342 CHAPTER 10 Materials
Fig.10.10
“Necking” of a test piece in the plastic range.
Fig.10.11
“Cup-and-cone” failure of a mild steel test piece.
Formildsteel,yieldingoccursatastressoftheorderof300N/mm^2 .Atfracture,thestrain(i.e.,the
elongation)isoftheorderof30percent.Thegradientofthelinearportionofthestress–straincurve
givesavalueforYoung’smodulusintheregionof200000N/mm^2.
The characteristics of the fracture are worthy of examination. In a cylindrical test piece, the two
halvesofthefracturedtestpiecehaveendswhichforma“cupandcone”(Fig.10.11).Theactualfailure
planesinthiscaseareinclinedatapproximately45◦totheaxisofloadingandcoincidewithplanesof
maximumshearstress.Similarly,ifaflattensilespecimenofmildsteelispolishedandthenstressed,a
patternoffinelinesappearsonthepolishedsurfaceatyield.Theselines,whichwerefirstdiscoveredby
Lüderin1854,intersectapproximatelyatrightanglesandareinclinedat45◦totheaxisofthespecimen,
therebycoincidingwithplanesofmaximumshearstress.Theseformsofyieldingandfracturesuggest
thatthecrystallinestructureofthesteelisrelativelyweakinshear,withyieldingtakingtheformofthe
slidingofonecrystalplaneoveranotherratherthanthetearingapartoftwocrystalplanes.
Thebehaviorofmildsteelincompressionisverysimilartoitsbehaviorintension,particularlyin
theelasticrange.Intheplasticrange,itisnotpossibletoobtainultimateandfractureloads,since,due
tocompression,theareaofcrosssectionincreasesastheloadincreases,producinga“barrelling”effect,
asshowninFig.10.12.Thisincreaseincross-sectionalareatendstodecreasethetruestress,thereby
increasing the load resistance. Ultimately a flat disc is produced. For design purposes, the ultimate
stressesofmildsteelintensionandcompressionareassumedtobethesame.
Highergradesofsteelhavegreaterstrengthsthanmildsteelbutarenotasductile.Theyalsopossess
thesameYoung’smodulussothatthehigherstressesareaccompaniedbyhigherstrains.
Aluminum
Aluminumandsomeofitsalloysarealsoductilematerials,althoughtheirstress–straincurvesdonot
have the distinct yield stress of mild steel. A typical stress–strain curve is shown in Fig. 10.13. The
points“a”and“b”againmarkthelimitofproportionalityandelasticlimit,respectively,butaredifficult
todetermineexperimentally.Instead,aproofstressisdefinedwhichisthestressrequiredtoproducea
givenpermanentstrainonremovaloftheload.InFig.10.13,alinedrawnparalleltothelinearportion
ofthestress–straincurvefromastrainof0.001(i.e.,astrainof0.1percent)intersectsthestress–strain