elastic-constants-ketul.ppt
Post on 19-Feb-2018
222 Views
Preview:
TRANSCRIPT
-
7/23/2019 Elastic-Constants-ketul.ppt
1/21
-
7/23/2019 Elastic-Constants-ketul.ppt
2/21
ElasticElastic
ConstantConstant
-
7/23/2019 Elastic-Constants-ketul.ppt
3/21
ELASTIC CONSTANTS INELASTIC CONSTANTS IN
ISOTROPIC MATERIALSISOTROPIC MATERIALS1.1.Elasticity ModulusElasticity Modulus (E)(E)
2. Poissons Ratio2. Poissons Ratio (())
3. S!a" Modulus3. S!a" Modulus (#)(#)
$. %ul& Modulus$. %ul& Modulus (')(')
-
7/23/2019 Elastic-Constants-ketul.ppt
4/21
1. Modulus o Elasticity E(*oun+s Modulus)
= E
Linear-elastic
E
F
Fsimpletension
test
Units:E: [GPa]
-
7/23/2019 Elastic-Constants-ketul.ppt
5/21
Slo,! o st"!ss st"ain ,lot (-ic isSlo,! o st"!ss st"ain ,lot (-ic is
,"o,o"tional to t! !lastic odulus),"o,o"tional to t! !lastic odulus)
d!,!nds on /ond st"!n+t o !tald!,!nds on /ond st"!n+t o !tal
Adapted from Fig. 6.7,
Callister 7e.
E0
-
7/23/2019 Elastic-Constants-ketul.ppt
6/21
2.2. Poissons "atioPoissons "atio
Units:: dimensionless
T
L
F
Fsimpletension
test
! is t"e ratio of
trans#erse contraction strain
to longit$dinal e%tension
strain in t"e direction of
stretc"ing force.
&it"er trans#erse strain or
longit$dional strain is
negati#e, 'is positi#eT
=
LT : Transverse Strain
L : Longitudional Strain
-
7/23/2019 Elastic-Constants-ketul.ppt
7/21
Virtually all common materialsVirtually all common materials
undergo a transverse contractionundergo a transverse contraction
when stretched in one direction and awhen stretched in one direction and a
transverse expansion whentransverse expansion when
compressed.compressed.
IIn an isotropic material the allowablen an isotropic material the allowable(theoretical)(theoretical) range of Poissons ratio isrange of Poissons ratio is
from !".# to $#.%& basedfrom !".# to $#.%& based onon the theorythe theory
of elasticityof elasticity..metals: ( ).**
ceramics:( ).+polmers:( ).)
-
7/23/2019 Elastic-Constants-ketul.ppt
8/21
G
= G
3. S!a" Modulus #3. S!a" Modulus #
simple
torsion
test
M
M
Units:G: [GPa]
-
7/23/2019 Elastic-Constants-ketul.ppt
9/21
$. %ul& Modulus '$. %ul& Modulus '
avg= KV
Vo avg
V
KVo
P
P
P
Initial Volume 'V#
Volume Change' V
Units:K: [GPa]
avgis the average
of three stressesapplied alongthree principaldirections.
-
7/23/2019 Elastic-Constants-ketul.ppt
10/21
= E
= G
avg=
KV
Vo
tresses
trains
ElasticConstants
*ormal
hear
Volumetric
-
7/23/2019 Elastic-Constants-ketul.ppt
11/21
Ea,l!Ea,l!4niaial Loadin+ o a P"isatic4niaial Loadin+ o a P"isatic
S,!ci!nS,!ci!n
At!"%!o"!
"#cm
"#
cm
"#cm
"#.+cm
,., cm
,., cm
5!t!"i
n! Eand
P'"###-gf
-
7/23/2019 Elastic-Constants-ketul.ppt
12/21
10cm
10cm
l/2=0.2cm
d/2=0.05cm
1000 kgf
P=1000 kgf
P=1000kgf /= 10*10
100
0=10kgf/cm2
E=
=
100.0
4
= 250 kgf/cm2
long=
ll0
= =0.04
0.410
lat=dd0 = = -0.01-0.110
= --0.010.0
4
=
0.25
-
7/23/2019 Elastic-Constants-ketul.ppt
13/21
For an isotroic mat!rial t"! str!ss-For an isotroic mat!rial t"! str!ss-
strain r!lations ar! as follo#s$strain r!lations ar! as follo#s$
-
7/23/2019 Elastic-Constants-ketul.ppt
14/21
RELATION %67 ' 8 ERELATION %67 ' 8 E
%onsid!r a c&'! #it" a &nit (ol&m!%onsid!r a c&'! #it" a &nit (ol&m!
1
1
1
)
%
+
ca&s!s an !longation in t"!dir!ction %) and contraction in t"!dir!ctions + , %.
"! n!# dim!nsions of t"! c&'!is $
%) dir!ction is 1
% dir!ction is 1-
+ dir!ction is 1-
-
7/23/2019 Elastic-Constants-ketul.ppt
15/21
00= 1= 1
Final (ol&m!Final (ol&m! fof t"! c&'! is no#$of t"! c&'! is no#$
111-1-1-1-==111-21-23322
22
= 1 - 2= 1 - 2332222-2-2223322
= 1 = 1 --22--22223322223322
is small 2, ar! small!r and can '!n!gl!ct!d.
f= 1 - 2 / = f - 0 = 1-2
6f !7&al t!nsil! str!ss!s ar! ali!d to!ac" of t"! ot"!r t#o airs of fac!s oft"! c&'! t"an t"! total c"ang! in (ol&m!#ill '! $
-
7/23/2019 Elastic-Constants-ketul.ppt
16/21
8
9 =/
=
1-2
=
1-2
E
1-2
9 =E
1-2
V ' /0 ("!12) '0 ("!12) 0 ("!12) 0 ("!12)$ $
=a(g
/0
-
7/23/2019 Elastic-Constants-ketul.ppt
17/21
:or!o(!r t"! r!lation:or!o(!r t"! r!lation'!t#!!n ; and E is $'!t#!!n ; and E is $
;
=
E
21
"! r!lation"! r!lation
'!t#!!n ; E and 9'!t#!!n ; E and 9
is $is $
E
1 1=
1
-
7/23/2019 Elastic-Constants-ketul.ppt
18/21
For (!r soft mat!rials s&c" as ast!sFor (!r soft mat!rials s&c" as ast!s
g!ls &tti!s 9 is (!r larg!g!ls &tti!s 9 is (!r larg!
>ot! t"at as 9>ot! t"at as 9 / 0 // 0 / //). 1 & 2 *G). 1 & 2 *G
3f 4 is #er large /3f 4 is #er large /55))2 )2 ) 889o #ol$me9o #ol$me
c"angec"ange
For mat!rials lik! m!tals ?'!rs , c!rtainFor mat!rials lik! m!tals ?'!rs , c!rtain
lastics 9 m&st '! consid!r!d.lastics 9 m&st '! consid!r!d.
-
7/23/2019 Elastic-Constants-ketul.ppt
19/21
:od&l&s of Elasticit $:od&l&s of Elasticit $
@ig" in co(al!nt como&nds s&c" as@ig" in co(al!nt como&nds s&c" as
diamonddiamond Ao#!r in m!tallic and ionic crstalsAo#!r in m!tallic and ionic crstals
Ao#!st in mol!c&lar amor"o&s solidsAo#!st in mol!c&lar amor"o&s solids
s&c" as lastics and r&''!r.s&c" as lastics and r&''!r.
-
7/23/2019 Elastic-Constants-ketul.ppt
20/21
Elastic Constants o So!Elastic Constants o So!
Mat!"ialsMat!"ialsEsiB10EsiB10CC;Pa;Pa
;siB10;siB10CC;Pa;Pa --
Cast IronCast Iron 1C1C
110110 D.4D.4 5050 0.1D0.1D
SteelSteel 00205205
11.11. 00 0.2C0.2C
AluminuAluminu
mm 1010 D0D0 .C.C 2525 0.0.
ConcreteConcrete 1.5-5.51.5-5.5 10-10-4040
0.C2-2.00.C2-2.0 4-4-1515
0.20.2
WoodWood Aong 1.1Aong 1.1
1212
0.110.11
0.D0.D
-
7/23/2019 Elastic-Constants-ketul.ppt
21/21
Tan& *ouTan& *ou
top related