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STEEL BALLS
Reporter: Ali Farajollahi
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IYPT 2010 Austria, I. R. Iran
The Question
• Colliding two large steel balls with
a thin sheet of material (e.g. paper)
in between may "burn" a hole in
the sheet.
• Investigate this effect for various
materials.
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IYPT 2010 Austria, I. R. Iran
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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IYPT 2010 Austria, I. R. Iran
Initial Observations
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IYPT 2010 Austria, I. R. Iran
Initial Observation
Burning
Waves
Radial rupture
Deformation
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IYPT 2010 Austria, I. R. Iran
Initial Observation
Tissue
Aluminum
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Styrofoam
IYPT 2010 Austria, I. R. Iran
Burning (Chemical) or
Rupture (Physical)?
– Temperature rises because of sheet
deflection
– 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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IYPT 2010 Austria, I. R. Iran
Material Strength Background
• Stress & Strain
F
 
A
l
 
l
F
Δl
l
• Poisson’s Ratio
x
 
y
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x
y
F
IYPT 2010 Austria, I. R. Iran
Static Loaded Balls
• To be able to simulate the
collision…
• Finding the deformation of two
steel balls under a specific load
F
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F
IYPT 2010 Austria, I. R. Iran
Static Loaded Balls
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IYPT 2010 Austria, I. R. Iran
Static Loaded Balls
• According to references, Contact
mechanics and Hertz theory, the
force and shape of two steel balls
can be calculated as follows:
r : Distance between a plot and center of contact
δ : Maximum length of deformation
α : Radius of contact
R : Half of the radius of the balls
E* : Young’s modulus
P0 : Pressure in the middle of contact
F : Force
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IYPT 2010 Austria, I. R. Iran
Dynamic collision simulation
• Simulating the system considering
to be quasi-static
– F will be calculated as explained
F  x
 2 a
m t
2
– Euler method was used
Updating
time
Updating
positions
Calculating
forces
Finding
acceleration
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IYPT 2010 Austria, I. R. Iran
Different Strains
• By assuming that the thickness of
sheet is negligible, we are able to
find different strains in the sheet.
F
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F
IYPT 2010 Austria, I. R. Iran
Different Strains
After collision
Before collision
θ
Before Collision
r
r
r+Δr
Δr
Maximum Collision
z
x
Top
Side
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IYPT 2010 Austria, I. R. Iran
Tensile Stress
r
r+Δr
P0 : Initial perimeter
P1 : Perimeter after collision
r : Initial radius
r+Δr : Increased radius
εx : Deformation through x-Axis
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IYPT 2010 Austria, I. R. Iran
Two Kinds of Behaviors
• Materials may rip because of
tensile or pressing stress
Δr
– σz: Pressing
– σy: Tensile
y 

dx
r

r


dr
z

r


dr
z

r
x
 
z
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IYPT 2010 Austria, I. R. Iran
Two Kinds of Behaviors
Pressing stress
m/s
m/s
Critical Pressure
m/s
m/s
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IYPT 2010 Austria, I. R. Iran
Two Kinds of Behaviors
Tensile stress
m/s
m/s
σy
m/s
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Critical Pressure
IYPT 2010 Austria, I. R. Iran
Experimental Setup
Holding the balls
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IYPT 2010 Austria, I. R. Iran
Experimental Setup
Using two electronic magnets to hold and release the balls on time
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IYPT 2010 Austria, I. R. Iran
Experiments
• Changing the release height,
calculating the velocity
• Scanning the holes, developing a
program with MATLAB to calculate
the area and radius of holes
• Compare with theory
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IYPT 2010 Austria, I. R. Iran
Experiments
• Paper, thickness of 0.2mm
• Released from different heights
5cm
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10cm
15cm
20cm
30cm
40cm
IYPT 2010 Austria, I. R. Iran
Experiments
0.7
0.6
Hole Radius (cm)
0.5
0.4
0.3
0.2
0.1
0
0
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5
10
15
20
25
Release Height (cm)
30
35
40
IYPT 2010 Austria, I. R. Iran
45
Experiments
• Paper thickness 0.1 mm
10cm
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15cm
20cm
30cm
40cm
IYPT 2010 Austria, I. R. Iran
Experiments
Release Height (cm)
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IYPT 2010 Austria, I. R. Iran
Experiments
• Balsa Wood 2.5mm Thick
10cm
15cm
20cm
35cm
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25cm
30cm
40cm
IYPT 2010 Austria, I. R. Iran
Experiments
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IYPT 2010 Austria, I. R. Iran
Comparison with Theory
• There are 2 main Causes,
– Pressure Stress
– Tensile Stress
• Calibrating the Critical Stress in
Both Causes
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IYPT 2010 Austria, I. R. Iran
Theory Comparison
• Paper 0.2 mm thick
• The Maximum contact area is smaller than the
experiments radius
Velocity (m/s)
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IYPT 2010 Austria, I. R. Iran
Theory Comparison
• Paper
• Tensile stress radius
Velocity (m/s)
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IYPT 2010 Austria, I. R. Iran
Theory Comparison
• Balsa Wood
• Pressing Stress Radius
Velocity (m/s)
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IYPT 2010 Austria, I. R. Iran
Theory Comparison
• Balsa Wood
• Tensile stress radius
Velocity (m/s)
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IYPT 2010 Austria, I. R. Iran
Conclusion
• Most of the phenomena happens
because of stresses in the sheet
• Burning is negligible in describing
the phenomena, although it exists.
• Materials are different in the
stresses they stand
– Paper is weak in tensile stress
– Balsa wood is weak in pressing stress
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IYPT 2010 Austria, I. R. Iran
References
• Mechanics of Materials, Egor P. Popov, 2nd
Edition, 1976.
• Contact mechanics, K.L. Johnson, Cambridge
University press, 1985.
• Halliday Fundamentals of physics, HallidayResnic-Walker, 1945.
• A First Course in Numerical Analysis, Anthony
Ralston-Philip Rabinowitz, 2nd Edition, 2001.
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IYPT 2010 Austria, I. R. Iran
IYPT 2010 Austria,
IYPT
National
2010 Austria,
team of I. R. Iran

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