Tensor Properties.pdf

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1、PartIIMaterialsScienceandMetallurgyTENSORPROPERTIESCourseC4DrACTwitchett12lectures+1examplesclassSYNOPSISIntroduction(11/2lectures)Reasonsforusingtensors.Tensorquantitiesandproperties(fieldandmattertensors).Electricalconductivityasasimpleexampleofatensorprop

2、erty.GeneralnotationandEinsteinsummationconvention.Transformationofaxes.Tensorrank.Anisotropyandsymmetry.Physicalsignificanceoftensorcomponents.Stressandstrain(21/2)Introductiontoelasticandplasticbehaviour,andtofailuremodesofmaterialsandstructures.Definition

3、ofstressatapoint.Tensornotationforstress.Examplesforuniaxialtensionandcompression,hydrostatictensionandcompression,pureshear.Stresstensorincylindricalco-ordinates.Resolutionofstresses:derivationofformulafornormalandshearstressesonaplane.Exampleofstressesonpl

4、aneinbarinuniaxialtension.Definitionofstrainatapoint.Distinctionbetweenrigidbodydisplacementandrotation,andshear.Symmetryofstraintensor.Propertiesofsymmetricalsecondranktensors:principalaxes.Diagonalisationofgeneraltensortofindprincipalstressesandstrains.Dia

5、gonalisationintwodimensions:theMohrcircleconstruction.Examples,includingrepresentationof3-Dstressstate.Hydrostaticanddeviatoriccomponentsofthestresstensor.Dilatationalanddeviatoriccomponentsofthestraintensor.Elasticity(2)Isotropicmedium:linearelasticitytheor

6、y,Hooke'sLaw,principleofsuperposition.Poisson'sratio,shearmodulus,bulkmodulus,Laméconstants,interrelationshipsofelasticconstants.Generalanisotropicmedium:stiffnessandcompliancetensors.Simplificationbysymmetry:matrixnotation.Strainenergydensity:symmetryofgene

7、ralstiffnessandcompliancematrices.Effectsofcrystalsymmetry.Physicalinterpretationofthreedeformationmodesinacubiccrystal.Anisotropyfactorforseveralmaterials.Methodsofexperimentalstressanalysis(11/2)Straingauges:fundamentalsunderlyinggaugefactor.Practicaldetai

8、ls.Analysisofstraingaugeresults.Photoelasticity:birefringence,stress-opticalco-efficients,isochromaticandisoclinicfringes,applications.Othermethodsofstressmeasurement:brittlecoatings,X-raydiffra