IYPT 2010 Austria, I. R. Iran Reporter: Ali Farajollahi 1

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. 2

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 3

IYPT 2010 Austria, I. R. Iran Initial Observations 4

IYPT 2010 Austria, I. R. Iran Initial Observation 5 Deformation Waves Radial rupture Burning

IYPT 2010 Austria, I. R. Iran Initial Observation 6 Aluminum Tissue 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 7

IYPT 2010 Austria, I. R. Iran Material Strength Background Stress & Strain Poissons Ratio 8 F F l ΔlΔl x y

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 9 FF

IYPT 2010 Austria, I. R. Iran Static Loaded Balls 10

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: 11 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* : Youngs modulus P 0 : Pressure in the middle of contact F : Force

IYPT 2010 Austria, I. R. Iran Dynamic collision simulation Simulating the system considering to be quasi-static –F will be calculated as explained –Euler method was used Updating time Calculating forces Finding acceleration Updating positions 12

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. 13 FF

IYPT 2010 Austria, I. R. Iran Different Strains 14 r Top r r+Δr After collision Before collision θ ΔrΔr Before Collision Side x z Maximum Collision

IYPT 2010 Austria, I. R. Iran Tensile Stress 15 r r+Δr P 0 : Initial perimeter P 1 : Perimeter after collision r : Initial radius r+Δr : Increased radius ε x : Deformation through x-Axis

IYPT 2010 Austria, I. R. Iran Two Kinds of Behaviors Materials may rip because of tensile or pressing stress –σ z : Pressing –σ y : Tensile 16 ΔrΔr

IYPT 2010 Austria, I. R. Iran Two Kinds of Behaviors 17 Critical Pressure Pressing stress m/s

IYPT 2010 Austria, I. R. Iran Two Kinds of Behaviors 18 σyσy m/s Tensile stress Critical Pressure

IYPT 2010 Austria, I. R. Iran Experimental Setup Holding the balls 19

IYPT 2010 Austria, I. R. Iran Experimental Setup Using two electronic magnets to hold and release the balls on time 20

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 21

IYPT 2010 Austria, I. R. Iran Experiments Paper, thickness of 0.2mm Released from different heights 22 5cm10cm 15cm20cm40cm30cm

IYPT 2010 Austria, I. R. Iran Experiments 23

IYPT 2010 Austria, I. R. Iran Experiments Paper thickness 0.1 mm 24 10cm15cm20cm30cm40cm

IYPT 2010 Austria, I. R. Iran Experiments 25 Release Height (cm)

IYPT 2010 Austria, I. R. Iran Experiments Balsa Wood 2.5mm Thick 26 10cm15cm20cm30cm 40cm 25cm 35cm

IYPT 2010 Austria, I. R. Iran Experiments 27

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 28

IYPT 2010 Austria, I. R. Iran Theory Comparison Paper 0.2 mm thick The Maximum contact area is smaller than the experiments radius 29 Velocity (m/s)

IYPT 2010 Austria, I. R. Iran Theory Comparison Paper Tensile stress radius 30 Velocity (m/s)

IYPT 2010 Austria, I. R. Iran Theory Comparison Balsa Wood Pressing Stress Radius 31 Velocity (m/s)

IYPT 2010 Austria, I. R. Iran Theory Comparison Balsa Wood Tensile stress radius 32 Velocity (m/s)

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 33

IYPT 2010 Austria, I. R. Iran References Mechanics of Materials, Egor P. Popov, 2nd Edition, Contact mechanics, K.L. Johnson, Cambridge University press, Halliday Fundamentals of physics, Halliday- Resnic-Walker, A First Course in Numerical Analysis, Anthony Ralston-Philip Rabinowitz, 2nd Edition,

IYPT 2010 Austria, I. R. IranIYPT 2010 Austria, National team of I. R. Iran