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Steel balls

3. Steel balls. Reporter: Ali Farajollahi. 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. Contents. Initial Observations Theoretical background

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Steel balls

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  1. 3 Steel balls Reporter: Ali Farajollahi

  2. 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.

  3. 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

  4. Initial Observations

  5. Initial Observation Burning Waves Radial rupture Deformation

  6. Initial Observation Tissue Aluminum Styrofoam

  7. 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

  8. Material Strength Background • Stress & Strain • Poisson’s Ratio F Δl l x y F

  9. Static Loaded Balls • To be able to simulate the collision… • Finding the deformation of two steel balls under a specific load F F

  10. Static Loaded Balls

  11. 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

  12. Dynamic collision simulation • Simulating the system considering to be quasi-static • F will be calculated as explained • Euler method was used

  13. Different Strains • By assuming that the thickness of sheet is negligible, we are able to find different strains in the sheet. F F

  14. Different Strains Before Collision After collision θ r Before collision r r+Δr Δr Maximum Collision z Top x Side

  15. Tensile Stress r r+Δr P0 : Initial perimeter P1 : Perimeter after collision r : Initial radius r+Δr : Increased radius εx : Deformation through x-Axis

  16. Two Kinds of Behaviors • Materials may rip because of tensile or pressing stress • σz: Pressing • σy: Tensile Δr

  17. Two Kinds of Behaviors Pressing stress m/s Critical Pressure m/s m/s m/s

  18. Two Kinds of Behaviors Tensile stress m/s m/s σy m/s Critical Pressure

  19. Experimental Setup Holding the balls

  20. Experimental Setup Using two electronic magnets to hold and release the balls on time

  21. 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

  22. Experiments • Paper, thickness of 0.2mm • Released from different heights 15cm 20cm 30cm 40cm 5cm 10cm

  23. Experiments

  24. Experiments • Paper thickness 0.1 mm 10cm 15cm 20cm 30cm 40cm

  25. Experiments Release Height (cm)

  26. Experiments • Balsa Wood 2.5mm Thick 10cm 15cm 20cm 25cm 30cm 35cm 40cm

  27. Experiments

  28. Comparison with Theory • There are 2 main Causes, • Pressure Stress • Tensile Stress • Calibrating the Critical Stress in Both Causes

  29. Theory Comparison • Paper 0.2 mm thick • The Maximum contact area is smaller than the experiments radius Pressing Stress Velocity (m/s)

  30. Theory Comparison • Paper • Tensile stress radius Tensile Stress Velocity (m/s)

  31. Theory Comparison • Balsa Wood • Pressing Stress Radius Pressing Stress Velocity (m/s)

  32. Theory Comparison • Balsa Wood • Tensile stress radius Tensile Stress Velocity (m/s)

  33. 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

  34. 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.

  35. Thank you for your attention

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