Summary
Summary Mechanical Properties of Matter
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- Institution
Handwritten cheat sheet for Mechanical Properties of Matter by JEE 2020, GATE, and CSIR topper.
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Mechanical properties of matexlongtudnal sreas (r) =AFE
|longihdnal stain (e)= 4L
Stress has same dimension ag oregsure andstun is
dimensionJess
oElastic doomaton:- Stesg and shain oxe popononal
ocach othex. dn oashz defoatio ) he cbjeet regains
is oniginal shape aftex he defung tte is remaed
T= Ye
This is knetwn_ag Hoche's Ao A
.y is he modulus of elashsty a Young's Modulus
.The modulue_mag be thougkt of as a materials
eskance to ehstic defoanaton
There ae Some matonale For cohich the initial stness
shain Cuse in not- ineax
he modulus is pxopchonal to the inbratzmic foce -
3epesnin cuve
"aith incKease in temp. the moduus decssnseg for
all but some subbes maBenals
olpastic defornation i- Shea2 js no mors propional
Jo shrain & permonent defoomotion
happens
Sain
, Astaught line is corstucted Il o the eaghc poaton of
he cuxve at oon urits in the strain aris The i stoess
coregponding to he intessechon of Hhis line &the cuve
1s19
defnedae te ield strength (og)
.UTS:- The ultimate tensile strength Curs) is the. stress a
he max, on he stresg- stoin cune.
Jhe matenal fractureg a much Jessor stess han
WTS
"Rrittle-A rmatexial ahich erpenencez verny itle ox
plagic deoatnation_upon fractuse. o t 9 Duchle
Brt
B
* Resilienee tis the capacaty afa
ooterial to absorb ene~ay whep stain
itt is defostmed eloshcaly he energy oabsexbed s stoed
ag elaghie potential enegy
.D=YA AL2
2
U
=l stresg x stain x volume
2 volus
U=Lx Shain'y
2.
densty
UL(stesgJ
2
Toushnesgi-tik the measuNS cf
of the abilite of a
noteial to absob enegy p to factue. s te ase
undex the sheee- stain curve upto pt. of Facte
, " dn situahons cwhere shess in the rod vaies alang
bewsect
the length of he xod the follecng may
Jshea) de Blential Gnexgy-A Jstsea)'dc
Elogakion AY 2y
tSheas
LA Face is applied ICtangential)to Area A
laithin eashe imit, the raho of sheaing stress to
sheazing strin ik called modaba af aiidiy
F= sheaing staess
e' Sheaaing strain
L
sheaming staain =Q t
Fxed D
FL
AR Ax
do this cage the body changes shape butis
volume xenains constatt.Only solids can erhibit a
A Toxsion:- t is a vasiaton ot pue sheas whein
suctue is teuisted
fied
Jength ' adius r ' fixed at Lend
Are AA'z l
angle of sheas Eangle of tust
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