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Determination elastic constants wit ultrasonic in bulk metallic glasses

  1. Jul 21, 2012 #1
    HAllo everyone,
    I had a problem with the measurement of young modulus and shear modulus with ultrasonic measurements( pulse-echo overlap technique)

    For my metallic glasses rods (amorphous material) I used these formula for the calculation:

    1. determination Shear modulus: G= ro * v trans^2
    where ro= density of material and v trans = transversale vawe packet velocity= 2*D * nu trans
    where D= height of the rods and nu trans= the found transversale frequency.

    2 for Young modulus the formula that I found was quite complex and say:
    first I calculated the longitudinale velocity with the same formula as for the transversale:
    v long = 2*D*nu long --> and here I'm not sure of this formula !!

    Then I used the following two equations:
    nu (= poisson ratio) = E/2*G -1 and v long = E(1- nu)/ro(1-nu-2*nu^2)
    to finally come to the following formula for the young modulus:
    E= ((2-3*v long ^2 * ro)/2*G)/((-v long ^2*ro/2*G^2) + 1/(2*G)

    Is it this formula correct? or maybe have you another for amorphous rods?!

    Thank in advance

  2. jcsd
  3. Aug 24, 2012 #2
    Longitudinal waves, still use
    but if the rod's radius is small versus the (quarter) wavelength, E'=E
    andif the rod is broad versus the wavelength, E'=E/[1-2μ2]
    where I misuse µ as Poisson't coefficient.
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