Experimental Mechanics of Solids E-Book

Cesar A. Sciammarella

• Herausgeber: John Wiley & Sons
• Kategorie: Fachliteratur
• Sprache: Englisch

Seitenzahl: 1302

Veröffentlichungsjahr: 2012

Beschreibung

Experimental solid mechanics is the study of materials to determine their physical properties. This study might include performing a stress analysis or measuring the extent of displacement, shape, strain and stress which a material suffers under controlled conditions. In the last few years there have been remarkable developments in experimental techniques that measure shape, displacement and strains and these sorts of experiments are increasingly conducted using computational techniques.

Experimental Mechanics of Solids is a comprehensive introduction to the topics, technologies and methods of experimental mechanics of solids. It begins by establishing the fundamentals of continuum mechanics, explaining key areas such as the equations used, stresses and strains, and two and three dimensional problems. Having laid down the foundations of the topic, the book then moves on to look at specific techniques and technologies with emphasis on the most recent developments such as optics and image processing. Most of the current computational methods, as well as practical ones, are included to ensure that the book provides information essential to the reader in practical or research applications.

Key features:

• Presents widely used and accepted methodologies that are based on research and development work of the lead author
• Systematically works through the topics and theories of experimental mechanics including detailed treatments of the Moire, Speckle and holographic optical methods
• Includes illustrations and diagrams to illuminate the topic clearly for the reader
• Provides a comprehensive introduction to the topic, and also acts as a quick reference guide

This comprehensive book forms an invaluable resource for graduate students and is also a point of reference for researchers and practitioners in structural and materials engineering.

Leseprobe

Contents

Cover

Title Page

Copyright

Dedication

About the Authors

Preface

Foreword

1: Continuum Mechanics – Historical Background

1.1 Definition of the Concept of Stress

1.2 Transformation of Coordinates

1.3 Stress Tensor Representation

1.4 Principal Stresses

1.5 Principal Stresses in Two Dimensions

1.6 The Equations of Equilibrium

1.7 Strain Tensor

1.8 Stress – Strain Relations

1.9 Equations of Compatibility

2: Theoretical Stress Analysis – Basic Formulation of Continuum Mechanics. Theory of Elasticity

2.1 Introduction

2.2 Fundamental Assumptions

2.3 General Problem

2.4 St. Venant’s Principle

2.5 Plane Stress, Plane Strain

2.6 Plane Stress Solution of a Simply Supported Beam with a Uniform Load

2.7 Solutions in Plane Strain and in Plane Stress

2.8 The Plane Problem in Polar Coordinates

2.9 Thick Wall Cylinders

3: Strain Gages – Introduction to Electrical Strain Gages

3.1 Strain Measurements – Point Methods

3.2 Electrical Strain Gages

3.3 Basics of Electrical Strain Gages

3.4 Gage Factor

3.5 Basic Characteristics of Electrical Strain Gages

3.6 Errors Due to the Transverse Sensitivity

3.7 Errors Due to Misalignment of Strain Gages

3.8 Reinforcing Effect of the Gage

3.9 Effect of the Resistance to Ground

3.10 Linearity of the Gages. Hysteresis

3.11 Maximum Deformations

3.12 Stability in Time

3.13 Heat Generation and Dissipation

3.14 Effect of External Ambient Pressure

3.15 Dynamic Effects

4: Strain Gages Instrumentation – The Wheatstone Bridge

4.1 Introduction

5: Strain Gage Rosettes: Selection, Application and Data Reduction

5.1 Introduction

5.2 Errors, Corrections, and Limitations for Rosettes

5.3 Applications of Gages to Load Cells

6: Optical Methods – Introduction

6.1 Historical Perspective and Overview

6.2 Fundamental Basic Definitions of Optics

6.3 The Electromagnetic Theory of Light

6.4 Properties of Polarized Light

6.5 The Jones Vector Representation

6.6 Light Intensity

6.7 Refraction of the Light

6.8 Geometrical Optics. Lenses and Mirrors

7: Optical Methods – Interference and Diffraction of Light

7.1 Connecting Light Interference with Basic Optical Concepts

7.2 Light Sources

7.3 Interference

7.4 Interferometers

7.5 Diffraction of the Light

8: Optical Methods – Fourier Transform

8.1 Introduction

8.2 Simple Properties

8.3 Transition to Two Dimensions

8.4 Special Functions

8.5 Applications to Diffraction Problems

8.6 Diffraction Patterns of Gratings

8.7 Angular Spectrum

8.8 Utilization of the FT in the Analysis of Diffraction Gratings

9: Optical Methods – Computer Vision

9.1 Introduction

9.2 Study of Lens Systems

9.3 Lens System, Coordinate Axis and Basic Layout

9.4 Diffraction Effect on Images

9.5 Analysis of the Derived Pupil Equations for Coherent Illumination

9.6 Imaging with Incoherent Illumination

9.7 Digital Cameras

9.8 Illumination Systems

9.9 Imaging Processing Systems

9.10 Getting High Quality Images

10: Optical Methods – Discrete Fourier Transform

10.1 Extension to Two Dimensions

10.2 The Whittaker-Shannon Theorem

10.3 General Representation of the Signals Subjected to Analysis

10.4 Computation of the Phase of the Fringes

10.5 Fringe Patterns Singularities

10.6 Extension of the Fringes beyond Boundaries

11: Photoelasticity – Introduction

11.1 Introduction

11.2 Derivation of the Fundamental Equations

11.3 Wave Plates

11.4 Polarizers

11.5 Instrument Matrices

11.6 Polariscopes

11.7 Artificial Birefringence

11.8 Polariscopes

11.9 Equations of the Intensities of the Plane Polariscope and the Circular Polariscope for a Stressed Plate

12: Photoelasticity Applications

12.1 Calibration Procedures of a Photoelastic Material

12.2 Interpretation of the Fringe Patterns

12.3 Determination of the Fringe Order

12.4 Relationship between Retardation Changes of Path and Sign of the Stress Differences

12.5 Isoclinics and Lines of Principal Stress Trajectories

12.6 Utilization of White Light in Photoelasticity

12.7 Determination of the Sign of the Boundary Stresses

12.8 Phase Stepping Techniques

12.9 RGB Photoelasticity

12.10 Reflection Photoelasticity

12.11 Full Field Analysis

12.12 Three Dimensional Analysis

12.13 Integrated Photoelasticity

12.14 Dynamic Photoelasticity

13: Techniques that Measure Displacements

13.1 Introduction

13.2 Formation of Moiré Patterns. One Dimensional Case

13.3 Formation of Moiré Patterns. Two Dimensional Case

13.4 Relationship of the Displacement Vector and the Strain Tensor Components

13.5 Properties of the Moire Fringes (Isothetic Lines)

13.6 Sections of the Surface of Projected Displacements

13.7 Singular Points and Singular Lines

13.8 Digital Moiré

13.9 Equipment Required to Apply the Moiré Method for Displacement and Strain Determination Utilizing Incoherent Illumination

13.10 Strain Analysis at the Sub-Micrometer Scale

13.11 Three Dimensional Moiré

13.12 Dynamic Moiré

14: Moiré Method. Coherent Ilumination

14.1 Introduction

14.2 Moiré Interferometry

14.3 Optical Developments to Obtain Displacement, Contours and Strain Information

14.4 Determination of All the Components of the Displacement Vector 3-D Interferometric Moiré

14.5 Application of Moiré Interferometry to High Temperature Fracture Analysis

15: Shadow Moiré & Projection Moiré – The Basic Relationships

15.1 Introduction

15.2 Basic Equation of Shadow Moiré

15.3 Basic Differential Geometry Properties of Surfaces

15.4 Connection between Differential Geometry and Moiré

15.5 Projective Geometry and Projection Moiré

15.6 Epipolar Model of the Two Projectors and One Camera System

15.7 Approaches to Extend the Moiré Method to More General Conditions of Projection and Observation

15.8 Summary of the Chapter

16: Moiré Contouring Applications

16.1 Introduction

16.2 Basic Principles of Optical Contouring Measuring Devices

16.3 Contouring Methods that Utilize Projected Carriers

16.4 Parallax Determination in an Area

16.5 Mathematical Modeling of the Parallax Determination in an Area

16.6 Limitations of the Contouring Model

16.7 Applications of the Contouring Methods

16.8 Double Projector System with Slope and Depth-of-Focus Corrections

16.9 Sensitivity Limits for Contouring Methods

17: Reflection Moiré

17.1 Introduction

17.2 Incoherent Illumination. Derivation of the Fundamental Relationship

17.3 Interferometric Reflection Moiré

17.4 Analysis of the Sensitivity that can be Achieved with the Described Setups

17.5 Determination of the Deflection of Surfaces Using Reflection Moiré

17.6 Applications of the Reflection Moiré Method

17.7 Reflection Moiré Application – Analysis of a Shell

18: Speckle Patterns and Their Properties

18.1 Introduction

18.2 First Order Statistics

18.3 Three Dimensional Structure of Speckle Patterns

18.4 Sensor Effect on Speckle Statistics

18.5 Utilization of Speckles to Measure Displacements. Speckle Interferometry

18.6 Decorrelation Phenomena

18.7 Model for the Formation of the Interference Fringes

18.8 Integrated Regime. Metaspeckle

18.9 Sensitivity Vector

18.10 Speckle Techniques Set-Ups

18.11 Out-of-Plane Interferometer

18.12 Shear Interferometry (Shearography)

18.13 Contouring Interferometer

18.14 Double Viewing. Duffy Double Aperture Method

19: Speckle 2

19.1 Speckle Photography

19.2 Point-Wise Observation of the Speckle Field

19.3 Global View

19.4 Different Set-Ups for Speckle Photography

19.5 Applications of Speckle Interferometry

19.6 High Temperature Strain Measurement

19.7 Four Beam Interferometer Sensitive to in Plane Displacements

20: Digital Image Correlation (DIC)

20.1 Introduction

20.2 Process to Obtain the Displacement Information

20.3 Basic Formulation of the Problem

20.4 Introduction of Smoothing Functions to Solve the Optimization Problem

20.5 Determination of the Components of the Displacement Vector

20.6 Important Factors that Influence the Packages of DIC

20.7 Evaluation of the DIC Method

20.8 Double Viewing DIC. Stereo Vision

21: Holographic Interferometry

21.1 Holography

21.2 Basic Elements of the Holographic Process

21.3 Properties of Holograms

21.4 Set up to Record Holograms

21.5 Holographic Interferometry

21.6 Derivation of the Equation of the Sensitivity Vector

21.7 Measuring Displacements

21.8 Holographic Moiré

21.9 Lens Holography

21.10 Holographic Moiré. Real Time Observation

21.11 Displacement Analysis of Curved Surfaces

21.12 Holographic Contouring

21.13 Measurement of Displacements in 3D of Transparent Bodies

21.14 Fiber Optics Version of the Holographic Moiré System

22: Digital and Dynamic Holography

22.1 Digital Holography

22.2 Determination of Strains from 3D Holographic Moiré Interferograms

22.3 Introduction to Dynamic Holographic Interferometry

22.4 Vibration Analysis

22.5 Experimental Set up for Time Average Holography

22.6 Investigation on Fracture Behavior of Turbine Blades Under Self-Exciting Modes

22.7 Dynamic Holographic Interferometry. Impact Analysis. Wave Propagation

22.8 Applications of Dynamic Holographic Interferometry

Index

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Library of Congress Cataloging-in-Publication Data

Sciammarella, Cesar A. Experimental mechanics of solids / Cesar A. Sciammarella, Federico M. Sciammarella. p. cm. Includes bibliographical references and index. ISBN 978-0-470-68953-0 (cloth : alk. paper) 1. Strength of materials. 2. Solids–Mechanical properties. 3. Structural analysis (Engineering) I. Sciammarella, F. M. (Federico M.) II. Title. TA405.S3475 2012 620.1′05–dc23 2011038404

A catalogue record for this book is available from the British Library.

ISBN: 978-0-470-68953-0

This book is dedicated to: Esther & Stephanie our loving wives and great supporters Eduardo a great son and older brother Sasha and Lhasa – faithful companions

About the Authors

Cesar A. Sciammarella was Director of the world renowned Experimental Mechanics Laboratory at the Illinois Institute of Technology for more than 30 years. Over that time he made pioneering developments in applying moiré, holography, and speckle interferometry methodologies as an experimental tool to solve industrial problems around the world. He recently completed a five year project funded by the Italian government to help the Politecnico of Bari develop its experimental mechanics lab and increase its future talent. Currently he is Research Professor at Northern Illinois University where he is working on various industrial projects involving optical contouring and experimental mechanics down at the nanometric level. This effort has taken him beyond the Rayleigh limit that traditionally was considered as the maximum resolution that could be obtained in optics in far field observations. His recent work has yielded measurements in the far field of nanocrystals and nanospheres with accuracies on the order of ±3.3 nm. His recent discoveries will no doubt lead this field as he has done in the past. He has been an active member in the Society of Experimental Mechanics where he has received almost every honor possible.

Federico M. Sciammarella joined the College of Engineering and Engineering Technology at Northern Illinois University in 2007 and is an assistant professor in the Mechanical Engineering Department. His two research areas are laser materials processing and experimental mechanics. One of several projects involves laser assisted machining (LAM) of ceramics through NIU's Rapid Optimization of Commercial Knowledge (ROCK) Project. The ROCK project enhances the capabilities of small companies by working through supply chains and with experts to improve their productivities and process. He has now spent some time using a novel optical method developed with his father and colleague Dr. Lamberti, Advanced Digital Moiré Contouring to measure surface roughness of the ceramic bars after the LAM process. Through its mission, the ROCK project, working with local companies, strive to develop niche technologies that will directly benefit the U.S. and by providing higher quality parts at reduced costs, improving supply logistics, and creating new manufacturing tools and methods that are critical to the continued growth of this nation.

Preface

The aim of this book, Experimental Mechanics of Solids, is to provide a comprehensive and in depth look at the various approaches possible to analyze systems and materials via experimental mechanics. This field has grown mostly through ideas, chance and pure intuition. This field is now mature enough that a comprehensive analysis on the nature of material properties is possible. Often we do things without too much thought and experimental mechanics is no exception.

The approach of this book is to break down each chapter into specific categories and provide some historical context so that the reader can understand how we have reached a certain level in the respective fields. The first two chapters provide some insight into the fundamental issues with regards to continuum mechanics and stress analysis that must be clear to the reader so that they may then make the appropriate decisions when performing field measurements. The next three chapters deal with the use and application of strain gages. There has been a lot of work done in this field so the aim was to provide some basic and practical information for the reader to be able to make sound choices with regards to a selection of gage and understanding the conditions for measurements. The remaining chapters deal with optical methods. Here for the first time ever the reader will see the unifying nature behind all these methods and should walk away with a more complete understanding of the various optical techniques. Most importantly, all the various examples that we have done over our careers are shared so that the reader can understand the advantages of one method over another in a given application.

Ultimately this book should serve as both a learning tool and a resource for industry when faced with difficult problems that only experimental mechanics can help solve. It is our hope that the students who read this book will understand what it takes to perform research in this field and provide inspiration for the future generations of experimentalists.

Our thanks go to Kristina Young M.S. who kindly rendered our illustrations.

Foreword

It is a great honor for me to write the foreword of Experimental Solid Mechanics authored by Prof. Cesar A. Sciammarella and Dr. Federico M. Sciammarella. I have been involved with the authors for the past 10 years. Professor C.A. Sciammarella has taught me optics and made me familiar with the use of optics in that wonderful field called Experimental Solid Mechanics. Dr. F.M. Sciammarella, my friend, was a PhD student when I visited Prof. C.A. Sciammarella's lab at the Illinois Institute of Technology. We took the class on Experimental Solid Mechanics taught by Prof. C.A. Sciammarella. Since then Fred and I collaborated on many pioneering studies carried out by the Professor.

I always asked Prof. Sciammarella to write a book with the purpose to disclose his enormous knowledge to young “fellows” who are interested in Experimental Solid Mechanics. In his five years at the Politecnico in Bari, the Professor was very busy carrying out frontier research and organizing international conferences that brought world renowned scientists to Bari. In spite of all of this hard work, Prof. Sciammarella found the time for conceiving the general organization of his book. In October 2008, when Prof. Sciammarella moved back to US we promised to continue working together. I am glad to say that Prof. Sciammarella, Dr. Sciammarella and myself still work together and will work together in the future, always investigating new exciting topics.

I have seen this book being developed day by day, chapter by chapter. Prof. Sciammarella and Dr. Sciammarella have shown me several chapters of their work. I remember the discussions we had in Chicago. There is no doubt that the quality of the book is outstanding. Apart from the technical content that is excellent in view of the high scientific reputation of the two authors, what has impressed me at the first reading is the clarity of the presentation which has plenty of useful examples. At the second reading, one realizes that the clarity is the obvious result of a total knowledge of the subject presented in the book. I now teach experimental mechanics and I am eager to suggest this new book to my students.

Thank you very much Professor and Fred for having given this book to us!

Dr. Luciano Lamberti Associate ProfessorDipartimento di Ingegneria Meccanica e GestionalePolitecnico di BariBARI, ITALY

1

Continuum Mechanics – Historical Background

The fundamental problem that faces a structural engineer, civil, mechanical or aeronautical is to make efficient use of the materials at their disposal to create shapes that will perform a certain function with minimum cost and high reliability whenever possible. There are two basic aspects of this process selection of materials, and then selection of shape. Material scientists, on the basis of the demand generated by applications, devote their efforts to creating the best possible materials for a given application. It is up to the designer of the structure or mechanical component to make the best use of these materials by selecting shapes that will simultaneously provide the transfer of forces acting on the structure or component in an efficient, safe and economical fashion. Today, a designer has a variety of tools to achieve these basic goals.

These tools have evolved historically through a heritage that can be traced back to the great builders of structures in 2700 BC Egypt, Greece and Rome, to the builders of cathedrals in the Middle Ages. Throughout the ancient and medieval period structural design was in the hands of master builders, helped by artisan masons and carpenters. During this period there is no evidence that structural theories existed. The design process was based on empirical evidence, founded many times in trial and error procedures done at different scales. The Romans achieved great advances in structural engineering, building structures that are still standing today, like the Pantheon, a masonry semi-spherical vault with a bronze ring to take care of tension stresses in the right place. It took many centuries to arrive at the beginning of a scientific approach to structures. It was the universal genius of the Renaissance Leonardo Da Vinci (1452–1519) one of the first designers that gives us evidence that scientific observations and rigorous analysis formed the basis of his designs. He was also an experimental mechanics pioneer and many of his designs were based on extensive materials testing.

The text that follows will introduce the names of the most outstanding contributors to some of the basic ideas of the mechanics of the continuum that we are going to review in this chapter. The next chapter provides background on those who contributed further in the nineteenth century and early twentieth. In the twentieth century many of the basic ideas were reformulated in a more rigorous and comprehensive mathematical framework. At the same time basic principles were developed to formulate solid mechanics problems in terms of approximate solutions through numerical computation: Finite Element, Boundary Element, Finite Differences.

The birth of the scientific approach to the design of structures can be traced back to Galileo Galilei. In 1638 Galileo published a manuscript entitled Dialogues Relating to Two New Sciences. This book can be considered as the precursor to the discipline Strength of Materials. It includes the first attempt to develop the theory of beams by analyzing the behavior of a cantilever beam. A close successor of Galileo was Robert Hook, curator of experiments at the Royal Society and professor of Geometry at Gresham College, Oxford. In 1676, he introduced his famous Hooke’s law that provided the first scientific understanding of elasticity in materials.

At this point it is necessary to mention the contribution of Sir Isaac Newton, with the first systematic approach to the science of Mechanics with the publication in 1687 of Philosophiae Naturalis Principia Mathematica. There is another important contribution of Newton and Gottfried Leibniz that helped in the development of structural engineering; they established the basis of Calculus, a fundamental mathematical tool in structural analysis.

From the eighteenth century, we must recall Leonard Euler, the mathematician who developed many of the tools that are used today in structural analysis. He, together with Bernoulli, developed the fundamental beam equation around 1750 by introducing the Euler-Bernoulli postulate of the plane sections which remain plane after deformation. Another important contribution of Euler was his developments concerning the phenomenon of buckling.

From the nineteenth century we recognize Thomas Young, English physicist and Foreign Secretary of the Royal Institute. Young introduced the concept of elastic modulus, the Young’s modulus, denoted as , in 1807. The complete formulation of the basis of the theory of elasticity was done by Simon-Denis Poisson who introduced the concept of what is called today Poisson’s ratio.