me215ch3_new1310

CHAPTER 3PROPERTIESIN TENSION AND COMPRESSIONME 215In daily life, engineering materials may be exposed to different type of loadings such as:tension, compression, bending, direct shear, torsional shear, fatigue, impact, creep etc To make sure that there is no failurefracture of the materials under such loads !e ha"e to kno! their load carrying limitscapacitiesThis re#uires testing these materials in laboratories to their upmost limits before they are actually employed in actual life$ctual ser"ice conditions ho!e"er, are usually different from laboratory test conditions, %o, results of laboratory tests !ill not be directly applicable to actual conditions&They ha"e to be someho! modified before used in actual conditionsThe tests done in laboratories ha"e to be performed under controllable conditions and comply to some standarts&Propertiesofmaterialsundersimpletensile and compressive loads are usually determined bytheuniaxialtypeTensionandCompression Tests.These tests'aretheeasiesttypeofteststoevaluatethe properties.'Representalmosttheconditionofprincipal stresses which are the reasons of failures.'Resultsofthetestcanbeutilizedforcombined stress situations.(ere is a simple tensile test procedure:Take a standart test specimenMake necessary measurements on specimen before the test)lace the specimen on testing machine$pply tensile load on the pecimen starting from *ero and increasing graduallyMake a note of load and elongation at different times of test)roceed until specimen fracturesMake necessary measurements on the fractured specimenForce, NL, mmF/o L /L! ! !"!! !.#$!! ". .. .. .Force, NL, mmF/o L /L! ! !"!! !.#$!! ". .. .. .+on"ert load "s elongation data to stress "s strain data and dra! stress "s strain cur"eTheterminationoftheelasticbehaviorofamaterialis %nown as &elastic limit& of a material. 'hentheloadisincreasedbeyondthispoint,the deformationofthespecimendoesnotdisappearupon releaseofloadandpartofthedeformationis permanent. (uch a deformation is called )plastic deformation&.For all types of materials there are two modes of behavior under loadin*.+lastic behavior,lastic behavior The characteristics of the elastic deformation are that the specimen returns to its ori*inal dimensions upon release of load. Theelasticlimitisde-nedasthe*reateststresswhichcanbe appliedwithoutresultin*inanypermanentstrainuponreleaseof load. +lastic limit is a property of the material and is of *reat importance indesi*napplications..ecausetheallowablestressvaluesin desi*n wor% are usually based on the elastic limit of materials.materialhasahi*helasticstren*thifitresistsloadswithout bein*deformedplastically/yieldin*0.1i*hstren*thmaterialsare selected for wei*ht savin*s.ELASTIC BEA!I"#For most of the en*ineerin* materials the elastic behavior of a material obeys 1oo%e2slaw3thereisalinearrelation between the stress and strain. (uchmaterialsarecalledlinearly elastic. (ome materials, li%e rubber, are notlinearlyelasticande4hibitanon3linear stress3strain curve as seen in the curve.Theelasticbehaviorofametalisnotnecessarilylinear up to elastic limit. The point mar%in* the end of the linear relationship is called the proportional limit of a metal.5n *eneral, a metal is said to be behavin* elastically if the oo$e%s la&isobeyedand the stress3strain responseis simultaneous6whenthestressreachesavalue)7&, materialisstrainedinstantaneouslytothevalue)8&as determined b the 1oo%e2s law. Let us consider some important features of the elastic portion of a Stress-Strain diagram:1. Stiffness(Elastic modulus)2. Resilience3. Yield strength (Elastic limit). !ltimate strength". #uctilit$%. &oughness inde' num(er). &rue stress-strain'. Sti(ness) 5t is the ratio of incremental normal stress to correspondin* direct strain for Tensile or 9ompressive stress. For linearly elastic materials this slope is constant and is e4pressed by the +lastic :odulus or ;oun*2s :odulus.+ < d7 / d8 7&.Ri*idity/di?erent from sti?ness05tisthedesi*nterminolo*ywhenthefunctional re@uirementsdemandthatthedeformations/notthe strain0be small.Itisnotapurelyamaterialpropertybuta function of both + and the *eometry factorsA L.+lasticmodulus/+0isalmostaconstantvalueforthe materials and chan*es with only few factors such as='Temperature increase , + decrease'Birectionally /anisotropy0 in rollin* e?ects+ valuesee Table C." and p"#D0+lastic:odulus,+,ran*esfromverylowvaluestovery hi*h values as in table below6+lastomers EEEEEEEEEEEE.EE "3F! %*/mm$Thermoplastics EEEEEEEEEE.EE "!! 3"F!! %*/mm$Thermosettin*s EEEEEEEEEEEE F!! 3$!!! %*/mm$9ast 5ron EEEEEEEEEEEEEEE G!!! 3$!!!! %*/mm$9arbon (teel EEEEEEEEEEEEE..$!!!! 3$#!!! %*/mm$9eramicsEEEEEEEEEEEEEEE."!!!!3#!!!! %*/mm$Refractory 1ard :etals EEEE.EEE E..up to H!!!! %*/mm$ + is determined by the bindin* forces between atoms. (ince these forces cannot be chan*ed without chan*in* the basic nature of the material, the elastic modulus is then one ofthemoststructure3insensitiveofthemechanical properties. 5t is only sli*htly a?ected by6lloyin* ddition1eat Treatment 9old 'or% $. Resilience= 5t is the capacity of a material for returnin* to ori*inal dimensions after elastic deformation.'or% done by F on an elastic bar is the area under Force vs deIection curve6' < J /FKe0F< Force, e< elastic deformationssumin*thatthematerialobeys1oo%e2slaw,thiswor%is converted into the elastic potential ener*y of the material' < J /7. 0/8.L0< cross3section area, L < len*th of the bar The ma4imum potential elastic ener*y is reached when the bar strained to its proportional/elastic limit (y.The resilience of a material, in the broad sense, is the area underthestress3straincurveuntiltheelasticlimitofthe material.L < J /(y$ / +0 %*3mm/mmC Thisistheareaunderstress3straincurveforthelinearlyelastic materials. n ideally resilient material is the one which has a hi*h elastic limit and low modulus of elasticity.Thou*hthede-nitionofmodulusofresilienceisbasedon elasticlimit/oryieldstren*th0ofamaterial,inpractice,thefull value of resilience is not utilized6 for the desi*n stresses have to be %eptbelowtheelasticlimittoavoidthefailureofthepartby e4cessive deformation /yieldin*0. Thetotalelasticener*ythatcanbeabsorbedbyanelementis dependent also upon the volume. Resilienceisanimportantpropertyindesi*napplicationswhere ener*yabsorptionisre@uired6suchassprin*s,partssubMectedto impact loadin*, vibratin* components, and so on.SPECIAL *E+I,ITI",S "+ TE ELASTIC LI-ITForsomeoftheen*ineerin*materials,the(ypointon7N8 curveisnotclearlyidenti-edsuchasfor6coldwor%edsteelsand non3ferrous metals. Bue to the importance of (y in desi*ns, two methods have been divised to appro4imately -nd (y point.a) Ofset yield strength: 1ard steels and non3ferrous metals do not havede-nedyieldlimit,thereforeastress,correspondin*toa de-nite strain/!."O or !.$O0 is commonly used instead of yield limit.Thisstressiscalledproofstressoro?setyieldlimit .o?set yield stren*th/a) Johnsonsapparentelasticlimit:thismethodisnotusedas widelyastheo?setmethodduetothe*reaterprobabilityof inaccuracy compared with the other method.(ometimesavalueof.