2 µm - eTheses Repository - University of Birmingham
(ii) for non-isothermal infiltration by a pure metal, taking into account the influence of preform deformability, and (iii) for isothermal infiltration, taking into account the influence of capillary phenomena (113) . Most models consider only the case of saturated flow, either by ignoring any capillary pressure drop or using the ‘slug-flow’ assumption, which implies that the infiltration front is abrupt. It has been shown that when the applied pressure is low or when the preform pore structure exhibits a broad size distribution, this assumption breaks down, as metal penetrates the preform in a gradual manner, filling the largest pores first. This case is relevant for industrial practice, because it is desirable to maintain the applied pressure as low as possible, to minimize preform damage and to reduce costs. In practical cases, the applied pressure is not established instantly but follows a more or less rapidly increasing function before the final infiltration pressure is established. For most relevant metal/reinforcement systems, isothermal metal infiltration is similar to drainage in soil mechanics (113) . During drainage, wetting water is displaced by non-wetting air out of a porous soil. In MMC infiltration, air generally constitutes the wetting phase and metal the non-wetting one. Non-saturated flow through porous media and drainage phenomena have been treated in the soil mechanics literature (111) . Based on soil mechanics, Dopler et al. (113) developed a model for isothermal infiltration of ceramic fibres based on capillary phenomena. The relationship between local pressure and non-wetting fluid velocity is classically described by Darcy’s law (Equation 25). When neglecting gravity it is valid for laminar flow in a porous medium in the following form: v0 = −K ⋅∇P Equation 25 where v0 is the superficial velocity of the non-wetting phase, defined as the volumetric flow rate, P is the pressure and K is the permeability tensor. 43
The permeability K can be expressed as a function of three independent terms: s r μ K K ⋅ K = Equation 26 where Ks is the specific preform permeability tensor, Kr is the relative permeability, varying with saturation between 0 and 1, and µ is the dynamic fluid viscosity. The tensor of specific permeability describes the geometrical arrangement of the porous medium. The different components of the tensor depend on the type of preform, its volume fraction, the diameter of the reinforcement phase, its arrangement and homogeneity. The component values of Ks can be measured by permeability experiments, using, for example water as a fluid (114) . There is no direct way to measure the relative preform permeability Kr. It is generally back- calculated from infiltration experiments or from calculations based on simplified porous preform geometries such as capillary tubes. A general form with two empirical parameters A and B can be given (113) as: K ⋅ B r = A S Equation 27 with S the saturation of the porous body. The evaluation of modelling results showed best agreement with A and B both equal to 1. The saturation S is defined as the ratio of filled void space to initial void space as follows: θl S = 1−θ c 44 Equation 28 where θl is the volume fraction of the intruded liquid and θc the volume fraction of the ceramic phase. The saturation is expressed, in general, in soil mechanics as a function of pressure. The functional relationship is measured by establishing a drainage curve for the considered system, which represents the degree of saturation either of the wetting or of the
Pressure Infiltration Behaviour and
Positive volume changes were predic
Figure 4.5 Droplet formation of the
with the metal alloy IM: examples a
As shown in Figure 4.9, apart from
4.3.2 Powder specific surface area
The particles of TO and MO were dis
oom temperature and 270°C, with a
obtain usable products when they we
strengths, whereas with 10 and 20 w
strength showed no significant diff
Relative change in dimension s x, s
(a) AOPC20 (b) AGPC15 2 µm (c) TOP
At higher magnification, Figure 4.2
intrusions started at 4 µm and end
As shown in Figure 4.27, the pore s
An overview of the specific values
1.71 to 1.98·10 6 m²/m³. The sim
logarithmic compression behaviour,
The volumetric stiffness Eiso of th
Figure 4.37 shows that the TOPC20 p
unhindered through the gap between
intrusions and the other areas were
4.8.1 Unreinforced matrix propertie
die, Tmelt,die , could not be recor
pressure was recorded as a function
the linear fits for AOPC20, TOPC20
4.8.6 Non destructive testing of MM
X-Y Y-Z Figure 4.51 Virtual cross-s
The metal filling the intragranular
the ceramic particles was not visib
etween the dark grey ceramic phases
The windows, one of which is marked
potential interfacial reactions, th
In order to determine the effect of
Infiltration depth L² L² (mm²) /
4.8.12 Microstructure of MMCs with
minor fraction of suboxides with hi
4.9. High pressure die casting infi
In the Y-Z plane section in Figure
4.9.2 Compression of preforms The c
Relative preform compression c pr (
decrease depended on the tooling us
Bending stress σ (MPa) / MPa 500 4
4.10.3 Influence of reinforcement t
Significant deformation developed i
a) b) 2 50 2 50 µm µm 2 50 2 50
5. DISCUSSION First the properties
The measured elastic modulus, Edyn
The MMCs showed similar wear with t
interfacial debonding: Peng et al.
The area Sml was derived using data
MMC. Due to the solidification shri
measurements which resulted in a lo
5.1.5 Influence of reactions No rea
5.2. Preform pore formation The tar
kinetics were reported to be rather
The newly formed water vapour led t
In order to achieve minimum porosit
the present work. These pressures w
indicated by zero values of the fre
influence on the pO2,calc. The lowe
during extended holding and acts as
Compared to Hg, the Al melt may con
preforms with IM, Figure 4.67. For
preform compression, cpr , increase
Specific Specific permeability Perm
Permeability (m²) / m² 1x10 -12 1
As the predominant fluid flow was a
In the CP mode, the Preform 1D code
Local Saturation saturation S () lo
listed in Table 5.1 and 5.3 were us
6. CONCLUSIONS 1. An aqueous proces
anged between 112 and 131° for the
8. REFERENCES 1. Altenpohl, D.: Alu
43. Davis, L.C. and Allison, J.E. :
85. Gennes, P.G. : “Wetting: Stat
127. Corbin, S.F., Lee, J. and Qiao
171. Gmelin, L. : Handbook of Inorg