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IYPT 2010 Austria, I. R. Iran
IYPT 2010 Austria, I. R. Iran
STEEL BALLS
Reporter: Ali Farajollahi
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The Question
Colliding two large steel balls witha thin sheet of material (e.g. paper)in between may "burn" a hole inthe sheet.
Investigate this effect for variousmaterials.
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Contents Initial Observations Theoretical background
Burning or Physical Rupture? Material Background
Theory: The balls Static loaded balls Balls collision simulation
Theory: The sheet Different strains
Experiments
Setup Comparison with Theory Different Materials & Behaviors
Conclusion
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Initial Observations
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Initial Observation
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Deformation
Waves
Radial rupture
Burning
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Initial Observation
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Aluminum
Tissue
Styrofoam
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Burning (Chemical) orRupture (Physical)?
Temperature rises because of sheetdeflection
Not enough energy to start flaming Not enough Oxygen in the contact
point
Burning occurs incompletely, but
the burnt amount is too low Main Happening: Physical Rupture
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Material Strength Background
Stress & Strain
Poissons Ratio
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l l
A
F
F
F
l
l
x y y
x
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Static Loaded Balls To be able to simulate the
collision Finding the deformation of two
steel balls under a specific load
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FF
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Static Loaded Balls
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Static Loaded Balls According to references, Contact
mechanics and Hertz theory, theforce and shape of two steel ballscan be calculated as follows:
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r : Distance between a plot and center of contact : Maximum length of deformation : Radius of contact R : Half of the radius of the ballsE* : Youngs modulus
P 0 : Pressure in the middle of contactF : Force
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Dynamic collision simulation Simulating the system considering
to be quasi-static F will be calculated as explained
Euler method was used
Updatingtime
Calculatingforces
Findingacceleration
Updating positions
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at
x
m
F 2
2
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Different Strains By assuming that the thickness of
sheet is negligible, we are able tofind different strains in the sheet.
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FF
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Different Strains
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r
Top
r
r+ r
After collision
Before collision
r
Before Collision
Side
x
zMaximum Collision
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Tensile Stress
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r
r+ r
P 0 : Initial perimeterP 1 : Perimeter after collisionr : Initial radiusr+ r : Increased radiusx : Deformation through x-Axis
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Two Kinds of Behaviors Materials may rip because of
tensile or pressing stress
z: Pressing
y: Tensile
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r
dr
r
dr
r
dx z z r y
r
z
x
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Two Kinds of Behaviors
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Critical Pressure
Pressing stress
m/sm/s
m/s
m/s
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Two Kinds of Behaviors
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y
m/s
m/s
m/s
Tensile stress
Critical Pressure
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Experimental Setup
Holding the balls
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Experimental Setup
Using two electronic magnets to hold and release the balls on time
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Experiments Changing the release height,
calculating the velocity
Scanning the holes, developing a
program with MATLAB to calculatethe area and radius of holes
Compare with theory
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Experiments Paper, thickness of 0.2mm
Released from different heights
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5cm 10cm 15cm 20cm 40cm30cm
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Experiments
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0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0 5 10 15 20 25 30 35 40 45
H o
l e R a
d i u s
( c m
)
Release Height (cm)
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Experiments
Paper thickness 0.1 mm
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10cm 15cm 20cm 30cm 40cm
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Experiments
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Release Height (cm)
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Experiments
Balsa Wood 2.5mm Thick
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10cm 15cm 20cm 30cm
40cm
25cm
35cm
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Experiments
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Comparison with Theory
There are 2 main Causes, Pressure Stress Tensile Stress
Calibrating the Critical Stress inBoth Causes
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Theory Comparison Paper 0.2 mm thick The Maximum contact area is smaller than the
experiments radius
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Velocity (m/s)
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Theory Comparison Paper
Tensile stress radius
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Velocity (m/s)
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Theory Comparison Balsa Wood
Pressing Stress Radius
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Velocity (m/s)
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Theory Comparison Balsa Wood
Tensile stress radius
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Velocity (m/s)
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Conclusion Most of the phenomena happens
because of stresses in the sheet
Burning is negligible in describingthe phenomena, although it exists.
Materials are different in thestresses they stand Paper is weak in tensile stress Balsa wood is weak in pressing stress
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References Mechanics of Materials, Egor P. Popov, 2nd
Edition, 1976. Contact mechanics, K.L. Johnson, Cambridge
University press, 1985. Halliday Fundamentals of physics, Halliday-
Resnic-Walker, 1945. A First Course in Numerical Analysis, Anthony
Ralston-Philip Rabinowitz, 2nd Edition, 2001.
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