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Thixoforming : Semi-solid Metal Processing

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216j 6 Modelling the Flow Behaviour of <strong>Semi</strong>-<strong>solid</strong> <strong>Metal</strong> Alloys<br />

u, T scalar<br />

h viscosity [Pa s]<br />

t shear stress [Pa]<br />

g_ shear rate [s 1 ]<br />

k consistency factor [Pa s n ]<br />

n power law coefficient (flow exponent)<br />

t0 yield stress; zero shear stress [Pa]<br />

t¥ infinite shear stress [Pa]<br />

h0 zero shear viscosity [Pas]<br />

h¥ infinite shear viscosity [Pa s]<br />

fS<br />

<strong>solid</strong> fraction (volume fraction <strong>solid</strong>)<br />

k degree of agglomeration<br />

ke degree of agglomeration equilibrium<br />

II second invariant<br />

S_ stress tensor<br />

D_ deformation rate tensor<br />

u_ velocity vector<br />

uS <strong>solid</strong> velocity [m s 1 ]<br />

uL liquid velocity [m s 1 ]<br />

subscript S <strong>solid</strong> phase<br />

subscript L liquid phase<br />

subscript B bulk phase<br />

c rate constant for k<br />

tw wall shear stress [Pa]<br />

Dp pressure drop [Pa]<br />

L length [m]<br />

a volumetric flow rate [m 3 s 1 ]<br />

H height [m]<br />

W width [m]<br />

C diameter [m]<br />

R radius [m]<br />

r radial coordinate [m]<br />

hap apparent viscosity [Pa s]<br />

n rotational speed [s 1 ]<br />

w angular velocity [rad s 1 ]<br />

G00 loss modulus [Pa]<br />

G0 storage modulus [Pa]<br />

S_ stress tensor<br />

Sij components of the stress tensor [Pa]<br />

e_ strain tensor<br />

eij<br />

_e<br />

components of the strain tensor<br />

strain rate tensor<br />

_e ij components of the strain rate tensor [s 1 ]

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