SOLID-SOLID IMPACT ANALYSIS
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Transcript SOLID-SOLID IMPACT ANALYSIS
Seminar on
Mokashi Imrankhan Sherkhan
Guided by: M S Bobji
Importance of Fracture Mechanics in
Tribology
Wear
Erosion
Surface Formation
Fracture 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 Propagation
Energy Approach
Potential Energy
Repulsion
Distance
Bond
Energy
Attraction
Equilibrium
Distance xo
Tension
Applied Force
Bond
Energy
l
k
Compression
+
+
xo
Cohesive
Force
Distance
Griffith’s Energy balance approach
•First documented paper on fracture
(1920) Considered as father of
Fracture Mechanics
Energy Approach Cont…
Surface energy Es = 2(2a B ᵞ)
ᵞ -Surface energy per unit area
B-Thickness of plate
Energy Approach Cont..
Total PE of Body with crack
U = UE – Uwork + US
Strain Energy
System always try to minimize its PE
Thick plate is more resistant
to fracture or thin?
J Integral
J Integral over a closed loop = 0
Path independent
Displacement Approach
Displacement Approach
From Hooke’s law, displacement field can be obtained as
u
2(1 )
r
1
KI
cos
sin 2
E
2
2 2
2
v
2(1 )
r
1
KI
sin
cos2
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
Stress Approach
Stress Intensity Factor
K a
for
K a
for
can be obtained from :
infinite plate
other geometry
1. handbook solution
2. approximate method
3. numerical method
Stress near crack tip
3
cos [1 sin sin ]
2
2
2
2r
x
K
y
K
xy
K
3
cos [1 sin sin ]
2
2
2
2r
3
sin cos cos
2
2
2
2r
ij
a
f ij ( )
2r
Plastic zone size
Plastic Zone Shapes
y
plane strain
x
plane stress
Mixed Loading
KI
K Ic
n1
K II
K IIc
n2
K III
K IIIc
n3
1
where KIc, KIIc, KIIIc, ni (i = 1, 2, 3) – parameters that characterize material near the concentrator,
determined experimentally
KI
K Ic
ni
K II = 1
K IIc
ni
ni
K II
K IIc
ni
K III
= 1
K IIIc
Cont…
KI
K Ic
ni
K
II
K IIc
ni
K
III
K IIIc
ni
1
(1)
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
FATIGUE FRACTURE
Every Coin has two 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 Proper
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 Proper Use
of Material (cont’)
•
Roof spans and windows were arched to maintain compressive loading
REFERENCES
A
book on “Fracture Mechanics” by Prashant
Kumar
“Introduction to Fracture Mechanics” book by C. H.
Wang
Finite Element Analysis
Stress analysis near crack
Quarter point element
J- integral