Expansion Mechanisms in Foaming Aluminum Melts

Abstract

The expansion of molten aluminum foam was studied to determine flow mechanisms in the cellular melt. The structure of the foaming melt evolved through a series of deformation stages before the foam stabilized and solidified. Changes in cell geometry during foam expansion were observed at different positions within the mold cavity and analyzed to determine flow mechanisms. The deformation patterns and cell shapes during foam expansion were observed macroscopically and microscopically from metallographic sections. Simple mechanical models described the salient features and mechanisms of the expansion process.

Appendices

Appendix A

1.1 Expansion ratio and rate

The expansion ratio (e(t)) and expansion rate ($\ifmmode\expandafter\dot\else\expandafter\.\fi{e}(t)$) of the foaming melt are functions of holding time in the process. These quantities can be expressed as

$$ e(t) = \frac{{V(t)}} {{V_{0} }},\quad \ifmmode\expandafter\dot\else\expandafter\.\fi{e}(t) = \frac{{de(t)}} {{dt}} = \frac{{dV(t)}} {{V_{0} dt}} $$

(A1)

where V ₀ and V(t) are the original volume and the dynamic volume of the foaming melt, respectively. Both parameters were measured.

For convenience of describing the kinetics, the logarithmic expansion ratio (E(t)) and logarithmic expansion rate ($\ifmmode\expandafter\dot\else\expandafter\.\fi{E}(t)$) can be defined as

$$ E(t) = \ln \frac{{V(t)}} {{V_{0} }},\quad \ifmmode\expandafter\dot\else\expandafter\.\fi{E}(t) = \frac{{dE(t)}} {{dt}} = \frac{{dV(t)}} {{V(t)dt}} $$

(A2)

The relations between E(t) and e(t), and between $\ifmmode\expandafter\dot\else\expandafter\.\fi{E}(t)$ and $\ifmmode\expandafter\dot\else\expandafter\.\fi{e}(t)$ are

$$ E(t) = \ln [e(t)],\quad \ifmmode\expandafter\dot\else\expandafter\.\fi{E}(t) = \frac{{\ifmmode\expandafter\dot\else\expandafter\.\fi{e}(t)}} {{e(t)}} = \frac{{d[\ln e(t)]}} {{dt}} $$

(A3)

Isothermal melt conditions permit one to observe foam expansion after the blowing agent is added. A device was employed for detecting the height of the expanding foam,[16] and in a cylindrical crucible, the height of the foam (H(t)) is a function of hold time. The relations between H(t), expansion ratio and expansion rate are

$$ e(t) = \frac{{H(t)}} {{H_{0} }} $$

$$ \ifmmode\expandafter\dot\else\expandafter\.\fi{e}(t) = \frac{{dH(t)}} {{H_{0} dt}} $$

$$ E(t) = \ln \frac{{H(t)}} {{H_{0} }} $$

$$ \ifmmode\expandafter\dot\else\expandafter\.\fi{E}(t) = \frac{{dH(t)}} {{H(t)dt}} $$

respectively, where H ₀ and H(t) are the original height and the dynamic height of the foaming melt, respectively.

Appendix B

1.1 Porosity

Perhaps the most critical characteristic of foam is the porosity (p)

$$ p = 1 - \frac{{V_{0} }} {V} = 1 - \frac{1} {e} $$

(B1)

The relation between the instantaneous specific density of the expanding foam ρ _f and the expansion ratio is

$$ \rho _{f} = \rho _{0} (1 - p) = \frac{{\rho _{0} }} {{e(t)}} $$

(B2)

where ρ ₀ is the density of the melt metal.