Basic of Axial Strain
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3.1 Normal (Axial) Stress and Strain Axial Strain | Axial Stress | Curve | Young's Modulus | Poisson's Ratio | Elastic Strain Energy | Fatigue » Axial Strain An axial bar of length L, and crosssectional area A, subjected to tensile force P, elongates by an amount, . The change in length divided by the initial length is termed ENGINEERING STRAIN (or simply strain). The symbol used for engineering strain in most texts is (epsilon). The strain in an axially loaded bar is defined as: Strain is positive in tension (>0 means <0) and negative in compression (<0); Strain is a nondimensional length a fraction. Because strain is small, it is often given as a percentage by multiplying by 100%: e.g., = 0.003 = 0.3%. » Axial Stress Consider the same bar as above. If a cut is taken perpendicular to the bar's axis, exposing an internal cross section of area A, the force per unit area on the face of this cut is termed STRESS. The symbol used for normal or axial stress in most engineering texts is (sigma). Stress in an axially loaded bar is: Stress is positive in tension (P>0) and negative in compression (P<0); English units: psi (pounds per square inch), or ksi (kilopounds per square inch); S.I. units: Pascal (Pa) (Newtons per square meter), or more commonly megapascal (MPa), (1 MPa = 1,000,000 Pa). » Stiffness; Young's Modulus Like a spring, all materials have a stiffness associated with them. In engineering, the stiffness of a material is defined through Hooke's Law: =E Where E is the YOUNG'S MODULUS or stiffness of the material.
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Transcript of Basic of Axial Strain
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08/05/2015 3.1AxialStrain
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3.1Normal(Axial)StressandStrainAxialStrain|AxialStress|Curve|Young'sModulus|Poisson'sRatio|ElasticStrainEnergy|Fatigue
AxialStrainAnaxialbaroflengthL,andcrosssectionalareaA,subjectedtotensileforceP,elongatesbyanamount,.ThechangeinlengthdividedbytheinitiallengthistermedENGINEERINGSTRAIN(orsimplystrain).Thesymbolusedforengineeringstraininmosttextsis(epsilon).Thestraininanaxiallyloadedbarisdefinedas:
Strainispositiveintension(>0means
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ValuesofEfordifferentmaterialsareobtainedexperimentallyfromstressstraincurves.Young'sModulusissimplytheslopeofthelinearregionofthestressstraincurve.ValuesofYoung'sModulusforvariousmaterialsaregiveninTable1ElasticConstants.Young'sModulusisgenerallylargeandusuallyexpressedineitherMsi(megapoundspersquareinch=thousandsofksi)orGPa(gigapascal).
StressStrainCurveThemostcommonwayofdepictingtherelationbetweenstressandstrainisthroughaSTRESSSTRAINCURVE.StressstraincurvesareobtainedexperimentallyandprovideusefulmaterialpropertiessuchasYoung'sModulus,yieldstrength,ultimatetensilestrength,etc.
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aStressStrainCurveis
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ProportionalLimit:thevalueofstresswhenthestressstraincurvenolongerfollowsHooke'sLaw.YieldStrength:thepracticalvalueoftheProportionalLimitfoundusingthe0.2%offsetrule.UltimateTensileStrength:themaximumvalueofstressthatamaterialcansupport.
Poisson'sRatioAsyoustretcharubberband,notonlydoesitelongate,butitgetsthinner.Thisholdstrueforstructuralcomponentsaswell,althoughitisdifficulttoseewiththenakedeye.ThisisreferredtoasthePoissonEffect.Mathematically,POISSON'SRATIOisexpressedasthenegativeratioofthetransversestrain(T)tothelongitudinalstrain(),wherethelongitudinalstrainisinthedirectionoftheappliedload:
TypicalvaluesofPoisson'sRatioforvariousmaterialsaregiveninTable1ElasticConstants.
ElasticStrainEnergyDensityTheelasticstrainenergydensitytheelasticstrainenergyperunitvolumestoredinanaxialmemberis:
ThemaximumvalueoftheelasticstrainenergyistheRESILIENCE.Itoccurswhenthestressintheaxialmemberreachestheyieldstrength:
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FatigueThestandardfatiguetest(zeromeanstress)hasastraintimehistorygraphasshownatright.Testsareperformedatdifferentstressamplitudesa,andthenumberofcyclestofailureisrecorded,Nf.Thepoints(NF,sa)areplottedandalinefitted.VariablesSf'andbaredeterminedfromthecurvefit.
ThefatiguestrengthofamaterialisthevalueofthestressamplitudeforagivenvalueofNfcanbecalculated:
Typically,forsteel,Nf=106cyclesandforaluminumNf=107cycles.Steelsalsohaveafatiguelimit...
Stresstimecurve.
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