STEEL BALLS Reporter Ali Farajollahi 1 IYPT 2010

STEEL BALLS 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 Burning Waves Radial rupture Deformation 5 IYPT 2010 Austria, I. R. Iran

Initial Observation Tissue Aluminum 6 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 F Δl l • Poisson’s Ratio x 8 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 9 F 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: 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 P 0 : Pressure in the middle of contact F : Force 11 IYPT 2010 Austria, I. R. Iran

Dynamic collision simulation • Simulating the system considering to be quasi-static – F will be calculated as explained Updating time – Euler method was used Updating positions Calculating forces Finding acceleration 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. F 13 F IYPT 2010 Austria, I. R. Iran

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

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

Two Kinds of Behaviors • Materials may rip because of tensile or pressing stress Δr – σz: Pressing – σy: Tensile 16 IYPT 2010 Austria, I. R. Iran

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

Two Kinds of Behaviors Tensile stress m/s σy m/s 18 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. 2 mm • Released from different heights 5 cm 22 10 cm 15 cm 20 cm 30 cm 40 cm 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 23 5 10 15 20 25 Release Height (cm) 30 35 40 IYPT 2010 Austria, I. R. Iran 45

Experiments • Paper thickness 0. 1 mm 10 cm 24 15 cm 20 cm 30 cm 40 cm IYPT 2010 Austria, I. R. Iran

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

Experiments • Balsa Wood 2. 5 mm Thick 10 cm 15 cm 20 cm 35 cm 26 25 cm 30 cm 40 cm 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 Velocity (m/s) 29 IYPT 2010 Austria, I. R. Iran

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

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

Theory Comparison • Balsa Wood • Tensile stress radius Velocity (m/s) 32 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, 2 nd 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, 2 nd Edition, 2001. 34 IYPT 2010 Austria, I. R. Iran

Thank you for your attention IYPT 2010 Austria, IYPT National 2010 Austria, team of I. R. Iran