- 1. CHAPTER 1 INTRODUCTION Squeeze casting, also known as
liquid-metal forging, is a process by which molten metal solidifies
under pressure within closed dies positioned between the plates of
a hydraulic press [1,2]. The applied pressure and the instant
contact of the molten metal with the die surface produce a rapid
heat transfer condition that yields a pore-free fine-grain casting
with mechanical properties approaching those of a wrought product.
Due to the elimination of air gap between the metal and die
interface, the heat transfer coefficient is increased, which
enhances cooling rates and solidification. The squeeze casting is
easily automated to produce near-net to net shape high- quality
components. The process was introduced in the United States in 1960
and has since gained widespread acceptance within the non ferrous
casting industry. Aluminium, Magnesium, Copper alloys components
are readily manufactured using this process. Several ferrous
components with relatively simple geometry for example, Nickel
hard-crusher wheel inserts have also been manufactured by the
squeeze casting process. Despite the shorter die life for complex
life for complex ferrous castings requiring sharp corners within
the die or punch, the process can be adopted for products where
better properties and savings in labour or material costs are
desired. 1.1 Background The process of mold design in the foundry
industry has long been based on the intuition and experience of
foundry engineers and designers. To bring the industry to a more
scientific basis the design process should be integrated with
scientific analysis such as fluid flow, heat transfer and stress
analysis. Perhaps the most effective way to do this is with the aid
of computer aided operation (CAO). Starting with the original
design, a computer model is used to stimulate the casting process.
Given a set of defect criteria, defects can be predicted
modification to the original design. After several iterations of
this design cycle and optimum design, free of defects should be
produced. From this procedure it will be possible to determine
whether a given mold design will produce a sound casting without
having to discover this in the foundry through the usual trial and
error process, which can be very tedious, time consuming and
expensive.
2. Figure 1.1 Schematic Diagram of Casting Design Process
Obviously the performance of this design cycle is based on the
accuracy of the casting simulation and the validity of the defect
prediction criteria. The promise of CAO has been that has we model
the physical process closer to reality, the simulation process
becomes more accurate, the defect criteria simpler and more
precise. However, this promise comes at a price. First, as a model
improves it becomes increasingly sensitive to the thermo physical
data. Often this data is difficult to obtain. Therefore several new
experimental techniques need to be developed. Second, as the
mathematics becomes more complex there is a need to either develop
efficient solution algorithm or invest in more powerful computer
resources. It is a balance of all these factor that will result in
a successful CAO application. The numerical simulation has
increasingly become an effective tool in the casting manufacturing,
by which some primitive and time-consuming procedures for finding
the appropriate set of process parameters are avoided. The aim of
this thesis is to improve the design cycle by investigating the
heat transfer aspects of solidification during squeeze casting
process. 1.2 Strategy of Thesis Design Casting Simulation Defect
prediction Design modification 3. Recently Sun [3] has carried out
extensive experiments on squeeze casting process of a different
wall-thickness 5-step casting under different pressure conditions.
Squeeze casting of magnesium alloy AM60 was performed under an
applied pressure 30, 60 and 90 MPa in a hydraulic press. With
measured temperatures, heat fluxes and IHTCs were evaluated using
the polynomial curve fitting method and numerical inverse method.
In this thesis, solidification process during squeeze casting
process is simulated using the commercial CFD software FLOW-3D for
the same set of parameters for which Sun [ ] has carried out
experiments. The heat transfer coefficients needed for metal/mold
inteface is taken from the polynomial fit developed by Sun [ ]
which is explained in detail in chapter 4 of this thesis. The
layout of the thesis is as follows: A literature review related to
modeling and experimental studies related to squeeze casting
process is presented in chapter 2. Chapter 3 explains the physics
behind the squeeze casting process, corresponding governing
equations and method of implementation using FLOW-3D,a commercial
CFD software. Examination of existing mathematical models to
determine their suitability. Chapter 4 explains in detail, the
experimental setup used by Sun [3] to calculate heat transfer
coefficients at the metal/die interface during squeeze casting
process under different applied pressures. Construction and/ or
importing of a mathematical model. Chapter 5 deals with the results
and discussion part of the simulations doen using FLOW-3D. This is
followed by conclusions in chapter 6. 1.3 Scope of Thesis The scope
of this thesis has been restricted to the investigation of
solidification process. In squeeze casting applied pressure plays
an important role. The main advantage of the deployment of high
pressure is that it enhances the heat transfer coefficients between
liquid metal and mold surface by several orders of magnitude. This
enhancement is realized due to the establishment of direct contact
between the liquid metal and the die wall. This fact has been
proved experimentally by Sun [3] where he has carried out extensive
experiments to record temperature profiles during squeeze casting
process of different wall- thickness 5-step casting under different
pressure conditions. The alloy chosen for his experiments were
magnesium alloy AM60 for the casting and steel die for the mold.
From the experimental data, he back calculated the heat transfer
coefficients at the metal/die interface using inverse approach and
by polynomianl fitting method. This work is directed 4. towards
using these heat transfer coefficients at the metal/die interface
for simulating the solidification process of different
wall-thickness 5-step casting under different pressure conditions
and to map the temperature profiles at different locations and try
to compare the results between simulation and experiments. CHAPTER
2 LITERATURE REVIEW 2.1 Squeeze Casting Casting is the most
economical route to transfer raw materials into readily usable
components. However, one of the major drawbacks for conventional or
even more advanced casting techniques, e.g., high pressure
die-casting is the formation of defects such as porosity.
Furthermore, segregation defects of hot tears. New casting
techniques have, therefore, been developed to compensate for these
shortcomings. Of the many such casting techniques available,
squeeze casting has greater potential to create less defective cast
components. Squeeze casting (SC) is a generic term to specify a
fabrication technique where solidification is promoted under high
pressure within a re-usable die. It is a metal-forming process,
which combines permanent mould casting with die forging into a
single operation where molten metal is solidified under applied
hydrostatic pressure. Although squeeze casting is now the accepted
term for this forming operation, it has been variously referred to
as "extrusion casting", "liquid pressing'', "pressure
crystallization'' and "squeeze forming''. The idea was initially
suggested by Chernov [2] in 1878 to apply steam pressure to molten
metal while being solidified. However, in spite of its century old
invention, commercialization of squeeze casting has been achieved
only quite recently and is mainly concentrated in Europe and Japan.
It is mainly used to fabricate high integrity engineering 5.
components with or without reinforcement. Hartley [2] reported a
technique developed by GKN Technology in UK for the pressurized
solidification of Al alloy in reusable dies. In this process a die
set is placed on a hydraulic press and preheated, and the exact
amount of molten alloy is poured into the lower half of the open
die set, the press closed so that the alloy fills the cavity and
the pressure maintained until complete solidification occurs (31-
108MPa pressure). External undercut forms can be produced, and
using retractable side cores, through-holes are possible. Since the
as-fabricated components can be readily used in service or after a
minor post-fabrication treatment, squeeze casting is also regarded
as a net or near net-shape fabrication route. Parallel to
commercialization, there are research centre throughout the world
that are actively researching further development and exploitation
of this net or near net shape fabrication process. This is
evidenced by the publication of more than 700 papers in various
engineering and scientific journals. These are mainly related to
Aluminium and Magnesium- based alloys with special emphasis on
metal matrix composites MMCs. According to Crouch[2], squeeze
casting is now the most popular fabrication route for MMC
artifacts. The annual 1215% growth rate of MMCs in the automotive,
aerospace, sport and leisure goods and other markets is a clear
indication of better usage of advanced manufacturing routes such as
squeeze casting. In addition, since squeeze casting may be carried
out without any feeding system, runners, gates, etc., and shrinkage
compensating units, risers, the yield is quite high with almost no
scrap for recycling. Finally, in contrast to forging, squeeze cast
components are fabricated in a single action operation with lesser
energy requirements. 2.1.1. Process outline The process of squeeze
casting involves the following steps: 1. A pre-specified amount of
molten metal is poured into a preheated die cavity, located on the
bed of a hydraulic press. 2. The press is activated to close off
the die cavity and to pressurize the liquid metal. This is carried
out very quickly, rendering solidification of the molten metalunder
pressure. 3. The pressure is held on till the metal is completely
solidified. This not only increases the rate of heat flow, but also
most importantly can eliminate macro/micro shrinkage porosity. 6.
In addition, since nucleation of gas porosity is
pressure-dependent, the porosityformation due to dissolved gases in
the molten metal isrestricted. 4. Finally the punch is withdrawn
and the component isejected out. 2.1.2.Mechanics of squeeze casting
2.1.2.1. The die A most crucial aspect in permanent mould castings
such as die-casting or squeeze casting is the die itself and, most
importantly, the design of the die including the selection of
suitable die material, the manufacturing process, appropriate heat
treatment and the maintenance practice. Squeeze casting dies are
exposed to severe thermal and mechanical cyclic loading, which may
cause thermal fatigue, cracking, erosion, corrosion, and
indentation. The nature and features of die are greatly influenced
by the particular alloy to be cast. Currently H13 tool steel is a
widely used material of constructions but generally die steels
should have good hot hardness, high temper resistance, adequate
toughness and especially a high degree of cleanliness and uniform
microstructure. 2.1.2.2. Different types of squeeze casting Two
basic forms of the process may be distinguished, depending on
whether the pressure is applied directly on to the solidifying cast
product via an upper or male die (punch)or the applied pressure is
exerted through an intermediate feeding system as schematically
shown in Fig.2.1: (i) the direct squeeze casting mode, and (ii) the
indirect squeeze casting mode. 7. Figure 2.1 Schematic diagram to
illustrate the direct and indirect modes of the squeeze casting
process. For the direct mode, two further forms may be
distinguished based on liquid metal displacement initiated by the
punch movement: (i) without metal movement, and(ii) with metal
movement. As illustrated in Figure1.2, the first form is suitable
for ingot type components where there is no metal movement, whilst
the second type involving metal movement, also known as the
backward process, is more versatile and can be used to cast a wide
range of shaped components. Figure 2.2 Schematic diagram to show
two forms of the direct squeeze casting process. 2.1.2.3. Various
modes of squeeze casting Squeeze casting can be classified
according to type of equipment used as : (i) vertical die closing
and injection, (ii) horizontal die closing and injection, (iii)
horizontal die closing and vertical injection, and (iv) vertical
die closing and horizontal injection. A further classification may
be envisaged as: (i) before the beginning of crystallization, and
(ii) after the beginning of crystallization, which may also be
described as semi-solid pressing. 8. Figure 2.3 summarizes the
various modes of the squeeze casting process. Figure 2.3 Various
modes of squeeze casting process 2.1.2.4 Process parameters The
most important process parameter is the alloy itself. The
composition and physical characteristics of the alloy are of
paramount importance due to their direct effects on the die life.
These include the melting temperature, and thermal conductivity of
the alloy together with the combined effect of the heat-transfer
coefficient and soldering onto the die material. Furthermore, the
alloy dictates the selection of casting parameters such as die
temperature, which has direct consequence on the die life.
Therefore, squeeze casting is usually employed for low melting
point temperature alloys of Aluminium and Magnesium. In addition to
the composition of a casting alloy, which determines its freezing
range and affects the quality of finished components, the casting
parameters should also be controlled very closely to achieve a
sound casting. The most dominant process parameters are die 9.
temperature and pouring temperature, and superheat, although the
level of applied pressure is also important. Since the metal is
cast under pressure, the inherent castability of the alloy is of
little or no concern. Other important parameters include the
cleanliness of the metal in relation to the presence of inclusions,
metal movement within the die which may induce turbulence, the die
coat, and the time interval over which the pressure is applied,
i.e., the so- called dead time. The die temperature is usually held
at between 200C and 300C for Aluminium and Magnesium alloys, whilst
the applied pressure varies between 50 and 150 MPa. The lubrication
medium, i.e., the die coat, is usually graphite based.
Heat-transfer coefficients are extremely high due to the casting
metal being pressed against the die wall. The control of following
process parameters is important for a good quality squeeze casting
components.[19]. Melt Volume Precision control of the metal volume
is required when filling the die cavity. This ensures dimensional
control. Casting Temperature Depends on the alloy and part
geometry. The starting point is normally 10-100C. above the
liquidus temperatures. Tooling temperatures ranging from 200-300 C
are normally used. The lower range is more suitable for thick
section casting. The punch temperature is kept 15 - 30C below the
lower die temperature to maintain sufficient clearance between them
for adequate vending. Excess punch to die clearance allows molten
metal to be extruded between them, eroding the surface. Time delay
is the duration between the actual poring of the metal and the
instant the punch contracts the molten pool and starts the
pressurization of the thin webs that are incorporated into the die
cavity. Because increased poring temperature maybe required to fill
these sections adequately upon pouring, a time delay will allow for
cooling of the molten pool before closing of the dies to avoid
shrink porosity. Pressure levels of 50-140 MPa are normally used.
There is an optimum pressure for each of the systems after this
there is no added advantage in mechanical properties. Pressure
duration varying from 30 - 120s has been found to be satisfactory
for castings weighing 9kg. However, the pressure duration is again
dependant on part geometry. Applied pressure after composite
solidification and temperature equalization will not contribute any
property enhancements and will only increase the cycle times. 10.
Lubrication for Aluminium, Magnesium and Copper alloys a good grade
of colloidal graphite spray lubricant has proved satisfactory when
sprayed on the warm dies priority casting. Care should be taken to
avoid excess build-up on narrow webs and fin areas where vent holes
are used. Care must be taken to prevent plugging of these vents for
ferrous casting, ceramic type coatings are required to prevent
welding between the casting and the metal die surface.
2.1.3.Advantages of Squeeze Casting With the current emphasis on
reducing materials consumption through virtually net shape
processing and the demand for higher strength parts for weight
savings, the emergence of Squeeze casting as a production process
has given materials and process engineers a new alternative to the
traditional approaches of casting and forging. By pressurizing
liquid metals while they solidify, near-net shapes can be achieved
in sound ,fully dense castings. The near-net and net shape
capabilities of these manufacturing process are the key advantages
of this process.Improved mechanical properties are additional
advantages of Squeeze cast parts. The close contact with the die
surface during solidification results in rapid solidification of
casting. This rapid solidification produces a fine secondary
dendrite arm spacing in the castings ,so that good strength and
ductility can be attained. These excellent properties are
relatively high in the as cast condition and are enhanced further
in the heat treatable alloys by the excellent response to solution
heat treatment. Since the process minimizes both gas porosity and
shrinkage cavities, excellent properties are attained. These
properties have been shown to be equivalent to wrought alloys in
many instances. Although this process has many advantages in
producing parts of light metals that can be utilized in structural
applications ,the full potential can only be realized after the
process has been optimized. Squeeze casting has been successfully
applied to a variety of ferrous and non ferrous alloys in
traditionally cast and wrought composition. Applications include
aluminum alloy pistons for engines and disc brakes; automotive
vehicles, truck hubs, barrel heads, and hubbed flanges; brass and
bronzes bushings and gears; steel missile components and
differential pinion gears; and a number of parts in cast iron,
including ductile iron mortar shells [3]. Squeeze casting is simple
and economical, and efficient in its use of raw material, and has
excellent potential for automated operation at high rates of
production. The process 11. generates the highest mechanical
properties attainable in a cast product. The micro structural
refinement and integrity of squeeze cast products are desirable for
many critical applications. Squeeze casting process gives new
opportunities to fabricate advanced materials, especially in the
field of composites. Squeeze casting can also be used to fabricate
bi-metals where, for instance, cast iron inserts can be
incorporated to increase wear resistance in aluminum alloy
components. Application to date have been wheels, pistons and
brakes discs [19]. 2.1.4. Applications of Squeeze Casting Squeeze
casting process has been explored for number of application using
various metals and alloys. Due to low density and high
strength-to-weight ratio, magnesium castings in the automotive
application increase rapidly. Currently, high pressure die
casting(HPDC) is the dominating production process for the most of
magnesium automotive components. Compared with the HPDC, the
squeeze casting process with high applied pressure is a promising
solution for thick magnesium castings. The squeeze casting has been
commercially succeeded in manufacturing parts include an Aluminium
dome , ductile Iron mortar shell, and a Steel bevel gear. Other
parts that have been Squeeze cast include stainless steel blades,
super alloy discs, Aluminium automotive wheels and pistons, and
gear blanks made of brass and bronze. Recently, this process has
also been adopted to make composite material at an affordable cost.
A porous ceramic pre-form is placed in the preheated die which is
later filled with the liquid metal and pressure is then. The
pressure, in this case, helps the liquid metal infiltrate the
porous ceramic perform, giving a sound metal ceramic composite. The
technological breakthrough of manufacturing metal-ceramic
composites, along with the ability to make complex parts by a
near-net shapes Squeeze casting process, suggest that this process
will find application where cost considerations and physical
properties of alloys are key factors [19].However, rare squeeze
cast magnesium components have been used in real engineering
applications. 2.1.5 Effect of pressure on the solidification
behaviour during squeeze casting process 12. The application of
pressure during solidification would be expected to affect phase
relationships in an alloy system. This may be deduced by
considering the Clausius-Clapeyron equation [2], f slff H VVT P T
)( (2.1) where Tf is the equilibrium freezing temperature, Vl and
Vs are the specific volumes of the liquid and solid, respectively,
and Hf is the latent heat of fusion. Substituting the appropriate
thermodynamic equation for volume, the effect of pressure on
freezing point may roughly be estimated as follows [2]: )exp( f f O
RT H PP (2.2) where P0, Hf and R are constants. Therefore, Tf
should increase with increasing pressure. On a mechanistic
approach, such change in freezing temperature is expected due to
the reduction in interatomic distance with increasing pressure and
thus restriction of atomic movement, which is the prerequisite for
melting/freezing. The inter-solubility of constituent elements
together with the solubility of impurity and trace elements is also
expected to increase with pressure. Fig 2.4The effect of rapid
cooling and the application of pressure on the Al-Si phase diagram.
13. The above mentioned theoretical predictions have been proven
experimentally where a liquidus temperature rise of up to 90 C has
been reported for pure Al/Si binary alloys at a pressure of 150
MPa. Furthermore, the eutectic point moves to the left, i.e., to
higher Si contents as indicated in Figure 2.4. The consequences of
such changes in the phase diagrams area significant improvement in
the microstructure and mechanical properties of SC-fabricated
components. The observed fine grained structure of squeeze castings
being principally due to the increase in heat-transfer
coefficients, i.e., greater cooling rates for the solidifying alloy
due to reduction in the air gap between the alloy and the die wall
and thus more effective contact area. The size of the air gap
between the solidifying alloy and the die wall and the degree of
undercooling, the two main features for fine structure, are
dependent on such process parameters as the pressure, the timing of
its application and the chemistry of the solidifying metal.
Certainly, the application of pressure reduces the air gap between
the solidifying metal and the metallic mould and thus increases the
contact area; effecting improvement in the heat-transfer
coefficient. Cho and Hong (1996) studied heat transfer coefficients
at the casting/die interface in squeeze casting and applied a
single load (50MPa) with die heating and concluded that heat
transfer coefficient increases with the application of pressure.
Casting parameters, as studied by different authors that have been
known to have signicant inuence on the squeeze cast products are
applied pressure, die pre-heat temperature and melt temperature. In
the work of Maleki et al. (2006), squeeze casting products decrease
in density at lower applied pressure and increases with higher
applied pressures [14]. They concluded that this increase becomes
less signicant at applied pressure of 100 MPa. In the report, it
was also observed that with increase in applied pressure, the cast
specimens grain size becomes smaller coupled with improved
hardness. The melt temperatures of between 6900 C and 6600 C might
just be enough for squeeze casting of Aluminium and Aluminium
alloys respectively, as observed by Yang (2003) [15]. It was
reported by Yang (2007) that the shorter the solidication time of
casting, the higher is its density, yield strength and ultimate
tensile strength [16]. Chattopadhyay (2007) applied a xed enthalpy
formulation to model solidication for a cylindrical geometry and
found that solidication time decreased asymptotically with increase
in heat transfer coefcient [4]. This phenomenon, he sited was due
to higher applied pressure on the solidifying cast product.
Investigating varying parameters of squeeze casting process and its
application, Ghomashchi and Vikhrov (2000) noted that many advances
in squeeze casting of Aluminium and low melting metals are leading
to the application of the process to high temperature alloys [2].
Santos et al. (2001) observed an increase in the heat transfer
coefcients 14. with increasing melt superheat for horizontal
directional solidication and a reverse for a vertical upward
directional solidication [17]. 2.2 Definition of the problem
Recently Sun [3] has carried out extensive experiments on squeeze
casting process of a different wall-thickness 5-step casting under
different pressure conditions. Squeeze casting of magnesium alloy
AM60 was performed under an applied pressure 30, 60 and 90 MPa in a
hydraulic press. With measured temperatures, heat fluxes and IHTCs
were evaluated using the polynomial curve fitting method and
numerical inverse method. In this thesis, solidification process
during squeeze casting process is simulated using the commercial
CFD software FLOW-3D for the same set of parameters for which Sun [
] has carried out experiments. The heat transfer coefficients
needed for metal/mold inteface is taken from the polynomial fit
developed by Sun [ ] which is explained in detail in chapter 4 of
this thesis. This work is directed towards using these heat
transfer coefficients at the metal/die interface for simulating the
solidification process of different wall-thickness 5-step casting
under different pressure conditions and to map the temperature
profiles at different locations and try to compare the results
between simulation and experiments. The cast material chosen for
this simulation is magnesium alloy AM60. The chemical composition
of AM60 is shown in Table I. The thermal properties of the related
materials in this study for performing the solidification
simulation is shown in Table II . Based on Yu(2007)s work, the
thermal conductivity(K) of AM60 has the linear relationship with
its temperature and follows equations(K=192.8-0.187T) in semisolid
temperature range(540C-615C) ; (K=0.0577T+60.85) below the solidus
temperature(615C). 15. Table I Chemical composition of Magnesium
Alloy AM60 Mg Al(%) Mn(%) Si(%) Cu()% Zn(%) balance 5.5-6.5 0.13
0.5 0.35 0.22 Table II Thermo physical properties of magnesium
alloy AM60 Properties Mg Alloy AM60 Solid Liquid Thermal
Conductivity (W/mK) 62 90 Specific Heat (J/Kg K) 1020 1180 Density
(Kg/m3 ) 1790 1730 Latent Heat (KJ/Kg) 373 Liquidus Temp at 0Mpa(C)
615 Solidus Temp at 0Mpa(C) 540 16. CHAPTER 3 MATHEMATICAL MODELING
OF CASTING PROCESS There are three forms of energy transport :
conduction (diffusion transport), convection (heat transmitted by
the mechanical motion of the fluid) and radiation (through space).
All three are active during solidification of casting. Energy
diffusion and convection occurs within the casting at the
metal/mould interface and within the mould. Energy is transported
by radiation from the mould to its environment which is typically
the air. 3.1 Heat transfer Heat transfer is the single most
important discipline in casting simulation. The solidification
process depends on heat transfer from the part to the mould and
from the mould to the environment. There are three possible modes
of heat transfer (1) conduction (2) convection and the (3)
radiation. The partial differential equation describing the process
is given by Q z T k zy T k yx T k xt T cp (3.1) The solution of the
above equation in a given domain requires knowledge of initial and
boundary conditions. 3.1.1. Initial and Boundary Conditions The
initial conditions define the temperature distribution throughout
the domain at some initial point in time. The simplest option is to
set the initial temperature depending on the estimated loss of
superheat during mould filling. The initial mould temperature
depends on the type of casting. Hence the mould temperature has to
be fixed accordingly. For investment castings, the mould is
preheated to a specified temperature which depend on the metal to
be cast. Initial conditions (t=0) used for the simulation are: The
pouring temperature of the molten alloy (MP of pure metal),Tmelt =
993K Temperature of the mould material , Tmould = 483K 17. The
boundary condition describe the condition that must be satisfied on
the boundaries of the domain. There are different types of
boundaries viz., mold exterior walls, metal/mold ,metal/insulator,
metal/chill, and metal/core interface and the metal free surfaces
while simulating the casting process . Boundary condition used for
the simulation: At the metal mold interface, the heat flux is
governed by (3.2) Thermal conductivity of the cast metal - Thermal
conductivity of the mold - interfacial heat transfer coefficient
Hence the boundary condition to be specified at the metal mold
interface is a heat transfer coefficient value 3.1.2 Mold exterior
During the casting process, the molds exterior surface is in
contact with air. Hence there exists a thermal boundary layer where
the temperature varies from the surface temperature to the fluid
free stream temperature. Either the temperature or heat flux can be
prescribed as a boundary condition at this surface. But the most
common approach is to approximate the heat flux at the solid
surface (mold exterior) using Newtons law of cooling as am TThq
(3.3) This is commonly referred to as the convective boundary
condition. In equation (3.3) the terms Tm, Ta, q and h corresponds
to the mold exterior temperature, ambient temperature, flux and
convective heat transfer coefficient respectively. 3.1.3.
Metal/mold or metal/chill or metal/insulator or metal/core
interface moldcasti erface mold mold erface cast cast TTh n T K n T
K intint 18. These boundaries are often referred to as interior
boundaries. Generally there is a temperature discontinuity at these
boundaries. For metal/mold interface the common approach is to
express the interfacial heat flux as mcgap TThq (3.4) where Tc, Tm,
hgap are the temperatures of the casting surface, mold surface and
the gap heat transfer coefficient. Generally the gap heat transfer
coefficient varies with respect to time or temperatures which are
usually determined either by experiments or by an inverse heat
transfer approach. 3.1.4. Metal free surfaces At the metal free
surface, the cast metal is exposed to the ambient. The heat
transfer at these surfaces can be modeled using a convective
boundary condition as given by equation (3.3). 3.2 Solidification
Solidification modeling involves the application of the heat
transfer concept along with the technique to account for the
release of latent heat during solidification[13]. The mold and any
other solid materials like chill, insulators etc. are modeled using
the standard heat conduction equation (equation 3.1). For the
solidifying metal, a special procedure is required to accurately
model the latent heat release. 3.2.1. Fraction of solid The extent
of solidification at any location within the casting is represented
by the fraction of solid, fs. At temperatures greater than or equal
to the liquidus temperature, the cast metal is in a completely
liquid state with a solid fraction value of zero. As the latent
heat is removed, the fraction of solid increases and reaches a
value of unity when the metal is in completely solid state. The
temperature at this point is called the solidus temperature. The
region where the solid fraction is between zero and unity is
referred to as the mushy zone. There are several ways to describe
the solid fraction variation between the liquidus and solidus
temperatures. The simplest approach is to assume that the solid
fraction varies linearly in the mushy zone. Alternatively, an
analytical expression such as Scheils equation 19. may be used. The
best approach is to determine the solid fraction-temperature
relationship using experimental measurements. The more accurate
method is using the solidification kinetics approach which involves
the time integration of a solid fraction evolution equation.
However solidification kinetics approach requires detailed
metallurgical data which may not be known. 3.2.2 Latent Heat The
release of latent heat during solidification is accounted for by a
heat generation term t f HQ s f (3.5) where Hf represents the
latent heat of solidification. This term is treated as a source
term and is determined from known parameters which is explained as:
The latent heat release rate is expressed as t T T f H t f H s f s
f (3.6) This term can be included in the left hand side of equation
(3.1) by defining an apparent specific heat as T f Hcc s fpapp
(3.7) For the case where the solid fraction is assumed to vary
linearly between liquidus and solidus, the above expression will be
or lspapp ls s fpapp TTTTcc TTT T f Hcc (3.8) Hence the governing
differential equation for solving solidification and heat transfer
during casting process becomes 20. z T k zy T k yx T k xt T capp
(3.9) with appropriate initial and boundary conditions. 3.3
Assumptions for the simulation (1) The die was assumed to be fully
filled with liquid alloy at the start of simulation. This is a
valid assumption when the cavity filling time is reasonably small
so that the heat loss during filling time is negligible. (2) A
uniform mold temperature was assumed for the simulation 21. 3.4
Flow 3D- An Overview FLOW-3D is a powerful and highly accurate
commercial CFD software that gives engineers valuable insight into
many of the physical processes. With special capabilities for
accurately predicting free-surface flows, FLOW-3D is the ideal CFD
software to use in design phase as well as in improving production
processes [ ]. It employs specially developed numerical techniques
to solve the equations of motion for fluids to obtain transient,
three-dimensional solutions to multi- scale, multi-physics flow
problems. An array of physical and numerical options allows users
to apply the code to a wide variety of fluid flow and heat transfer
phenomena. It is an easy-to-use simulation software designed to:
Accurately simulate filling and solidification processes Pinpoint
probable defects and problems before casting Identify viable
designs more quickly Decrease the number of design iterations
Improve scrap rates Reduce overall casting costs Flow-3D employs
specially developed numerical techniques to solve the equations of
motion for fluids to obtain transient, three-dimensional solutions
to multi-scale, multi-physics flow problems. An array of physical
and numerical options allows users to apply the code to a wide
variety of fluid flow and heat transfer phenomena. Fluid motion is
described with non-linear, transient, second-order differential
equations. The fluid equations of motion must be employed to solve
these equations. The science (and often art) of developing these
methods is called computational fluid dynamics. A numerical
solution of these equations involves approximating the various
terms with algebraic expressions. The resulting equations are then
solved to yield an approximate solution to the original problem.
The process is called simulation. An outline of the numerical
solution algorithms available in FLOW-3D follows the section on the
equations of motion. Typically, a numerical model starts with a
computational mesh, or grid. It consists of a 22. number of
interconnected elements, or cells. These cells subdivide the
physical space into small volumes with several nodes associated
with each such volume. The nodes are used to store values of the
unknowns, such as pressure, temperature and velocity. The mesh is
effectively the numerical space that replaces the original physical
one. It provides the means for defining the flow parameters at
discrete locations, setting boundary conditions and, of course, for
developing numerical approximations of the fluid motion equations.
The FLOW-3D approach is to subdivide the flow domain into a grid of
rectangular cells, sometimes called brick elements. A computational
mesh effectively discretizes the physical space. Each fluid
parameter is represented in a mesh by an array of values at
discrete points. Since the actual physical parameters vary
continuously in space, a mesh with a fine spacing between nodes
provides a better representation to the reality than a coarser one.
We arrive then at a fundamental property of a numerical
approximation: any valid numerical approximation approaches the
original equations as the grid spacing is reduced. If an
approximation does not satisfy this condition, then it must be
deemed incorrect. Reducing the grid spacing, or refining the mesh,
for the same physical space results in more elements and nodes and,
therefore, increases the size of the numerical model. But apart
from the physical reality of fluid flow and heat transfer, there is
also the reality of design cycles, computer hardware and deadlines,
which combine in forcing the simulation engineers to choose a
reasonable size of the mesh. Reaching a compromise between
satisfying these constraints and obtaining accurate solutions by
the user is a balancing act that is a no lesser art than the CFD
model development itself. Rectangular grids are very easy to
generate and store because of their regular, or structured, nature.
Nonuniform grid spacing adds flexibility when meshing complex flow
domains. The computational cells are numbered in a consecutive
manner using three indices: i in the x- direction, j in the
y-direction and k in the z direction. This way each cell in a
three-dimensional mesh can be identified by a unique address (i, j,
k), similar to coordinates of a point in the physical space.
Structured rectangular grids carry additional benefits of the
relative ease of the development of numerical methods, transparency
of the latter with respect to their relationship to the original
physical problem and, finally, accuracy and stability of the
numerical solutions. The oldest numerical algorithms based on the
finite difference and finite volume methods have been originally
developed on such meshes. They form the core of the numerical
approach in FLOW-3D. The finite difference method is based on the
properties of the Taylor expansion and on the straightforward
application of the definition of derivatives. It is the oldest of
the methods applied to obtain numerical solutions to differential
equations, and the first application is considered to have been
developed by Euler in 1768. The finite volume method derives
directly from the integral form of 23. the conservation laws for
fluid motion and, therefore, naturally possesses the conservation
properties. Rather than point wise approximations on a grid, FVM
approximates the average integral value on a reference volume. FVM
partitions the computational domain into control volumes (which are
not necessarily the cells of the mesh).It then discretizes the
integral formulation of the conservation laws over each control
volume (making use of the Gaussdivergence theorem). It then solves
the resulting set of algebraic equations or updates the values of
the dependent variables. The key to the method is that the integral
form of the conservation law can be rewritten; using the Gauss
Divergence Theorem. In other words, the rate of change of mass in
the control volume is equal to the net mass flux through its
boundary. The domain of the current problem is divided into finite
control volumes using cubic cells. 3.5Simulation strategy The steps
involved in simulating the casting solidification process using
FLOW3D are shown in the flowchart: Geometry modeling of the casting
Identification of the material type of each component Activating
physical models Applying Initial and Boundary Conditions
Preprocessor Simulation Run Simulation Meshing the geometry 24.
Figure 3.1 Flowchart for implementation of solidification
simulation in FLOW-3D As a first step the solidification simulation
of 5-step casting with the following dimensions for the steps: step
1 of dimensions 100 X 30 X 3 mm, step 2 of dimension 100 X 30 X 5
mm, step 2 of dimension 100 X 30 X 8 mm, step 4 of dimension 100 X
30 X 12 mm, step 2 of dimension 100 X 30 X 20 mm, is carried out
using FLOW-3D. The whole casting geometry was created as a solid
model in AutoCAD along with the bottom cylindrical shape sleeve of
diameter 100 mm. This solid model was first converted to an .stl
file . This file was used as the computational domain in the CFD
software FLOW 3-D. The implementation of solidification simulation
in FLOW -3D is briefly explained here: 3.5.1 Geometry modeling of
the casting The first task is to create the computational domain
for casting and mold. The mold box is created as a rectangular
component using the primitive Box in FLOW-3D. Appropriate
dimensions were chosen so that it covers the casting geometry in
all directions. For the present simulation the dimensions of the
mold box chosen was 160 X 140 X 270 mm. This is identified as
component 1 and is a solid component. The 5-step casting geometry
was then imported as an .stl file in FLOW-3D as a subcomponent to
component 1 and this is identified as subcomponent 1. Since it is
easier to work with SI units, appropriate transformations were done
to convert the scale of the geometry from mm to m. Once the stl
file is imported, the somponent type is transformed from solid to
complement as shown in Figure 3.2. Analyzing Results 25. Figure 3.2
FLOW-3D GUI for creating computational domain 3.5.2 Identification
of the material type The component1 is chosen as mold material and
is made of steel and hence the material type loaded is Steel AISI
P- 20 from the materials tab - solid database. The fluid 1 which
corresponds to metal cavity (subcomponent 1 ) is chosen as the cast
alloy and for the present simulation it was chosen as AM60
Magnesium alloy. The schematic view of the material database of
FLOW-3D is shown in Figures 3.3 and 3.4 . Figure 3.3 FLOW-3D GUI
for material selection - solids 26. Figure 3.4 FLOW-3D GUI for
material selection - fluids 3.5.3 Meshing the geometry The first
step in defining a particular domain is to determine the type of
coordinate system to use for the mesh. Two types are available in
FLOW-3D: Cartesian and cylindrical. The choice of mesh (cylindrical
or Cartesian) does affect some of the geometry definitions. The
selection of coordinate system applies to all mesh blocks.
Cartesian meshes accommodate general geometries rather well and are
therefore best for most problems. They are the default setting as
indicated in the Mesh Type drop-down box. Cylindrical meshes can
provide considerable improvements over Cartesian meshes for certain
geometries that lend themselves to a cylindrical description,
especially when the problem can be considered axisymmetric.
Existing mesh block definitions may be modified in the tree
structure. The resolution is controlled by the value specified for
either the size of cell, or the total number of cells, or the
number of the cells specified in each coordinate direction. When
the geometry becomes complex shaped , intermediate mesh planes can
be defined, as well as cell sizes for the domain between any two
mesh planes. Figure 3.5(a) depicts the mesh domain in FLOW-3D and
Figure 3.5(b) shows the mesh information for the computational
domain. 27. Fig 3.5 (a) Meshed computational domain (b) mesh
information dialog box For the present simulation, cell size chosen
is 2 mm in each direction. Hence the total number of cells in the
computational domain was around 245000 cells in the mesh. 3.5.4
Activating physical models The physical models were activated from
physics tab where the gravity, heat transfer and solidification
models were activated for the current simulation. In the gravity
model the value of acceleration due to gravity was entered in the
desired direction. For the present simulation a value of -9.8 m/s2
was given in the y -direction. In the heat transfer model the full
energy equation option is chosen with implict numerical
approximation Figure 3.6 shows the GUI of 28. FLOW-3D for
implementation of physics. Fig 3.6 Dialog box of FLOW-3D where the
physical models are activated. 3.5.5 Applying initial and boundary
conditions For the present simulation it was assumed that the
cavity was initially filled with liquid alloy. Hence the whole
cavity which is considered as fluid domain was assigned the same
initial temperature. The initial temperature of the fluid was
specified as 993K using the initial conditions setting tab of
FLOW-3D. The mold temperature was specified as 483 K using the
initial conditions setting tab of FLOW-3Dfor mold material. All the
external boundaries which corresponds to mold exterior was set to
symmetry boundary condition. The interface between mold and metal
is treated as a boundary and a typical value of heat transfer
coefficient is specified . 29. 3.5.6 Numerics Tab The user can
adjust parameters associated with the numerical methods used during
a simulation in the Numerics Tab of FLOW-3D. There are six control
options; (i) Time step controls - use the entry boxes in this group
to change the initial time step size , minimum time step and the
maximum time step. (ii) Pressure solver options - radio button to
choose the desired pressure iteration scheme. (iii) Explicit /
Implicit solver options - To change the numerical options
associated with viscosity, heat transfer,elastic stress,surface
tension,and the bubblepressure. Also the user can use the
convergence controls buttons to modify the default convergence
criteria if desired, when implicit options are selected. (iv)
Volume of Fluid Advection - radio button option for choosing
advection scheme for volume of fluid (v) Momentum Advection Group -
radio button option for choosing the approximations for partial
derivatives in momentum equations. (vi) Fluid Flow Options - radio
button option through which the user can opt either for fluid flow
or no fluid flow. The user has the option to choose either constant
fluid velocity or zero fluid velocity for the fluid domain.
Otherwise the full momemtum equations will be solved. Figure 3.7
shows the GUI corresponding to numeric option in FLOW-3D. 30.
Figure 3.7 GUI for numerics in FLOW-3D 3.5.7 Output Tab The output
tab of FLOW-3D is used for generating results for post processing.
The user has the option to generate result files based on either
time, or fill fraction or solidified fraction. The user also has
the option to choose what data he needs to store in the results
file like temperature, solid fraction, liquid fraction, wall
temperature, wall heat flux etc. Also through probes GUI, the user
can generate data corresponding to a particular location at all
time intervals of the simulation. The GUI correponding to output
tab of FLOw-3D is shown in Figure 3.8. 31. Figure 3.8 GUI for
output tab in FLOW-3D 3.5.8 Simulation Manager The GUI
corresponding to the Simulate tab of FLOW-3D is shown in Figure
3.9. Using this tab, the user can either start the "preprocess
simulation" or "run simulation" option. If the user chooses
"preprocess simulation", FLOW3D solver checks whether there are any
errors associated with physics setting, meshing, property setting
etc. If there are any errors , the solver comes out with error
messages. If there are no errors, a file by name "flsgrf.*" is
created and this file is the one which is used for running the
solver. 32. Figure 3.9 GUI for output tab in FLOW-3D. Once the
pre-processing is done the user can use the "run simulation" option
to start the solver run. The "run simulation" option opens another
window as shown in Figure 3.10 which shows the progress of the
simulation and the data files available for post processing is also
shown in this window. Figure 3.10 Simulation window of FLOW-3D. 33.
One of the most valuable additions to the "Simulation Manager" tab
is the introduction of a robust "Queue Manage tab" which is shown
in Figure 3.11. The "Queue Manager" is especially useful for
managing many simulations with changing priorities. For example,
the "Queue Manager" allows simulations to be added to the queue,
reordered, paused, restarted, and terminated. These actions are
performed using the buttons located below the Queue Manager. Figure
3.11 Queue manager tab FLOW-3D. 3.5.9 Post-processing The post
processing option in FLOW-3D is carried out using the "analyze tab"
which is shown in Figure 3.12. Here the user has to load the
simulation file for which post processing has to be done. The post
processor of FLOW-3D can generate one dimensional, two dimensional
and three dimensional contour plots, history plots like cooling
curves at specified locations or spatial plots of temperature etc.
If the user wants to generate text files of the data generated
through simulation, he can do so by exporting the data as .txt
file. Further movies can be generated for visualizing the mold
filling, solidification profile etc. The post 34. processing window
of FLOW-3D is shown in Figure 3.13. Figure 3.12 Analyse tab
FLOW-3D. 35. Figure 3.12 GUI for choosing options for post
processing in FLOW-3D. 36. CHAPTER 4 CASE STUDY EXPERIMENTAL
RESULTS REPORTED BY SUN ET AL FOR ESTIMATION OF HEAT TRANSFER
COEFFICIENT DURING SQUEEZE CASTING PROCESS 4.1 INTRODUCTION In this
chapter, the experimental results of Sun et al [ ] is presented
where they have done experiments to record the thermal histories at
certain locations and how they back calculated the heat transfer
coefficient between metal/die interface by using polynomial
extrapolation method. 4.2 EXPERIMENTAL SETUP 4.2.1 5-Step Casting A
5-step shape casting was designed by Sun et al specifically to
record the thermal histories at certain locations during squeeze
casting process.. Figure 4.1 shows the 3-D model of 5- step casting
used for their experimental study. It consists of 5 step casting,
with dimensions of 100 x 30 x3 mm, 100 x 30 x 5 mm, 100 x 30 x 8
mm, 100 x 30 x12 mm, 100 x 30 x 20 mm accordingly. The molten metal
was allowed to fill ths cavity from the bottom by a cylindrical
shape sleeve with diameter 100 mm. Fig 4.1 3-D model of 5-step
casting with the round-shape gating system [ Sun et al., [ ]] (a)
XZ view; (b) YZ view; (c) isometric view 37. 2.2 Configuration of
die and installation of measurement unit. To measure the
temperatures and pressures at the casting-die interface accurately
and effectively, a special thermocouple holder was developed. It
hosted 3 thermocouples simultaneously to ensure accurate placement
of thermocouples in desired locations of each step. The
thermocouple holders were manufactured using the same material P20
as the die to ensure that the heat transfer process would not be
distorted. Figure 4.2 illustrates schematically the configuration
of the upper die (left and right parts) mounted on the top ceiling
of the press machine. It also reveals the geometric installation of
pressure transducers and thermocouple holders. Pressures within the
die cavity were measured using Kistler pressure transducers 6175A2
with operating temperature 850C and pressures up to 200 MPa. As
shown in Figure 4.2, pressure transducers and temperature
thermocouples were located opposite to each other so that
measurements from sensors could be directly correlated due to the
symmetry of the step casting. Five pressure transducers and
temperature measuring unit were designated as PT1 through PT5, TS1
through TS5, respectively. Each unit was inserted into the die and
adjusted until the front wall of the sensor approached the cavity
surface. The geometry shape of thermocouples holders was purposely
designed the same as the pressure transducer, so that they could be
exchangeable at different locations. Figure 4.2 Configuration of
the upper die and the geometric installation of hermocouple and
pressure transducers. (Sun et al., [ ]) 38. Figure 4.3 Installation
of upper - die and geometric installation of thermocouples and
pressure transducers. (Sun et al., [ ]) As shown in Figure 4.3, the
thermocouple head was bent down to 90 degree and attached to the
die surface tightly. The designed installation method minimized the
disturbance of the temperature field in the step casting cavity. On
the right part of the die, the thermocouples was installed to
measure casting surface (T-surf) and inside die
temperatures(T1,T2,T4). To ensure the accuracy, temperature
measurements were also carried out simultaneously in both the right
and the left parts of the die. This thermocouple head bending
method enables to acquire relatively accurate data of the casting
surface temperature. 4.2.2 Casting Process The integrated system
included a 75 tons laboratory hydraulic press, upper-lower die, an
that the mold assembly is composed of three parts. The two upper
dies of the casting cavity is split along the center. The bottom
sleeve has a diameter of 0.1016 m and a height of 0.127 m. The
chill vent was located on the top of the step casting, which can
discharge the gas inside the upper die cavity. Both the upper die
and the bottom sleeve were heated by cartridge heaters. 39. Fig 4.4
Schematic diagram of squeeze casting machine used by Sun et al., [
] Before pouring, the dies were pre-heated to 210C using four
heating cartridges installed inside the dies. The experimental
procedure included pouring molten magnesium alloy AM60 into the
bottom sleeve with a pouring temperature 720C, closing the dies,
cavity filling, squeezing solidification with the applied pressure,
lowering the sleeve die, splitting the two parts of the upper die.
Finally the 5-step casting can be shaken out from the cavity. The
temperatures inside the die and casting were measured by Omega KTSS
-116U thermocouples with response time below 10 ms. Real-time
in-cavity local pressures and temperature data were recorded by a
Lab VIEW based data acquisition system. The mold coating used in
step castings is Boron Nitride lubrication (Type Sf) which was
sprayed manually onto the surface of the mold cavity before heating
the dies to the initial temperature. To minimize the thermal
barrier effect of mold coating, the coating thickness applied in
this study was relatively thin (below 50 m). 4.3. Determination Of
IHTC by Polynomial Curve Fitting Method. To evaluate the IHTC
effectively as a function of solidification time in the squeeze
casting process, the finite difference method (FDM) was employed as
follows based on the heat transfer equations. Since the thickness
of each step is much smaller than the width or length of the step,
it can be assumed that the heat transfer at each step is
one-dimensional. The heat transfer across the nodal points of the
step casting and die is shown in Figure 4.5. The temperatures were
measured at 2, 4, 6, 8 mm beneath die surface and the heat flux
transferred to the die mould can be evaluated by heat transfer
equations. 40. Fig 4.5 One-dimensional heat transfer at the
interface between the casting and die, where temperature
measurements were performed (Sun et al. [ ]) Fig 4.6 5-step
castings solidifying under applied pressure 30, 60, and 90MPa. (Sun
et al., [ ] From the temperature versus time curves obtained at
each position inside the die, the temperature at the die surface
(X0 = 0mm) can be extrapolated by using polynomial curve fitting
method. After the completion of filling, by selecting a particular
time of solidification process, the values of temperatures were
read from the temperature-time data at position X1, X2, X3, and X4
as shown in Figure 4.5. A polynomial curve with various measured
temperatures against distance X were plotted and extrapolated by a
polynomial trend line. The temperature at the die surface was
determined by substituting the value of X=0 in the polynomial curve
fitting. The polynomial equation thus obtained is 41. given below
which predicts the temperature values at various distances inside
the die at a chosen time. y = 0.0635x3 + 0.1759x2 - 16.495x +
308.43 This procedure is repeated for a number of time increments
to get series of such temperatures with corresponding times at
metal - die interface, at metal surface, die surface, and at
various positions inside the die.