D.H. Lammlein PhD Dissertation - Vanderbilt University

Flow stress in aluminum alloys is dependent on temperature and strain-rate.
Sellars and Tegart [6] proposed an initial formulation which represented the TMAZ
region as a rigid, visco-plastic fluid. Sheppard and Wright [39] modified their
formulation into the following commonly used form:
Z
Q
= & ε exp( ) = A(sin ασ ) n
e
RT
or equivalently [43]
⎡ ⎤
1 − ⎢⎛
Z 1
⎞ n
1
= ⎜ ⎟ ⎥
⎛ Q ⎞
σ
e
sinh
Z = ε& exp⎜
⎟
α ⎢⎝
A ⎠ ⎥
⎝ RT ⎠
⎣ ⎦
where α, A, n are material constants (α = 0.045 (Mpa) -1 , Q = 145 kJ mol -1 , A = 8.8632E6
s -1 , n = 3.55), σ e is the equivalent steady state flow stress (Mpa), R the gas constant (R =
8.314 mol -1 K -1 ), T the absolute temperature (K), Q is the activation energy (J mol -1 ) and Z
is the Zener-Hollomon parameter. The material constants used are determined using a
standard compression test. The material viscosity is defined in the following manner:
σ
e
µ =
3 & ε
The visco-plastic model holds at temperatures reasonably below the metals solidus
temperature. As the material approaches the solidus temperature significant softening
occurs. Seidel and Reynolds [51] proposed reducing the flow strength in a linear fashion
from its value at some arbitrary temperature, T m , to zero at the solidus temperature, T s .
[51] and [22] define the so-called empirical softening regime by setting T m at 50°C below
the solidus temperature.
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