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2 µm - eTheses Repository - University of Birmingham

2 µm - eTheses Repository - University of Birmingham

Equation 27 leads to

Equation 27 leads to Equation 50, which was used for modelling dynamic preform infiltration in the following section. Kr = S Equation 50 5.4.5. Dynamic preform infiltration model In Richards’ model, phase changes during infiltration in the liquid or porous solid are generally neglected and isothermal conditions are assumed. The latter was not the case for the present experiments. In the constant flux infiltrations, a plunger was used to press the melt into the pores of the preform. In order to achieve dense MMCs, pores in the sub-micron scale had to be infiltrated. The gap between the plunger and the die was about 10 µm and, as a result, when under isothermal conditions at temperatures above the solidus, the melt would be forced out of this gap rather than filling the porosity. The gaps between the plunger and die and the die parting line were sealed by solidifying the melt in the gap achieved by using die temperatures below the metal solidus (143) . The die was held at 250°C in HPDC and ISQC and at 450°C in DSQC. The latter was still about 100°C below the solidus of the alloy IS and sufficient as no melt was lost in any of the experiments. The temperature profile recorded in the centre (Tcentre) near the preform during infiltration in DSQC (Figure 4.46) and the measured solidus of 566°C of the alloy IS (Figure 4.45) suggested that the melt was in the liquid state for more than 10 s inside the preform. In the constant flux mode, infiltration took less than 1 s to fill the entire porosity of the preform and therefore it was assumed that no premature solidification occurred. Therefore an isothermal process of a rigid porous preform was assumed during infiltration modelling. Consequently, momentum and energy balance equations became irrelevant and the solid metal fraction was considered to be nil throughout. 227

As the predominant fluid flow was along the high permeability x-axis of the preforms fabricated using pore forming agents (e.g. AOPC20), a one-dimensional flow was assumed for the present simple infiltration model. Richards’ equation for variably saturated soil water flow has a clear physical basis. Therefore, it is generally applicable and can be used for fundamental research and scenario analysis. The equation is difficult to solve because of its parabolic form in combination with strong non- linearity of the soil hydraulic functions which relate water content, soil water pressure head and hydraulic conductivity. The results depend largely on the structure of the numerical scheme and the applied time and space steps (185) . Special attention has to be paid to the procedure with respect to the boundary conditions. Both finite difference and finite element methods are used to solve Richards’ equation. In one dimensional modelling, the finite difference approach is advantageous because it needs no mass lumping to prevent oscillations and is easier to implement in numerical routines. A mass conservative finite volume scheme was used to solve Richards’ equation. As shown in Figure 5.10, fixed nodes and temporal spacing were used. The spatial and temporal discretization was performed as shown graphically in Figure 5.10. The subscript i is the node number which is increasing toward higher x-values whereas the superscript j is the time level and Δt j = t j+1 - t j . All the nodes were in the centre of the control volumes with Δxu = xi־1 , Δxl = xi - xi+1 and Δxi the cell thickness. The spatial averages of K were calculated as geometrical means on the border of the control volumes. The values of K and S were taken at the old time level j (explicit linearization), which made it possible to calculate the new pressure p and simultaneously p I j+1 without iteration. Details of the finite difference code used for preform infiltration modelling have been published by Pokora (186) . 228

  • Page 1 and 2:

    Pressure Infiltration Behaviour and

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    ABSTRACT In the pressure infiltrati

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    CONTENTS 1. INTRODUCTION 1 2. LITER

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    4.8.3 Evaluation of infiltration be

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    Symbol Meaning γRv surface energy

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    Symbol Meaning TYS tensile yield st

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    these materials are the detrimental

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    2. LITERATURE REVIEW 2.1. Materials

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    changes in the oxide film chemistry

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    or inside the bulk fluid only. Inte

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    that are most effective in decreasi

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    initiation stress of 25 %. Further,

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    Beffort (36) suggested that even th

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    einforcement interface and reinforc

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    It is interesting to note that, for

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    20 Table 2.1 Compilation of the mec

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    General models to predict fracture

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    with values observed by others for

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    The work of adhesion characterises

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    and vapour, is difficult to evaluat

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    system Al-Al2O3 is 10 -49 Pa at 700

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    In the Al-Cu system, although the p

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    The heat of reaction ΔGr may be es

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    al. (100) who found non-wetting beh

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    capillary or threshold pressure has

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    using constant gas pressure. Infilt

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    The superficial velocity v0 in the

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    The permeability K can be expressed

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    2.4. Preform fabrication Composites

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    According to Kniewallner (51) even

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    2.4.3. Foamed preforms Another inte

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    structure. This is shown schematica

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    2.5.1. Gas pressure infiltration (G

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    MMCs infiltrated with an Al-9Mg or

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    layer oxide films. The Weber number

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    Long et al. (50) suggested that v0

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    3. EXPERIMENTAL PROCEDURE The influ

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    sintered at 1550°C, which represen

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    using a AVT-Horn (Aalen, Germany) m

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    squares fit function within the MAP

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    areas, SsBET ,of the powders were m

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    with dimensions of 65 mm x 46 mm x

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    The preform sintering process was o

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    in the evaporation of mercury at lo

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    The compressive strength, σc , of

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    as the measured mean value 0.23. Th

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    for 90 s to ensure complete solidif

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    ottom punch surface. The temperatur

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    A graphic presentation of the relat

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    detected. This operation took appro

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    modulus Edyn of the unreinforced al

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    calculated using the methods outlin

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    Positive volume changes were predic

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    Figure 4.5 Droplet formation of the

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    with the metal alloy IM: examples a

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    As shown in Figure 4.9, apart from

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    4.3.2 Powder specific surface area

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    The particles of TO and MO were dis

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    oom temperature and 270°C, with a

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    obtain usable products when they we

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    strengths, whereas with 10 and 20 w

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    strength showed no significant diff

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    Relative change in dimension s x, s

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    (a) AOPC20 (b) AGPC15 2 µm (c) TOP

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    At higher magnification, Figure 4.2

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    intrusions started at 4 µm and end

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    As shown in Figure 4.27, the pore s

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    An overview of the specific values

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    1.71 to 1.98·10 6 m²/m³. The sim

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    logarithmic compression behaviour,

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    The volumetric stiffness Eiso of th

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    Figure 4.37 shows that the TOPC20 p

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    unhindered through the gap between

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    intrusions and the other areas were

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    4.8.1 Unreinforced matrix propertie

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    die, Tmelt,die , could not be recor

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    pressure was recorded as a function

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    the linear fits for AOPC20, TOPC20

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    4.8.6 Non destructive testing of MM

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    X-Y Y-Z Figure 4.51 Virtual cross-s

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    The metal filling the intragranular

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    the ceramic particles was not visib

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    etween the dark grey ceramic phases

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    The windows, one of which is marked

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    potential interfacial reactions, th

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    In order to determine the effect of

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    Infiltration depth L² L² (mm²) /

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    4.8.12 Microstructure of MMCs with

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    minor fraction of suboxides with hi

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    4.9. High pressure die casting infi

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    In the Y-Z plane section in Figure

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    4.9.2 Compression of preforms The c

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    Relative preform compression c pr (

  • Page 187 and 188: decrease depended on the tooling us
  • Page 189 and 190: Bending stress σ (MPa) / MPa 500 4
  • Page 191 and 192: 4.10.3 Influence of reinforcement t
  • Page 193 and 194: Significant deformation developed i
  • Page 195 and 196: a) b) 2 50 2 50 µm µm 2 50 2 50
  • Page 197 and 198: 5. DISCUSSION First the properties
  • Page 199 and 200: The measured elastic modulus, Edyn
  • Page 201 and 202: The MMCs showed similar wear with t
  • Page 203 and 204: interfacial debonding: Peng et al.
  • Page 205 and 206: The area Sml was derived using data
  • Page 207 and 208: MMC. Due to the solidification shri
  • Page 209 and 210: measurements which resulted in a lo
  • Page 211 and 212: 5.1.5 Influence of reactions No rea
  • Page 213 and 214: 5.2. Preform pore formation The tar
  • Page 215 and 216: kinetics were reported to be rather
  • Page 217 and 218: The newly formed water vapour led t
  • Page 219 and 220: In order to achieve minimum porosit
  • Page 221 and 222: the present work. These pressures w
  • Page 223 and 224: indicated by zero values of the fre
  • Page 225 and 226: influence on the pO2,calc. The lowe
  • Page 227 and 228: during extended holding and acts as
  • Page 229 and 230: Compared to Hg, the Al melt may con
  • Page 231 and 232: preforms with IM, Figure 4.67. For
  • Page 233 and 234: preform compression, cpr , increase
  • Page 235 and 236: Specific Specific permeability Perm
  • Page 237: Permeability (m²) / m² 1x10 -12 1
  • Page 241 and 242: In the CP mode, the Preform 1D code
  • Page 243 and 244: Local Saturation saturation S () lo
  • Page 245 and 246: listed in Table 5.1 and 5.3 were us
  • Page 247 and 248: 6. CONCLUSIONS 1. An aqueous proces
  • Page 249 and 250: anged between 112 and 131° for the
  • Page 251 and 252: 8. REFERENCES 1. Altenpohl, D.: Alu
  • Page 253 and 254: 43. Davis, L.C. and Allison, J.E. :
  • Page 255 and 256: 85. Gennes, P.G. : “Wetting: Stat
  • Page 257 and 258: 127. Corbin, S.F., Lee, J. and Qiao
  • Page 259: 171. Gmelin, L. : Handbook of Inorg
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