
1
cosh
cosh
cosh
cosh
(8)
Where,
120
120
2
12 1
1
K
k K
,
120
120
2
12 2
2
K
k K
,
20
120
2
12 1
3
K
k K
,
20
120
2
12 2
4
K
k K
and
220
20
K
Characteristic equation:
120 230
2
1
120 230
2
2
2
4
K K
r r K K S
ki
(9)
Where, 12 230 23 120 r K K ,
2
12 23 20 S ( )
Now, shearing stress τ1 and τ2 at interfaces are
determined by using equation (7). Peeling stress at
the interfaces is given by:
x
a
x
P a 2
2
1
1 1
(10)
x
b
x
P b 2
2
1
2 1
(11)
Where,
D
D h D h Dh
a
2
1 1 1 2 1
1
,
D
D h h
a
2
1 2 3
2
,
D
D h h
b
2
3 1 2
1
and
D
D h D h Dh
b
2
3 2 3 3 3
2
cosh( ) cosh( )
cosh( ) cosh( )
2 2
(2)
1 1 2
(1)
2
2
2 2
(2)
1 1 1
(1)
1
1
A k k x A k k x
x
A k k x A k k x
x
III. NUMERICAL INVESTIGATIONS
a. Verification OF ANALYTICAL RESULTS
The grid independent study has been made with
different grids to yield consistent values of Sujan et
al. [15]. In the present numerical investigation the
SOLID 45 element is used for the 3D modeling of
solid structures. The element is defined by eight
nodes having three degrees of freedom at each node:
translations in the nodal x, y, and z directions.
However, element SLOID 45 is selected for the
analysis of the interfacial stresses between bi-layered
and tri-layered assembly because of the element has
plasticity, creep, swelling, stress stiffening, large
deflection, and large strain capabilities.
During the course of present research, the
present methodology is verified in terms of interfacial
stresses like shearing stresses and peeling stresses, In
order to validate the predictive capability and
accuracy of the present methodology, computations
are performed using the configuration and boundary
conditions of the analytical and numerical
investigation by Sujan [15] on effects tri-material
assembly without bonding is selected. The results
presented in the paper in terms of shearing and
peeling stresses for without bonding material
between interfacial materials. It is seen from the
literature that, Sujan [15] used SOLID45 elements
with (7000 elements) constant mesh for ¼ of the total
model due to double symmetrical model. The authors
have made assumptions during the analysis of both
analytical and numerical investigations which were
explained in part
Fig. 2 Convergence of shearing stresses with grid
refinement.
Since the system is double symmetric, for 3D
analysis one quarter of the model is analyzed. For 3D
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model, Sujan [15] used for layer 1: 10 x 10 x 5 + 40 x 10 x 5 = 2500, for layer 2: 10 x 10 x 3 + 40 x 10 x 3 = 1500 and 10 x10 x 6 + 40 x 10 x 6 = 3000 elements for layer 3 (total number of elements = 7000). The BRICK 8 noded SOLID 45 element with uniform grid is selected for the numerical analysis. Different grid sizes with total number of elements 5000, 6000, 7000, 8000 and 9000 constant mesh have been studied. The grid with 7000 elements gave results identical to that of 8000 and above shown in Fig. 2. In view of this, 7000 elements grid is used in all further computations. Fig. 3 shows the one quarter of 3D model for the numerical analysis. It may be noted that Sujan [15] have used a constant mesh of 7000 for their study. Fig. 3 One quarter of 3D model after mapped meshing. Table 1 Compression of shearing stress of previous work with present work for uniform temperature at (1-2) and (2-3) interfaces.
x/L
Interface (1-2)
Interface (2-3)
Sujan [15]
Present study
Sujan [15]
Present study
0.9
6.60
6.45
-5
-4.98
0.92
7.99
7.82
-4.43
-4.39
0.94
10.42
10.32
-5.61
-5.55
0.96
13.66
13.74
-8.18
-8.09
0.98
17.99
18.15
-9.69
-9.59
1
23.82
24.54
-8.23
-8.1
A comparison of the interfacial shear stress for layers 1-2 and 2-3 are made with Sujan et al. [15]. Table 1 and 2 show the comparison of interfacial shear stresses of layer 1-2 and 2-3 subjected to constant temperature respectively. It is observed from table 1 that there is a good agreement between the present results and that of Sujan et al. [15] for interfaces of 1-2 and 2-3 with maximum discrepancy of 2.2%.
IV. RESULTS AND DISCUSSION
The tri-layered assembly with bond subjected to differential temperature at the interfaces is shown in Fig. 1. The analytical computations are carried out for the thickness of the bond varied from 0.001 to 0.004mm in order to find the variations of the interfacial shear and peeling stresses. Fig. 4.1 Shearing stress along the interface of layer (1-2) for uniform temperature model, (ΔT = -120c) and differential uniform temperature model, (ΔT1 = - 120C, ΔT2 = - 120C, and ΔT3 = - 60C). Fig. 4.1 represents shearing stress along the interface of layer (1-2) for the cases of uniform temperature change (UTC), and differential uniform temperature change (DUTC). From the comparison of analytical values between UTC and DUTC, it can be seen that for DUTC, shearing stress is considerably lower compared to UTC at all identical points along the interface of layer (1-2). However, analytical comparison shows that for DUTC, shearing stress reduces almost 18% in average compared to UTC. The numerical (FEM) simulation is also represented in Fig. 4.1. The variations of interfacial shearing stresses are similar to that of analytical one. However, FEM comparisons shows that for DUTC the shearing stress reduced almost 20% in average at the interface 1-2 compared to UTC. Thus, it is observed from the Fig. 4.1 that there is a good agreement between the analytical and numerical simulations with maximum discrepancy of 3%. Fig. 4.2 Shearing stress along the interface of layer (2-3) for uniform temperature model, (ΔT = -120c) and differential uniform temperature model, (ΔT1 = - 120c, ΔT2 = - 120c, and ΔT3 = - 60c).
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Fig. 4.2 represents the analytical and numerical simulations of shearing and peeling stresses along the interface of layer (2-3) for the cases of UTC and DUTC. Analytical comparison between these two shows that for DUTC, shearing stress is substantially lower compared to UTC at all identical positions along the interface of layer (2-3). The shear stress is increased monotonically with increase of length. For instance, at location x/L = 0.80, for DUTC shearing stress is lower by 0.65 MPa compared to UTC, at x/L = 0.9 the value increases to 1.67 MPa, and at the free end (x/L = 1), the difference increases as much as almost 50%. However, analytical comparison shows that for DUTC, shearing stress reduce almost 40% in average at the interface layer (2-3) compared to UTC. However, the FEM comparison shows that for DUTC, shearing stress reduces almost 38.5% in average at the interface of layer (2-3) compared to UTC. Thus, again almost similar trend of variation is reflected for analytical and numerically simulated results. Fig. 4.3 Peeling stress along the interface of layer (1- 2) for uniform temperature model, (ΔT = -120C) and differential uniform temperature model, (ΔT1 = - 120C, ΔT2 = - 120C, and ΔT3 = - 60C). The analytical and numerical simulations of peeling stresses of interfacial layers (1-2) subjected to UTC and DUTC is shown in Fig. 4.3. It is observed that the analytical comparison shows that the peeling stresses for DUTC considerably lower compared to UTC at all identical locations along the interface beyond x/L > 0.6 However, analytical comparison shows that for ,peeling stress reduces almost 60%in average at the interface of layer 1-2 compared to analytical with exception of 3 locations near the free edge and represent FEM simulation for respectively. Fig. 4.4 Peeling Stress along the Interface of Layer (2 -3) for Uniform Temperature Model,(ΔT = - 120C) and Differential Uniform Temperature Model, (ΔT1 = -120C, ΔT2 = - 120C, and ΔT3 = - 60C) However, analytical comparison shows that for analytical, peeling stress reduces almost 35% in average at the interface of layer 2 and layer 3 compared to FEM respectively. The comparison between the two graphs shows that at location x/L = 0.8.However, FEM comparison shows that peeling stress reduces almost 30% in average at the interface of layer 2 and layer 3 compared to analytical. Although beyond x/L=0.96 till the free end the peeling stress changes sign as was observed earlier. Fig. 4.5 Shearing stress along the interface of layer (1-2) with temperature ratio (m1). Fig. 4.5 shows analytical comparison of shearing stress along the interface of layer 1-2 for different values of m1 with m2 = 1. It is observed that at x/L = 0.8, for m1 = 2 shearing stress reduces by 0.8 MPa compared to m1 = 1. At x/L = 0.9 the difference increases to 4.14 MPa and at x/L = 1, the difference increases as much as 14.96 MPa or 60%
The variation of shearing stress along the interface of layer 2-3 for different values of m1 with
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m2 = 1 . It can be observed that at x/L = 0.8, for m1 = 2 shearing stress reduces by 0.48 MPa compared to m1 = 1. At x/L = 0.9, the difference increases to 2.03 MPa and at x/L = 1, the difference further increases to 2.59 MPa or 20%. Fig. 4.6 Shearing stress along the interface of layer (2-3) with temperature ratio (m1). Fig. 4.6 represents shearing and peeling stresses based on various values of m1 where m2 is maintained constant. Here 1 is varied from 16x10-6 /C to 3.2x10-6 /C in four stages to produce the value of n1 = 0.2, 0.3, 0.4, and 0.5 maintaining m2 (=2/3) constant. Thus, again almost similar trend of variation is reflected for analytical and numerically simulated results. Fig. 4.7 Peeling stress along the interface of layer (1-2) with temperature ratio (m1).
Fig. 4.7 shows analytical comparison of peeling stress for different values of m1 with m2 = 1. For the combination of the layers in this case, along the interface of layer 1 and layer 2, the peeling stress is compressive in nature. It can be observed that at x/L = 0.8, for m1=2 peeling stress reduces by 0.22 MPa compared to m1 = 1. From x/L=0.8 the difference starts decreasing until location x/L= 0.94 where the stress values are almost identical. From x/L = 0.94 towards the free end we can observe a reverse trend where peeling stress value for m1=2 starts increasing compared to m1 = 1 and at x/L = 1, the difference increases to 2.39 MPa or 62%. Fig. 4.8 Peeling stress along the interface of layer (2-3) with temperature ratio (m1). Fig. 4.8 shows the variation of peeling stress along the interface of layer 2 and layer 3 for different values of m1 with m2 = 1 is shown in Fig. 4.8. For the combination of the layers in this case, the peeling stress is compressive in nature. It can be observed that at x/L = 0.8, for m1 = 2 peeling stress reduces by 0.30 MPa compared to m1 = 1. At x/L = 0.9 the difference increases to 0.75 MPa and at x/L = 1, the difference further increases to 1.95 MPa. However, it is found that for m1=2, peeling stress reduces almost 30% compared to m1 = 1 at any identical location at that interface. Thus, it is evident that the different levels of temperatures in the layers has significant influence in the shearing and peeling stress development and should be accounted while calculating interfacial stresses in a tri-material assembly. Fig. 4.9 Shearing stress along the interface of layer (1-2) with coefficient of thermal expansion ratio (n1).
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Fig. 4.9 shows analytical comparison of shearing stress along the interface of layer (1-2 )for different values of n1 where n2 is maintained constant. It can be observed that with increasing the value of n1, shearing stress decreases considerably at the interface. For instance, at location x/L = 0.8 for n1 = 0.5 shearing stress reduces by 1.03 MPa compared to n1 = 0.2. At x/L=0.9, the difference increases to 4.03 MPa and at x/L = 1, the difference further increases as much as 18.86 MPa or 73%. Fig. 4.10 Peeling stress along the interface of layer (2-3) with coefficient of thermal expansion ratio (n1). Fig 4.10 shows that The variation of peeling stress along the interface of layer 2 and layer 3 for different values of n1 with constant n2 is shown in Fig. 4.12. For the combination of the layers, the peeling stress is compressive in nature in this case. It is observed that at x/L = 0.8, for n1 = 0.5 peeling stress reduces by 0.38 MPa compared to n1 = 0.2. At x/L = 0.9 the difference increases to 0.96 MPa and at x/L = 1, the difference further increases to 2.32 MPa or 35%. However, it is found that for n1=0.5, peeling stress reduces by around 36% in average compared to n1=0.2 at any identical location at that interface.
V. CONCLUSION
Thorough validation of both analytical and numerical analysis is carried out for both the shearing and peeling stress. The results obtained from the analysis leads to following conclusion.
1. Analytical and Numerical results showed that shearing stress are reduced in the range of 60% - 70% at (1-2) interface and 35% - 40% at (2-3) interface near the free end due to the influence of bond layer. Thus, it indicates that near the vicinity of the free end, the bond layer consideration may influence significantly on interfacial stress.
2. It is observed that, peeling stress are continuously reduced in the range of 10% - 20% at (1-2) interface and 13% - 25% at (2-3) interface due to the influence of bond layer. Thus, it indicates that,
the bond layer consideration may influence significantly on interfacial stress.
3. The shearing stresses decreased considerably at the interface with the increase of bond layer thickness. For instance, shearing stress decreased 40% - 50% at (1-2) interface and 25% - 40% at (2-3) interface respectively at the free end for a bond thickness of 0.01mm compared to zero bond thickness.
4. The peeling stresses decreased considerably at the interface with the increase of bond layer thickness. For instance, peeling stress decreased by 14% - 20% at both (1-2) interface and (2-3) interface respectively at the free end for a bond thickness of 0.01mm compared to zero bond thickness.
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