Definition, Stress-Strain Curve, Hooke's Law, SI Units - Byju's

A stress-strain curve is a graphical way to show the reaction of a material when a load is applied. It shows a comparison between stress and ... PhysicsSolidDeformationStressAndStrain StressAndStrain Youmayhavenoticedthatcertainobjectsstretcheasily,butstretchingobjectssuchasanironrodsoundsimpossible,right?Inthisarticle,wewillhelpyouunderstandwhyafewobjectsaremoremalleablethanothers.Mainly,wewilldiscussStress-StrainCurvebecausetheyhelpusknowtheamountofloadorstressthatamaterialcanhandlebeforeitstretchesandbreaks. TableofContents WhatisStress? TypesofStress TensileStress CompressiveStress WhatisStrain? TypesofStrain TensileStrain CompressiveStrain Stress-StrainCurve ProportionalLimit ElasticLimit YieldPoint UltimateStressPoint FractureorBreakingPoint Hooke’sLaw ElasticModuliofMaterials FrequentlyAskedQuestions–FAQs WhatisStress? Stressisdefinedasforceperunitareawithinmaterialsthatarisefromexternallyappliedforces,unevenheating,orpermanentdeformationandthatpermitsanaccuratedescriptionandpredictionofelastic,plastic,andfluidbehaviour. Stressisgivenbythefollowingformula: \(\begin{array}{l}\sigma=\frac{F}{A}\end{array}\) where,\(\begin{array}{l}\sigma\end{array}\)isthestressapplied,FistheforceappliedandAistheareaofforceapplication. Theunitofstressis\(\begin{array}{l}N/m^{2}\end{array}\). TypesofStress Stressappliedtoamaterialcanbeoftwotypesasfollows: TensileStress ThedeformationorelongationofasolidbodyduetoapplyingatensileforceorstressisknownasTensilestrain.Inotherwords,tensilestrainisproducedwhenabodyincreasesinlengthasappliedforcestrytostretchit. ReadMore:TensileStress CompressiveStress Compressivestrainisthedeformationinasolidduetotheapplicationofcompressivestress.Inotherwords,compressivestrainisproducedwhenabodydecreasesinlengthwhenequalandoppositeforcestrytocompressit. ReadMore:CompressiveStress WhatisStrain? Strainistheamountofdeformationexperiencedbythebodyinthedirectionofforceapplied,dividedbytheinitialdimensionsofthebody. Thefollowingequationgivestherelationfordeformationintermsofthelengthofasolid: \(\begin{array}{l}\epsilon=\frac{\deltal}{L}\end{array}\) where,\(\begin{array}{l}\epsilon\end{array}\)isthestrainduetostressapplied,\(\begin{array}{l}\deltal\end{array}\)isthechangeinlengthandListheoriginallengthofthematerial. Thestrainisadimensionlessquantityasitjustdefinestherelativechangeinshape. TypesofStrain Strainexperiencedbyabodycanbeoftwotypesdependingonstressapplicationasfollows: TensileStrain Tensilestrainisthechangeinlength(orarea)ofabodyduetotheapplicationoftensilestress. CompressiveStrain CompressiveStrainisthechangeinlength(orarea)ofabodyduetotheapplicationofcompressivestrain. Stress-StrainCurve Whenwestudysolidsandtheirmechanicalproperties,informationregardingtheirelasticpropertiesismostimportant.Wecanlearnabouttheelasticpropertiesofmaterialsbystudyingthestress-strainrelationships,underdifferentloads,inthesematerials. Thematerial’sstress-straincurvegivesitsstress-strainrelationship.Inastress-straincurve,thestressanditscorrespondingstrainvaluesareplotted.Anexampleofastress-straincurveisgivenbelow. ExplainingStress-StrainGraph Thedifferentregionsinthestress-straindiagramare: (i)ProportionalLimit Itistheregioninthestress-straincurvethatobeysHooke’sLaw.Inthislimit,thestress-strainratiogivesusaproportionalityconstantknownasYoung’smodulus.ThepointOAinthegraphrepresentstheproportionallimit. (ii)ElasticLimit Itisthepointinthegraphuptowhichthematerialreturnstoitsoriginalpositionwhentheloadactingonitiscompletelyremoved.Beyondthislimit,thematerialdoesn’treturntoitsoriginalposition,andaplasticdeformationstartstoappearinit. (iii)YieldPoint Theyieldpointisdefinedasthepointatwhichthematerialstartstodeformplastically.Aftertheyieldpointispassed,permanentplasticdeformationoccurs.Therearetwoyieldpoints(i)upperyieldpoint(ii)loweryieldpoint. (iv)UltimateStressPoint Itisapointthatrepresentsthemaximumstressthatamaterialcanendurebeforefailure.Beyondthispoint,failureoccurs. (v)FractureorBreakingPoint Itisthepointinthestress-straincurveatwhichthefailureofthematerialtakesplace. Hooke’sLaw Inthe19th-century,whilestudyingspringsandelasticity,EnglishscientistRobertHookenoticedthatmanymaterialsexhibitedasimilarpropertywhenthestress-strainrelationshipwasstudied.Therewasalinearregionwheretheforcerequiredtostretchthematerialwasproportionaltotheextensionofthematerial,knownasHooke’sLaw. Hooke’sLawstatesthatthestrainofthematerialisproportionaltotheappliedstresswithintheelasticlimitofthatmaterial. Mathematically,Hooke’slawiscommonlyexpressedas: F=–k.x WhereFistheforce,xistheextensionlength,andkistheconstantofproportionalityknownasspringconstantinN/m. ReadMore:Hooke’sLaw Seethevideobelowtolearnaboutthestress-straincurveandHooke’slaw. ElasticModuliofMaterials ThefollowingtableliststheYoung’smodulus,shearmodulusandbulkmodulusforcommonmaterials. Material Young’smodulus(E)inGPa Shearmodulus(G)inGPa Bulkmodulus(K)inGPA Glass 55 23 37 Steel 200 84 160 Iron 91 70 100 Lead 16 5.6 7.7 Aluminium 70 24 70 Note:GPaisgigapascaland1GPa=1,00,00,00,000Pa. RelatedReading Poisson’sratio Young’sModulus YieldStrength PlasticDeformation FrequentlyAskedQuestions–FAQsWhatdoesthestress-straincurveshow?Astress-straincurveisagraphicalwaytoshowthereactionofamaterialwhenaloadisapplied.Itshowsacomparisonbetweenstressandstrain.Whatistheuseofthestress-straindiagram? Thestress-straindiagramprovidesagraphicalmeasurementofthestrengthandelasticityofthematerial.Also,thebehaviourofthematerialscanbestudiedwiththehelpofthestress-straindiagram,whichmakesiteasywiththeapplicationofthesematerials.Whatistherelationbetweenstressandstrain? Therelationbetweenstressandstrainisthattheyaredirectlyproportionaltoeachotheruptoanelasticlimit.Hooke’slawexplainstherelationshipbetweenstressandstrain.AccordingtoHooke’slaw,thestraininasolidisproportionaltotheappliedstressandthisshouldbewithintheelasticlimitofthatsolid.Whatisyieldpointinstress-straingraph?Yieldpointisdefinedasthepointatwhichthematerialstartstodeformplastically.Aftertheyieldpointispassed,permanentplasticdeformationoccurs.Howtomakeastress-straincurve? Thestress-straincurveisobtainedbygraduallyapplyingloadtoatestcouponandmeasuringthedeformation,fromwhichthestressandstraincanbedetermined. StaytunedtoBYJU’SandFallinLovewithLearning! TestyourknowledgeonStressAndStrain Q5 PutyourunderstandingofthisconcepttotestbyansweringafewMCQs.Click‘StartQuiz’tobegin! Selectthecorrectanswerandclickonthe“Finish”buttonCheckyourscoreandanswersattheendofthequiz StartQuiz Congrats! VisitBYJU’SforallPhysicsrelatedqueriesandstudymaterials Yourresultisasbelow 0outof0arewrong 0outof0arecorrect 0outof0areUnattempted ViewQuizAnswersandAnalysis PHYSICSRelatedLinks UseOfRectifier WhatIsQuark EnergyTransformationExamplesInDailyLife GalvanometerDiagram TypesOfSatelliteCommunication ParallelSeries UsesOfInfraredWaves RefractionOfLightClass10Notes ApplicationOfDcGenerator WaveDefinitionPhysics 3Comments LuphoMshumi July16,2020at3:54am Thankyou.Itisclear,simpleandeasytounderstand Reply Girishharihar October19,2020at5:13pm Streesandstraindifference Reply sushmitha October19,2020at7:50pm Learnaboutthedifferencebetweenstressandstrainhere. 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