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The Magic of Ice Dorthe Dahl-Jensen

The Magic of Ice Dorthe Dahl-Jensen. NGRIP. GRIP. Dye3. Isotropic Flow Law: Glens Flow Law  ij = As e n-1 s ij (15) trace( s 2 ) = 2s e 2 = (s x 2 +s y 2 +s z 2 +2(s xy 2 +s xz 2 +s yz 2 )) The strain rate is thus not only linearly related to the stress deviator in the given

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The Magic of Ice Dorthe Dahl-Jensen

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  1. The Magic of Ice Dorthe Dahl-Jensen

  2. NGRIP GRIP Dye3

  3. Isotropic Flow Law: Glens Flow Law ij = Asen-1sij (15) trace(s2) = 2se2 = (sx2+sy2+sz2+2(sxy2+sxz2+syz2)) The strain rate is thus not only linearly related to the stress deviator in the given direction, but also to the quadratic sum of all the stress deviators acting on the material. It is a non-linear equation. The flow law exponent n is normally set to 3. The flow law parameter A is a function of temperature (the Arrhenius Equation) A = Aoexp(-Q/RT) T is the temperature in Kelvin R is the gas constant (8.314 Jmol-1K-1) Q is the activation energy for creep (60 kJ/mol)

  4. εx = Um-1(μσx - 1/2(2μ-λ)σy - 1/2λσz) εy = Um-1(-1/2(2μ-λ) σx + μσy - 1/2λσz) εz = Um-1((-1/2λ(σx+σy) + λσz) εxz = 1/2Um-1ντxz εyz = 1/2Um-1ντyz εxy = 1/2Um-1(4μ-λ)τxy) where U = 1/2(2μ-λ)(σx-σy)2 + 1/2λ((σy-σz)2 + (σz-σx)2) + ν(τyz2+τxz2) + (4μ-λ)τxy2 The m in this theory relates to the n in Glen’s law: m=(n+1)/2. For the isotropic case, λ = μ = 1/3ν.

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