Mokashi Imrankhan Sherkhan Guided by: M S Bobji Seminar on.
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Transcript of Mokashi Imrankhan Sherkhan Guided by: M S Bobji Seminar on.
Mokashi Imrankhan Sherkhan
Guided by: M S Bobji
Seminar on
Importance of Fracture Importance of Fracture Mechanics in TribologyMechanics in Tribology
WearErosionSurface Formation
Fracture Mechanics approachFracture Mechanics approach
Energy Based : Energy release rate(G) and J integral
Stress Based : Stress intensity factor (K)
Displacement Based : Crack tip opening displacement (CTOD)
Modes of Crack PropagationModes of Crack Propagation
Energy ApproachEnergy Approach
+ +
xo
BondEnergy
CohesiveForce
l
EquilibriumDistance xo
Pot
ent
ialE
nerg
y
Distance
Repulsion
Attraction
Tension
Compression
App
lied
For
ce
k
BondEnergy
Distance
Griffith’s Energy balance approachGriffith’s Energy balance approach
•First documented paper on fracture (1920) Considered as father of Fracture Mechanics
Energy Approach Cont…Energy Approach Cont…
Surface energy Es = 2(2a B ᵞ)
ᵞ -Surface energy per unit areaB-Thickness of plate
Energy Approach Cont..Energy Approach Cont..
Total PE of Body with crack
U = UE – Uwork + US
Strain EnergySystem always try to minimize its PE
Thick plate is more Thick plate is more resistant to fracture or resistant to fracture or thin?thin?
J IntegralJ Integral J Integral over a closed loop = 0 Path independent
Displacement Displacement ApproachApproach
From Hooke’s law, displacement field can be obtained as
2I
2I
2(1 ) r 1u K cos sin
E 2 2 2 2
2(1 ) r 1v K sin cos
E 2 2 2 2
where u, v = displacements in x, y directions
(3 4 ) for plane stress problems
3 for plane strain problems
1
Displacement ApproachDisplacement Approach
Stress ApproachStress Approach
Stress Intensity FactorStress Intensity Factor
for infinite plate
for other geometry
can be obtained from : 1. handbook solution
2. approximate method
3. numerical method
aK
aK
Stress near crack tipStress near crack tip
]sinsin[cos2
3
21
22
r
Kx
]sinsin[cos2
3
21
22
r
Ky
2
3
222
coscossinr
Kxy
)( ijij fr
a
2
Plastic zone size
x
y
plane strain
plane stress
Plastic Zone ShapesPlastic Zone Shapes
Mixed LoadingMixed Loading
13
III
III2
II
II1
I
I
n
c
n
c
n
c K
K
K
K
K
K
where KIc, KIIc, KIIIc, ni (i = 1, 2, 3) – parameters that characterize material near the concentrator,
determined experimentally
in
c
in
c K
K
K
K
II
II
I
I = 1
in
c
in
c K
K
K
K
III
III
II
II = 1
Cont…Cont…
Diagrams of the deformed body limiting-equilibrium state the conditions of mixed (I+II), (I+III) fracture mechanisms
Curve 1 – according to formula (1) when KIII = 0 and ni = 4, curve 2
according formula (1) when KIII = 0
and ni = 2
Curves 1 and 2 are plotted according to formula (1) when ni = 4 and ni =2
correspondingly
1III
III
II
II
I
I
iii n
c
n
c
n
c K
K
K
K
K
K(1)
FATIGUE FRACTUREFATIGUE FRACTURE
Every Coin has two Every Coin has two sides…sides…
Useful Fracture Metal cutting Rock cutting in Mining “Biting” of candies
Unwanted Fracture Fracture of Liberty ships in World
war II Fracture of wheels, axles and rails
Fracture Avoidance with Fracture Avoidance with Proper Use of MaterialProper Use of Material
Pyramid of Egypt Schematic Roman Bridge Design
• The primary construction material prior to 19th were timber, brick and mortar
• Arch shape producing compressive stress stone have high compressive strength
Fracture Avoidance with Fracture Avoidance with Proper Use of Material (cont’)Proper Use of Material (cont’)
• Roof spans and windows were arched to maintain compressive loading
REFERENCESREFERENCES
A book on “Fracture Mechanics” by Prashant Kumar“Introduction to Fracture Mechanics” book by C. H. Wang
Finite Element AnalysisFinite Element Analysis
Stress analysis near crack Quarter point element
J- integral