TABLE OF CONTENTS. Mechanics of Composite Materials, Second Edition Autar K Kaw University of South Florida, Tampa, USA

Size: px
Start display at page:

Download "TABLE OF CONTENTS. Mechanics of Composite Materials, Second Edition Autar K Kaw University of South Florida, Tampa, USA"

Transcription

1 Mechanics of Composite Materials, Second Edition Autar K Kaw University of South Florida, Tampa, USA TABLE OF CONTENTS 1. INTRODUCTION TO COMPOSITE MATERIALS 1.1 Introduction Classification Polymer Matrix Composites Metal Matrix Composites Ceramic Matrix Composites Carbon-Carbon Composites Recycling Mechanics Terminology... General References... Videos MACROMECHANICAL ANALYSIS OF A LAMINA 2.1 Introduction Review of Definitions...

2 2.1.1 Stress Strain Elastic Moduli Strain Energy Hooke's Law for Different Types of Materials Anisotropic Material Monoclinic Material Orthotropic Material (Orthoganally Anisotropic)/ Specially Orthotropic Transversely Isotropic Material Isotropic Material Hooke's Law for a Two Dimensional Unidirectional Lamina Plane Stress Assumption Reduction of Hooke's Law in Three Dimensions to Two Dimensions Relationship of Compliance and Stiffness Matrix to Engineering Elastic Constants of a Lamina Hooke's Law for a Two Dimensional Angle Lamina Engineering Constants of an Angle Lamina Invariant Form of Stiffness and Compliance Matrices for an Angle Lamina Strength Failure Theories of an Angle Lamina Maximum Stress Failure Theory Strength Ratio Failure Envelopes Maximum Strain Failure Theory Tsai-Hill Failure Theory Tsai-Wu Failure Theory...

3 2.8.7 Comparison of Experimental Results with Failure Theories Hygrothermal Stresses and Strains in a Lamina Hygrothermal Stress-Strain Relationship for a Unidirectional Lamina Hygrothermal Stress-Strain Relationship for an Angle Lamina... Appendix A: Matrix Algebra... Appendix B: Transformation of Stresses and Strains MICROMECHANICAL ANALYSIS OF A LAMINA 3.1 Introduction Volume and Mass Fractions, Density and Void Content Volume Fractions Mass Fractions Density Void Content Evaluation of the Four Elastic Moduli Strength of Materials Approach Longitudinal Young s Modulus Transverse Young s Modulus Major Poisson s Ratio In-Plane Shear Modulus Semi-Empirical Models...

4 Longitudinal Young s Modulus Transverse Young s Modulus Major Poisson s Ratio In-Plane Shear Modulus Elasticity Approach Longitudinal Young s Modulus Transverse Young s Modulus Major Poisson s Ratio In-Plane Shear Modulus Elastic Moduli of Lamina with Transversely Isotropic Fibers Ultimate Strengths of a Unidirectional Lamina Longitudinal Tensile Strength Longitudinal Compressive Strength Transverse Tensile Strength Transverse Compressive Strength In-Plane Shear Strength Coefficients of Thermal Expansion of a Unidirectional Lamina Longitudinal Thermal Expansion Coefficient Transverse Thermal Expansion Coefficient 3.5 Coefficients of Moisture Expansion of a Unidirectional Lamina MACROMECHANICAL ANALYSIS OF A LAMINATE

5 4.1 Introduction Laminate Code Stress-Strain Relations for a Laminate One Dimensional Isotropic Beam Stress-Strain Relations Strain-Displacement Equations Strain and Stress in a Laminate Stress and Moment Resultants Related to Mid-Plane Strains and Curvatures In-Plane and Flexural Modulus of a Laminate In-Plane Engineering Constants of a Laminate Flexural Engineering Constants of a Laminate Hygrothermal Effects in a Laminate Hygrothermal Stresses and Strains Coefficients of Thermal and Moisture Expansion of Laminates Warpage of Laminates FAILURE, ANALYSIS AND DESIGN OF LAMINATES 5.1 Introduction Special Cases of Laminates Symmetric Laminates...

6 5.2.2 Cross-Ply Laminates Angle-Ply Laminates Antisymmetric Laminates Balanced Laminates Quasi-Isotropic Laminates Failure Criteria For a Laminate Design of Laminated Composite Other Mechanical Design Issues Sandwich Composites Long Term Environmental Effects Interlaminar Stresses Impact Fracture Resistance Fatigue Resistance... 6.ANALYSIS OF BEAMS 6.1 Introduction. 6.2 Symmetrical Beams. 6.3 Nonsymetrical Beams

7 .. Index to Subjects

ME 582 Advanced Materials Science. Chapter 2 Macromechanical Analysis of a Lamina (Part 2)

ME 582 Advanced Materials Science. Chapter 2 Macromechanical Analysis of a Lamina (Part 2) ME 582 Advanced Materials Science Chapter 2 Macromechanical Analysis of a Lamina (Part 2) Laboratory for Composite Materials Research Department of Mechanical Engineering University of South Alabama, Mobile,

More information

Mechanics of Composite Materials, Second Edition Autar K Kaw University of South Florida, Tampa, USA

Mechanics of Composite Materials, Second Edition Autar K Kaw University of South Florida, Tampa, USA Mechanics of Composite Materials, Second Edition Autar K Kaw University of South Florida, Tampa, USA What programs are in PROMAL? Master Menu The master menu screen with five separate applications from

More information

QUESTION BANK Composite Materials

QUESTION BANK Composite Materials QUESTION BANK Composite Materials 1. Define composite material. 2. What is the need for composite material? 3. Mention important characterits of composite material 4. Give examples for fiber material 5.

More information

Hygrothermal stresses in laminates

Hygrothermal stresses in laminates Hygrothermal stresses in laminates Changing environment conditions (temperature and moisture) have an important effect on the properties which are matrix dominated. Change in temperaturet and moisture

More information

Chapter 2 - Macromechanical Analysis of a Lamina. Exercise Set. 2.1 The number of independent elastic constants in three dimensions are: 2.

Chapter 2 - Macromechanical Analysis of a Lamina. Exercise Set. 2.1 The number of independent elastic constants in three dimensions are: 2. Chapter - Macromechanical Analysis of a Lamina Exercise Set. The number of independent elastic constants in three dimensions are: Anisotropic Monoclinic 3 Orthotropic 9 Transversely Orthotropic 5 Isotropic.

More information

Computational Analysis for Composites

Computational Analysis for Composites Computational Analysis for Composites Professor Johann Sienz and Dr. Tony Murmu Swansea University July, 011 The topics covered include: OUTLINE Overview of composites and their applications Micromechanics

More information

PROMAL2012 SOFTWARE PACKAGE A USER GUIDE

PROMAL2012 SOFTWARE PACKAGE A USER GUIDE PROMAL2012 SOFTWARE PACKAGE A USER GUIDE 1. This manual is only for VISTA, WINDOWS 7 and WINDOWS 8 users. The PROMAL2012 software and manual are available at http://www.eng.usf.edu/~kaw/promal2012/ 2.

More information

Composite Structures. Indian Institute of Technology Kanpur

Composite Structures. Indian Institute of Technology Kanpur Mechanics of Laminated Composite Structures Nachiketa Tiwari Indian Institute of Technology Kanpur Lecture 23 Analysis of an Orthotropic Ply Lecture Overview Introduction Engineering constants for an 2

More information

Stress, Strain Stress strain relationships for different types of materials Stress strain relationships for a unidirectional/bidirectional lamina

Stress, Strain Stress strain relationships for different types of materials Stress strain relationships for a unidirectional/bidirectional lamina Chapter 2 Macromechanical Analysis of a Lamina Stress, Strain Stress strain relationships for different types of materials Stress strain relationships for a unidirectional/bidirectional lamina Islamic

More information

Laminated Composite Plates and Shells

Laminated Composite Plates and Shells Jianqiao Ye Laminated Composite Plates and Shells 3D Modelling With 62 Figures Springer Table of Contents 1. Introduction to Composite Materials 1 1.1 Introduction 1 1.2 Classification of Composite Materials

More information

FINITE ELEMENT ANALYSIS OF COMPOSITE MATERIALS

FINITE ELEMENT ANALYSIS OF COMPOSITE MATERIALS FINITE ELEMENT ANALYSIS OF COMPOSITE MATERIALS Ever J. Barbero Department of Mechanical and Aerospace Engineering West Virginia University USA CRC Press Taylor &.Francis Group Boca Raton London New York

More information

Getting Started with Composites Modeling and Analysis

Getting Started with Composites Modeling and Analysis Getting Started with Composites Modeling and Analysis IN THIS WEBINAR: PRESENTED BY: Orthotropic materials and how to define them Composite Laminate properties and modeling Composite failure theories and

More information

Module III - Macro-mechanics of Lamina. Lecture 23. Macro-Mechanics of Lamina

Module III - Macro-mechanics of Lamina. Lecture 23. Macro-Mechanics of Lamina Module III - Macro-mechanics of Lamina Lecture 23 Macro-Mechanics of Lamina For better understanding of the macromechanics of lamina, the knowledge of the material properties in essential. Therefore, the

More information

Fracture Mechanics, Damage and Fatigue: Composites

Fracture Mechanics, Damage and Fatigue: Composites University of Liège Aerospace & Mechanical Engineering Fracture Mechanics, Damage and Fatigue: Composites Ludovic Noels Computational & Multiscale Mechanics of Materials CM3 http://www.ltas-cm3.ulg.ac.be/

More information

MECHANICS OF COMPOSITE STRUCTURES

MECHANICS OF COMPOSITE STRUCTURES MECHANICS OF COMPOSITE STRUCTURES LÁSZLÓ P. KOLLÁR Budapest University of Technology and Economics GEORGE S. SPRINGER Stanford University PUBLISHED BY THE PRESS SYNDICATE OF THE UNIVERSITY OF CAMBRIDGE

More information

Effect of Thermal Stresses on the Failure Criteria of Fiber Composites

Effect of Thermal Stresses on the Failure Criteria of Fiber Composites Effect of Thermal Stresses on the Failure Criteria of Fiber Composites Martin Leong * Institute of Mechanical Engineering Aalborg University, Aalborg, Denmark Bhavani V. Sankar Department of Mechanical

More information

Presented By: EAS 6939 Aerospace Structural Composites

Presented By: EAS 6939 Aerospace Structural Composites A Beam Theory for Laminated Composites and Application to Torsion Problems Dr. BhavaniV. Sankar Presented By: Sameer Luthra EAS 6939 Aerospace Structural Composites 1 Introduction Composite beams have

More information

Module 5: Laminate Theory Lecture 17: Laminate Constitutive Relations. The Lecture Contains: Laminate Constitutive Relations

Module 5: Laminate Theory Lecture 17: Laminate Constitutive Relations. The Lecture Contains: Laminate Constitutive Relations Lecture 17: Laminate Constitutive Relations The Lecture Contains: Laminate Constitutive Relations Classification of Laminates Cross-Ply Laminates Specially Orthotropic Laminates Examples Homework References

More information

ME 7502 Lecture 2 Effective Properties of Particulate and Unidirectional Composites

ME 7502 Lecture 2 Effective Properties of Particulate and Unidirectional Composites ME 75 Lecture Effective Properties of Particulate and Unidirectional Composites Concepts from Elasticit Theor Statistical Homogeneit, Representative Volume Element, Composite Material Effective Stress-

More information

Bending of Simply Supported Isotropic and Composite Laminate Plates

Bending of Simply Supported Isotropic and Composite Laminate Plates Bending of Simply Supported Isotropic and Composite Laminate Plates Ernesto Gutierrez-Miravete 1 Isotropic Plates Consider simply a supported rectangular plate of isotropic material (length a, width b,

More information

five Mechanics of Materials 1 ARCHITECTURAL STRUCTURES: FORM, BEHAVIOR, AND DESIGN DR. ANNE NICHOLS SUMMER 2017 lecture

five Mechanics of Materials 1 ARCHITECTURAL STRUCTURES: FORM, BEHAVIOR, AND DESIGN DR. ANNE NICHOLS SUMMER 2017 lecture ARCHITECTURAL STRUCTURES: FORM, BEHAVIOR, AND DESIGN DR. ANNE NICHOLS SUMMER 2017 lecture five mechanics www.carttalk.com of materials Mechanics of Materials 1 Mechanics of Materials MECHANICS MATERIALS

More information

Composite Laminate Modeling

Composite Laminate Modeling omposite Laminate Modeling White Paper for Femap and NX Nastran Users Venkata Bheemreddy, Ph.D., Senior Staff Mechanical Engineer Adrian Jensen, PE, Senior Staff Mechanical Engineer WHAT THIS WHITE PAPER

More information

Passive Damping Characteristics of Carbon Epoxy Composite Plates

Passive Damping Characteristics of Carbon Epoxy Composite Plates Journal of Materials Science and Engineering A 6 (-) 35-4 doi:.765/6-63/6.-.5 D DAVID PUBLISHING Passive Damping Characteristics of Carbon Epoxy Composite Plates Dileep Kumar K * and V V Subba Rao Faculty

More information

A Constitutive Framework for the Numerical Analysis of Organic Soils and Directionally Dependent Materials

A Constitutive Framework for the Numerical Analysis of Organic Soils and Directionally Dependent Materials Dublin, October 2010 A Constitutive Framework for the Numerical Analysis of Organic Soils and Directionally Dependent Materials FracMan Technology Group Dr Mark Cottrell Presentation Outline Some Physical

More information

PURE BENDING. If a simply supported beam carries two point loads of 10 kn as shown in the following figure, pure bending occurs at segment BC.

PURE BENDING. If a simply supported beam carries two point loads of 10 kn as shown in the following figure, pure bending occurs at segment BC. BENDING STRESS The effect of a bending moment applied to a cross-section of a beam is to induce a state of stress across that section. These stresses are known as bending stresses and they act normally

More information

Materials and Structures. Indian Institute of Technology Kanpur

Materials and Structures. Indian Institute of Technology Kanpur Introduction to Composite Materials and Structures Nachiketa Tiwari Indian Institute of Technology Kanpur Lecture 34 Thermal Stresses in Plates Lecture Overview Introduction Mechanical and Thermal Strains

More information

2.2 Relation Between Mathematical & Engineering Constants Isotropic Materials Orthotropic Materials

2.2 Relation Between Mathematical & Engineering Constants Isotropic Materials Orthotropic Materials Chapter : lastic Constitutive quations of a Laminate.0 Introduction quations of Motion Symmetric of Stresses Tensorial and ngineering Strains Symmetry of Constitutive quations. Three-Dimensional Constitutive

More information

LAMINATED COMPOSITE PLATES

LAMINATED COMPOSITE PLATES LAMINATED COMPOSITE PLATES David Roylance Department of Materials Science and Engineering Massachusetts Institute of Technology Cambridge, MA 02139 February 10, 2000 Introduction This document is intended

More information

Module 7: Micromechanics Lecture 34: Self Consistent, Mori -Tanaka and Halpin -Tsai Models. Introduction. The Lecture Contains. Self Consistent Method

Module 7: Micromechanics Lecture 34: Self Consistent, Mori -Tanaka and Halpin -Tsai Models. Introduction. The Lecture Contains. Self Consistent Method Introduction In this lecture we will introduce some more micromechanical methods to predict the effective properties of the composite. Here we will introduce expressions for the effective properties without

More information

SIMULATION OF PROGRESSIVE FAILURE PREDICTION OF FILAMENT WOUND COMPOSITE TUBES SUBJECTED TO MULTIPLE LOADING WITH MEMBRANE-FLEXION COUPLING EFFECTS

SIMULATION OF PROGRESSIVE FAILURE PREDICTION OF FILAMENT WOUND COMPOSITE TUBES SUBJECTED TO MULTIPLE LOADING WITH MEMBRANE-FLEXION COUPLING EFFECTS VOL. 5, NO. 4, APRIL 010 ISSN 1819-6608 006-010 Asian Research Publishing Network (ARPN). All rights reserved. SIMULATION OF PROGRESSIVE FAILURE PREDICTION OF FILAMENT WOUND COMPOSITE TUBES SUBJECTED TO

More information

Tensile Properties of Thermoplastic-Laminated Composites Based on a Polypropylene Matrix Reinforced with Continuous Twaron Fibers

Tensile Properties of Thermoplastic-Laminated Composites Based on a Polypropylene Matrix Reinforced with Continuous Twaron Fibers Tensile Properties of Thermoplastic-Laminated Composites Based on a Polypropylene Matrix Reinforced with Continuous Twaron Fibers J. L. MENA-TUN, P. I. GONZALEZ-CHI Centro de Investigación Científica de

More information

Mechanical Behavior of Composite Tapered Lamina

Mechanical Behavior of Composite Tapered Lamina International Journal of Engineering Research and Development e-issn: 2278-067X, p-issn: 2278-800X, www.ijerd.com Volume 10, Issue 8 (August 2014), PP.19-27 Mechanical Behavior of Composite Tapered Lamina

More information

Predicting Failure of Multiangle Composite Laminates

Predicting Failure of Multiangle Composite Laminates Predicting Failure of Multiangle Composite Laminates Preliminary discussion (not in textbook): Micromechanics failure analyses vs Macromechanics failure analyses Fiber Architecture of Some Common Composite

More information

As an example we consider the stacking and analysis of a 2-ply symmetric laminate. First we clear the Matlab space and close figures.

As an example we consider the stacking and analysis of a 2-ply symmetric laminate. First we clear the Matlab space and close figures. Program Lam 1 Introduction The collection of Matlab command and function files in the package lam allows the stacking and analysis of a laminate. In fact only a representative piece of a laminate is considered,

More information

Composite Structures. Indian Institute of Technology Kanpur

Composite Structures. Indian Institute of Technology Kanpur Mechanics of Laminated Composite Structures Nachiketa Tiwari Indian Institute of Technology Kanpur Lecture 21 Behavior of Ribbon Fiber Composites Ribbon Reinforced Composites: Introduction Quite often,

More information

PLY LEVEL UNCERTAINTY EFFECTS ON FAILURE OF COMPOSITE

PLY LEVEL UNCERTAINTY EFFECTS ON FAILURE OF COMPOSITE 7th European Workshop on Structural Health Monitoring July 8-11, 2014. La Cité, Nantes, France More Info at Open Access Database www.ndt.net/?id=17206 PLY LEVEL UNCERTAINTY EFFECTS ON FAILURE OF COMPOSITE

More information

Mechanical and Thermal Properties of Coir Fiber Reinforced Epoxy Composites Using a Micromechanical Approach

Mechanical and Thermal Properties of Coir Fiber Reinforced Epoxy Composites Using a Micromechanical Approach Mechanical and Thermal Properties of Coir Fiber Reinforced Epoxy Composites Using a Micromechanical Approach Sandhyarani Biswas Department of Mechanical Engineering, N.I.T Rourkela, INDIA Abstract: Now-a-days,

More information

EFFECT OF LAMINATION ANGLE AND THICKNESS ON ANALYSIS OF COMPOSITE PLATE UNDER THERMO MECHANICAL LOADING

EFFECT OF LAMINATION ANGLE AND THICKNESS ON ANALYSIS OF COMPOSITE PLATE UNDER THERMO MECHANICAL LOADING Journal of MECHANICAL ENGINEERING Strojnícky časopis, VOL 67 (217), NO 1, 5-22 EFFECT OF LAMINATION ANGLE AND THICKNESS ON ANALYSIS OF COMPOSITE PLATE UNDER THERMO MECHANICAL LOADING Arnab Choudhury 1,

More information

Module 4: Behaviour of a Laminae-II. Learning Unit 1: M1. M4.1 Mechanics of Composites. M4.1.1 Introduction to Mechanics of Composites

Module 4: Behaviour of a Laminae-II. Learning Unit 1: M1. M4.1 Mechanics of Composites. M4.1.1 Introduction to Mechanics of Composites Module 4: Behaviour of a Laminae-II Learning Unit 1: M1 M4.1 Mechanics of Composites M4.1.1 Introduction to Mechanics of Composites The relation between ply uniaxial strengths and constituent properties

More information

VALIDATION of CoDA SOFTWARE for COMPOSITES SYNTHESIS AND PRELIMINARY DESIGN (or GETTING COMPOSITES USED - PART 2 )

VALIDATION of CoDA SOFTWARE for COMPOSITES SYNTHESIS AND PRELIMINARY DESIGN (or GETTING COMPOSITES USED - PART 2 ) VALIDATION of CoDA SOFTWARE for COMPOSITES SYNTHESIS AND PRELIMINARY DESIGN (or GETTING COMPOSITES USED - PART 2 ) Graham D Sims and William R Broughton Composites Design Data and Methods, Centre for Materials

More information

Comparison of Ply-wise Stress-Strain results for graphite/epoxy laminated plate subjected to in-plane normal loads using CLT and ANSYS ACP PrepPost

Comparison of Ply-wise Stress-Strain results for graphite/epoxy laminated plate subjected to in-plane normal loads using CLT and ANSYS ACP PrepPost Comparison of Ply-wise Stress-Strain results for graphite/epoxy laminated plate subjected to in-plane normal loads using CLT and ANSYS ACP PrepPost 1 Mihir A. Mehta, 2 Satyen D. Ramani 1 PG Student, Department

More information

Lecture 15 Strain and stress in beams

Lecture 15 Strain and stress in beams Spring, 2019 ME 323 Mechanics of Materials Lecture 15 Strain and stress in beams Reading assignment: 6.1 6.2 News: Instructor: Prof. Marcial Gonzalez Last modified: 1/6/19 9:42:38 PM Beam theory (@ ME

More information

Influence of the filament winding process variables on the mechanical behavior of a composite pressure vessel

Influence of the filament winding process variables on the mechanical behavior of a composite pressure vessel Influence of the filament winding process variables on the mechanical behavior of a composite pressure vessel G. Vargas 1 & A. Miravete 2 1 Universidad Pontificia Bolivariana, Facultad de Ingeniería Mecánica,

More information

ON THE NUMERICAL ANALYSIS OF COMPOSITE MATERIAL

ON THE NUMERICAL ANALYSIS OF COMPOSITE MATERIAL The 4th International Conference Advanced Composite Materials Engineering COMAT 8- October, Brasov, Romania O THE UMERICAL AALYSIS OF COMPOSITE MATERIAL D.D. icoara Transilvania University, City Brasov,

More information

American Society for Testing and Materials (ASTM) Standards. Mechanical Testing of Composites and their Constituents

American Society for Testing and Materials (ASTM) Standards. Mechanical Testing of Composites and their Constituents Mechanical Testing of Composites and their Constituents American Society for Testing and Materials (ASTM) Standards Tests done to determine intrinsic material properties such as modulus and strength for

More information

Materials and Structures. Indian Institute of Technology Kanpur

Materials and Structures. Indian Institute of Technology Kanpur Introduction to Composite Materials and Structures Nachiketa Tiwari Indian Institute of Technology Kanpur Lecture 16 Behavior of Unidirectional Composites Lecture Overview Mt Material ilaxes in unidirectional

More information

MODELING OF THE BEHAVIOR OF WOVEN LAMINATED COMPOSITES UNTIL RUPTURE

MODELING OF THE BEHAVIOR OF WOVEN LAMINATED COMPOSITES UNTIL RUPTURE MODELING OF THE BEHAVIOR OF WOVEN LAMINATED COMPOSITES UNTIL RUPTURE Jean Paul Charles, Christian Hochard,3, Pierre Antoine Aubourg,3 Eurocopter, 375 Marignane cedex, France Unimeca, 6 rue J. Curie, 3453

More information

Composite models 30 and 131: Ply types 0 and 8 calibration

Composite models 30 and 131: Ply types 0 and 8 calibration Model calibration Composite Bi-Phase models 30 and 3 for elastic, damage and failure PAM-CRASH material model 30 is for solid and 3 for multi-layered shell elements. Within these models different ply types

More information

PRELIMINARY PREDICTION OF SPECIMEN PROPERTIES CLT and 1 st order FEM analyses

PRELIMINARY PREDICTION OF SPECIMEN PROPERTIES CLT and 1 st order FEM analyses OPTIMAT BLADES Page 1 of 24 PRELIMINARY PREDICTION OF SPECIMEN PROPERTIES CLT and 1 st order FEM analyses first issue Peter Joosse CHANGE RECORD Issue/revision date pages Summary of changes draft 24-10-02

More information

LAMINATED COMPOSITE PLATES

LAMINATED COMPOSITE PLATES LAMINATED COMPOSITE PLATES David Roylance Department of Materials Science and Engineering Massachusetts Institute of Technology Cambridge, MA 02139 February 10, 2000 Introduction This document is intended

More information

9 Strength Theories of Lamina

9 Strength Theories of Lamina 9 trength Theories of Lamina 9- TRENGTH O ORTHOTROPIC LAMINA or isotropic materials the simplest method to predict failure is to compare the applied stresses to the strengths or some other allowable stresses.

More information

Smart Materials, Adaptive Structures, and Intelligent Mechanical Systems

Smart Materials, Adaptive Structures, and Intelligent Mechanical Systems Smart Materials, Adaptive Structures, and Intelligent Mechanical Systems Bishakh Bhattacharya & Nachiketa Tiwari Indian Institute of Technology Kanpur Lecture 19 Analysis of an Orthotropic Ply References

More information

Module 7: Micromechanics Lecture 25: Strength of Materials Approach. Introduction. The Lecture Contains. Effective Transverse Modulus

Module 7: Micromechanics Lecture 25: Strength of Materials Approach. Introduction. The Lecture Contains. Effective Transverse Modulus Introduction In the previous lecture we have introduced the concept of Representative Volume Element or Unit Cell. This is the basic building block in a micromechanical study. Further, we explained the

More information

Finite Element Analysis of Graphite/Epoxy Composite Pressure Vessel

Finite Element Analysis of Graphite/Epoxy Composite Pressure Vessel Journal of Materials Science and Chemical Engineering, 2017, 5, 19-28 http://www.scirp.org/journal/msce ISSN Online: 2327-6053 ISSN Print: 2327-6045 Finite Element Analysis of Graphite/Epoxy Composite

More information

A Software Tool for Mechanics of Composite Materials*

A Software Tool for Mechanics of Composite Materials* Int. J. Engng Ed. Vol. 13, No., p. 433±441, 17 04-14X/1 $3.00+0.00 Printed in Great Britain. # 17 TEMPUS Publications. A Software Tool for Mechanics of Composite Materials* AUTAR K. KAW and GARY WILLENBRING

More information

An integrated approach to the design of high performance carbon fibre reinforced risers - from micro to macro - scale

An integrated approach to the design of high performance carbon fibre reinforced risers - from micro to macro - scale An integrated approach to the design of high performance carbon fibre reinforced risers - from micro to macro - scale Angelos Mintzas 1, Steve Hatton 1, Sarinova Simandjuntak 2, Andrew Little 2, Zhongyi

More information

Strength Prediction Of Composite Laminate

Strength Prediction Of Composite Laminate Strength Prediction Of Composite te Prof. Yogananda. A 1, Mr. R. Vijayakumar 2 Assistant Professor, Department of Mechanical Engineering, East West Institute of Technology, Bangalore. Research Scholar,

More information

Mechanics of Materials Primer

Mechanics of Materials Primer Mechanics of Materials rimer Notation: A = area (net = with holes, bearing = in contact, etc...) b = total width of material at a horizontal section d = diameter of a hole D = symbol for diameter E = modulus

More information

Materials and Structures. Indian Institute of Technology Kanpur

Materials and Structures. Indian Institute of Technology Kanpur Introduction to Composite Materials and Structures Nachiketa Tiwari Indian Institute of Technology Kanpur Lecture 15 Behavior of Unidirectional Composites Lecture Overview Mt Material ilaxes in unidirectional

More information

Analysis of Composite Pressure Vessels

Analysis of Composite Pressure Vessels Analysis of Composite Pressure Vessels Reza Mohammadzadeh Gheshlaghi 1 Mohammad Hassan Hojjati Hamid Reza Mohammadi Daniali 3 1 Engineering Research Centre, Tabriz, Iran,3 Department of Mechanical Engineering,

More information

STRESSES WITHIN CURVED LAMINATED BEAMS OF DOUGLAS-FIR

STRESSES WITHIN CURVED LAMINATED BEAMS OF DOUGLAS-FIR UNITED STATES DEPARTMENT OF AGRICULTURE. FOREST SERVICE - FOREST PRODUCTS LABORATORY - MADISON, WIS. STRESSES WITHIN CURVED LAMINATED BEAMS OF DOUGLAS-FIR NOVEMBER 1963 FPL-020 STRESSES WITHIN CURVED LAMINATED

More information

Module-6: Laminated Composites-II. Learning Unit-1: M6.1. M 6.1 Structural Mechanics of Laminates

Module-6: Laminated Composites-II. Learning Unit-1: M6.1. M 6.1 Structural Mechanics of Laminates Module-6: Laminated Composites-II Learning Unit-1: M6.1 M 6.1 Structural Mechanics of Laminates Classical Lamination Theory: Laminate Stiffness Matrix To this point in the development of classical lamination

More information

INTERNATIONAL JOURNAL OF APPLIED ENGINEERING RESEARCH, DINDIGUL Volume 2, No 1, 2011

INTERNATIONAL JOURNAL OF APPLIED ENGINEERING RESEARCH, DINDIGUL Volume 2, No 1, 2011 Interlaminar failure analysis of FRP cross ply laminate with elliptical cutout Venkateswara Rao.S 1, Sd. Abdul Kalam 1, Srilakshmi.S 1, Bala Krishna Murthy.V 2 1 Mechanical Engineering Department, P. V.

More information

Chapter 2: Elasticity

Chapter 2: Elasticity OHP 1 Mechanical Properties of Materials Chapter 2: lasticity Prof. Wenjea J. Tseng ( 曾文甲 ) Department of Materials ngineering National Chung Hsing University wenjea@dragon.nchu.edu.tw Reference: W.F.

More information

Fracture Mechanics of Composites with Residual Thermal Stresses

Fracture Mechanics of Composites with Residual Thermal Stresses J. A. Nairn Material Science & Engineering, University of Utah, Salt Lake City, Utah 84 Fracture Mechanics of Composites with Residual Thermal Stresses The problem of calculating the energy release rate

More information

DAMAGE MECHANICS MODEL FOR OFF-AXIS FATIGUE BEHAVIOR OF UNIDIRECTIONAL CARBON FIBER-REINFORCED COMPOSITES AT ROOM AND HIGH TEMPERATURES

DAMAGE MECHANICS MODEL FOR OFF-AXIS FATIGUE BEHAVIOR OF UNIDIRECTIONAL CARBON FIBER-REINFORCED COMPOSITES AT ROOM AND HIGH TEMPERATURES DAMAGE MECHANICS MODEL FOR OFF-AXIS FATIGUE BEHAVIOR OF UNIDIRECTIONAL CARBON FIBER-REINFORCED COMPOSITES AT ROOM AND HIGH TEMPERATURES M. Kawai Institute of Engineering Mechanics University of Tsukuba,

More information

Mechanics of Materials

Mechanics of Materials Mechanics of Materials Notation: a = acceleration = area (net = with holes, bearing = in contact, etc...) SD = allowable stress design d = diameter of a hole = calculus symbol for differentiation e = change

More information

Chapter 6: Mechanical Properties of Metals. Dr. Feras Fraige

Chapter 6: Mechanical Properties of Metals. Dr. Feras Fraige Chapter 6: Mechanical Properties of Metals Dr. Feras Fraige Stress and Strain Tension Compression Shear Torsion Elastic deformation Plastic Deformation Yield Strength Tensile Strength Ductility Toughness

More information

LAMINATION THEORY FOR THE STRENGTH OF FIBER COMPOSITE MATERIALS

LAMINATION THEORY FOR THE STRENGTH OF FIBER COMPOSITE MATERIALS XXII. LAMINATION THEORY FOR THE STRENGTH OF FIBER COMPOSITE MATERIALS Introduction The lamination theory for the elastic stiffness of fiber composite materials is the backbone of the entire field, it holds

More information

MECHANICS OF MATERIALS. EQUATIONS AND THEOREMS

MECHANICS OF MATERIALS. EQUATIONS AND THEOREMS 1 MECHANICS OF MATERIALS. EQUATIONS AND THEOREMS Version 2011-01-14 Stress tensor Definition of traction vector (1) Cauchy theorem (2) Equilibrium (3) Invariants (4) (5) (6) or, written in terms of principal

More information

IJSER 1. INTRODUCTION. M.Elhadary

IJSER 1. INTRODUCTION. M.Elhadary 1591 A new failure criterion for GRP composite materials subjected to in-phase and out-of-phase biaxial fatigue loading under different stress ratios M.Elhadary Abstract this studying the fatigue behavior

More information

The stiffness of plates

The stiffness of plates The stiffness of plates 1. Introduction The word plate is a collective term for elements in which forces can be transferred in two directions. Floors, walls, bridge slabs and laminates are all plates.

More information

Non-conventional Glass fiber NCF composites with thermoset and thermoplastic matrices. F Talence, France Le Cheylard, France

Non-conventional Glass fiber NCF composites with thermoset and thermoplastic matrices. F Talence, France Le Cheylard, France 20 th International Conference on Composite Materials Copenhagen, 19-24th July 2015 Non-conventional Glass fiber NCF composites with thermoset and thermoplastic matrices. Thierry Lorriot 1, Jalal El Yagoubi

More information

MODELING OF CONCRETE MATERIALS AND STRUCTURES. Kaspar Willam

MODELING OF CONCRETE MATERIALS AND STRUCTURES. Kaspar Willam MODELING OF CONCRETE MATERIALS AND STRUCTURES Class Meeting #1: Fundamentals Kaspar Willam University of Colorado at Boulder Notation: Direct and indicial tensor formulations Fundamentals: Stress and Strain

More information

Enhancing Prediction Accuracy In Sift Theory

Enhancing Prediction Accuracy In Sift Theory 18 TH INTERNATIONAL CONFERENCE ON COMPOSITE MATERIALS Enhancing Prediction Accuracy In Sift Theory J. Wang 1 *, W. K. Chiu 1 Defence Science and Technology Organisation, Fishermans Bend, Australia, Department

More information

Elastic Moduli characterization of composites using the Impulse Excitation Technique

Elastic Moduli characterization of composites using the Impulse Excitation Technique White paper: Technical-scientific Informative Elastic Moduli characterization of composites using the Impulse ATCP Physical Engineering Sonelastic Division wwwsonelasticcom Authors: Lucas Barcelos Otani

More information

Passive Damping Characteristics of Carbon Epoxy Composite Plates

Passive Damping Characteristics of Carbon Epoxy Composite Plates Journal of aterials Science and Engineering A 6 (1-2) (2016) 35-42 doi: 10.17265/2161-6213/2016.1-2.005 D DAVID PUBLISHIG Passive Damping Characteristics of Carbon Epoxy Composite Plates Dileep Kumar K

More information

Calculation of Damage-dependent Directional Failure Indices from the Tsai-Wu Static Failure Criterion

Calculation of Damage-dependent Directional Failure Indices from the Tsai-Wu Static Failure Criterion Van Paepegem, W. and Degrieck, J. (3. alculation of Damage-dependent Directional Failure Indices from the sai-wu Static Failure riterion. omposites Science and echnology, 63(, 35-3. alculation of Damage-dependent

More information

Finite Element Analysis of Composite Laminate By Using ABDH Matrix(Stiffness Matrix)

Finite Element Analysis of Composite Laminate By Using ABDH Matrix(Stiffness Matrix) Finite Element Analysis of Composite Laminate By Using ABDH Matrix(Stiffness Matrix) Nikhil J. Chaudhari 1 Post Graduate Student Department of Mechanical Engineering Veermata Jijabai Technological Institute

More information

KINK BAND FORMATION OF FIBER REINFORCED POLYMER (FRP)

KINK BAND FORMATION OF FIBER REINFORCED POLYMER (FRP) KINK BAND FORMATION OF FIBER REINFORCED POLYMER (FRP) 1 University of Science & Technology Beijing, China, niukm@ustb.edu.cn 2 Tsinghua University, Department of Engineering Mechanics, Beijing, China,

More information

2 To whom all correspondences should be addressed:

2 To whom all correspondences should be addressed: Composite Modeling and Analysis of FDM Prototypes for Design and Fabrication of Functionally Graded Parts Longmei Li, Q. Sun, C. Bellehumeur 1,andP.Gu 2 Department of Mechanical and Manufacturing Engineering

More information

Multi Disciplinary Delamination Studies In Frp Composites Using 3d Finite Element Analysis Mohan Rentala

Multi Disciplinary Delamination Studies In Frp Composites Using 3d Finite Element Analysis Mohan Rentala Multi Disciplinary Delamination Studies In Frp Composites Using 3d Finite Element Analysis Mohan Rentala Abstract: FRP laminated composites have been extensively used in Aerospace and allied industries

More information

Module 3: 3D Constitutive Equations Lecture 10: Constitutive Relations: Generally Anisotropy to Orthotropy. The Lecture Contains: Stress Symmetry

Module 3: 3D Constitutive Equations Lecture 10: Constitutive Relations: Generally Anisotropy to Orthotropy. The Lecture Contains: Stress Symmetry The Lecture Contains: Stress Symmetry Strain Symmetry Strain Energy Density Function Material Symmetry Symmetry with respect to a Plane Symmetry with respect to two Orthogonal Planes Homework References

More information

Analytical study of sandwich structures using Euler Bernoulli beam equation

Analytical study of sandwich structures using Euler Bernoulli beam equation Analtical stud of sandwich structures using Euler Bernoulli beam equation Hui Xue and H. Khawaja Citation: AIP Conference Proceedings 1798, 020076 (2017); doi: 10.1063/1.4972668 View online: http://dx.doi.org/10.1063/1.4972668

More information

MECHANICS OF MATERIALS

MECHANICS OF MATERIALS CHATR Stress MCHANICS OF MATRIALS and Strain Axial Loading Stress & Strain: Axial Loading Suitability of a structure or machine may depend on the deformations in the structure as well as the stresses induced

More information

A STRUCTURE DESIGN OF CFRP REAR PRESSURE BULKHEAD WITHOUT STIFFENERS

A STRUCTURE DESIGN OF CFRP REAR PRESSURE BULKHEAD WITHOUT STIFFENERS Xi an, 2-25 th August 217 A STRUCTURE DESIGN OF CFRP REAR PRESSURE BULKHEAD WITHOUT STIFFENERS LI Zhongyang 1, LI Dong 2 Mailbox72-35, Yanliang District, Xian, China, Email: zhongyangli@live.com Keywords:

More information

Lecture 4 Honeycombs Notes, 3.054

Lecture 4 Honeycombs Notes, 3.054 Honeycombs-In-plane behavior Lecture 4 Honeycombs Notes, 3.054 Prismatic cells Polymer, metal, ceramic honeycombs widely available Used for sandwich structure cores, energy absorption, carriers for catalysts

More information

Laminated Beams of Isotropic or Orthotropic Materials Subjected to Temperature Change

Laminated Beams of Isotropic or Orthotropic Materials Subjected to Temperature Change United States Department of Agriculture Forest Service Forest Products Laboratory Research Paper FPL 375 June 1980 Laminated Beams of Isotropic or Orthotropic Materials Subjected to Temperature Change

More information

Department of Mechanical Engineering, National Institute of Technology Rourkela, Rourkela , India

Department of Mechanical Engineering, National Institute of Technology Rourkela, Rourkela , India Composites, Article ID 629175, 12 pages http://dx.doi.org/10.1155/2014/629175 Research Article Effect of Fiber Geometry and Representative Volume Element on Elastic and Thermal Properties of Unidirectional

More information

TRIALS WITH A SIMPLIFIED METHOD FOR BUCKLING AND ULTIMATE STRENGTH ANALYSIS OF COMPOSITE PLATES

TRIALS WITH A SIMPLIFIED METHOD FOR BUCKLING AND ULTIMATE STRENGTH ANALYSIS OF COMPOSITE PLATES DEPT. OF MATH., UNIVERSITY OF OSLO RESEARCH REPORT IN MECHANICS, No. 1 ISSN 0801-9940 December 2012 TRIALS WITH A SIMPLIFIED METHOD FOR BUCKLING AND ULTIMATE STRENGTH ANALYSIS OF COMPOSITE PLATES by Qiao

More information

Thermal buckling and post-buckling of laminated composite plates with. temperature dependent properties by an asymptotic numerical method

Thermal buckling and post-buckling of laminated composite plates with. temperature dependent properties by an asymptotic numerical method hermal buckling and post-buckling of laminated composite plates with temperature dependent properties by an asymptotic numerical method F. Abdoun a,*, L. Azrar a,b, E.M. Daya c a LAMA, Higher School of

More information

NUMERICAL FEM ANALYSIS FOR THE PART OF COMPOSITE HELICOPTER ROTOR BLADE

NUMERICAL FEM ANALYSIS FOR THE PART OF COMPOSITE HELICOPTER ROTOR BLADE Journal of KONES Powertrain and Transport, Vol. 19, No. 1 2012 NUMERICAL FEM ANALYSIS FOR THE PART OF COMPOSITE HELICOPTER ROTOR BLADE Hubert D bski Lublin University of Technology, Department of Machine

More information

Fig. 1. Circular fiber and interphase between the fiber and the matrix.

Fig. 1. Circular fiber and interphase between the fiber and the matrix. Finite element unit cell model based on ABAQUS for fiber reinforced composites Tian Tang Composites Manufacturing & Simulation Center, Purdue University West Lafayette, IN 47906 1. Problem Statement In

More information

Influence of fibre proportion and position on the machinability of GFRP composites- An FEA model

Influence of fibre proportion and position on the machinability of GFRP composites- An FEA model Indian Journal of Engineering & Materials Sciences Vol. 12, October 2005, pp. 443-450 Influence of fibre proportion and position on the machinability of GFRP composites- An FEA model D Abdul Budan* Department

More information

BIAXIAL STRENGTH INVESTIGATION OF CFRP COMPOSITE LAMINATES BY USING CRUCIFORM SPECIMENS

BIAXIAL STRENGTH INVESTIGATION OF CFRP COMPOSITE LAMINATES BY USING CRUCIFORM SPECIMENS BIAXIAL STRENGTH INVESTIGATION OF CFRP COMPOSITE LAMINATES BY USING CRUCIFORM SPECIMENS H. Kumazawa and T. Takatoya Airframes and Structures Group, Japan Aerospace Exploration Agency 6-13-1, Ohsawa, Mitaka,

More information

Most of the material in this package is based on a recently published book. This is:

Most of the material in this package is based on a recently published book. This is: Mechanics of Composite Materials Version 2.1 Bill Clyne, University of Cambridge Boban Tanovic, MATTER Assumed Pre-knowledge It is assumed that the student is familiar with simple concepts of mechanical

More information

Mechanical Properties

Mechanical Properties Mechanical Properties Elastic deformation Plastic deformation Fracture I. Elastic Deformation S s u s y e u e T I II III e For a typical ductile metal: I. Elastic deformation II. Stable plastic deformation

More information

ME 2570 MECHANICS OF MATERIALS

ME 2570 MECHANICS OF MATERIALS ME 2570 MECHANICS OF MATERIALS Chapter III. Mechanical Properties of Materials 1 Tension and Compression Test The strength of a material depends on its ability to sustain a load without undue deformation

More information

Chapter 3. Load and Stress Analysis

Chapter 3. Load and Stress Analysis Chapter 3 Load and Stress Analysis 2 Shear Force and Bending Moments in Beams Internal shear force V & bending moment M must ensure equilibrium Fig. 3 2 Sign Conventions for Bending and Shear Fig. 3 3

More information

8 Properties of Lamina

8 Properties of Lamina 8 Properties of Lamina 8- ORTHOTROPIC LAMINA An orthotropic lamina is a sheet with unique and predictable properties and consists of an assemblage of fibers ling in the plane of the sheet and held in place

More information