10.7 Properties of Materials 341Fig.10.9
Stress–strain curve for mild steel.
Low Carbon Steel (Mild Steel)
Anominalstress–straincurveformildsteel,aductilematerial,isshowninFig.10.9.From0to“a”,
thestress–straincurveislinear,thematerialinthisrangeobeyingHooke’slaw.Beyond“a,”thelimit
of proportionality, stress is no longer proportional to strain, and the stress–strain curve continues to
“b,”theelasticlimit,whichisdefinedasthemaximumstressthatcanbeappliedtoamaterialwithout
producingapermanentplasticdeformationorpermanentsetwhentheloadisremoved.Inotherwords,
ifthematerialisstressedbeyond“b”andtheloadthenremoved,aresidualstrainexistsatzeroload.
Formanymaterials,itisimpossibletodetectadifferencebetweenthelimitofproportionalityandthe
elasticlimit.From0to“b,”thematerialissaidtobeintheelasticrange,whilefrom“b”tofracture,the
materialisintheplasticrange.Thetransitionfromtheelastictotheplasticrangemaybeexplainedby
consideringthearrangementofcrystalsinthematerial.Astheloadisapplied,slippingoccursbetween
thecrystalswhicharealignedmostcloselytothedirectionofload.Astheloadisincreased,moreand
morecrystalsslipwitheachequalloadincrementuntilappreciablestrainincrementsareproducedand
theplasticrangeisreached.
A further increase in stress from “b” results in the mild steel reaching itsupper yield pointat
“c,”followedbyarapidfallinstresstoitslower yield pointat “d.” The existence of a lower yield
point for mild steel is a peculiarity of the tensile test wherein the movement of the ends of the test
pieceproducedbythetestingmachinedoesnotproceedasrapidlyasitsplasticdeformation;theload
thereforedecreases,asdoesthestress.From“d”to“f,”thestrainincreasesataroughlyconstantvalue
of stress untilstrain hardeningagain causes an increase in stress. This increase in stress continues,
accompaniedbyalargeincreaseinstrainto“g,”theultimatestress,σult,ofthematerial.Atthispoint,
the test piece begins, visibly, to “neck,” as shown in Fig. 10.10. The material in the test piece in the
region of the “neck” is almost perfectly plastic at this stage, and from this point onward to fracture,
thereisareductioninnominalstress.