This document outlines a course on the mechanics of flexible materials. The course covers fundamentals of polymers and stresses/strains. It also covers textile materials, including mechanical properties of fibers, yarns and nonwovens. Assessment includes quizzes, assignments, a midterm and final exam. The course aims to explain how internal structure, external factors and assumptions relate to the mechanical behavior of flexible materials.
Here are the steps to solve this problem:
1) Calculate true stress (σ) and true strain (ε) at each load using the given diameter values:
σ = Load/Current cross-sectional area
ε = ln(Initial diameter/Current diameter)
2) Plot true stress vs true strain curve
3) Determine values from the curve:
1) True stress at maximum load = Highest stress value on curve
2) True fracture stress = Stress at fracture point
3) True fracture strain = Strain at fracture point
4) True uniform strain = Strain value where necking begins
5) True necking strain = Strain at start of necking region
6) Ultimate
This experiment tested the tensile properties of steel, aluminum, and two polymeric materials. Specimens of each material were pulled apart in a tensile testing machine at a constant strain rate to measure properties like yield strength, tensile strength, and elongation. The engineering stress-strain and true stress-strain curves were plotted and compared for each material. Values for properties like Young's modulus, yield stress, and tensile strength were determined from the curves and compared to literature values. Sources of experimental error were also discussed.
The document discusses two-dimensional finite element analysis. It describes triangular and quadrilateral elements used for 2D problems. The derivation of the stiffness matrix is shown for a three-noded triangular element. Shape functions are presented for triangular and quadrilateral elements. Examples are provided to calculate strains for a triangular element and to determine temperatures at interior points using shape functions.
Introduction to finite element analysisTarun Gehlot
The document provides an introduction to finite element analysis (FEA) or the finite element method (FEM). It describes FEA as a numerical method used to solve engineering and mathematical physics problems that cannot be solved through analytical methods due to complex geometries, loadings, or material properties. FEA involves discretizing a complex model into smaller, simpler elements connected at nodes, then applying the governing equations to obtain a numerical solution for the unknown primary variable (usually displacement) at nodes. Secondary variables like stress are then determined from nodal displacements. The process involves preprocessing, solving, and postprocessing steps.
This document discusses the basics of strength of materials. It defines solid mechanics as the branch of mechanics dealing with the behavior of solid materials under external forces or internal forces caused by temperature changes, phase changes, or other agents. It describes several key mechanical properties of materials including ductility, hardness, impact resistance, plasticity, fracture toughness, elasticity, endurance strength, creep resistance, and more. It also defines stress, strain, and explains Hooke's law relating stress and strain within a material's elastic limit according to its modulus of elasticity.
This document provides an overview of engineering mechanics. It defines mechanics as the branch of physics dealing with rest and motion. Mechanics can be divided into classical mechanics, relativistic mechanics, and wave mechanics. Engineering mechanics is further divided into solid mechanics and fluid mechanics. Solid mechanics includes rigid body mechanics and deformable body mechanics. Rigid body mechanics contains statics and dynamics. Dynamics contains kinematics and kinetics. The document also outlines Newton's laws of motion, the law of universal gravitation, and other fundamental laws and concepts of mechanics. Finally, it discusses common units used in mechanics like the MKS, CGS, and FPS systems.
This document summarizes key parameters that can be determined from a true stress-true strain curve obtained from tensile testing of a material sample. These parameters include:
- True stress and true strain at maximum load, which represent the material's ultimate tensile strength and strain at necking.
- True fracture stress and true fracture strain, which represent the stress and strain at fracture after significant necking has occurred.
- True uniform strain, representing the strain up to maximum load before necking.
- True local necking strain, representing the additional strain from maximum load to fracture during necking.
- Strain hardening exponent and strength coefficient, materials constants that describe work hardening behavior and
Here are the steps to solve this problem:
1) Calculate true stress (σ) and true strain (ε) at each load using the given diameter values:
σ = Load/Current cross-sectional area
ε = ln(Initial diameter/Current diameter)
2) Plot true stress vs true strain curve
3) Determine values from the curve:
1) True stress at maximum load = Highest stress value on curve
2) True fracture stress = Stress at fracture point
3) True fracture strain = Strain at fracture point
4) True uniform strain = Strain value where necking begins
5) True necking strain = Strain at start of necking region
6) Ultimate
This experiment tested the tensile properties of steel, aluminum, and two polymeric materials. Specimens of each material were pulled apart in a tensile testing machine at a constant strain rate to measure properties like yield strength, tensile strength, and elongation. The engineering stress-strain and true stress-strain curves were plotted and compared for each material. Values for properties like Young's modulus, yield stress, and tensile strength were determined from the curves and compared to literature values. Sources of experimental error were also discussed.
The document discusses two-dimensional finite element analysis. It describes triangular and quadrilateral elements used for 2D problems. The derivation of the stiffness matrix is shown for a three-noded triangular element. Shape functions are presented for triangular and quadrilateral elements. Examples are provided to calculate strains for a triangular element and to determine temperatures at interior points using shape functions.
Introduction to finite element analysisTarun Gehlot
The document provides an introduction to finite element analysis (FEA) or the finite element method (FEM). It describes FEA as a numerical method used to solve engineering and mathematical physics problems that cannot be solved through analytical methods due to complex geometries, loadings, or material properties. FEA involves discretizing a complex model into smaller, simpler elements connected at nodes, then applying the governing equations to obtain a numerical solution for the unknown primary variable (usually displacement) at nodes. Secondary variables like stress are then determined from nodal displacements. The process involves preprocessing, solving, and postprocessing steps.
This document discusses the basics of strength of materials. It defines solid mechanics as the branch of mechanics dealing with the behavior of solid materials under external forces or internal forces caused by temperature changes, phase changes, or other agents. It describes several key mechanical properties of materials including ductility, hardness, impact resistance, plasticity, fracture toughness, elasticity, endurance strength, creep resistance, and more. It also defines stress, strain, and explains Hooke's law relating stress and strain within a material's elastic limit according to its modulus of elasticity.
This document provides an overview of engineering mechanics. It defines mechanics as the branch of physics dealing with rest and motion. Mechanics can be divided into classical mechanics, relativistic mechanics, and wave mechanics. Engineering mechanics is further divided into solid mechanics and fluid mechanics. Solid mechanics includes rigid body mechanics and deformable body mechanics. Rigid body mechanics contains statics and dynamics. Dynamics contains kinematics and kinetics. The document also outlines Newton's laws of motion, the law of universal gravitation, and other fundamental laws and concepts of mechanics. Finally, it discusses common units used in mechanics like the MKS, CGS, and FPS systems.
This document summarizes key parameters that can be determined from a true stress-true strain curve obtained from tensile testing of a material sample. These parameters include:
- True stress and true strain at maximum load, which represent the material's ultimate tensile strength and strain at necking.
- True fracture stress and true fracture strain, which represent the stress and strain at fracture after significant necking has occurred.
- True uniform strain, representing the strain up to maximum load before necking.
- True local necking strain, representing the additional strain from maximum load to fracture during necking.
- Strain hardening exponent and strength coefficient, materials constants that describe work hardening behavior and
1) The document discusses effective modal mass and modal participation factors, which are methods for determining how readily a vibration mode of a system can be excited. Modes with higher effective masses can be more easily excited by base excitation.
2) It provides definitions and equations for calculating effective modal mass and modal participation factors. These include the mass matrix, stiffness matrix, eigenvectors, influence vector, coefficient vector, modal participation factor matrix, and effective modal mass.
3) An example calculation is shown for a two degree-of-freedom system to demonstrate how to compute its eigenvalues, eigenvectors, and then the effective modal masses and participation factors of each mode. The first mode is found to have much higher effective mass
constant strain triangular which is used in analysis of triangular in finite element method with the help of shape function and natural coordinate system.
The document discusses a presentation on a universal testing machine. It describes how the machine is used to apply tensile, compressive, and shear forces to test materials and measure their properties. It explains that the machine uses load cells, crossheads, and columns to grip specimens and apply and measure forces. The document outlines the working principle of the machine and procedures for tensile and compression tests.
Strength of Materials Lecture - 2
Elastic stress and strain of materials (stress-strain diagram)
Mehran University of Engineering and Technology.
Department of Mechanical Engineering.
This document discusses key concepts in strength of materials including stress, strain, true stress and strain, stress-strain curves, tensile and compressive stress, lateral and volumetric strain, Poisson's ratio, Young's modulus, modulus of rigidity, ductile and brittle materials. Some key points covered are:
- True stress is calculated based on the instantaneous area during loading while engineering stress uses the original area.
- Stress-strain curves relate the stress and strain in a material.
- Ductile materials exhibit a large percentage of elongation before failure while brittle materials break suddenly with little yielding.
- Properties like Young's modulus, shear modulus, and Poisson's ratio describe a material's elastic properties
This document contains lecture notes on the finite element method from Dr. Atteshamuddin S. Sayyad. It covers the fundamentals of elasticity theory including assumptions, basic terms like stresses and strains, equilibrium equations, and strain-displacement relationships. The notes provide definitions and equations for normal and shear stresses and strains, the state of stress and strain at a point, and developing the governing equations of equilibrium in three dimensions from an infinitesimal element.
- The document discusses one-dimensional finite element analysis.
- It describes the derivation of shape functions for linear one-dimensional elements like a bar element. Shape functions define the variation of displacement within the element.
- The stiffness matrix, which represents the element's resistance to deformation, is also derived for a basic linear bar element. It is shown to be symmetric and its properties are discussed.
- Examples are provided to demonstrate calculating displacements at points within a one-dimensional element using the shape functions.
This presentation is for mechanical engineering/ civil engineering students to help them understand the different type of destructive mechanical testing of materials. The tensile testing, hardness, impact test procedures are explained in detail.
The document provides an introduction to the finite element method (FEM). It discusses that FEM is a numerical technique used to approximate solutions to boundary value problems defined by partial differential equations. It can handle complex geometries, loadings, and material properties that have no analytical solution. The document outlines the historical development of FEM and describes different numerical methods like the finite difference method, variational method, and weighted residual methods that FEM evolved from. It also discusses key concepts in FEM like discretization into elements, node points, and interpolation functions.
*Plain stress-strain,
*axi-symmetric problems in 2D elasticity
*Constant Strain Triangles (CST)- Element stiffness matrix, Assembling stiffness Equation, Load vector, stress and reaction forces calculations. (numerical treatment only on constant strain triangles)
*Post Processing Techniques- *Check and validate accuracy of results,
* Average and Un-average stresses,
*Special tricks for post processing,
*Interpretation of results and design modifications,
*CAE reports.
This document gives the class notes of Unit 6: Bending and shear Stresses in beams. Subject: Mechanics of materials.
Syllabus contest is as per VTU, Belagavi, India.
Notes Compiled By: Hareesha N Gowda, Assistant Professor, DSCE, Bengaluru-78.
Some basic defintions of the topics used in Strength of Materials subject. Pictorial presentation is more than details. Many examples are provided as well.
Introduction to the non destructive testing explains the methods for evaluating and verifying many types of Materials as plastics, structures, metals, chemicals, leakage, physical properties. It's very used in the concrete engineering world and in the scientific world.
Unit 1-stress, strain and deformation of solidskarthi keyan
This document discusses stress and strain in materials due to external forces. It defines stress as the effect of external forces on materials, and strain as the deformation or change in shape of materials under stress. It describes different types of stresses like tensile, compressive, and shear stresses, as well as different types of strains. Hooke's law and Poisson's ratio are explained, which relate stress to strain in materials. The concept of factor of safety is also introduced.
Incremental sheet forming (ISF) is a metal forming process that uses localized deformation from a tool to form a sheet of metal into a 3D shape through a series of small increments. ISF has potential advantages over other sheet metal forming processes as it does not require dies, allows for localized production and reworking, and uses lower forming forces. However, ISF is not widely used in industry due to challenges achieving optimal mechanical capabilities and accuracy without expensive tool path optimization or workpiece support, and limitations of current machinery and tooling designs. The document outlines ongoing research projects at IfM to address these challenges through areas like tool force prediction, sandwich panel forming, real-time process control, and flexible workpiece support to
CE72.52 - Lecture 2 - Material BehaviorFawad Najam
This document discusses material behavior and properties that are important for structural analysis and design. It defines various types of material stiffness, from material stiffness to cross-section stiffness to member and structure stiffness. It also discusses stress-strain relationships and different material models, including linear elastic, nonlinear elastic, plastic, and viscoelastic models. Finally, it covers key material properties like strength, stiffness, ductility, time-dependent behavior, damping properties, and how these properties depend on the material composition and loading conditions.
fracture mechanics and damage tolerance .Why do high strain rate, low temperature and triaxial state of stress promote brittle fracture?Method of Crack/Crack Like Defect Analysis
This document outlines the structure and properties of materials, including monolithic, composite, and hierarchical materials. It discusses the structure of materials, strength of real materials, and material response to stress, including linear elastic behavior and viscoelastic behavior. The document also covers dislocation theory, fracture theory including Griffith theory and fracture toughness, fatigue behavior such as fatigue crack initiation and propagation, and creep behavior including the different creep stages.
1) The document discusses effective modal mass and modal participation factors, which are methods for determining how readily a vibration mode of a system can be excited. Modes with higher effective masses can be more easily excited by base excitation.
2) It provides definitions and equations for calculating effective modal mass and modal participation factors. These include the mass matrix, stiffness matrix, eigenvectors, influence vector, coefficient vector, modal participation factor matrix, and effective modal mass.
3) An example calculation is shown for a two degree-of-freedom system to demonstrate how to compute its eigenvalues, eigenvectors, and then the effective modal masses and participation factors of each mode. The first mode is found to have much higher effective mass
constant strain triangular which is used in analysis of triangular in finite element method with the help of shape function and natural coordinate system.
The document discusses a presentation on a universal testing machine. It describes how the machine is used to apply tensile, compressive, and shear forces to test materials and measure their properties. It explains that the machine uses load cells, crossheads, and columns to grip specimens and apply and measure forces. The document outlines the working principle of the machine and procedures for tensile and compression tests.
Strength of Materials Lecture - 2
Elastic stress and strain of materials (stress-strain diagram)
Mehran University of Engineering and Technology.
Department of Mechanical Engineering.
This document discusses key concepts in strength of materials including stress, strain, true stress and strain, stress-strain curves, tensile and compressive stress, lateral and volumetric strain, Poisson's ratio, Young's modulus, modulus of rigidity, ductile and brittle materials. Some key points covered are:
- True stress is calculated based on the instantaneous area during loading while engineering stress uses the original area.
- Stress-strain curves relate the stress and strain in a material.
- Ductile materials exhibit a large percentage of elongation before failure while brittle materials break suddenly with little yielding.
- Properties like Young's modulus, shear modulus, and Poisson's ratio describe a material's elastic properties
This document contains lecture notes on the finite element method from Dr. Atteshamuddin S. Sayyad. It covers the fundamentals of elasticity theory including assumptions, basic terms like stresses and strains, equilibrium equations, and strain-displacement relationships. The notes provide definitions and equations for normal and shear stresses and strains, the state of stress and strain at a point, and developing the governing equations of equilibrium in three dimensions from an infinitesimal element.
- The document discusses one-dimensional finite element analysis.
- It describes the derivation of shape functions for linear one-dimensional elements like a bar element. Shape functions define the variation of displacement within the element.
- The stiffness matrix, which represents the element's resistance to deformation, is also derived for a basic linear bar element. It is shown to be symmetric and its properties are discussed.
- Examples are provided to demonstrate calculating displacements at points within a one-dimensional element using the shape functions.
This presentation is for mechanical engineering/ civil engineering students to help them understand the different type of destructive mechanical testing of materials. The tensile testing, hardness, impact test procedures are explained in detail.
The document provides an introduction to the finite element method (FEM). It discusses that FEM is a numerical technique used to approximate solutions to boundary value problems defined by partial differential equations. It can handle complex geometries, loadings, and material properties that have no analytical solution. The document outlines the historical development of FEM and describes different numerical methods like the finite difference method, variational method, and weighted residual methods that FEM evolved from. It also discusses key concepts in FEM like discretization into elements, node points, and interpolation functions.
*Plain stress-strain,
*axi-symmetric problems in 2D elasticity
*Constant Strain Triangles (CST)- Element stiffness matrix, Assembling stiffness Equation, Load vector, stress and reaction forces calculations. (numerical treatment only on constant strain triangles)
*Post Processing Techniques- *Check and validate accuracy of results,
* Average and Un-average stresses,
*Special tricks for post processing,
*Interpretation of results and design modifications,
*CAE reports.
This document gives the class notes of Unit 6: Bending and shear Stresses in beams. Subject: Mechanics of materials.
Syllabus contest is as per VTU, Belagavi, India.
Notes Compiled By: Hareesha N Gowda, Assistant Professor, DSCE, Bengaluru-78.
Some basic defintions of the topics used in Strength of Materials subject. Pictorial presentation is more than details. Many examples are provided as well.
Introduction to the non destructive testing explains the methods for evaluating and verifying many types of Materials as plastics, structures, metals, chemicals, leakage, physical properties. It's very used in the concrete engineering world and in the scientific world.
Unit 1-stress, strain and deformation of solidskarthi keyan
This document discusses stress and strain in materials due to external forces. It defines stress as the effect of external forces on materials, and strain as the deformation or change in shape of materials under stress. It describes different types of stresses like tensile, compressive, and shear stresses, as well as different types of strains. Hooke's law and Poisson's ratio are explained, which relate stress to strain in materials. The concept of factor of safety is also introduced.
Incremental sheet forming (ISF) is a metal forming process that uses localized deformation from a tool to form a sheet of metal into a 3D shape through a series of small increments. ISF has potential advantages over other sheet metal forming processes as it does not require dies, allows for localized production and reworking, and uses lower forming forces. However, ISF is not widely used in industry due to challenges achieving optimal mechanical capabilities and accuracy without expensive tool path optimization or workpiece support, and limitations of current machinery and tooling designs. The document outlines ongoing research projects at IfM to address these challenges through areas like tool force prediction, sandwich panel forming, real-time process control, and flexible workpiece support to
CE72.52 - Lecture 2 - Material BehaviorFawad Najam
This document discusses material behavior and properties that are important for structural analysis and design. It defines various types of material stiffness, from material stiffness to cross-section stiffness to member and structure stiffness. It also discusses stress-strain relationships and different material models, including linear elastic, nonlinear elastic, plastic, and viscoelastic models. Finally, it covers key material properties like strength, stiffness, ductility, time-dependent behavior, damping properties, and how these properties depend on the material composition and loading conditions.
fracture mechanics and damage tolerance .Why do high strain rate, low temperature and triaxial state of stress promote brittle fracture?Method of Crack/Crack Like Defect Analysis
This document outlines the structure and properties of materials, including monolithic, composite, and hierarchical materials. It discusses the structure of materials, strength of real materials, and material response to stress, including linear elastic behavior and viscoelastic behavior. The document also covers dislocation theory, fracture theory including Griffith theory and fracture toughness, fatigue behavior such as fatigue crack initiation and propagation, and creep behavior including the different creep stages.
207682663-Composite-Material-An-Introduction.pptxAbinash Behera
The document provides an introduction to composite materials, including:
1. A brief history of composite materials from natural occurrences to modern developments.
2. A definition of composite materials as a combination of two materials and a basic composition of a composite including a matrix and reinforcements.
3. A classification of composites based on the matrix phase (polymer, metal, ceramic) and the type of reinforcements used (fibers, particulates, flakes, whiskers).
4. An overview of how to characterize the mechanical properties of composites including rule of mixtures, loading orientation, and methods to estimate properties like modulus of elasticity, strength, and thermal expansion.
The document summarizes Travis Hilbig's masters thesis defense on using molecular dynamics (MD) simulations to model the scratching of polymeric materials. The study aims to (1) create a model of high density polyethylene (HDPE), (2) simulate scratching on the material, (3) analyze penetration depth and recovery, and (4) determine factors influencing scratch behavior. MD simulations represent interactions using Lennard-Jones potentials parameterized for HDPE's intramolecular and intermolecular interactions. The results will provide insight into scratch resistance of polymers to optimize structures for applications.
FRACTURE MECHANICS OF NANO-SILICA PARTICLES IN REINFORCED EPOXIES Jordan Suls
This document summarizes a study that used finite element modeling to examine how different levels of particle dispersion (evenly dispersed, moderately clumped, and severely clumped) affect the fracture mechanics of nanosilica particle reinforced epoxies. Three models were created in Abaqus with the different dispersion levels and subjected to tensile loading. The results found that the evenly dispersed model had the highest fracture toughness, as indicated by its ability to withstand a greater force at similar displacements. This was because the clumped models developed large stress regions around the clumps that caused earlier debonding of the particle-matrix interfaces and faster crack propagation.
Composites are materials made from two or more constituent materials with different physical or chemical properties. The materials remain separate within the finished structure to produce properties that are superior to those of the individual components. Composites consist of a reinforcement material, such as fibers, sheets or particles, embedded within a matrix material that maintains the relative positions of the reinforcements and allows for load transfer from the matrix to the reinforcement. Common reinforcement materials include glass, carbon and organic fibers while matrix materials include polymers, metals and ceramics. Composites offer advantages over traditional materials like high strength, light weight, design flexibility and resistance to corrosion.
Introduction to Mechanical Metallurgy (Our course project)Rishabh Gupta
The document summarizes key concepts in materials science and engineering. It discusses:
1. The importance of selecting high quality materials for better product design and performance.
2. The four main components in materials science - processing, structure, properties, and performance - and how they interrelate.
3. The main classes of materials - metals, ceramics, polymers, composites, semiconductors, and elastomers - and some of their key characteristics.
4. Crystal structures of metals and how they are classified based on atomic packing efficiency. Factors that determine a material's density are also covered.
This document discusses the mechanical and tribological characterization of short fiber reinforced polymer composites. Two types of fibers were studied as reinforcements in an epoxy matrix: glass fibers and banana fibers. Composites with varying weight percentages of each fiber type were fabricated and tested. Their physical properties like density and void content were measured. Mechanical properties including microhardness, compressive strength, tensile strength, flexural strength, and impact strength were also evaluated using standard tests. The experimental results from these characterizations were reported and comparisons made between the glass fiber and banana fiber reinforced composites.
FINITE ELEMENT ANALYSIS OF JUTE AND BANANA FIBERS REINFORCED COMPOSITES FOR M...Rahul Kshirsagar
The presentation contains the determination of mechanical properties of Jute and Banana Fibre reinforced biocomposites experimentally and validation of the same properties using finite element analysis software. Both the results obtained found to be in good agreement with each other. Furthermore, the percentage error in between these two values has calculated.
The document discusses the functions and desired properties of matrices in composite materials. Matrices hold fibers together, protect them from the environment, distribute loads evenly between fibers, and improve properties like impact resistance. Desired matrix properties include low moisture absorption, shrinkage, and thermal expansion. The document also discusses polymer matrix composites, classifications of polymers, factors affecting composite properties, and manufacturing processes for composites with thermoplastic and thermosetting matrices.
This document discusses dental polymers, including their classification, properties, and uses. It provides information on the basic nature of polymers and how they are formed through polymerization reactions. Key points include:
- Polymers are formed from monomers through chemical reactions, creating large molecular weight macro molecules. Their form determines if they are fibers, rigid solids, or elastomers.
- Common dental polymers include polymethyl methacrylate (PMMA), which is used in denture bases and other prosthetic appliances.
- Polymers have various desirable properties for dental applications, including being biologically compatible, strong, dimensionally stable, and easy to handle.
- Polymer properties depend on factors like molecular
This document discusses the mechanical properties of viscoelastic materials. It covers topics like stress/strain behavior, creep, toughness, reinforcement, and modifiers. It explains how polymer chemistry, structures, and properties influence product performance. Key factors that determine a plastic's mechanical response are intermolecular forces, temperature, time under load, degree of crystallinity, and molecular weight. A plastic can behave as an elastic solid, viscoelastic solid, viscoelastic fluid, or viscous fluid depending on these factors. Tests like tensile testing, impact testing, and dynamic mechanical analysis are used to characterize mechanical properties.
This document provides an introduction and overview of the Material Science course being taught by Dr. R. Sarjila at Auxilium College in Vellore. The course covers 5 units: phase diagrams, defects, optical properties, elastic behavior and polymers/ceramics, and laser physics. Key concepts in unit 1 include binary phase diagrams, solid solutions, and eutectic systems. Unit 2 discusses point defects, diffusion, and dislocations. Subsequent units cover additional material properties and applications. The document lists relevant textbooks and references and concludes with an introduction to phase diagrams and the Gibbs phase rule.
This book was originally prepared in 2012 and updated recently in 2015. The
objective of the present book is to present a complete and up ± to ± date coverage of
composite laminates properties and literature reviews through the usage of a wide
spectrum of old and recent bibliography.
The material presented in this book is intended to serve as an introduction and
literature review of composite laminated plates. In chapter one, the introduction was
presented from the points of view of fundamental definitions of fibrous composite
laminates and micromechanical properties of fibers and matrix materials. At the end
of the chapter the objectives of the present work were cited.
Chapter two contains a comprehensive literature review which includes
continuous developments in the theories of laminated plates. Also, a survey of
numerical techniques which could be used in the analysis of laminated plates.
Chapter three contains the conclusion of the present book. In this chapter the
important observations and findings were explained clearly.
The book is suitable as a review on theories of plates, numerical and / or
analytical techniques subjected to bending, buckling and vibration of laminated
plates.
Materials Technology for Engineers pre-test 1 notesmusadoto
Materials are probably more deep-seated in our culture than most of us realize. Transportation, housing, clothing, communication, recreation, and food production virtually every segment of our everyday lives is influenced to one degree or another by materials. Historically, the development and advancement of societies have been intimately tied to the members’ ability to produce and manipulate materials to fill their needs. In fact, early civilizations have been designated by the level of their materials development (i.e., Stone Age, Bronze Age). The earliest humans had access to only a very limited number of materials, those that occur naturally: stone, wood, clay, skins, and so on. With time they
discovered techniques for producing materials that had properties superior to those of the natural ones; these new materials included pottery and various metals. Furthermore, it was discovered that the properties of a material could be altered by heat treatments and by the addition of other substances. At this point, materials utilization was totally a selection process, that is, deciding from a given, rather limited set of materials the one that was best suited for an application by virtue of its characteristics. It was not until relatively recent times that scientists came to understand the relationships between the structural elements of materials and their properties. This knowledge acquired in the past 60 years or so, has empowered them to fashion, to a large degree, the characteristics of materials. Thus, tens of
thousands of different materials have evolved with rather specialized characteristics that meet the needs of our modern and complex society; these include metals, plastics, glasses, and fibers. The development of many technologies that make our existence so comfortable
has been intimately associated with the accessibility of suitable materials. An advancement
in the understanding of a material type is often the forerunner to the stepwise progression of a technology. For example, automobiles would not have been possible without the availability of inexpensive steel or some other comparable substitute. In our contemporary era, sophisticated electronic devices rely on components that are made from what are called semiconducting materials.
Biomaterials and biosciences biometals.pptxKoustavGhosh26
This document provides an introduction to materials, including:
1. It discusses the evolution of materials from the Stone Age to today's Silicon Age and how materials drive modern society.
2. It explains that materials science studies the relationship between structure and properties of materials, while materials engineering designs materials for specific properties and applications.
3. It briefly introduces common materials like metals, ceramics, polymers, and composites, describing their basic structures and properties.
This document provides an overview of the Fibre Physics course offered at Gujarat Technological University. The course covers the physical properties of textile fibers including their structure, moisture absorption, tensile properties, optical properties, frictional properties, electrical properties, and thermal properties. It is a 3-credit course taught over 3 lecture hours per week. Student assessment includes tests, assignments, and an end of semester exam worth a total of 100 marks. The content is divided into 5 modules focusing on fiber structure, moisture absorption, tensile properties, optical and frictional properties, and electrical and thermal properties. Upon completing the course, students should have an understanding of the key physical properties of different textile fibers.
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1. 4/29/2011
Mechanics of Flexible Materials
By Hammad Mohsin
1
Course Outline
A)FUNDAMENTALS & POLYMERS
Module 1 Introduction to Mechanics of Materials
• Role of Mechanics of Materials in Engineering
Role of Mechanics of Materials in Engineering,
Stresses and Deformations, True Stress and True
Strain
Module 2 Study of Stress and Strain
• Stress ‐ Strain Diagrams of Ductile and Brittle
g
Materials, Isotropic and An‐isotropic Materials,
Modulus of Elasticity, Modulus of Rigidity, Elastic and
Plastic Behavior of Materials, Non Linear Elasticity,
Linear Elasticity, 2
1
2. 4/29/2011
• Stress and Strain in Changed Thermal Conditions,
Repeated Loading, Bending of Elasto‐plastic
Materials, Analysis of Stresses and Deformations
Module 3 Molecular basis of Rubberlike elasticity
• Structure of a Typical Network, Elementary
Molecular Theories, More Advanced Molecular
Theories Phenomenological Theories and
Molecular Structure, Swelling of Networks and
Responsive Gels Enthalpic and Entropic
p p p
Contributions to Rubber Elasticity: Force‐
Temperature Relations , Direct Determination of
Molecular Dimensions
3
Module 4 Strength of Elastomers
• Initiation of Fracture, Threshold Strengths and
Extensibilities, Fracture Under Multiaxial
Stresses , Crack Propagation, Tensile Rupture,
Repeated Stressing: Mechanical Fatigue,
Repeated Stressing Mechanical Fatigue
Surface Cracking by Ozone, Abrasive Wear.
Module 5 Failure Prevention
• Analysis of polymer product failure Design
Analysis of polymer product failure, Design
aids for preventing brittle failure, Defect
analysis HDPE pipe durability.
4
2
3. 4/29/2011
B) TEXTILE MATERIALS
Module 6 Mechanical Properties of Textile Fibres
• Tensile Recovery, Elastic Performance Coefficient in
Tension, Inter Fibre Stress and its Transmission,
, ,
Stress analysis of stable fibre, filaments, influence
of twist on yarn modulus
• Plasticity of textile fibers based on effect of load,
time, temperature superposition.
Module 7 Mechanics of Yarns:
• Mechanics of Bent Yarns, Flexural Rigidity, Fabric
Wrinkling, Stiffness in Textile Fabrics. Creasing and
Crease‐proofing of Textiles 5
• Module 8 Compression of Textile Materials
• Study of Resilience, Friction between Single
Fibres, Friction in Plied Yarns
• Module 9 Mechanical Properties of Non
Wovens and composite materials
6
3
4. 4/29/2011
Books
• Neilsen L., Landel R.,“Mechanical Properties of Polymers
and Composites” (1994)
• Moalli J “Plastic Failure: Analysis and Prevention” (2001)
Moalli J Plastic Failure: Analysis and Prevention (2001)
• Mark J, Erman B., Elrich F “Science and Technology of
Rubbers” (2005)
• Ferdinand P Beer, E Russell Jhonston Jr., Jhon T Dewolf
“Mechanics of Materials” (2004)
• Jinlian Hu “Structure and Mechanics of Woven Fabrics”
Jinlian Hu Structure and Mechanics of Woven Fabrics
(2004)
• AE Bogdanovich, C M Pastore “Mechanics of Textile and
Laminated Composites” (1996)
7
Assessment
• Quizzes: 10%
• Class participation & Discussion 10%
• Assignments : 10%
• Midterm: 30%
• Final: 40%
8
4
5. 4/29/2011
Cause
& effect
model
9
Material Properties
1. Elastic
a. Elastic Behavior causes a
a. Elastic Behavior causes a
material to return to its
original shape after being
deformed.
10
5
6. 4/29/2011
b. Completely elastic behavior
F = kx
Force
k is called the elastic
modulus
(F)
Distance (x)
11
2. Viscous
a. Viscous behavior is related to the rate of
deformation.
d f ti
⎛ Δx ⎞
F = η⎜ ⎟
⎝ Δt ⎠
Viscosity Rate of deformation
12
6
7. 4/29/2011
fast
f t
force, F
slow
distance, x
13
3. Viscoelastic
a. Fibers exhibit viscoelastic behavior
b. force required to deform a material
dependents amount of deformation and rate
at which the material is deformed
fast
F viscous
slow
elastic
x 14
7
8. 4/29/2011
B. Internal Structure
1. Chemical Composition
Sequence and kind of atoms in structure
Sequence and kind of atoms in structure
2. Crystallinity
Polymer chains or sections packed together
3. Orientation
Alignment of chains along fiber axis
C. Thermal Properties
C Thermal Properties
Melting Temperature
2. Glass Transition Temperature
Most polymers are thermoplastic – they soften
before melting
15
D. Physical Properties
Breaking Strength
Force required to break a fiber
Force required to break a fiber
2. Breaking Elongation
Amount of stretch before breaking
3. Modulus
Resistance to deformation
4. Toughness
Amount of energy absorbed
5. Elasticity
Ability to recover after being deformed
16
8
9. 4/29/2011
17
Structural factors=> Mechanical
Behavior
l. Molecular weight
2. Cross‐linking and branching
2 Cross‐linking and branching
3. Crystallinity and crystal morphology
4. Copolymerization (random, block, and graft)
5. Plasticization
6. Molecular orientation
7. Fillers
7 Fillers
8. Blending
9. Phase separation and orientation in blocks,
grafts, and blends
18
9
10. 4/29/2011
External Factors Mechanical
Properties
1. Temperature
2. Time, frequency, rate of stressing or straining
3. Pressure
4. Stress and strain amplitude
5. Type of deformation (shear, tensile, biaxial, e tc. )
6. Heat treatments or thermal history
6 Heat treatments or thermal history
7. Nature of surrounding atmosphere, especially
moisture content
19
5 assumptions ‐> Mechanical Behavior
1) Linearity: Two types of linearity are normally
assumed: A) Material linearity (Hookean stress
assumed: A) Material linearity (Hookean stress‐
strain behavior) or linear relation between stress
and strain; B) Geometric linearity or small strains
and deformation.
2) Elastic: Deformations due to external loads are
completely and instantaneously reversible upon
load removal.
load removal.
3) Continuum: Matter is continuously distributed
for all size scales, i.e. there are no holes or voids.
4) Homogeneous: Material properties are the same
at every point or material properties are invariant
upon translation. 20
10
11. 4/29/2011
5) Isotropic: Materials which have the same
mechanical properties in all directions at an
h i l ti i ll di ti t
arbitrary point or materials whose properties
are invariant upon rotation of axes at a point.
Amorphous materials are isotropic.
21
Stress‐ Strain > Definations
• Dog Bone is used and material properties such as
• 1) Young’s modulus, 2) Poisson’s ratio, 3) failure (yield) stress and
) g , ) , ) (y )
strain.
• The specimen may be cut from a thin flat plate of constant
thickness or may be machined from a cylindrical bar.
• The “dogbone” shape is to avoid stress concentrations from
loading machine connections and to insure a homogeneous state
of stress and strain within the measurement region.
• The term homogeneous here indicates a uniform state of stress
or strain over the measurement region, i.e. the throat or reduced
central portion of the specimen.
22
11
12. 4/29/2011
• The engineering (average) stress can be
calculated by dividing the applied tensile
l l t d b di idi th li d t il
force, P, (normal to the cross section) by the
area of the original cross sectional area A0 as
follows,
Stress
23
Strain
• The engineering (average) strain in the direction
of the tensile load can be found by dividing the
change in length, ∆L, of the inscribed rectangle by
the original length L0,
• The term lambda in the above equation is called
the extension ratio and is sometimes used for
large deformations e.g., Low modulus rubber
24
12
13. 4/29/2011
True Stresses and Strain
• True stress and strain are calculated using the
instantaneous (deformed at a particular load)
i t t (d f d t ti l l d)
values of the cross‐sectional area, A, and the
length of the rectangle, L,
25
Young Modulus
• Young’s modulus, E, may be determined from
the slope of the stress‐strain curve or by
th l f th t t i b
dividing stress by strain,
26
13
14. 4/29/2011
• the axial deformation over length L0 is,
• Poisson’s ratio, , is defined as the absolute
value of the ratio of strain transverse, єy, to
the load direction to the strain in the load
direction, є x ,
Where strain transverse
‐ve for Applied tensile load, 27
Shear
• L = length of the cylinder,
• T = applied torque,
• r = radial distance,
• J = polar second moment of area
• G = shear modulus.
• =shear stress, = angle of twist,
• =shear strain, 28
14
15. 4/29/2011
• The shear modulus, G, is the slope of the shear
stress‐strain curve and may be found from,
where the shear strain is easily found by measuring
only the angular rotation, , in a given length, L.
The shear modulus is related to Young’s modulus
• As Poisson’s ratio, , varies between 0.3 and 0.5 for
most materials, the shear modulus is often
approximated by, G ~ E/3. 29
Typical Stress Strain Properties
30
15
16. 4/29/2011
Yield point
• if the stress exceeds the proportional limit a
residual or permanent deformation may remain
when the specimen is unloaded and the material is
p
said to have “yielded”.
• The exact yield point may not be the same as the
proportional limit and if this is the case the location
is difficult to determine.
• As a result, an arbitrary “0.2% offset” procedure is
often used to determine the yield point in metals
31
• That is, a line parallel to the initial tangent to
the stress‐strain diagram is drawn to pass
th t t i di i d t
through a strain of 0.002 in./in.
• The yield point is then defined as the point C
of intersection of this line and the stress‐strain
diagram.
g
• This procedure can be used for polymers but
the offset must be much larger than 0.2%
definition used for metals.
32
16
18. 4/29/2011
• If the strain scale of Fig. (a) is expanded as
illustrated in Fig. (b),
• the stress‐strain diagram of mild steel is
approximated by two straight lines;
• i) for the linear elastic portion and
• ii) is horizontal at a stress level of the lower
yield point. 35
• This characteristic of mild steel to “flow”,
“neck” “d
“ k” or “draw” without rupture when the
” ith t t h th
yield point has been exceeded has led to the
concepts of plastic, limit or ultimate design.
36
18
19. 4/29/2011
Idealized Stress‐ Strain
• a linear elastic perfectly brittle material is assumed
to have a stress‐strain diagram fig (a)
• a perfectly elastic‐plastic material with the stress‐
strain diagram Fig (b) mild steel or Poly C 37
• Metals (and polymers) often have nonlinear
• stress‐strain behavior as shown in Fig. (a). These
are sometimes modeled with a bilinear diagram
as shown in Fig. (b) and are referred to as a
perfectly linear elastic strain hardening material.38
19
20. 4/29/2011
Mathematical Definitions
Definition of a Continuum: A basic assumption
of elementary solid mechanics is that a
f l t lid h i i th t
material can be approximated as a continuum.
That is, the material (of mass M) is
continuously distributed over an arbitrarily
small volume, V, such that,
39
Mathematical/ Physical Def. of
Normal and Shear Stress
• Consider a body in
equilibrium under the
ilib i d th
action of external
forces
• F1, F2, F3, F4 = Fi as
shown in Fig.g
40
20
21. 4/29/2011
• If a cutting plane is
passed through the
d th h th
body as
• shown in Fig,
equilibrium is
maintained on the
remaining portion
by internal forces
distributed over the
surface S. 41
• At any arbitrary point p,
• the incremental resultant force, ∆Fr, on the
cut surface can be broken up into a normal
force in the direction of the normal, n, to
surface S and
• a tangential force parallel to surface S.
• The normal stress and the shear stress at
point p is mathematically defined as,
i i h i ll d fi d
42
21
22. 4/29/2011
Alternatively, the resultant
force, ∆Fr, at point p can
be divided by the area, ∆
A,
and the limit taken to
and the limit taken to
obtain the stress resultant
σr as shown in Fig. Normal
and tangential
components of this stress
resultant will then be the
normal stress σn and
shear stress τs at point p
on the area A.
43
• If a pair of cutting planes a differential distance
apart are passed through
• the body parallel to each of the three coordinate
yp
planes, a cube will be identified.
• Each plane will have normal and tangential
components of the stress resultants.
• The tangential or shear stress resultant on each
plane can further be represented by two
components in the coordinate directions.
44
22
23. 4/29/2011
• The internal stress
state is then
represented by
three stress
components on
components on
each coordinate
plane as shown in
Fig. Therefore at
any point in a body
there will be nine
h ill b i
stress components.
These are often
identified in matrix
form such that, 45
Using equilibrium, it is easy to show that the
stress matrix is symmetric,
t ti i ti
or
• leaving only six independent stresses existing at
a material point. 46
23
24. 4/29/2011
Physical and Mathematical Def. of
Normal & Shear Strain
• If there is stress acting on the body. For
example
l
47
• Both shearing and normal deformation may occur
with displacements.
• u is the displacement component in the x
direction and v is the displacement component in
the y direction.
the y direction
48
24
25. 4/29/2011
• The unit change in the x dimension will be the
strain єxx and is given by,
• If we apply similarly for y and z direction, and
assume that change of angle is very small then
∆u will be ignored. Then in 3 co‐ordinate
system normal strains are defined as:‐
49
Shear strains
• Shear strains are defined as the distortion of
the original 90º angle at the origin or the sum
of the angles Ѳ1 + Ѳ2. That is, again using the
small deformation assumption,
• After solving in all 3 directions shear strain is
50
25
26. 4/29/2011
• Like stresses, nine components of strain exist
at a point and these can be represented in
matrix form as,
• Again, it is possible to show that the strain
g , p
matrix is symmetric or that,
• Hence there are only six independent strains. 51
26