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MECH-237 Lab 1 – SPIRNG 2014---------------------------------------------------

Tension Test of Metals

Name: Andreas Christoforou

Date: 03/06/2014

New Jersey Institute of e!hno"o#y

141 $ummit $t% Newar&% NJ 0'103

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Contents

A(stra!t )**)******************************)))*3Introdu!tion + ,ro!edure***************************))))4

heory *****************************)*****)))'-10

esu"ts and Ana"ysis *****************************))11Dis!ussion + Con!"usion****************************12

eferen!es**********************************14

A..endi**********************************))1

List of Figures

i#ure 1: $tee" Aisi &oo under "oadin#

i#ure 2: ree !ut of stee" Aisi &oo

i#ure 3: $tress-strain re"ationshi. under tensi"e "oadin#

i#ure 4: odu"us of esi"ien!e

i#ure : odu"us of tou#hness

i#ure 6: $tress-$train dia#ram of hot ro""ed stee"

i#ure ': modu"us of e"asti!ity of Aisi stee"

i#ure : stress 5 strain re"ation of Cast Iron

i#ure : Cast Iron after ne!&in#

List of Tables

a("e 1: Ca"!u"ations and estimation of im.ortant 7a"ues

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Abstract

In order for en#ineerin# students to (e su!!essfu" in their fie"d it is si#nifi!ant for

them to a!8uire a #ood understandin# for materia" ana"ysis in the !ourse of their studies)

he uniaia" tension test is one of the most fundamenta" tests in !i7i" en#ineerin#

s.e!ifi!a""y de7ised for determinin# me!hani!a" materia" .ro.erties that are re"ated to

for!es a!tin# on (odies in a uniform dire!tion9 .ro.erties su!h as the oun#;s odu"us%

the ie"d stress% the ensi"e $train to ai"ure% and the <"timate ensi"e $tren#th are

e.e!ted to (e understood (y the students) In the !ourse of this "a(oratory e.eriment%

two materia" s.e!imens were tested and ana"yed on their stress-strain re"ationshi.s: $tee"

Aisi &oo and Cast iron CI 20) his "a(oratory e.eriment is meant to !on7ey a (asi!

understandin# for materia" testin# su!h as the (eha7ior of the two materia"s (y !om.arin#

the stress-strain !ur7es o(tained from the resu"ts) =owe7er% this "a. is meant to tri##er

further interest in the study of materia" en#ineerin#)

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Introduction

he tensi"e test is a method to measure the me!hani!a" .ro.erties of materia"s) It

re"ates the effe!t of a uniaia" tensi"e "oad >for!e? on the e"on#ation >!han#e in "en#th? of

a standard s.e!imen)

he .rimary o(@e!ti7e of this "a( was to ana"ye how the two different s.e!imens

stee" Aisi &oo and !ast iron CI 20 rea!ted under in!reasin# "oad) he test s.e!imens

wi"" (e "oaded durin# the .ro!edure) e are e.e!ted to (e a("e to e."ain "oad-etension

and stress-strain re"ationshi.s and (e a("e to e7a"uate the 7a"ues of u"timate tensi"e

stren#th% yie"d stren#th% B e"on#ation% fra!ture strain% du!ti"ity and oun#s odu"us of

the two meta"s when su(@e!ted to tension odu"us of esi"ien!e and ou#hness) A"so% to

e."ain the (eha7ior when the (ars were "oaded and !om.are the modu"us of e"asti!ity for

ea!h of them) At the end we to des!ri(e the (eha7ior of the two materia"s studied)

he two sam."es were su(@e!ted to in!reasin# aia" "oads usin# a me!hani!a"

testin# ma!hine) he !om.utation of e8uations and ana"ysis of the resu"ts are e.e!ted

for this "a.) y re7iewin# the res.e!ti7e stress 7s) strain #ra.hs% we !an easi"y !a"!u"ate

the oun#;s odu"us% the ie"d stress% the ensi"e $train to ai"ure% and the <"timate

ensi"e $tren#th and stren#th of the materia")

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Procedure

irst in the stee" Aisi &oo aia" tensi"e test% a s.e!imen of stee" was fastened to the

testin# #ri.s of the estin# ma!hine) Its to. and (ottom se!tions were !onsidera("y wider

in diameter than that of the narrow midd"e se!tion% whi!h the etensometer was atta!hed

to) Durin# the tensi"e test% the (ottom se!tion of the s.e!imen was stati!a""y atta!hed to

the testin# ma!hine;s frame whereas the to. se!tion was ti#ht"y #ri..ed and .u""ed on (y

the ma!hine;s !rosshead) he test was desi#ned to simu"ate 7aryin# sta#es of "oadin# and

un"oadin#) he ma!hine;s !rosshead mo7ed at a 7ery s"ow% !onstant u.ward motion for

"oadin# and then to a !onstant downward motion for un"oadin#) As the ma!hine re.orted

information on "oadin# for!e% an e"e!tri!a" etensometer a!!urate"y measured and

re.orted the sam."e;s o7era"" e"on#ation o7er then its #au#e "en#th and automati!a""y

!a"!u"ated its strain) he Aisi stee" was "oaded and (efore yie"d .oint9 then "oaded a#ain

.assin# the yie"d .oint9 fina""y it "oaded a#ain unti" to ru.ture) he data for the Aisi stee"

was re!orded in time inter7a"s of "ess than a se!ond durin# the !ourse of the test unti"

fai"ure o!!urred in the narrow mid-se!tion of the s.e!imen)

he same .ro!edure was fo""owed for the Cast iron)

hen the two meta"s are su(@e!ted to a tensi"e "oadin#% the meta" wi"" under#o e"asti! and

."asti! deformation) Initia""y% the meta" wi"" e"asti!a""y deform #i7in# a "inear re"ationshi.

of "oad and etension)

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i#ure 1: $tee" Aisi &oo under "oadin# i#ure 2: ree !ut of stee" Aisi &oo

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Analysis of test Results:

he fi#ure (e"ow shows the stress-strain re"ationshi. of meta"s under uniaia" tensi"e

"oadin#)

i#ure 3: $tress-strain re"ationshi. under uniaia" tensi"e "oadin#

o""owin# the stress-strain re"ationshi. from fi#)1 we !an use the fo""owin# e8uations to

o(tain our resu"ts and ma&e the !om.arison of the two meta"s)

he aia" stress E in the test s.e!imens is !a"!u"ated (y di7idin# the "oad , (y the initia"

!ross-se!tiona" area A0

and the e8uation for stress fo""ows as%

>e8) 1?

he strain !an (e !a"!u"ated with the fo""owin# e8uation%

>e8)2?here% σ is the en#ineerin# stress

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ε is the en#ineerin# strain P is the eterna" tensi"e "oad

δ is the e"on#ation

Ao is the ori#ina" !ross-se!tiona" area of the s.e!imen Lo is the ori#ina" "en#th of the s.e!imen

Lf is the fina" "en#th of the s.e!imen

Comment: hen the initia" area of the s.e!imen is used in these !a"!u"ations% the

resu"tin# stress is !a""ed en#ineerin# stress) A more ea!t 7a"ue of the aia" stress% &nown

as the true stress% !an (e !a"!u"ated (y usin# the a!tua" area of (ar whi!h !an (e!ome

si#nifi!ant"y "ess than the initia" area) Fo#i!a""y% if we use the a!tua" area of (ar when it is

in!reasin# due to tension the true stress wi"" (e hi#her as it !an (e !on!"uded from

e8uation 1) A"so the same !on!e.ts a!!ounts for the strain) If the initia" #a#e "en#th is

used then the en#ineerin# strain is o(tained) Fo#i!a""y% the distan!e (etween the #a#e

mar&s in!reases due to the tension and the a!tua" distan!e is used to !a"!u"ate strain

whi!h is !a""ed the true strain) he true strain wou"d (e hi#her than the en#ineerin# strain

as e8uation 2 shows that strain is di7ided (y "en#th) In this re.ort I wi"" (e usin# the

en#ineerin# stress and strain to ana"ye my resu"ts)

Durin# e"asti! deformation% the en#ineerin# stress-strain re"ationshi. fo""ows the =oo&s

Faw and the s"o.e of the !ur7e indi!ates the oun#s modu"us >G?)

>e8) 3?

here E is the modu"us of e"asti!ity >oun#;s modu"us?

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hen the yie"din# o!!urs at the (e#innin# of ."asti! deformation the yie"d stress% Ey% !an

(e o(tained (y di7idin# the "oad at yie"din# >,y? (y the ori#ina" !ross-se!tiona" area of

the s.e!imen >Ao? (y the e8uation%

>e8) 4 ?

here σy is the yie"din# stress

Py is the yie"din# "oad

he du!ti"ity of the two meta"s in tension !an (e !hara!teried (y e"on#ation and (y

the redu!tion in area at the !ross-se!tion where fra!ture o!!urs) he .er!ent e"on#ation is

defined as fo""ows: > e8) ?

he redu!tion in diameter !an (e !a"!u"ated (y su(tra!t initia" #a#e diameter from the

fina"% di7ide it (y the initia" and then mu"ti."y (y 100)

he .er!ent e"on#ation for the hot ro""ed stee" was &ind of hi#h as it was a(out 3)B%

!om.are it with the !ast iron there wasn;t any e"on#ation at a"" and its fina" diameter

remain the same)

y simi"ar way we !a"!u"ated the .er!ent redu!tion of the !ross se!tiona" area)

e a"so ha7e to find the odu"us of esi"ien!e whi!h is the maimum e"asti! ener#y

a(sor(ed (y a materia" when a "oad is a.."ied) hi!h is defined as fo""ows:

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(eq.6)

here σy is the yie"d stren#th

i#ure 4: odu"us of esi"ien!e

Hn the other hand odu"us of tou#hness re.resents the ener#y .er unit 7o"ume re8uired

to !ause the materia" to ru.ture) It is !"ear that the tou#hness of a materia" is re"ated to

its du!ti"ity as we"" as to its u"timate stren#th% and that the !a.a!ity of a stru!ture to

withstand an im.a!t "oad de.ends u.on the tou#hness of the materia" used)

i#ure : odu"us of tou#hness

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>e8)'?

a("e 1: Ca"!u"ations and estimation of im.ortant 7a"ues

Detai"s Aisi &oo stee" Cast iron CI 20

Diameter >in? ')3' )02

au#e "en#th >in? 2)00 2Cross se!tiona" area >in? 0)14' 0)1'

,ro.ortiona" "imit >&si? K 4 1)

oun# odu"us >&si? K 2600 13'1

Foad at yie"d .oint >&i.s? 10) 0)3'

ie"d stren#th >&si? 1) 1)

ie"d $train 0)000064 0)00013

aimum "oad >&i.? 1) 0)'2'

<"timate tensi"e stress >&si? ') 3)6

$train at <"timum 0) 0)00023

BG"on#ation in 2L 6)2 0

B redu!tion of area )46 0odu"us of resi"ien!e >.si? 0)061 0)12

odu"us of tou#hness >&si? 2' 0)33

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he fo""owin# fi#ures whi!h I wi"" (e showin# were o(tained usin# i!rosoft G!e" and

from the !o""e!ted data of the two materia"s)

i#ure 6 (e"ow shows the $tress-$train dia#ram of stee" durin# the e"asti! (eha7ior andthe yie"din# re#ion)

H(ser7in# the (eha7ior of the stee" in fi#ure 6 I rea"ied that the .ro.ortiona" "imit was

hard to find sin!e the !ur7e did not (end enou#h to distin#uish the "inear re"ationshi.

from the f"atten out .art as shown in the fi#ure) herefore% I assumed that the

,ro.ortiona" "imit was 7ery !"ose to the u..er yie"d .oint) Durin# "oadin# the stress-strain

dia#ram fo""owed the "inear re"ationshi. as shown in fi#ure 6) I !a"!u"ated the odu"us of

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e"asti!ity (y usin# a"" the data .oints from the (e#innin# u. to the .ro.ortiona" "imit (y

fittin# a "inear "ine (etween the .oints) hen the s"o.e of that "ine is the odu"us of

e"asti!ity of the stee" as shown in fi#ure ')

i#ure ': modu"us of e"asti!ity of Aisi stee"

i#ure (e"ow shows the $tress-$train dia#ram of !ast iron durin# the e"asti! and

(e#innin# of the ."asti! (eha7ior) It was a "itt"e easier to find the .ro.ortiona" "imit and

yie"d stren#th !om.are it with the Aisi stee" )=owe7er% the materia" sti"" under#oes "ar#e

strains after its .ro.ortiona"ity "imit and an ar(itrary yie"d stress may (e determined (y

offset method) herefore% I !a"!u"ated the yie"d stren#th (y usin# 0)2B strain as an offset

method) I o(tained the e8uation of the "ine usin# the same s"o.e G and (y assumin# that

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the 7a"ues of strain and stress in the ne#ati7e 8uadrant wi"" (e the same as in the .ositi7e

8uadrant sin!e the re"ationshi. is "inear)

)

i#ure : stress 5 strain re"ation of Cast Iron

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i#ure : Cast Iron after ne!&in#

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iscussion

=ot-ro""ed% AI$I stee"esu"ts of the $tress 7s) $train re"ation for the hot ro"" $tee" !an (e seen in fi#ures 2 and 3

(ut a"so from fi#ure A1 from the a..endi A) he s.e!imen e"on#ates "inear"y unti" yie"d

stress) I o(tained this .oint as the maimum .oint (efore the de!rease in "oad !arryin#

!a.a!ity to a "ower yie"d .oint as shown in i#ure 2) he yie"din# for!e !orres.onds tothe 7a"ue of ,y M 10)>&i.s? whi!h I o(tained from e8) 4) After this .oint% the s.e!imen

wi"" no "on#er return to its ori#ina" "en#th if the "oad is ta&en away) A"so% after this .oint

the materia" e.erien!es e"on#ation under !onstant "oadin# !onditions (e!ause it is"o!ated in the ."asti! re#ion) he hot ro"" stee" (e!omes .erfe!t"y ."asti! and it !an

deform without an in!rease in the a.."ied "oad)) he oun#;s odu"us >G? was!a"!u"ated to (e around 2600 &si) After the materia" .asses its ."asti!ity the stee" (e#ins tostrain harden) he stress that !auses the initiation of strain hardenin# is the same as the

yie"din# stress) Durin# the strain hardenin# the s.e!imen !an su..ort more "oad unti" it

rea!hes a maimum stress) he maimum stress was EuM')&si and the) he 7a"ues for

modu"us of e"asti!ity% u"timate tension stren#th% yie"d tension stren#th and .er!ente"on#ation o(tained in this re.ort were 7ery simi"ar to those in the A..endi in the

(oo&)

CI 20 Cast Iron:

As it !an (e seen from fi#ures and the Cast Iron s.e!imen initia""y deformed "inear"y

with res.e!t to the a.."ied for!e durin# the first "oadin#) he Cast Iron s.e!imen (e#unto yie"d around EyM1)&si as it was !a"!u"ated usin# the 0)2B offset method) he yie"din#

for!e !orres.onds to the 7a"ue of ,yM 0)3' &i.s whi!h I o(tained from e8) 4) he

oun#;s odu"us of rass was !a"!u"ated to (e around ''2&si) he maimum $tren#th

of the Cast Iron s.e!imen was !a"!u"ated to (e EuM3)6&si) After this is rea!hed% themateria" is a(out to fai")) he ,uM0)'2'&i.s) he 7a"ues for modu"us of e"asti!ity%

u"timate tension stren#th% yie"d tension stren#th and .er!ent e"on#ation o(tained in this

re.ort were not mat!hin# to those in the A..endi in the (oo&) =owe7er% there are a "otof ty.es of !ast iron whi!h !ou"d (e different)) As I mentioned (efore there different (rass

meta"s that !ou"d (e used and the s.e!ifi! one we used was not too stron# and that;s why

it (ro&e 7ery fast (e!ause its modu"us of e"asti!ity was 7ery sma"")

rass 7s Car(on $tee":

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Conclusion

he $tress-$train #ra.h in fi#ure A3 from the a..endi A shows that the Car(on stee"e.erien!ed more ."asti! deformation than the rass% and this is ref"e!ted (y the hi#her

.er!enta#e e"on#ation) he .er!ent e"on#ation for stee" was 2)3B and that of rass was

11B) Com.arin# the im.ortant stresses su!h Ey% Eu% Efra!ture of the two s.e!imens the

Car(on stee" is stron#er (e!ause it withstands a hi#her stress (efore fai"ure than therass) Car(on stee" is more du!ti"e (e!ause the strain under its !ur7e is #reater than that

of a"uminum) he ad7anta#e of du!ti"ity is that 7isi("e distortions may o!!ur if the "oads

(e!ome too "ar#e% thus .ro7idin# an o..ortunity to ta&e remedia" a!tion (efore an a!tua"fra!ture o!!urs) he Car(on stee" a"so dis."ayed a hi#her tou#hness than the a"uminum

stee"% whi!h is re.resented (y the "ar#er area (eneath the stress strain #ra.h) he Car(onstee" had a "ar#er ne!&in# re#ion than the rass stee"% whi!h e."ains the #reaterredu!tion in !ross se!tiona" area at the .oint of fra!ture) Ne!&in# is a .ro.erty of a du!ti"e

materia") In !on!"usion% Car(on stee" !an (e re#arded as a more Du!ti"e materia" than

rass)

he materia"s se"e!ted for a desi#n often wi"" determine the fa(ri!ation .ro!esses that !an

(e used to manufa!ture the .rodu!t% its .erforman!e !hara!teristi!s% and its re!y!"a(i"ity

and en7ironmenta" im.a!t) As a resu"t% en#ineers shou"d a!8uire a ro(ust understandin#of materia" !hara!teristi!s and the !riteria that one shou"d use in ma&in# materia"

se"e!tions)L

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A!!endi" A:

References

erdinand ,) eer% G) usse"" Johnston% Jr)% John ) Dewo"f% Da7id ) aure&)e!hani!s of ateria"s) !raw-=i"" Com.anies% In!)% 2012% 6 th Gdition) 1221 A7enue

of the Ameri!as% New or&) Cha.ter 1)

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