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Understand foam porosity

  1. Jun 3, 2015 #1
    1. The problem statement, all variables and given/known data
    This should be a pretty simple question but I can't find a straight answer in the literature. I want to simulate a 3D model of a metal foam by starting with an aluminum block and filling it with randomly placed spherical holes of constant volume. The foam should have a porosity of 20 ppi (pores per inch) and a volume ratio of 25% aluminum. How many pores should there be, and what are their sizes?

    2. Relevant equations
    20 pores per inch
    25% aluminum, 75% void by volume

    3. The attempt at a solution
    I'm not clear on precisely what "ppi" means. Does 20 ppi imply that a 1 inch cube of aluminum should contain 20^3 = 8000 pores? And that each pore should have a volume of 0.75/8000 = 0.00009375 in^3? This seems pretty obvious but I want to make sure before I proceed. Thank you for your help!
     
  2. jcsd
  3. Jun 5, 2015 #2

    CWatters

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    Assume the pores are spherical. Work out what the radius of each pore would be. Can you put them on a 1/20" pitch/grid without them intersecting each other :-)

    I'm afraid I'm not familiar with packing theories.
     
    Last edited: Jun 5, 2015
  4. Jun 5, 2015 #3

    CWatters

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    Google suggests Cubic Close packing can achieve 74% packing density but I'm not quite sure how you calculate the PPI in that configuration..

    http://mathworld.wolfram.com/SpherePacking.html
     
  5. Jun 5, 2015 #4
    The pores in a foam are allowed to overlap with each other. This isn't a sphere packing problem though. This is a question of the expected value of the volume these pores will occupy.
     
  6. Jun 5, 2015 #5

    NascentOxygen

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    Yes, that is how I see it. As far as averages go, it should make no difference whether the pores are neatly arrayed in equi-spaced rows and columns, or randomly positioned. So, take the easy route, consider them all neatly arrayed in 3D ranks. :smile:

    Work out the radius each would have if it were spherical, and compare this dimension with their centre-to-centre spacing to see whether the model seems realistic for your application.
     
  7. Jun 6, 2015 #6

    CWatters

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    If the pores overlap each other won't the volume ratio be incorrect. (eg some of the volume is double counted).

    PS I believe they do overlap.
     
    Last edited: Jun 6, 2015
  8. Jun 6, 2015 #7

    NascentOxygen

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    Will the expected overlap be likely to alter the prescribed composition of 25% by more than ±1 sig fig?
     
  9. Jun 8, 2015 #8

    CWatters

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    If I did the sums right the volume of a single pore after deducting the 6 overlaps is

    8.86 * 10^-5 cubic inches compared to
    9.38 * 10^-5 calculated by ignoring the overlap

    8.86 * 10^-5 * 8000 = 0.71

    eg 71% rather than the 75% requested.
     
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