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Solid Mechanics and Its Applications Emmanuel E. Gdoutos Experimental Mechanics An Introduction Solid Mechanics and Its Applications FoundingEditor G.M.L.Gladwell Volume 269 SeriesEditors J.R.Barber,DepartmentofMechanicalEngineering,UniversityofMichigan,Ann Arbor,MI,USA AndersKlarbring,MechanicalEngineering,LinköpingUniversity,Linköping, Sweden Thefundamentalquestionsarisinginmechanicsare:Why?,How?,andHowmuch? The aim of this series is to provide lucid accounts written by authoritative researchersgivingvisionandinsightinansweringthesequestionsonthesubjectof mechanicsasitrelatestosolids.Thescopeoftheseriescoverstheentirespectrum of solid mechanics. Thus it includes the foundation of mechanics; variational formulations; computational mechanics; statics, kinematics and dynamics of rigid and elastic bodies; vibrations of solids and structures; dynamical systems and chaos;thetheoriesofelasticity,plasticityandviscoelasticity;compositematerials; rods,beams,shellsandmembranes;structuralcontrolandstability;soils,rocksand geomechanics; fracture; tribology; experimental mechanics; biomechanics and machinedesign.Themedianlevelofpresentationisthefirstyeargraduatestudent. Some texts are monographs defining the current state of the field; others are accessible to final year undergraduates; but essentially the emphasis is on readabilityandclarity. Springer and Professors Barber and Klarbring welcome book ideas from authors.Potentialauthorswhowishtosubmitabookproposalshouldcontact Dr. Mayra Castro, Senior Editor, Springer Heidelberg, Germany, email:[email protected] Indexed by SCOPUS, Ei Compendex, EBSCO Discovery Service, OCLC, ProQuestSummon,GoogleScholarandSpringerLink. Moreinformationaboutthisseriesathttps://link.springer.com/bookseries/6557 Emmanuel E. Gdoutos Experimental Mechanics An Introduction EmmanuelE.Gdoutos AcademyofAthens Athens,Greece ISSN0925-0042 ISSN2214-7764 (electronic) SolidMechanicsandItsApplications ISBN978-3-030-89465-8 ISBN978-3-030-89466-5 (eBook) https://doi.org/10.1007/978-3-030-89466-5 ©TheEditor(s)(ifapplicable)andTheAuthor(s),underexclusivelicensetoSpringerNature SwitzerlandAG2022 Thisworkissubjecttocopyright.AllrightsaresolelyandexclusivelylicensedbythePublisher,whether thewholeorpartofthematerialisconcerned,specificallytherightsoftranslation,reprinting,reuse ofillustrations,recitation,broadcasting,reproductiononmicrofilmsorinanyotherphysicalway,and transmissionorinformationstorageandretrieval,electronicadaptation,computersoftware,orbysimilar ordissimilarmethodologynowknownorhereafterdeveloped. Theuseofgeneraldescriptivenames,registerednames,trademarks,servicemarks,etc.inthispublication doesnotimply,evenintheabsenceofaspecificstatement,thatsuchnamesareexemptfromtherelevant protectivelawsandregulationsandthereforefreeforgeneraluse. Thepublisher,theauthorsandtheeditorsaresafetoassumethattheadviceandinformationinthisbook arebelievedtobetrueandaccurateatthedateofpublication.Neitherthepublishernortheauthorsor theeditorsgiveawarranty,expressedorimplied,withrespecttothematerialcontainedhereinorforany errorsoromissionsthatmayhavebeenmade.Thepublisherremainsneutralwithregardtojurisdictional claimsinpublishedmapsandinstitutionalaffiliations. ThisSpringerimprintispublishedbytheregisteredcompanySpringerNatureSwitzerlandAG Theregisteredcompanyaddressis:Gewerbestrasse11,6330Cham,Switzerland ThisbookisdedicatedtomywifeMariaand mychildrenEleftheriosand Alexandra-Kalliope Preface Experimental mechanics is a branch of engineering mechanics. Its objective is to use experiments to characterize the mechanical behavior of materials, structures, and systems. It uses advanced techniques and technologies to study the response andfailureofmaterialsandstructureswiththeobjectiveofimprovingtheirperfor- mance and the efficient use of materials with minimum cost and high reliability. Displacements,strains,andstressesaremeasured. Experimentalmechanicsisnotacounterparttotheoreticalandanalyticalmethods, butratherencompassesthemandgoesbeyondbystudyingthetruecharacteristicsof theproblems.Theoreticalmethodsarerestrictedtoidealizedproblems,whilenumer- icalmethods,likefiniteelements,arerestrictedbytheirunderlyingmodels.Experi- mentalmechanicsgoesfurtherbydeterminingthestrainsandstressesofmachines and structures in operation, which is impossible in other methods without knowledge of the nature of the applied forces, the boundary and initial conditions, and thematerialbehavior.Thesefactorsarenotknowninmanystructuresinoperation likeaircrafts,spacecrafts,bridges,dams,etc.Experimentaldataareusedtovalidate theoretical and numerical analyses of systems manufactured from complex, inho- mogeneousmaterials,likecomposites,concrete,biologicalmaterials,soil,etc.The quote:“Onegoodtestisworthathousandexpertopinions”byWernherVonBraun comprisestheessenceofexperimentalmechanics. Experimental mechanics has been helped tremendously by the advent of computers and optoelectronics which had an enormous effect on optical methods. Digitalimageprocessingtookadvantageofcomputertechnology.Moirétechniques havealsogreatlybenefited.Thespecimengratingcouldbetransferredtoacomputer screenandbesuperimposedwiththereferencegrating,ataskperformedpreviously onthespecimen.Ofseismicimpactonexperimentalmethodswasthedevelopmentof thedigitalimagecorrelation(DIC)methodformeasurementofdisplacements.Points onthesurfaceoftheobjectunderstudyarecorrelatedbeforeandafterdeformation with algorithms run by computers. The method can be used in structures covering the macro-, micro, and nano-scale levels. DIC has been commercialized and it is relativelyeasyforthenoviceexperimentalisttosetuptheopticalarrangement,use thesoftwareandobtainresults. vii viii Preface Thepurposeofthisbookistopresentinaclear,simple,straightforward,novel, andunifiedmannerthemostusedmethodsofexperimentalmechanicsofsolidsfor thedeterminationofdisplacements,strains,andstresses.Emphasisisgivenonthe principles of operation of the various methods, not on their applications to engi- neeringproblems.Formoreinformationonthemethodspresentedinthebook,there isanextensivebibliographyattheendofeachchapter.Thebookisdividedinto16 chapters. Chapter 1 presents the principle of operation of strain gages, the potentiometer andWheatstonebridgecircuitsformeasuringsmallresistancechanges,andthestrain gagerosettesforthecompletedeterminationofthestateofstrainatapoint. Chapter 2 presents the basic background for the understanding of the optical methodsofexperimentalmechanics.Topicscoveredincludeahistoricaloverview, geometricopticsdealingwithreflection,refraction,mirrorsandlenses,waveoptics dealingwithHuygens’sprinciple,electromagnetictheoryoflight,polarization,inter- ference,anddiffractionphenomena.Thesetopicsarecoveredinafundamentalway easily understood by an undergraduate student. The chapter is comprehensive and no further knowledge of optics is necessary for the study of optical methods of experimentalmechanicsinthesubsequentchapters. Chapter3presentsthebasicprinciplesofthegeometricmoiréphenomenonandits applicationsinexperimentalmechanics.Followingthedefinitionofthebasicterms themoiréphenomenon,themathematicalformationofmoiréfringes,therelationship betweenlinegratingsandmoiréfringes,themoirépatternsformedbycircular,radial andlinegratings,themeasurementofin-planeandout-of-planedisplacementsand slopes,thesharpeningofmoiréfringesandthemoiréofmoiréeffectarepresented. Chapter4presentstwohigh-sensitivitymethods,themethodofcoherentorinter- mediate moiré and the method of moiré interferometry. Unlike geometric moiré whichisbasedonthephenomenonofobstructionoflight,thetwomethodsarebased onwaveopticsandusethephenomenaofdiffractionbyagrating,two-beaminter- ference,andFouriertransformationbyalens.Topicscoveredinthischapterinclude: diffractionbytwosuperimposedparallelgratingsandformationofmoirépatterns, opticalfiltering,andfringemultiplicationobtainedbythemethodsofcoherentmoiré andmoiréinterferometry. Chapter 5 presents two moiré methods that use remote gratings for the deter- mination of the gradients of the out-of-plane displacements or the sum of the two in-plane principal stresses for opaque or transparent materials, respectively. The moirépatternsarecreatedbyprojectingtherulingsofonegratingontotherulings ofasecondgratingafterinteractionwiththespecimen.Thefirstmethodisbasedon geometricmoiréanduseswhitelight,whilethesecondisbasedonthediffractionof lightandusescoherentlight. Chapter6presentstheequationsofthemethodofcausticsforreflectingsurfaces toobtainthecausticscreatedbyaxisymmetricellipsoidmirrors.Theseequationsare appliedforthedeterminationofstressintensityfactorsintwo-dimensionalopening- modeandmixed-modecrackproblems. Chapter 7 presents the basics of photoelastic stress analysis including: optical patternsobtainedintheplaneandcircularpolariscopes,theisochromaticandisoclinic Preface ix fringe patterns and their properties, the compensation methods, the stress separa- tionsmethods,thefringemultiplicationandsharpening,thetransitionfrommodel toprototype,thethree-dimensionalphotoelasticityandthephotoelasticcoatings. Chapter8presentstheMach-Zehnder,theMichelson,andtheFizeau-typeinter- ferometersforstressanalysis.Theopticalpatternsobtainedbytheseinterferometers arestudiedusingtheJonescalculus.Attheendofthechapter,agenericinterpretation oftheopticalpatternsobtainedbyallinterferometersispresented. Chapter9presentstheprinciplesofholographyandholographicinterferometry and its applications to photoelastic materials. The equations of the recording and reconstructionprocessesusingtheJonescalculusandagenericexplanationofboth holographyandholographicinterferometryarepresented. Chapter 10 presents the operation of optical fibers for transfer of light and describes the interferometric and Bragg grating optical fiber sensors for strain measurement. Chapter11presentsthespeckleeffectandthemethodsofspecklephotography, speckleinterferometry,shearography,andelectronicspecklepatterninterferometry (ESPI)forthedeterminationofdisplacements. Chapter12presentstheessentialstepsofdigitalimagecorrelation(DIC)including thespecklepatterning,theimagedigitizationprocess,theintensityinterpolation,and thecorrelationofimages. Chapter13presentsthetheoreticalbasisofthethermoelasticeffect,theinfrared detectors for measuring very small temperature changes, the conditions of adia- baticity, the specimen preparation, the stress separation methods, and applications ofthermalstressanalysis. Chapter14presentstheprinciplesofcontactmechanicsandthemajormethods of indentation testing at the macro-, micro-, and nano- levels used to measure the hardness,themodulusofelasticity,andthecriticalstressintensityfactor. Chapter 15 presents the basic principles and advantages and disadvantages of the following six major nondestructive testing methods: Dye penetrant, magnetic particles,eddycurrents,X-raydiffraction,ultrasonics,andacousticemission. Finally,Chap.16presentsthehole-drillingmethodofmeasuringresidualstresses. The method involves monitoring the change of strains produced when a hole is drilled in a component containing residual stresses. The relevant equations for the determinationoftheresidualstressesfromtherelievedstrainswhenaholeisdrilled areestablishedforuniaxialandbiaxialresidualstresses. Today’s experimentalistarmedwithastrongbackground innumericalmethods andcomputertechniquesanddeepunderstandingofthebasicexperimentalmethods shouldhavethetoolsnecessarytosolveproblemsofstructuralbehaviorandmaterial characterization atthenano-,micro-,andmacro-scalelevels.Needlesstosay,that the most valuable virtues of an experimentalist are not his/her technical skills, but honestyandintegrity.Experimentalresultsshouldbepresentedasobtainedfromthe tests,unbiasedofanyrelationswithanalyticalsolutions,incasetheyexist.Thismost valuablevirtueshouldbecultivatedinclassroomsandlaboratories. Thebookprovidesthebasicsofthemostusedmethodsofexperimentalmechanics formeasuringdisplacements,strains,andstresses.Itisintendedtobeaninstrument x Preface oflearning,ratherthanareview ofpublished contributions.Itishoped thatitwill beusednotonlyasalearningtoolbutalsoasaninspirationandbasisonwhichthe researcher,theengineer,theexperimentalist,thestudentcandeveloptheirnewown ideastopromoteresearchinexperimentalmechanicsofsolids. ThebookwaswrittenduringtheCOVID19pandemic.Iwanttotakethisoppor- tunitytothankmywifeMariaandmychildrenEleftheriosandAlexandra-Kalliope for their love and support during the writing of the book. A great word of thanks goestoDr.PanayiotisDanoglidisoftheUniversityofTexasatArlingtonforhishelp inthepreparationofthefiguresofthebookinaspeedyandefficientway.Hishard workanddedicationaregreatlyappreciated. Athens,Greece EmmanuelE.Gdoutos 2021