Experimental Stress Analysis for Materials and Structures: Stress Analysis Models for Developing Design Methodologies

509 Pages·2015·21.87 MB·English

by  Alessandro Freddi

Springer Series in Solid and Structural Mechanics 4
Alessandro Freddi
Giorgio Olmi
Luca Cristofolini
Experimental
Stress Analysis
for Materials
and Structures
Stress Analysis Models for Developing
Design Methodologies
Springer Series in Solid and Structural
Mechanics
Volume 4
Series editors
Michel Frémond, Rome, Italy
Franco Maceri, Rome, Italy
More information about this series at http://www.springer.com/series/10616
Alessandro Freddi Giorgio Olmi
(cid:129)
Luca Cristofolini
Experimental Stress
Analysis for Materials
and Structures
Stress Analysis Models for Developing
Design Methodologies
123
Alessandro Freddi Luca Cristofolini
Department of IndustrialEngineering Department of IndustrialEngineering
Universityof Bologna Universityof Bologna
Bologna Bologna
Italy Italy
GiorgioOlmi
Department of IndustrialEngineering
Universityof Bologna
Bologna
Italy
ISSN 2195-3511 ISSN 2195-352X (electronic)
Springer Series inSolidand StructuralMechanics
ISBN 978-3-319-06085-9 ISBN 978-3-319-06086-6 (eBook)
DOI 10.1007/978-3-319-06086-6
LibraryofCongressControlNumber:2015932851
SpringerChamHeidelbergNewYorkDordrechtLondon
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Nichts ist so praktisch wie eine gute Theorie
—Kurt Lewin (1890–1947)
(There is nothing so practical as a good
theory)
but:
Nothing helps scientific thought like a good
Experiment.
Engineering and Physics cannot be thought
of without models which represent the real
world to the best of our knowledge.
—Friedrich Pfeiffer, Hartmut Bremer
(2015) CISM–AIMETA–Udine.
Since the birth of modern science, the
hypothesis as well as its experimental
verification have a mathematical nature, both
being expressed by a set of physical
measurable—not qualitative—quantities…..
—Emanuele Severino (1984)
Modern Philosophy
Rizzoli Inc., Italy
Foreword
A model is an abstract mathematical description of a more or less complex entity,
which is important in engineering sciences to investigate and predict the entity
behavior in relation to performance, reliability, and safety. Correct modeling of a
technical entity, whether material, structure, device, equipment or system, is thus
fundamental to engineering purposes. This holds, in particular, for mechanical
structures or systems, for which experiments to support modeling are often
unavoidable, following the definition of inverse problem from the measurement of
effects to identification of causes given in the preface of this book. In these cases,
design of experiment is an essential tool to verify, develop, or refine models.
Experimentandexperiencegreatlyhelpinfindingsimplificationsmakingthemodel
justascomplexasnecessarytocontainallrelevantparameters.However,inmodel
building, physical and statistical validation of model assumptions should precede
data analysis. In this book Professor Freddi, supported by two of his closest col-
laborators,hascondensedtheexperiencesgainedinalongacademicactivityinthis
field in cooperation with the industry. The book gives a careful introduction to
methods and tools used in Experimental Stress Analysis, opening the door to new
investigationsonfailuremechanismsitisusefulformechanicalengineersinpractice
as well as a textbook, notleast for thelarge numberof solved practical examples.
Firenze and Zürich, April 2015 Alessandro Birolini
Ph.D. Professor Emeritus of Reliability
Engineering at the ETH Zurich
vii
Preface
The contents presented in this book are, in the opinion of the authors, an essential
conceptualbasisforthetrainingofprofessionalmechanicalengineersinthefieldof
experimentalmethodsappliedtotheoryofstructures.Ourintentionisnottogivean
overviewofalltheexperimentalmethodsusedinstressanalysis,aswepresentonly
those that we have utilized for research purposes and scientific and technical
consulting. Experimental analysis methods are based on different branches of sci-
ence such as mechanics, electronics, optics, information theory, etc.: excellent
specialized books are available written by specialists from different areas, which
focus exclusively on methods. This book is a complementary reading to such
specializedworks,inthatitgivesanoutlineofsomemethodsandshowshowtheir
applicationsmakeitpossibletounderstandthefoundationofaproblemevenbefore
obtainingadetailedsolution.Forthislattertask,thecomputingmethodsthatcover
nearly every need in solving particular cases are the best.
Whilehistoricallyexperimentalanalysiswasdevelopedasasurreptitioustooldue
toalackofanalyticalsolutionstostructuralproblems,todayitisaninstrumentfor
clarifying the limitations of analytical theories, but primarily, due to the inverse
nature of experimentation, for identifying unknown parameters, integrating exper-
imental data into analytical models. ExperimentalStressAnalysis was classically
regarded asa collection ofexperimental methods dedicatedto themeasurement of
deformations ofloaded bodies, and then to thecorresponding states ofstress.This
has been modified into a methodology to build acceptable models for setting up
phenomenological theories and supporting design practices.
Itiscommontospeakofdesignforsafety,reliability,ordesigntopreventhigh
cyclefatigue,lowcyclefatigue,crackpropagation,multi-modefailures,etc.Onthe
basis of years of teaching and consulting experience, we believe that the ultimate
goalofexperimentalanalysisisnotonlytheknowledgeofastateofstressbutalso
the design and assessment of the integrity of structural systems.
Thereisanotherissueherethatmustbedealtwith:ExperimentalStressAnalysis
requires a variety of devices, testing machines, etc. that may be available on the
market, often packaged in the form of black boxes. Self-made equipments give
ix
x Preface
many more opportunities for adjusting to specific problems and have an unparal-
leledrolefortrainingtheexperimentalistandalsoforeducationinstructuraldesign.
The laboratory practice is highly educational for this purpose since it is concep-
tually similar to the practice of design. Both deal with problems in which a lot of
data is unknown. This book is therefore oriented to applications, which require a
self-made laboratory equipment on the assumption that it may offer a useful aid to
help graduate students develop sensitivity to quickly discovering the few control-
ling variables and the essential tests for solving the problem.
Accordingtoitsinversemethodologynature,experimentalanalysishasrecently
foundnewtasksinthesolutionofreliabilityproblems.Theestimationofreliability,
andthereforealsotheanswertothequestionofapossibleextensionoflife,requires
experiments in order to identify the causes of defects and failures and to measure
the failure rate. Therefore, the role of experimentation is not one of simple verifi-
cation of a theoretical prediction, but is a continuous monitoring and control of
processesandaninvaluabletoolfor theestimationofthelifeoftechnicalsystems.
Finally, we did not use the more accredited and common label of Experimental
Mechanics as the title to cover the topics of this book. Generic nominalization
might lead to a confused definition of boundaries and to misunderstandings:
important topics, such as Experimental Vibrations Analysis, have for many years
constituteddisciplinesintheirownrightandarenotcoveredinthisbook.Alongthe
same line, there is no reason to limit Experimental Mechanics to solid bodies.
Referencestoexperimentalstressanalysiscanbefoundinmaterialsproducedby
scientific societies in various countries, such as SEM (American Association of
Experimental Mechanics) in the USA, GESA (Gesellschaft für Experimentelle
Spannung Analyse) in Germany, GAMAC (Avancement des Methodes d’Analyse
desContraintes)inFrance,BSSM(BritishSocietyforStrainMeasurement)intheUK,
AIAS (Italian Association of Stress Analysis) in Italy, EURASEM (European
AssociationforExperimentalMechanics)forEurope,theDanubia-AdriaSymposium
forCentralEurope,andtheInternationalCommitteeIMEKOTC15(Experimental
Mechanics) with related YSESM, (Youth Symposium for Experimental Solid
Mechanics)expresslydevotedtoyoungresearchers.
Bologna, April 2015 Alessandro Freddi
Giorgio Olmi
Luca Cristofolini
Contents
Part I A Brief Review of the Experimental Methods Utilized
in the Book
1 Introduction to Inverse Problems . . . . . . . . . . . . . . . . . . . . . . . . 3
1.1 Premise. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.1.1 General Rules. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.1.2 Rules for Inverse Problems . . . . . . . . . . . . . . . . . . . 4
1.2 Forward and Inverse Problems for Elastic
Discretized Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.2.1 Quality Indicators of Inverse Solutions . . . . . . . . . . . 13
1.2.2 Inverse Solution for Systems in Matrix Form. . . . . . . 14
1.3 Systems in Functional Form. . . . . . . . . . . . . . . . . . . . . . . . . 17
1.3.1 Regularization Method of Tikhonov-Phillips. . . . . . . . 18
1.3.2 Regularization Using Regularization Matrix. . . . . . . . 19
1.3.3 Further Reading . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2 Introduction to the Application of Strain Gages. . . . . . . . . . . . . . 23
2.1 Properties of Strain Gages . . . . . . . . . . . . . . . . . . . . . . . . . . 23
2.1.1 Relationship Between Strain and Resistance
Change . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
2.1.2 Materials for Metal Strain Gages . . . . . . . . . . . . . . . 26
2.1.3 Resistance Values. . . . . . . . . . . . . . . . . . . . . . . . . . 28
2.1.4 Transverse Sensitivity and Strain Gage Factor . . . . . . 32
2.1.5 Influence of a Temperature Variation . . . . . . . . . . . . 34
2.1.6 Compensation for Thermal Output . . . . . . . . . . . . . . 36
2.2 Strain Gage Rosettes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
2.2.1 Three-Gage Rectangular ð0(cid:2)45(cid:2)90(cid:2)Þ Rosettes . . . . . 39
2.2.2 Three-Gage ð0(cid:2)120(cid:2)240(cid:2)Þ
or ð0(cid:2)60(cid:2)120(cid:2)Þ Rosettes . . . . . . . . . . . . . . . . . . . . 41
xi