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Measurement of Neck Development in Tensile Testing Using Projection Moire Wright State University CORE Scholar Mechanical and Materials Engineering Faculty Publications Mechanical and Materials Engineering 1982 Measurement of Neck Development in Tensile Testing Using Projection Moire Raghavan Srinivasan Wright State University - Main Campus, [email protected] C. S. Hartley C. Raju J. Clave Follow this and additional works at: https://corescholar.libraries.wright.edu/mme Part of the Materials Science and Engineering Commons, and the Mechanical Engineering Commons Repository Citation Srinivasan, R., Hartley, C. S., Raju, C., & Clave, J. (1982). Measurement of Neck Development in Tensile Testing Using Projection Moire. Optical Engineering, 21 (4), 655-662. https://corescholar.libraries.wright.edu/mme/123 This Article is brought to you for free and open access by the Mechanical and Materials Engineering at CORE Scholar. It has been accepted for inclusion in Mechanical and Materials Engineering Faculty Publications by an authorized administrator of CORE Scholar. For more information, please contact [email protected]. Measurement ofof neck development in tensile testing using projection moire R. Srinivasan Abstract. TheThe projectionprojection moiremoire techniquetechnique affordsaffords anan accurateaccurate methodmethod of State University of New YorkYork measuring the geometry of the neckednecked region inin aa tensiletensile specimen.specimen. Correc-Correc­ DeptDept. ofof MaterialsMaterials Science and Engineering tions toto the measured stress, necessary toto accountaccount forfor thethe triaxialitytriaxiality introducedintroduced Stony Brook, New York 11794 by thethe neck, requirerequire valuesvalues forfor thethe radius of curvature of the specimen at the minimum section. The spacing of fringes resultingresulting fromfrom thethe interferenceinterference C. S. Hartley between a grating projected on the specimen surface andand aa master grating notnot Louisiana StateState UniversityUniversity only provide information which permitspermits calculationcalculation ofof thethe radiusradius butbut alsoalso Dept. ofof MechanicalMechanical Engineering demonstrates any changes in symmetry resulting fromfrom plasticplastic deformation.deformation. Baton Rouge, LouisianaLouisiana 7080370803 Results obtained by testingtesting specimens of copper and mild steel having initially straight andand initially curved curved profilesprofiles indicateindicate that that Bridgman's Bridgman's approach approach providesprovides B. B. Raju a self-consistentself- consistent correctioncorrection forfor triaxiality.triaxiality. However, comparison of incremental J. ClaveClave tests with continuouscontinuous teststests indicatesindicates thatthat thethe developmentdevelopment ofof neckneck geometry may be sensitivesensitive to the strain rate.rate. University of Florida Dept. ofof MaterialsMaterials Science and Engineering Keywords: incoherent optical techniques in experimentalexperimental mechanics; mechanics; projection moire; Gainesville, Florida 32611 plasticity; necking.necking. Optical Engineering 2121(4), (4), 655-662655 -662 (July/August(July /August 1982). CONTENTS the neck; 2) thethe stress distribution distribution across thethe minimum crosscross section 1. Introduction changes from from aa uniform,uniform, uniaxial statestate of stressstress toto a nonuniform, 2. PrinciplesPrinciples ofof measurement measurement multiaxial statestate of stress.stress. A correction for thethe crosscross sectionsection of the 2.1. Projection moire method deforming regionregion requiresrequires onlyonly an an instantaneousinstantaneous measurement,measurement, but 2.2. TheoryTheory of thethe methodmethod correction forfor triaxiality ofof the the stressstress distribution introducedintroduced by the 2.3. MeasurementMeasurement of profile radiusradius neck demandsdemands more more carefulcareful analysis.analysis. Additional Additional complications maymay 3. ExperimentalExperimental procedureprocedure arise if plastic anisotropy causes causes the specimen shape toto deviatedeviate from from its 3.1. Apparatus initialinitial axisymmetry. 3.2. Calibration of thethe instrument Two approachesapproaches havehave been used to correct stressstress-strain -strain datadata forfor 3.3. ProcedureProcedure necking. Direct methods rely on elimination ofof the the neckneck by machining 4. ResultsResults or cold workingworking specimensspecimens atat various stages of of thethe testtest afterafter flowflow 5. DiscussionDiscussion localizationlocalization hashas occurred.1occurred. 1 "-33 IndirectIndirect measurements utilizeutilize analytical 5.1. Calibration expressions relatedrelated toto the shape ofof thethe specimenspecimen to to correctcorrect thethe appar­appar- 5.2. MeasurementsMeasurements onon specimensspecimens ent stress for for triaxiality.triaxiality.44 "-77 AllAll indirect methodsmethods requirerequire simultaneous 6. ConclusionsConclusions measurements ofof thethe dimensions dimensions ofof thethe minimumminimum cross section normalnormal 7. AcknowledgmentsAcknowledgments to thethe loadingloading axisaxis andand R,R, thethe radiusradius ofof curvaturecurvature ofof the the specimenspecimen 8. AppendixAppendix A:A: generalgeneral equations of the moire fringes profile measured atat thethe minimumminimum section. The most widely used method,method, 9. ReferencesReferences suggested by by Bridgman,Bridgman,66 statesstates that that forfor an axisymmetric specimenspecimen 1. INTRODUCTIONINTRODUCTION aatt = aa { {[1[1 ++ (R/ (R/2a)] 2a)] Znfa [1[l ++ (a(a/2R)]}~ /2R)]}-1, (1) Uniaxial tensile tests of of ductile ductile materialsmaterials oftenoften exhibitexhibit a periodperiod of flow of flow where aatt is thethe correctedcorrected uniform true true axial axial stress stress and and a a is is thethe measured localization, called "necking, "prior to fracture of the specimen. Because called "necking," prior to fracture of the specimen. Because true axial stressstress on the minimum cross cross section,section, respectively;respectively; aa repre-repre­ of this phenomenon, of this phenomenon, aa specimen having having an an initiallyinitially uniformuniform gaugegauge sents thethe radius radius ofof thethe minimumminimum crosscross-sectional -sectional dimension. dimension. AnAn exten­exten- section, suchsuch as as a a right right circularcircular cylinder, developsdevelops a locally reducedreduced sion to specialspecial casescases of nonaxisymmetrynonaxisymmetry hashas beenbeen proposedproposed byby cross section,section, whichwhich decreases in in size size until until failure. failure. Necking introduces introduces Eisenberg.?Eisenberg.7 two important considerationsconsiderations intointo thethe analysisanalysis of tensile deformation: Obtaining accurate experimental values of R presentspresents aa difficultdifficult 1) thethe volumevolume ofof thethe deformingdeforming region decreases from from thatthat of the entireentire problem. MostMost techniquestechniques relyrely onon incrementalincremental tests, tests, betweenbetween whichwhich gauge sectionsection to to a a smaller, smaller, generally generally unknown unknown value value in in the the vicinity vicinity ofof measurements areare made by optical8optical8 oror mechanical mechanical methods.2.3,6,9 methods.2' 3'6'9 Continuous measurements requirerequire calibrationcalibration with anan incrementalincremental Invited Paper 10IO-109 -109 receivedreceived Mar.Mar. 31,1982;31,1982; revisedrevised manuscriptmanuscript received Apr. 14,1982;14,1982; accepted for publication Apr. 14,1982;14, 1982; receivedreceived by Managing Editor Apr.Apr. 26,26, 1982.1982. technique toto ensure accuracy.accuracy.'°10 Finally, choicechoice of anan appropriateappropriate © 1982 SocietySociety of of Photo-Optical Photo -Optical Instrumentation Instrumentation Engineers. analytical correction requires detaileddetailed knowledgeknowledge of of thethe evolution evolution of of OPTICAL ENGINEERING ENGINEERING / July/August / July /August 1982 1982 / Vol./ Vol. 21 21 No. No. 4 /4 / 655 Downloaded From: http://opticalengineering.spiedigitallibrary.org/ on 06/25/2013 Terms of Use: http://spiedl.org/terms SRINIVASAN, HARTLEY, RAJU, CLAVE specimenSpecimen Projected lide Fig. 2. ImageImage ofof aa specimen:specimen: a) without referencereference grid;grid; b)b) with reference reference grid Projector Carera grid. Reference grid Projection axi s Viewing axis Fig. 1. Schematic diagramdiagram of the projectionprojection moiremoire apparatus.apparatus. the specimen shape during the test.test. The present work describes anan application of the projection moire technique to determine R and toto verifyverify axialaxial symmetry.symmetry. ThisThis proce-proce­ dure offers aa powerfulpowerful methodmethod ofof obtainingobtaining measurementsmeasurements required for analytical corrections and for quantitative measurementsmeasurements ofof thethe spec-spec­ imen shape. 2.2, PRINCIPLESPRINCIPLES OFOF MEASUREMENTMEASUREMENT 2.1. ProjectionProjection moiremoire methodmethod The projection moire method isis a modification ofof the shadowshadow moiremoire method. Shadow moire requires the grating toto bebe at leastleast as large as the surface being studied, making it inconvenient for largelarge struc-struc­ tures. Projection moiremoire overcomesovercomes this limitationlimitation byby projectingprojecting anan image of aa grid on thethe surface being studied, using a slide projector. This method is, therefore, capable of handling both largelarge andand smallsmall structures. The projection moire
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