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Numerical Simulation of Pressure Infiltration Process for Making Metal Matrix Composites Using Dual-Scale Fabrics

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Abstract

Correct modeling of flow and solidification of metal melt in the pressure infiltration process (PIP) is important for accurate simulation and process optimization of the mold-filling process during the making of metal matrix composites. The fiber reinforcements used in this process often consist of fiber tows or bundles that are woven, stitched, or braided to create a dual-scale preform. The physics of melt flow in the dual-scale preform is very different from that in a single-scale preform created from a random distribution of fibers. As a result, the previous PIP simulations, which treat the preform as being single scale, are inaccurate. A pseudo dual-scale approach is presented where the melt flow through such dual-scale porous media is modeled using the conventional single-scale approach using two distinctly different permeabilities in tows and gaps. A three-dimensional finite difference model is developed to model the flow of molten metal in the dual- and single-scale preforms. To track the fluid front during the mold filling and infiltration, the volume of fluid method is used. A source-based method is used to deal with transient heat transfer and phase changes. The computational code is validated against an analytical solution and a published result. Subsequent study reveals that infiltration of an idealized dual-scale preform is marked by irregular flow fronts and an unsaturated region behind the front due to the formation of gas pockets inside fiber tows. Unlike the single-scale preform characterized by sharp temperature gradients near mold walls, the dual-scale preforms are marked by surging of high-temperature melts between tows and by the presence of sharp gradients on the gap-tow interfaces. The parameters such as the (gap-tow) permeability ratio, the (gap-tow) pore volume ratio, and the inlet pressure have a strong influence on the formation of the saturated region in the dual-scale preform.

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Notes

  1. Preform is another name for the near-net-shape reinforcement “package” inserted in a PIP mold.

  2. A true dual-scale approach will involve formulating a set of macroscopic governing equations for the inter-tow (gap) flows and coupling them with the intra-tow flows using the volume-averaging method, as was done in References 9 and 10.

  3. A contact angle greater than 90 deg for (liquid metal + fiber) system is responsible for the non-wetting nature of the liquid metal and is responsible for significant porosity in MMCs produced using PIP.

  4. In the tow region packed with aligned fibers, the permeability tensor will be transversely isotropic, i.e., its value along the fiber will be different from its value in the plane perpendicular to the fiber axis.

  5. In the isotropic gap region, K x  = K y  = K z .

  6. A phase average is the volumetric integral of a flow quantity within an averaging volume divided by the total averaging volume. An intrinsic phase average, on the other hand, is the volumetric integral of a flow quantity within an averaging volume divided by the pore volume within the averaging volume. See[49] for a description of the phase-average and intrinsic phase-average quantities in porous media.

  7. Henceforth, the term pressure will mean the pore-averaged pressure, while the term velocity will stand for the Darcy or phase-averaged velocity.

  8. The behavior of air pockets formed in dual-scale porous media will perhaps be more complicated than what is presumed here. During infiltration, the trapped gas pockets have a tendency to wriggle out of tows, move very quickly through the gaps, and while moving have a tendency to spilt or merge with other air pockets.[10] However, if the travel of the open flow front through the mold is not significant, then such a behavior may not be seen and the gas pockets inside tows model will perhaps be adequate.

  9. A slight difference between the analytical and numerical solutions may be attributed to the fudging of flow fronts as predicted by the VOF method.

  10. The dissolution of the gases is possible when the gas pressure rises beyond the saturated vapor pressures of its various components. Flushing down of gas pockets is also possible if the gas pressure rises beyond a critical pressure that facilitates the movement of the pocket after sufficient shrinkage. Both these phenomena have not been incorporated in our present numerical simulation.

  11. The existence of such sharp temperature gradient may result in the formation of columnar coarse grains, while the rest of the solidification region may be characterized by the equiaxed fine grains.

  12. Note that the global tow saturation seems to converge to about 0.7 when the permeability ratio is going to infinity (Figure 17); rather one would expect it to converge to zero, if the tows are perfectly impermeable. We did quite a few simulations with varying grid densities to resolve this issue, but were unsuccessful. It seems that this problem of liquid going inside the tows even when the permeability of tows is much smaller than that of gaps is related to the fudging or diffusing of flow fronts by the use of the VOF method. This is perhaps the reason why the tows cannot be perfectly dry when the permeability ratio is going to infinity. Hence, this effect is essentially a weakness of the numerical scheme chosen to model tow impregnation by the liquid metal.

Abbreviations

c p :

Specific heat at constant pressure

F :

Volume fraction of fluid

f s :

Volume fraction of solidified metal

H :

Mold height

∆h m :

Latent heat of metal matrix

K x :

Permeability component in x direction

K y :

Permeability component in y direction

K z :

Permeability component in z direction

K tow :

Permeability at the intra-tows region

K gap :

Permeability at the inter-tows region

k c :

Thermal conductivity of composites

k f :

Thermal conductivity of fibers

k m :

Thermal conductivity of metal

L :

Mold length

N tow :

Number of tows

P :

Average pressure

P c :

Capillary pressure

P gage :

Gage pressure

P gas :

Pressure inside air pocket

P in :

Inlet pressure

P s :

Suction pressure

Pep :

Peclet number

q in :

Inlet flow rate

r e :

Equivalent capillary radius

r f :

Fiber radius

Re:

Reynolds number

S tow :

Volume of tows occupied by metal/total tow volume

T gas :

Temperature inside air pocket

T in :

Melt inlet temperature

T m :

Melting temperature of pure metal

T pre :

Preform initial temperature

T w :

Mold wall temperature

t :

Infiltration time

t fill :

Mold-filling time

u, v, w :

Volume-averaged velocity components

V f :

Volume fraction of fiber

V sf :

Volume fraction of solid materials

VSaturated by metal,i :

Volume saturated by metal

V tow,i :

Volume of tow

W :

Mold width

x, y, z :

Cartesian coordinates

x(t)front :

Location of flow front

α :

Wetting angle

ε :

Preform porosity

γ l :

Surface tension of liquid

θ :

Dimensionless temperature

ρ :

Density

μ :

Dynamic viscosity

c:

Composite

f:

Fiber

front:

Infiltration front

i:

Index of tow number

in:

Inlet position

m:

Metal matrix

p:

Preform

*:

Non-dimensionalized quantity

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Acknowledgments

The authors would like to acknowledge financial support from the Research Growth Initiative (RGI) program of the Graduate School of the University of Wisconsin-Milwaukee and Catalyst Grant by the Bradley Foundation. Helpful comments from Professor Pradeep Rohatgi, Drs. Ben Schultz, and J.B. Ferguson are appreciated.

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Authors and Affiliations

  1. Laboratory for Flow and Transport Studies in Porous Media, Department of Mechanical Engineering, University of Wisconsin-Milwaukee, Milwaukee, WI, 53211, USA

    Bo Wang (Professor) & Krishna M. Pillai (Associate Professor)

  2. School of Materials Science and Engineering, Shanghai University, Shanghai, 200072, P.R. China

    Bo Wang (Professor)

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  1. Bo Wang
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Correspondence to Krishna M. Pillai.

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Manuscript submitted February 9, 2012.

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Wang, B., Pillai, K.M. Numerical Simulation of Pressure Infiltration Process for Making Metal Matrix Composites Using Dual-Scale Fabrics. Metall Mater Trans A 44, 5834–5852 (2013). https://doi.org/10.1007/s11661-013-1955-9

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