Numerical_simulation_of_casting_solidifi

Prévia do material em texto

Journal of Materials Processing Technology 178 (2006) 29–33
Numerical simulation of casting solidification in
permanent metallic molds
T.R. Vijayaram, S. Sulaiman, A.M.S. Hamouda ∗, M.H.M. Ahmad
Department of Mechanical and Manufacturing Engineering, Faculty of Engineering, Universiti Putra Malaysia,
UPM 43400 Serdang, Selangor Darul Ehsan, Poskod 43400, Malaysia
Received 26 May 2005; accepted 26 September 2005
Abstract
Casting solidification is actually the transformation of liquid phase to solid phase with the liberation of latent heat of fusion. During this
metallurgical process, it induces casting defects like shrinkage, porosity and hot tears. To eradicate and eliminate these problems, accurate casting
design and proper design of gating system is necessary. This can be predicted and designed by means of computer simulation of casting solidification.
This review paper discusses about the simulation process of casting solidification with the aid of an example, which will help the foundry engineers
and industrial metallurgists to optimize the design parameters, better understand the temperature history of the solidifying casting and hence to
identify the hot spot region with the aid of obtained time-temperature contours. These results will be used to get defect free as cast products on
implementing the above findings attained from the simulation process. In this paper, the importance of heat transfer in the simulation process
is presented. This paper reviews the details of computer simulation of solidification of castings in metallurgical engineering foundries. Since,
computers became widely available in industry, researchers have been working on the development of programs to simulate the solidification of
castings.
© 2005 Elsevier B.V. All rights reserved.
Keywords: Casting solidification; Computer simulation software; Hot tears; Hot spots; Solid–liquid interface
1. Introduction
Metallurgical phase transformation plays a vital role in the
solidification of castings [1]. Computer simulation of casting
solidification of metals and alloys is a complex phenomenon
[2,3]. The assumptions and constraints used for simulation are
considered as a vital one [8,23]. In the casting process, the
metal–mold interface will have an air gap which affects the dis-
sipation of heat flow from the casting to the mold [7,8]. But the
application of pressure during the solidification process reduces
the air gap and forms a tight contact between the casting and the
mold [4,5]. This condition releases the heat at a faster rate and
produces fine grain structured castings [9]. To identify the con-
ditions and optimum values, simulation of solidification process
is done by running indigenously developed computer software
for the casting process selected for investigation [6,11]. The
program output provides the details on time-temperature profile
∗ Corresponding author. Tel.: +60 3 89466330; fax: +60 3 86567122.
E-mail address: hamouda@eng.upm.edu.my (A.M.S. Hamouda).
and heat transfer coefficient values which plays a key role in the
effective design of castings [10,11].
2. Aim of computer modeling of solidification of
castings:
Many computer simulation programs now exist, but some
require computers of a power not generally available to practical
foundry men, while others take an unacceptably long time to
obtain meaningful results. The aim of computer modeling is to
[56]:
• Predict the pattern of solidification, indicating where shrink-
age cavities and associated defects may arise.
• Simulate solidification with the casting in various positions,
so that the optimum position may be selected.
• Calculate the volumes and weights of all the different mate-
rials in the solid model.
• Provide a choice of quality levels, allowing, for example, the
highlighting or ignoring of micro-porosity.
0924-0136/$ – see front matter © 2005 Elsevier B.V. All rights reserved.
doi:10.1016/j.jmatprotec.2005.09.025
mailto:hamouda@eng.upm.edu.my
dx.doi.org/10.1016/j.jmatprotec.2005.09.025
https://www.researchgate.net/publication/243403058_The_Physics_Of_Liquid_Metals?el=1_x_8&enrichId=rgreq-e4300068c37c53cc17bd152d276047d2-XXX&enrichSource=Y292ZXJQYWdlOzIyODQ1MzIwNTtBUzoxMDY1NDQwNTQxNDUwMjdAMTQwMjQxMzQ5MDY4OQ==
https://www.researchgate.net/publication/241281190_Materials_Science_and_Technology?el=1_x_8&enrichId=rgreq-e4300068c37c53cc17bd152d276047d2-XXX&enrichSource=Y292ZXJQYWdlOzIyODQ1MzIwNTtBUzoxMDY1NDQwNTQxNDUwMjdAMTQwMjQxMzQ5MDY4OQ==
https://www.researchgate.net/publication/225249320_Mathematical_modeling_of_porosity_formation_in_solidification?el=1_x_8&enrichId=rgreq-e4300068c37c53cc17bd152d276047d2-XXX&enrichSource=Y292ZXJQYWdlOzIyODQ1MzIwNTtBUzoxMDY1NDQwNTQxNDUwMjdAMTQwMjQxMzQ5MDY4OQ==
https://www.researchgate.net/publication/285166715_Fundamentals_of_Solidification?el=1_x_8&enrichId=rgreq-e4300068c37c53cc17bd152d276047d2-XXX&enrichSource=Y292ZXJQYWdlOzIyODQ1MzIwNTtBUzoxMDY1NDQwNTQxNDUwMjdAMTQwMjQxMzQ5MDY4OQ==
https://www.researchgate.net/publication/250154928_Coarsening_in_Solidification_Processing?el=1_x_8&enrichId=rgreq-e4300068c37c53cc17bd152d276047d2-XXX&enrichSource=Y292ZXJQYWdlOzIyODQ1MzIwNTtBUzoxMDY1NDQwNTQxNDUwMjdAMTQwMjQxMzQ5MDY4OQ==
30 T.R. Vijayaram et al. / Journal of Materials Processing Technology 178 (2006) 29–33
• Perform over a range of metals, including steel, white iron,
grey iron and ductile iron and non-ferrous metals.
3. Literature review
From the existing and recent literature citations it is found
that the currently available casting solidification simulation soft-
ware’s have not taken all constraints and conditions required for
the realistic simulation process [12–14]. This matters more and
influences critically on the output results [31]. Normally simu-
lation is done for simple shape castings particularly cylindrical
and of slab type [15,55]. Very limited complicated shape cast-
ings of real engineering components have taken for this research
work and yet not applied all constraints and complete boundary
conditions [16,17]. According to the literature reviewed, it is
clear that the casting solidification simulation is done only to
metals and alloys [18–20]. Little work has been done so far on
the simulation of metal matrix composites due to the complex-
ity involved in it [21,22]. The movement and the velocity of the
solidification front are determined by considering the assumed
boundary conditions and constraints [23,24].
4. Significance of casting solidification simulation of
metals, alloys and composite materials
Solidification of castings varies for different materials. Pure
metal and eutectic alloys solidifies at constant temperature. But
alloys of binary and ternary type solidify over a range of tempera-
ture. The result of the simulation process helps to design the cast-
ings effectively by identifying the defect locations from the geo-
metrical features of the components [3]. In the case of particulate
composite materials, it is used to determine the particle distribu-
tion uniformity during the solidification of composites [25–28].
The solidification front velocity decides the particle pushing and
engulfment in the composite casting solidifying process [29,30].
By simulation, the time versus temperature helps to visualize
the temperature contours and distribution inside the solidifying
composites [31–33]. So, the effect of the particle hindrance by
the solid–liquid interface can be thoroughly studied. The distur-
bance of the interface by the paniculate decides its distribution
inside the composite casting [34,35]. Similarly, for the optimum
processing of fiber-reinforced composites by squeeze casting,
the infiltration of the liquid alloy into the fiber is simulated to
get the details of the infiltration level and the characteristics of
viscosity, surface tension and wett-ability of the alloy with the
fiber [36]. By generating practical conditions in the software,
one can predict the optimum values likesqueeze pressure, die
temperature, molten metal or alloy pouring temperature and per-
form preheating temperature [37–40]. This helps us to identify
whether complete infiltration has taken place or not during solid-
ification process.
5. Steps involved in the development of casting
solidification simulation software
• Problem identification.
• Shape and size of the cast component.
• Identifying the type of metal casting process.
• Selecting the type of mesh element.
• Identifying the type of mold and cast material.
• Direction of heat flow.
• Applying the boundary conditions and constraints.
• Identifying the physical, chemical and mechanical properties
of the mold and cast material.
• Discretizing the selected casting into smaller nodal elements.
• Applying pre processor.
• Writing the heat transfer equations.
• Developing the stiffness matrices.
• Writing the codings by selecting a suitable higher-level pro-
gramming language.
• Run the program.
• Getting the output results.
• Applying post processor to refine and for better results.
6. Available numerical techniques for casting
solidification simulation process
• Finite difference method (FDM)
• Finite element method (FEM)
• Boundary element method (BEM)
Finite difference method is the oldest numerical mathemat-
ical technique used to generate the solidification simulation by
discretizing the casting and mold arrangement into smaller equal
elements [41–43]. For an element, the small linear distance in
the X-direction is taken as ‘Delta X’ and the vertical distance
in the Y-direction is taken as ‘Delta Y’ The air gap resistance
is considered here and one of the above mentioned numerical
methods is applied to get the solution [22,44,45]. Besides, it
is a common procedure to write the basic heat transfer equa-
tions for the nodal elements based on the mode of conduction,
convection and radiation [46]. By using finite element method
different types of mesh elements are generated by discretization
and hence stiffness matrices are developed to predict the velocity
of the moving solid–liquid interface, time-temperature distribu-
tion and particle distribution in the case of composites casting
solidification processing [47,48]. Recently, boundary element
method is adopted to get accurate result outputs and this is con-
sidered as an advanced technique by engineering scientists and
technologists [49,50].
7. List of assumptions and constraints to be considered
in casting solidification simulation software package
development
• Latent heat of fusion.
• Unidirectional heat flow.
• Thermal resistance–air gap consideration.
• Assuming the absence of crests and troughs in the metal–mold
interface.
• Isotropic conditions.
• Uniformity of properties in all directions consideration.
• Square element consideration in mesh generation.
• Location of nodes at the centre of the element.
https://www.researchgate.net/publication/250675976_Modeling_of_feeding_behavior_of_solidifying_Al7Si03Mg_alloy_plate_casting?el=1_x_8&enrichId=rgreq-e4300068c37c53cc17bd152d276047d2-XXX&enrichSource=Y292ZXJQYWdlOzIyODQ1MzIwNTtBUzoxMDY1NDQwNTQxNDUwMjdAMTQwMjQxMzQ5MDY4OQ==
https://www.researchgate.net/publication/226287992_Finite_element_of_solidification_problems?el=1_x_8&enrichId=rgreq-e4300068c37c53cc17bd152d276047d2-XXX&enrichSource=Y292ZXJQYWdlOzIyODQ1MzIwNTtBUzoxMDY1NDQwNTQxNDUwMjdAMTQwMjQxMzQ5MDY4OQ==
https://www.researchgate.net/publication/37426216_Modelling_of_microstructure_formation_in_solidification_processes?el=1_x_8&enrichId=rgreq-e4300068c37c53cc17bd152d276047d2-XXX&enrichSource=Y292ZXJQYWdlOzIyODQ1MzIwNTtBUzoxMDY1NDQwNTQxNDUwMjdAMTQwMjQxMzQ5MDY4OQ==
https://www.researchgate.net/publication/225694269_Heat_transfer-solidification_kinetics_modeling_of_solidification_of_castings?el=1_x_8&enrichId=rgreq-e4300068c37c53cc17bd152d276047d2-XXX&enrichSource=Y292ZXJQYWdlOzIyODQ1MzIwNTtBUzoxMDY1NDQwNTQxNDUwMjdAMTQwMjQxMzQ5MDY4OQ==
https://www.researchgate.net/publication/230256958_Modelization_of_phase_change_by_fictitious_heat_flow?el=1_x_8&enrichId=rgreq-e4300068c37c53cc17bd152d276047d2-XXX&enrichSource=Y292ZXJQYWdlOzIyODQ1MzIwNTtBUzoxMDY1NDQwNTQxNDUwMjdAMTQwMjQxMzQ5MDY4OQ==
https://www.researchgate.net/publication/260086364_Computer-Aided_Differential_Thermal_Analysis_of_Spheroidal_and_Compacted_Graphite_Cast_Irons?el=1_x_8&enrichId=rgreq-e4300068c37c53cc17bd152d276047d2-XXX&enrichSource=Y292ZXJQYWdlOzIyODQ1MzIwNTtBUzoxMDY1NDQwNTQxNDUwMjdAMTQwMjQxMzQ5MDY4OQ==
https://www.researchgate.net/publication/234328085_Conduction_of_Heat_in_SolidS?el=1_x_8&enrichId=rgreq-e4300068c37c53cc17bd152d276047d2-XXX&enrichSource=Y292ZXJQYWdlOzIyODQ1MzIwNTtBUzoxMDY1NDQwNTQxNDUwMjdAMTQwMjQxMzQ5MDY4OQ==
https://www.researchgate.net/publication/234328085_Conduction_of_Heat_in_SolidS?el=1_x_8&enrichId=rgreq-e4300068c37c53cc17bd152d276047d2-XXX&enrichSource=Y292ZXJQYWdlOzIyODQ1MzIwNTtBUzoxMDY1NDQwNTQxNDUwMjdAMTQwMjQxMzQ5MDY4OQ==
https://www.researchgate.net/publication/222445716_Finite_element_mesh_generation_methods_A_review_and_classification?el=1_x_8&enrichId=rgreq-e4300068c37c53cc17bd152d276047d2-XXX&enrichSource=Y292ZXJQYWdlOzIyODQ1MzIwNTtBUzoxMDY1NDQwNTQxNDUwMjdAMTQwMjQxMzQ5MDY4OQ==
https://www.researchgate.net/publication/223389615_Computer_simulation_of_the_effects_of_alloy_variables_on_the_grain_structures_of_castings?el=1_x_8&enrichId=rgreq-e4300068c37c53cc17bd152d276047d2-XXX&enrichSource=Y292ZXJQYWdlOzIyODQ1MzIwNTtBUzoxMDY1NDQwNTQxNDUwMjdAMTQwMjQxMzQ5MDY4OQ==
https://www.researchgate.net/publication/229789264_Finite_Element_Solution_of_Non-Linear_Heat_Conduction_Problems_with_Special_Reference_to_Phase_Change?el=1_x_8&enrichId=rgreq-e4300068c37c53cc17bd152d276047d2-XXX&enrichSource=Y292ZXJQYWdlOzIyODQ1MzIwNTtBUzoxMDY1NDQwNTQxNDUwMjdAMTQwMjQxMzQ5MDY4OQ==
https://www.researchgate.net/publication/227768350_Fixed_Grid_Techniques_for_Phase_Change_Problems_A_Review?el=1_x_8&enrichId=rgreq-e4300068c37c53cc17bd152d276047d2-XXX&enrichSource=Y292ZXJQYWdlOzIyODQ1MzIwNTtBUzoxMDY1NDQwNTQxNDUwMjdAMTQwMjQxMzQ5MDY4OQ==
https://www.researchgate.net/publication/225599976_The_Air-Gap_Formation_at_the_Casting-Mold_Interface_and_the_Heat_Transfer_Mechanism_through_the_Gap?el=1_x_8&enrichId=rgreq-e4300068c37c53cc17bd152d276047d2-XXX&enrichSource=Y292ZXJQYWdlOzIyODQ1MzIwNTtBUzoxMDY1NDQwNTQxNDUwMjdAMTQwMjQxMzQ5MDY4OQ==
https://www.researchgate.net/publication/241281190_Materials_Science_and_Technology?el=1_x_8&enrichId=rgreq-e4300068c37c53cc17bd152d276047d2-XXX&enrichSource=Y292ZXJQYWdlOzIyODQ1MzIwNTtBUzoxMDY1NDQwNTQxNDUwMjdAMTQwMjQxMzQ5MDY4OQ==
https://www.researchgate.net/publication/260086296_Computer-aided_Cooling_Curve_Analysis_Principles_and_Applications_in_Metal_Casting?el=1_x_8&enrichId=rgreq-e4300068c37c53cc17bd152d276047d2-XXX&enrichSource=Y292ZXJQYWdlOzIyODQ1MzIwNTtBUzoxMDY1NDQwNTQxNDUwMjdAMTQwMjQxMzQ5MDY4OQ==
https://www.researchgate.net/publication/225483016_The_use_of_heat_flow_modeling_to_explore_solidification_phenomena?el=1_x_8&enrichId=rgreq-e4300068c37c53cc17bd152d276047d2-XXX&enrichSource=Y292ZXJQYWdlOzIyODQ1MzIwNTtBUzoxMDY1NDQwNTQxNDUwMjdAMTQwMjQxMzQ5MDY4OQ==
https://www.researchgate.net/publication/234467296_Radiation_Heat_Transfer?el=1_x_8&enrichId=rgreq-e4300068c37c53cc17bd152d276047d2-XXX&enrichSource=Y292ZXJQYWdlOzIyODQ1MzIwNTtBUzoxMDY1NDQwNTQxNDUwMjdAMTQwMjQxMzQ5MDY4OQ==
https://www.researchgate.net/publication/234228377_Summary_of_Thermal_Properties_for_Casting_Alloys_and_Mold_Materials?el=1_x_8&enrichId=rgreq-e4300068c37c53cc17bd152d276047d2-XXX&enrichSource=Y292ZXJQYWdlOzIyODQ1MzIwNTtBUzoxMDY1NDQwNTQxNDUwMjdAMTQwMjQxMzQ5MDY4OQ==
https://www.researchgate.net/publication/229808565_An_Improved_Algorithm_for_Heat_Conduction_Problems_with_Phase_Change?el=1_x_8&enrichId=rgreq-e4300068c37c53cc17bd152d276047d2-XXX&enrichSource=Y292ZXJQYWdlOzIyODQ1MzIwNTtBUzoxMDY1NDQwNTQxNDUwMjdAMTQwMjQxMzQ5MDY4OQ==
https://www.researchgate.net/publication/225249320_Mathematical_modeling_of_porosity_formation_in_solidification?el=1_x_8&enrichId=rgreq-e4300068c37c53cc17bd152d276047d2-XXX&enrichSource=Y292ZXJQYWdlOzIyODQ1MzIwNTtBUzoxMDY1NDQwNTQxNDUwMjdAMTQwMjQxMzQ5MDY4OQ==https://www.researchgate.net/publication/229747879_An_efficient_algorithm_for_analysis_of_nonlinear_heat_transfer_with_phase_changes?el=1_x_8&enrichId=rgreq-e4300068c37c53cc17bd152d276047d2-XXX&enrichSource=Y292ZXJQYWdlOzIyODQ1MzIwNTtBUzoxMDY1NDQwNTQxNDUwMjdAMTQwMjQxMzQ5MDY4OQ==
https://www.researchgate.net/publication/284672671_Effects_of_solidification_parameters_on_the_feeding_efficiency_of_A356_aluminum_alloy?el=1_x_8&enrichId=rgreq-e4300068c37c53cc17bd152d276047d2-XXX&enrichSource=Y292ZXJQYWdlOzIyODQ1MzIwNTtBUzoxMDY1NDQwNTQxNDUwMjdAMTQwMjQxMzQ5MDY4OQ==
https://www.researchgate.net/publication/284672671_Effects_of_solidification_parameters_on_the_feeding_efficiency_of_A356_aluminum_alloy?el=1_x_8&enrichId=rgreq-e4300068c37c53cc17bd152d276047d2-XXX&enrichSource=Y292ZXJQYWdlOzIyODQ1MzIwNTtBUzoxMDY1NDQwNTQxNDUwMjdAMTQwMjQxMzQ5MDY4OQ==
https://www.researchgate.net/publication/290104372_Finite_element_simulation_of_solidification_problems?el=1_x_8&enrichId=rgreq-e4300068c37c53cc17bd152d276047d2-XXX&enrichSource=Y292ZXJQYWdlOzIyODQ1MzIwNTtBUzoxMDY1NDQwNTQxNDUwMjdAMTQwMjQxMzQ5MDY4OQ==
https://www.researchgate.net/publication/284038309_Variations_of_heat_transfer_coefficients_during_solidification_of_castings_in_metallic_moulds?el=1_x_8&enrichId=rgreq-e4300068c37c53cc17bd152d276047d2-XXX&enrichSource=Y292ZXJQYWdlOzIyODQ1MzIwNTtBUzoxMDY1NDQwNTQxNDUwMjdAMTQwMjQxMzQ5MDY4OQ==
https://www.researchgate.net/publication/279893660_APPLICATION_OF_A_COMPUTER_SIMULATION_SYSTEM_TO_ALUMINUM_PERMANENT_MOLD_CASTINGS?el=1_x_8&enrichId=rgreq-e4300068c37c53cc17bd152d276047d2-XXX&enrichSource=Y292ZXJQYWdlOzIyODQ1MzIwNTtBUzoxMDY1NDQwNTQxNDUwMjdAMTQwMjQxMzQ5MDY4OQ==
https://www.researchgate.net/publication/291987141_NUMERICAL_SIMULATION_OF_CASTING_SOLIDIFICATION?el=1_x_8&enrichId=rgreq-e4300068c37c53cc17bd152d276047d2-XXX&enrichSource=Y292ZXJQYWdlOzIyODQ1MzIwNTtBUzoxMDY1NDQwNTQxNDUwMjdAMTQwMjQxMzQ5MDY4OQ==
https://www.researchgate.net/publication/250154928_Coarsening_in_Solidification_Processing?el=1_x_8&enrichId=rgreq-e4300068c37c53cc17bd152d276047d2-XXX&enrichSource=Y292ZXJQYWdlOzIyODQ1MzIwNTtBUzoxMDY1NDQwNTQxNDUwMjdAMTQwMjQxMzQ5MDY4OQ==
https://www.researchgate.net/publication/284859680_Numerical_Heat_Transfer_and_Fluid_Flow?el=1_x_8&enrichId=rgreq-e4300068c37c53cc17bd152d276047d2-XXX&enrichSource=Y292ZXJQYWdlOzIyODQ1MzIwNTtBUzoxMDY1NDQwNTQxNDUwMjdAMTQwMjQxMzQ5MDY4OQ==
T.R. Vijayaram et al. / Journal of Materials Processing Technology 178 (2006) 29–33 31
• Pressurization rate, molten metal temperature and squeeze
pressure consideration in the case of squeeze casting process.
8. Procedure for applying solidification simulation
program
The procedure for carrying out a casting solidification simu-
lation program analysis is listed below [56]:
• Using the casting drawing, determine model scale and ele-
ment size.
• Make the solid model of the casting.
• Make the solid model of the proposed production method
(feeders, chills, insulators etc.). Use the program’s own
feeder-size calculator of required.
• Carry out thermal analysis to establish the order of solidifica-
tion.
• Carry out solidification simulation to a set quality standard,
for the selected alloy incorporating shrinkage percentage, in
gate effects etc. this results in the model being changed to
the predicted final shape (internal and external) of the cast-
ing showing size, shape and location of shrinkage cavities in
castings and feeders.
• Examine the predicted shrinkage (the equivalent of NDT) by
viewing and plotting of 3D ‘X-rays’ and sections of the model
in 2D slices or 3D sections and relating predicted defects to
solidification contours and required quality standards.
• If the predicted defects do not meet the required quality stan-
dard, develop an improved production method and repeat the
procedures. These trial-and-error sampling procedures can be
carried out very rapidly, allowing the operator to indulge in
any number of “what–if experiments”.
Basically, casting solidification simulation software program
performs firstly, the solid modeling, consecutively, the thermal
analysis and solifdifation simulation. During the simulation pro-
cess, the effect of varying molding position, ingate position,
mold materials, chills, insulating and exothermic materials can
be modelled, allowing the optimum method of making the cast-
ing to be predicted [56].
9. Experimental method and description for generating
time-temperature data
A model of squeeze casting process is analyzed for generat-
ing time-temperature data during the solidification process. In
squeeze casting process, the pressure is applied until the casting
gets solidified completely in the mold [51–53]. So, air gap is
seen only when the pressure is absence and it is not observed
when the pressure is applied [54,55]. The main components of
the experimental set-up for generating time-temperature data are
listed below.
• Data acquisition system (DAS).
• ADU Converter.
• Amplifier.
• Solidification simulation software.
• Metallic mold.
• Thermocouple leads.
• A suitable induction melting furnace to melt the metal or alloy
ingot.
• A suitable computer system with sufficient memory capacity.
• A graphic plotter.
The real experimental procedure of the solidification simula-
tion system is explained in a simplified manner with the aid of an
example. The selected metallic mold with the casting cavity is
placed on the floor and sufficient number of hole provisions are
made on it to insert the thermocouple lead wires on the selected
locations of the inside casting surface and at the interior loca-
tions apart by opted distances. The extended thermocouple wires
from the mold are connected to the input terminals of the data
acquisition system and the corresponding output leads are linked
to an amplifier to amplify the signals [45,46]. A suitable material
is melted temperature. The final output of the amplified signal
is fed to the computer which is supported by the solidification
simulation software package [33]. The used computer software
helps to generate the time-temperature data readings and it is
shown in Table 1. By using suitable graphic package, the data is
Table 1
Generated time-temperature data
Time Temperature
0 1400
30 1380
60 310
90 1260
120 1200
150 1100
180 1150
210 1040
240 980
270 900
300 840
330 660
360 660
390 660
420 660
450 660
480 660
510 660
540 660
570 660
600 660
630 600
660 520
690 480
720 420
750 380
780 340
810 300
840 260
870 230
900 200
930 170
960 140
990 100
1020 70
https://www.researchgate.net/publication/222445716_Finite_element_mesh_generation_methods_A_review_and_classification?el=1_x_8&enrichId=rgreq-e4300068c37c53cc17bd152d276047d2-XXX&enrichSource=Y292ZXJQYWdlOzIyODQ1MzIwNTtBUzoxMDY1NDQwNTQxNDUwMjdAMTQwMjQxMzQ5MDY4OQ==
https://www.researchgate.net/publication/223389615_Computer_simulation_of_the_effects_of_alloy_variables_on_the_grain_structures_of_castings?el=1_x_8&enrichId=rgreq-e4300068c37c53cc17bd152d276047d2-XXX&enrichSource=Y292ZXJQYWdlOzIyODQ1MzIwNTtBUzoxMDY1NDQwNTQxNDUwMjdAMTQwMjQxMzQ5MDY4OQ==
https://www.researchgate.net/publication/233845152_Bubbles_Drops_and_Particles?el=1_x_8&enrichId=rgreq-e4300068c37c53cc17bd152d276047d2-XXX&enrichSource=Y292ZXJQYWdlOzIyODQ1MzIwNTtBUzoxMDY1NDQwNTQxNDUwMjdAMTQwMjQxMzQ5MDY4OQ==
32 T.R. Vijayaram et al. / Journal of Materials Processing Technology 178 (2006) 29–33
Graph 1. Time-temperature curve generated from the computer solidification
simulation of a eutectic alloy.
further converted into a time-temperature plot which is shown
below in Graph 1.
The obtained time-temperature profile varies for different
materials poured in the liquid form in the mold. It is influenced
by the type of the poured metal or alloy or composite material
melted [5]. The behavior of recaleasence, latent heat of liber-
ation of the material during the phase transformation, melting
point, liquidus temperature, solidus temperature and solidifica-tion time can be studied from the generated graph [49,8,10].
10. Applications of casting solidification simulation
software programs
Casting solidification simulation software’s are in regular use
by aluminium, copper, iron and steel foundries using processes
ranging from green-sand, resin-and shell-bonded sand to invest-
ment and gravity die casting. Applications include [56]:
• Large steel castings such as heavy weighing turbine housings
and stern frames where improved yields and reduced fettling
costs were achieved.
• Critical high pressure valve castings.
• Repetition castings such as ductile iron crank shafts, where
modeling increases the chance of achieving ‘right first time’
methoding, so reducing the lead time for new castings.
Solidification simulation software’s are not only used by
foundry method engineers but also casting designers and
purchasers are using the software’s having experienced signif-
icant improved quality from their simulation software-using
suppliers.
11. Conclusion
Casting solidification simulation process is used to iden-
tify the defective locations in the castings from the generated
time-temperature contours. It is concluded that casting solidi-
fication simulation technology is used to eliminate defects like
shrinkage, porosity and to locate the hot spot regions which
helps to design the components effectively. Besides, it is used
to determine the solidification time and behavior of different
materials accurately. Hence, it is used to determine the cooling
rate influenced by the grain structure of castings. Solidification
simulation of castings provides time-temperature data, temper-
ature contours, hot spot locations, degree of recalescence, latent
heat of fusion and solidification time. The time-temperature plot
explains the effect of under cooling of solidifying castings which
reflects more on the inside microstructures responsible for mate-
rial properties
Acknowledgement
The authors express their sincere gratitude to the Department
of Mechanical and Manufacturing Engineering, Faculty of Engi-
neering, Universiti Putra Malaysia for the consent to publish this
paper.
References
[1] T. Iida, R.I.L. Guthrie, The Physics of Liquid Metals, Clarendon Press,
Oxford, 1988.
[2] A. Vogel, R.D. Doherty, B. Cantor, Solidification and Casting of Metals,
The Metals Society, London, 1979, pp. 518–525.
[3] M.C. Flemings, Solidification Processing, McGraw-Hill, New York,
1974.
[4] H.L. Lee, R.D. Doherty, E.A. Feest, J.M. Titchmarsh, Solidification
Technology in the Foundry and Cast House, The Metals Society, Lon-
don, 1983, p. 119.
[5] C. Beckermann, Modeling of macro segregation: applications and future
needs, Int. Mater. Rev. 47 (5) (2002) 243–261.
[6] J.D. Hunt, Solidification and Casting of Metals, Metals Society, London,
1979.
[7] W. Kurz, D.J. Fisher, Fundamentals of Solidification, Trans Tech Publi-
cations, Aedermannsdorf, Switzerland, 1989.
[8] ASM Hand Book, Casting, ASM International, vol. 15, 1988.
[9] R. Heine, Principles of Metal Casting, McGraw-Hill, 1999.
[10] S. Kalpakjian, S.R. Schmid, Manufacturing Engineering and Technology,
4th ed., International Edition Prentice-Hall, 2001.
[11] Numerical simulation of casting solidification in automotive applications,
in: C. Kim, C.-W. Kim (Eds.), Proceedings of the 18th Annual Automo-
tive Materials Symposium Sponsored by Detroit Section of TMS, May
1-2, 1991. Michigan State University, U.S.A., The Minerals, Metals and
Materials Society, TMS, U.S.A., 1991.
[12] J. Henzel, J. Keverian, Comparison of calculated and measured solidifi-
cation patterns in a variety of castings, AFS (Am. Foundry men’s Soc.)
Cast Met. Res. J. (1) (1965) 19–30.
[13] R.D. Pehlke, M.J. Kirt, R.E. Marrone, D.J. Cook, Numerical simulation
of casting solidification, Trans. Am. Foundry men’s Soc. (81) (1972)
517–523.
[14] K.G. Upadhya, D.M. Stefanescu, K. Lieu, D.P. Yegar, Computer-aided
cooling curve analysis, principles and applications in metal casting,
Trans. Am. Foundry men’s Soc. (97) (1989) 61–66.
[15] V.R. Voller, C.R. Swaminathan, B.G. Thomas, Fixed grid techniques
for phase change problems: a review, Int. J. Numer. Methods Eng. 30
(1990) 875–898.
[16] J. Isaac, G.P. Reddy, Variation of Heat Transfer Coefficients During
Solidification of Castings in Metallic Molds, British Foundry man, 1985,
pp. 465–468.
[17] Y. Nishida, W. Droste, S. Engler, The air-gap formation process at the
casting-mold interface and the heat transfer mechanism through the gap,
Metall. Trans. 17B (1986) 833–844.
[18] I.Y. Kodra, M. Sayawaki, A generalized automatic mesh generation
scheme for finite element method, Int. J. Numer. Methods Eng. 15 (1980)
713–731.
[19] C.S. Wei, J.T. Berry, Solidification simulation based on the edge function
approach, Trans. Am. Foundry men’s Soc. 91 (1983) 509–514.
[20] Z. Abdullah, M. Salaudean, K. Davis, Modeling permanent mould cast-
ing processes, Cast Met. (3) (1990) 7–14.
[21] Y.W. Lee, E. Chang, C.F. Chien, Modeling of feeding behavior of solid-
ifying Al–7Si–0.3Mg alloy plate castings, Metall. Trans. 21B (1990)
715–722.
https://www.researchgate.net/publication/250675976_Modeling_of_feeding_behavior_of_solidifying_Al7Si03Mg_alloy_plate_casting?el=1_x_8&enrichId=rgreq-e4300068c37c53cc17bd152d276047d2-XXX&enrichSource=Y292ZXJQYWdlOzIyODQ1MzIwNTtBUzoxMDY1NDQwNTQxNDUwMjdAMTQwMjQxMzQ5MDY4OQ==
https://www.researchgate.net/publication/250675976_Modeling_of_feeding_behavior_of_solidifying_Al7Si03Mg_alloy_plate_casting?el=1_x_8&enrichId=rgreq-e4300068c37c53cc17bd152d276047d2-XXX&enrichSource=Y292ZXJQYWdlOzIyODQ1MzIwNTtBUzoxMDY1NDQwNTQxNDUwMjdAMTQwMjQxMzQ5MDY4OQ==
https://www.researchgate.net/publication/250675976_Modeling_of_feeding_behavior_of_solidifying_Al7Si03Mg_alloy_plate_casting?el=1_x_8&enrichId=rgreq-e4300068c37c53cc17bd152d276047d2-XXX&enrichSource=Y292ZXJQYWdlOzIyODQ1MzIwNTtBUzoxMDY1NDQwNTQxNDUwMjdAMTQwMjQxMzQ5MDY4OQ==
https://www.researchgate.net/publication/227768350_Fixed_Grid_Techniques_for_Phase_Change_Problems_A_Review?el=1_x_8&enrichId=rgreq-e4300068c37c53cc17bd152d276047d2-XXX&enrichSource=Y292ZXJQYWdlOzIyODQ1MzIwNTtBUzoxMDY1NDQwNTQxNDUwMjdAMTQwMjQxMzQ5MDY4OQ==
https://www.researchgate.net/publication/227768350_Fixed_Grid_Techniques_for_Phase_Change_Problems_A_Review?el=1_x_8&enrichId=rgreq-e4300068c37c53cc17bd152d276047d2-XXX&enrichSource=Y292ZXJQYWdlOzIyODQ1MzIwNTtBUzoxMDY1NDQwNTQxNDUwMjdAMTQwMjQxMzQ5MDY4OQ==
https://www.researchgate.net/publication/227768350_Fixed_Grid_Techniques_for_Phase_Change_Problems_A_Review?el=1_x_8&enrichId=rgreq-e4300068c37c53cc17bd152d276047d2-XXX&enrichSource=Y292ZXJQYWdlOzIyODQ1MzIwNTtBUzoxMDY1NDQwNTQxNDUwMjdAMTQwMjQxMzQ5MDY4OQ==
https://www.researchgate.net/publication/225599976_The_Air-Gap_Formation_at_the_Casting-Mold_Interface_and_the_Heat_Transfer_Mechanism_through_the_Gap?el=1_x_8&enrichId=rgreq-e4300068c37c53cc17bd152d276047d2-XXX&enrichSource=Y292ZXJQYWdlOzIyODQ1MzIwNTtBUzoxMDY1NDQwNTQxNDUwMjdAMTQwMjQxMzQ5MDY4OQ==
https://www.researchgate.net/publication/225599976_The_Air-Gap_Formation_at_the_Casting-Mold_Interface_and_the_Heat_Transfer_Mechanism_through_the_Gap?el=1_x_8&enrichId=rgreq-e4300068c37c53cc17bd152d276047d2-XXX&enrichSource=Y292ZXJQYWdlOzIyODQ1MzIwNTtBUzoxMDY1NDQwNTQxNDUwMjdAMTQwMjQxMzQ5MDY4OQ==
https://www.researchgate.net/publication/225599976_The_Air-Gap_Formation_at_the_Casting-Mold_Interface_and_the_Heat_Transfer_Mechanism_through_the_Gap?el=1_x_8&enrichId=rgreq-e4300068c37c53cc17bd152d276047d2-XXX&enrichSource=Y292ZXJQYWdlOzIyODQ1MzIwNTtBUzoxMDY1NDQwNTQxNDUwMjdAMTQwMjQxMzQ5MDY4OQ==
https://www.researchgate.net/publication/260086296_Computer-aided_Cooling_Curve_Analysis_Principles_and_Applications_in_Metal_Casting?el=1_x_8&enrichId=rgreq-e4300068c37c53cc17bd152d276047d2-XXX&enrichSource=Y292ZXJQYWdlOzIyODQ1MzIwNTtBUzoxMDY1NDQwNTQxNDUwMjdAMTQwMjQxMzQ5MDY4OQ==
https://www.researchgate.net/publication/260086296_Computer-aided_Cooling_Curve_Analysis_Principles_and_Applications_in_Metal_Casting?el=1_x_8&enrichId=rgreq-e4300068c37c53cc17bd152d276047d2-XXX&enrichSource=Y292ZXJQYWdlOzIyODQ1MzIwNTtBUzoxMDY1NDQwNTQxNDUwMjdAMTQwMjQxMzQ5MDY4OQ==https://www.researchgate.net/publication/260086296_Computer-aided_Cooling_Curve_Analysis_Principles_and_Applications_in_Metal_Casting?el=1_x_8&enrichId=rgreq-e4300068c37c53cc17bd152d276047d2-XXX&enrichSource=Y292ZXJQYWdlOzIyODQ1MzIwNTtBUzoxMDY1NDQwNTQxNDUwMjdAMTQwMjQxMzQ5MDY4OQ==
https://www.researchgate.net/publication/234228377_Summary_of_Thermal_Properties_for_Casting_Alloys_and_Mold_Materials?el=1_x_8&enrichId=rgreq-e4300068c37c53cc17bd152d276047d2-XXX&enrichSource=Y292ZXJQYWdlOzIyODQ1MzIwNTtBUzoxMDY1NDQwNTQxNDUwMjdAMTQwMjQxMzQ5MDY4OQ==
https://www.researchgate.net/publication/284038309_Variations_of_heat_transfer_coefficients_during_solidification_of_castings_in_metallic_moulds?el=1_x_8&enrichId=rgreq-e4300068c37c53cc17bd152d276047d2-XXX&enrichSource=Y292ZXJQYWdlOzIyODQ1MzIwNTtBUzoxMDY1NDQwNTQxNDUwMjdAMTQwMjQxMzQ5MDY4OQ==
https://www.researchgate.net/publication/284038309_Variations_of_heat_transfer_coefficients_during_solidification_of_castings_in_metallic_moulds?el=1_x_8&enrichId=rgreq-e4300068c37c53cc17bd152d276047d2-XXX&enrichSource=Y292ZXJQYWdlOzIyODQ1MzIwNTtBUzoxMDY1NDQwNTQxNDUwMjdAMTQwMjQxMzQ5MDY4OQ==
https://www.researchgate.net/publication/284038309_Variations_of_heat_transfer_coefficients_during_solidification_of_castings_in_metallic_moulds?el=1_x_8&enrichId=rgreq-e4300068c37c53cc17bd152d276047d2-XXX&enrichSource=Y292ZXJQYWdlOzIyODQ1MzIwNTtBUzoxMDY1NDQwNTQxNDUwMjdAMTQwMjQxMzQ5MDY4OQ==
https://www.researchgate.net/publication/285166715_Fundamentals_of_Solidification?el=1_x_8&enrichId=rgreq-e4300068c37c53cc17bd152d276047d2-XXX&enrichSource=Y292ZXJQYWdlOzIyODQ1MzIwNTtBUzoxMDY1NDQwNTQxNDUwMjdAMTQwMjQxMzQ5MDY4OQ==
https://www.researchgate.net/publication/285166715_Fundamentals_of_Solidification?el=1_x_8&enrichId=rgreq-e4300068c37c53cc17bd152d276047d2-XXX&enrichSource=Y292ZXJQYWdlOzIyODQ1MzIwNTtBUzoxMDY1NDQwNTQxNDUwMjdAMTQwMjQxMzQ5MDY4OQ==
https://www.researchgate.net/publication/291987141_NUMERICAL_SIMULATION_OF_CASTING_SOLIDIFICATION?el=1_x_8&enrichId=rgreq-e4300068c37c53cc17bd152d276047d2-XXX&enrichSource=Y292ZXJQYWdlOzIyODQ1MzIwNTtBUzoxMDY1NDQwNTQxNDUwMjdAMTQwMjQxMzQ5MDY4OQ==
https://www.researchgate.net/publication/291987141_NUMERICAL_SIMULATION_OF_CASTING_SOLIDIFICATION?el=1_x_8&enrichId=rgreq-e4300068c37c53cc17bd152d276047d2-XXX&enrichSource=Y292ZXJQYWdlOzIyODQ1MzIwNTtBUzoxMDY1NDQwNTQxNDUwMjdAMTQwMjQxMzQ5MDY4OQ==
https://www.researchgate.net/publication/291987141_NUMERICAL_SIMULATION_OF_CASTING_SOLIDIFICATION?el=1_x_8&enrichId=rgreq-e4300068c37c53cc17bd152d276047d2-XXX&enrichSource=Y292ZXJQYWdlOzIyODQ1MzIwNTtBUzoxMDY1NDQwNTQxNDUwMjdAMTQwMjQxMzQ5MDY4OQ==
https://www.researchgate.net/publication/250154928_Coarsening_in_Solidification_Processing?el=1_x_8&enrichId=rgreq-e4300068c37c53cc17bd152d276047d2-XXX&enrichSource=Y292ZXJQYWdlOzIyODQ1MzIwNTtBUzoxMDY1NDQwNTQxNDUwMjdAMTQwMjQxMzQ5MDY4OQ==
https://www.researchgate.net/publication/250154928_Coarsening_in_Solidification_Processing?el=1_x_8&enrichId=rgreq-e4300068c37c53cc17bd152d276047d2-XXX&enrichSource=Y292ZXJQYWdlOzIyODQ1MzIwNTtBUzoxMDY1NDQwNTQxNDUwMjdAMTQwMjQxMzQ5MDY4OQ==
T.R. Vijayaram et al. / Journal of Materials Processing Technology 178 (2006) 29–33 33
[22] E.N. Pan, C.S. Lim, C.R. Loper, Effects of solidification parameters on
the feeding efficiency of A 356 Aluminium alloy, Trans. Am. Foundry
men’s Soc. (98) (1990) 735–746.
[23] K. Kubo, R.D. Pehlke, Mathematical modeling of porosity formation in
solidification, Metall. Trans. B 16B (1985) 359–366.
[24] G. Comini, S. Del Guidice, R.W. Lewis, O.C. Zienkiewicz, Finite ele-
ment solution of non-linear heat conduction problems with special ref-
erence to phase change, Int. J. Numer. Methods Eng. 8 (1974) 613–624.
[25] T.W. Clyne, The use of heat flow modeling to explore solidification
phenomena, Metall. Trans. B 13B (1982) 471–478.
[26] M.J. Beffel, J.O. Wilkes, R.D. Pehlke, Finite element simulation of cast-
ing processes, Trans. Am. Foundry men’s Soc. 94 (1986) 757–764.
[27] K. Morgan, R.W. Lewis, O.C. Zienkiewicz, An improved algorithm for
heat conduction problems with phase change, Int. J. Numer. Methods
Eng. 12 (1987) 1191–1195.
[28] R.W. Lewis, P.M. Roberts, Finite element simulation of solidification
problems, Appl. Sci. Res. 44 (1987) 61–92.
[29] J.T. Berry, R.D. Pehlke, Modeling Solidification Heat Transfer Metals
Hand Book, Casting, vol. 15, 9th ed., ASM International, Metals Park,
Ohio, U.S.A., 1988, pp. 858–866.
[30] R.W. Ruddle, The solidification of castings, Inst. Met. (1957) 377.
[31] H.S. Carslaw, J.C. Jaeger, Conduction of Heat in Solids, 2nd ed., Claren-
don Press, London, 1959.
[32] S. Bourne, J.A. Spittle, Solidification Processing, Institute of Metals,
London, 1987, pp. 291–293.
[33] J.A. Spittle, S.G.R. Brown, Computer simulation of the effects of alloy
variables on the grain structure of castings, Acta Metall. 37 (7) (1989)
1803–1810.
[34] D.M. Stefanescu, G. Upadhya, D. Bandyopadhyay, Heat transfer-
solidification kinetics modeling of solidification of castings, Metall.
Trans. 21A (1990) 997.
[35] C.S. Kanetkar, D.M. Stefanescu, Macro-micro modeling of solidifica-
tion of hypoeutectic and eutectic Aluminium–Silicon alloys, Trans. Am.
Foundry men’s Soc. 96 (1988) 591–598.
[36] M. Rappaz, Modeling of microstructure formation in solidification pro-
cesses, Int. Mater. Rev. 34 (3) (1989) 93–123.
[37] W.D. Rolph, K.J. Bathe, An efficient algorithm for analysis of non-linear
heat transfer with phase change, Int. J. Numer. Methods Eng. 18 (1982)
119–134.
[38] J. Roose, O. Storrer, Modelization of phase changes by fictitious heat
flow, Int. J. Numer. Methods Eng. 20 (1984) 217–225.
[39] I.G. Chan, D.D. Stefanescu, Computer-aided differential thermal analysis
of spheroidal and compacted graphite cast iron, Trans. Am. Foundry
men’s Soc. 92 (1984) 947–964.
[40] R.W. Heine, J.J. Uiker, D. Gantenbein, Geometric modeling of mold
aggregate, superheat, edge effects, feeding distance, chills and solidifi-
cation microstructure, Trans. Am. Foundry men’s Soc. 92 (1984) 135–
150.
[41] Y. Ohtsuka, K. Mizuno, J. Yamada, Application of a computer simulation
system to Aluminium permanent mold castings, Trans. Am. Foundry
men’s Soc. 82 (1989) 635–646.
[42] Suhas V. Patankar, Numerical Heat Transfer and Fluid Flow, Hemisphere
Publishing Corporation, New York, 1980.
[43] General Information—Chemical compositions, mechanical and phys-
ical properties of SAE Aluminium casting alloys, SAE Information
Report J 452, January 1989, SAE Hand Book, vol. 1, 1991, pp. 10.06–
10.14.
[44] E.M. Sparrow, R.D. Cess, Radiation Heat Transfer, Hemisphere Publish-
ing Corporation, New York, U.S.A., 1978.
[45] K. Ho-Le, Finite element mesh generation methods: a review and clas-
sification, Comput. Aided Des. 20 (1988) 27–38.
[46] P.M. Finnigan, A.F. Hathaway, W.E. Lorensen, CATFEM: computer
assisted tomography to finite element modeling, Comput. Eng. 2 (ASME
1990) (1990) 153–160.
[47] W. Oldfield, A quantitative approach to casting solidification: freezing
of cast iron, Trans. Am. Soc. Met. (59) (1966) 945–959.
[48] C.E. Bates, G.L. Oliver, R.H. McSwain, Volumetric changes during
freezing of ductile irons, Trans. Am. Foundry men’s Soc. (86) (1977)
289–298.
[49] R.D. Pehlke, A. Jeyarajan, H. Wada, Summary of Thermal Properties
for Cast Alloys and Mold Materials, The University of Michigan, Ann
Arbor, 1982.
[50] J.A. Dantzig, J. Wiese, S.C. Lu, Modeling of heat flow in sand castings,
part-1 and part-2, Metall. Trans. 16B (1985) 195–209.
[51] V. Ekpoom, R.W. Heine, Thermal analysis (DHA) of cast iron, Trans.
Am. Foundry men’s Soc. 89 (1981) 27–38.
[52] A.J. Surula, T. Rantala, A. Louro, Possibility of controlling the qual-
ity of SG-Irons by computerized thermal analysis, in: FOCOMP 1986
Conference, Krakar, Poland, June 1986.
[53] J.R. Cuthill, et al., Computerized metallurgical data base, The Metall.
Soc. (1988) 3.
[54] R. Clift, J.R. Grace, M.E. Weber, Bubbles Drops and Particles, Academic
Press, 1978, pp. 314–318.
[55]R.L. Lewis, S. Liou, D. Ye, Literature review of solidification simulation
in the design of sand castings, Res. J 17 (1987) 1–11.
[56] The Foseco Foundry man’s Hand Book, Foseco, revised and edited by
John R Brown, 10th ed., Butterworth-Heinemann, Foseco International
Ltd., Birmingham, U.K., 1994.
https://www.researchgate.net/publication/37426216_Modelling_of_microstructure_formation_in_solidification_processes?el=1_x_8&enrichId=rgreq-e4300068c37c53cc17bd152d276047d2-XXX&enrichSource=Y292ZXJQYWdlOzIyODQ1MzIwNTtBUzoxMDY1NDQwNTQxNDUwMjdAMTQwMjQxMzQ5MDY4OQ==
https://www.researchgate.net/publication/37426216_Modelling_of_microstructure_formation_in_solidification_processes?el=1_x_8&enrichId=rgreq-e4300068c37c53cc17bd152d276047d2-XXX&enrichSource=Y292ZXJQYWdlOzIyODQ1MzIwNTtBUzoxMDY1NDQwNTQxNDUwMjdAMTQwMjQxMzQ5MDY4OQ==
https://www.researchgate.net/publication/225694269_Heat_transfer-solidification_kinetics_modeling_of_solidification_of_castings?el=1_x_8&enrichId=rgreq-e4300068c37c53cc17bd152d276047d2-XXX&enrichSource=Y292ZXJQYWdlOzIyODQ1MzIwNTtBUzoxMDY1NDQwNTQxNDUwMjdAMTQwMjQxMzQ5MDY4OQ==
https://www.researchgate.net/publication/225694269_Heat_transfer-solidification_kinetics_modeling_of_solidification_of_castings?el=1_x_8&enrichId=rgreq-e4300068c37c53cc17bd152d276047d2-XXX&enrichSource=Y292ZXJQYWdlOzIyODQ1MzIwNTtBUzoxMDY1NDQwNTQxNDUwMjdAMTQwMjQxMzQ5MDY4OQ==
https://www.researchgate.net/publication/225694269_Heat_transfer-solidification_kinetics_modeling_of_solidification_of_castings?el=1_x_8&enrichId=rgreq-e4300068c37c53cc17bd152d276047d2-XXX&enrichSource=Y292ZXJQYWdlOzIyODQ1MzIwNTtBUzoxMDY1NDQwNTQxNDUwMjdAMTQwMjQxMzQ5MDY4OQ==
https://www.researchgate.net/publication/230256958_Modelization_of_phase_change_by_fictitious_heat_flow?el=1_x_8&enrichId=rgreq-e4300068c37c53cc17bd152d276047d2-XXX&enrichSource=Y292ZXJQYWdlOzIyODQ1MzIwNTtBUzoxMDY1NDQwNTQxNDUwMjdAMTQwMjQxMzQ5MDY4OQ==
https://www.researchgate.net/publication/230256958_Modelization_of_phase_change_by_fictitious_heat_flow?el=1_x_8&enrichId=rgreq-e4300068c37c53cc17bd152d276047d2-XXX&enrichSource=Y292ZXJQYWdlOzIyODQ1MzIwNTtBUzoxMDY1NDQwNTQxNDUwMjdAMTQwMjQxMzQ5MDY4OQ==
https://www.researchgate.net/publication/260086364_Computer-Aided_Differential_Thermal_Analysis_of_Spheroidal_and_Compacted_Graphite_Cast_Irons?el=1_x_8&enrichId=rgreq-e4300068c37c53cc17bd152d276047d2-XXX&enrichSource=Y292ZXJQYWdlOzIyODQ1MzIwNTtBUzoxMDY1NDQwNTQxNDUwMjdAMTQwMjQxMzQ5MDY4OQ==
https://www.researchgate.net/publication/260086364_Computer-Aided_Differential_Thermal_Analysis_of_Spheroidal_and_Compacted_Graphite_Cast_Irons?el=1_x_8&enrichId=rgreq-e4300068c37c53cc17bd152d276047d2-XXX&enrichSource=Y292ZXJQYWdlOzIyODQ1MzIwNTtBUzoxMDY1NDQwNTQxNDUwMjdAMTQwMjQxMzQ5MDY4OQ==
https://www.researchgate.net/publication/260086364_Computer-Aided_Differential_Thermal_Analysis_of_Spheroidal_and_Compacted_Graphite_Cast_Irons?el=1_x_8&enrichId=rgreq-e4300068c37c53cc17bd152d276047d2-XXX&enrichSource=Y292ZXJQYWdlOzIyODQ1MzIwNTtBUzoxMDY1NDQwNTQxNDUwMjdAMTQwMjQxMzQ5MDY4OQ==
https://www.researchgate.net/publication/234328085_Conduction_of_Heat_in_SolidS?el=1_x_8&enrichId=rgreq-e4300068c37c53cc17bd152d276047d2-XXX&enrichSource=Y292ZXJQYWdlOzIyODQ1MzIwNTtBUzoxMDY1NDQwNTQxNDUwMjdAMTQwMjQxMzQ5MDY4OQ==
https://www.researchgate.net/publication/234328085_Conduction_of_Heat_in_SolidS?el=1_x_8&enrichId=rgreq-e4300068c37c53cc17bd152d276047d2-XXX&enrichSource=Y292ZXJQYWdlOzIyODQ1MzIwNTtBUzoxMDY1NDQwNTQxNDUwMjdAMTQwMjQxMzQ5MDY4OQ==
https://www.researchgate.net/publication/222445716_Finite_element_mesh_generation_methods_A_review_and_classification?el=1_x_8&enrichId=rgreq-e4300068c37c53cc17bd152d276047d2-XXX&enrichSource=Y292ZXJQYWdlOzIyODQ1MzIwNTtBUzoxMDY1NDQwNTQxNDUwMjdAMTQwMjQxMzQ5MDY4OQ==
https://www.researchgate.net/publication/222445716_Finite_element_mesh_generation_methods_A_review_and_classification?el=1_x_8&enrichId=rgreq-e4300068c37c53cc17bd152d276047d2-XXX&enrichSource=Y292ZXJQYWdlOzIyODQ1MzIwNTtBUzoxMDY1NDQwNTQxNDUwMjdAMTQwMjQxMzQ5MDY4OQ==
https://www.researchgate.net/publication/223389615_Computer_simulation_of_the_effects_of_alloy_variables_on_the_grain_structures_of_castings?el=1_x_8&enrichId=rgreq-e4300068c37c53cc17bd152d276047d2-XXX&enrichSource=Y292ZXJQYWdlOzIyODQ1MzIwNTtBUzoxMDY1NDQwNTQxNDUwMjdAMTQwMjQxMzQ5MDY4OQ==
https://www.researchgate.net/publication/223389615_Computer_simulation_of_the_effects_of_alloy_variables_on_the_grain_structures_of_castings?el=1_x_8&enrichId=rgreq-e4300068c37c53cc17bd152d276047d2-XXX&enrichSource=Y292ZXJQYWdlOzIyODQ1MzIwNTtBUzoxMDY1NDQwNTQxNDUwMjdAMTQwMjQxMzQ5MDY4OQ==
https://www.researchgate.net/publication/223389615_Computer_simulation_of_the_effects_of_alloy_variables_on_the_grain_structures_of_castings?el=1_x_8&enrichId=rgreq-e4300068c37c53cc17bd152d276047d2-XXX&enrichSource=Y292ZXJQYWdlOzIyODQ1MzIwNTtBUzoxMDY1NDQwNTQxNDUwMjdAMTQwMjQxMzQ5MDY4OQ==
https://www.researchgate.net/publication/229789264_Finite_Element_Solution_of_Non-Linear_Heat_Conduction_Problems_with_Special_Reference_to_Phase_Change?el=1_x_8&enrichId=rgreq-e4300068c37c53cc17bd152d276047d2-XXX&enrichSource=Y292ZXJQYWdlOzIyODQ1MzIwNTtBUzoxMDY1NDQwNTQxNDUwMjdAMTQwMjQxMzQ5MDY4OQ==
https://www.researchgate.net/publication/229789264_Finite_Element_Solution_of_Non-Linear_Heat_Conduction_Problems_with_Special_Reference_to_Phase_Change?el=1_x_8&enrichId=rgreq-e4300068c37c53cc17bd152d276047d2-XXX&enrichSource=Y292ZXJQYWdlOzIyODQ1MzIwNTtBUzoxMDY1NDQwNTQxNDUwMjdAMTQwMjQxMzQ5MDY4OQ==
https://www.researchgate.net/publication/229789264_Finite_Element_Solution_of_Non-Linear_Heat_Conduction_Problems_with_Special_Reference_to_Phase_Change?el=1_x_8&enrichId=rgreq-e4300068c37c53cc17bd152d276047d2-XXX&enrichSource=Y292ZXJQYWdlOzIyODQ1MzIwNTtBUzoxMDY1NDQwNTQxNDUwMjdAMTQwMjQxMzQ5MDY4OQ==
https://www.researchgate.net/publication/225483016_The_use_of_heat_flow_modeling_to_explore_solidification_phenomena?el=1_x_8&enrichId=rgreq-e4300068c37c53cc17bd152d276047d2-XXX&enrichSource=Y292ZXJQYWdlOzIyODQ1MzIwNTtBUzoxMDY1NDQwNTQxNDUwMjdAMTQwMjQxMzQ5MDY4OQ==
https://www.researchgate.net/publication/225483016_The_use_of_heat_flow_modeling_to_explore_solidification_phenomena?el=1_x_8&enrichId=rgreq-e4300068c37c53cc17bd152d276047d2-XXX&enrichSource=Y292ZXJQYWdlOzIyODQ1MzIwNTtBUzoxMDY1NDQwNTQxNDUwMjdAMTQwMjQxMzQ5MDY4OQ==
https://www.researchgate.net/publication/233845152_Bubbles_Drops_and_Particles?el=1_x_8&enrichId=rgreq-e4300068c37c53cc17bd152d276047d2-XXX&enrichSource=Y292ZXJQYWdlOzIyODQ1MzIwNTtBUzoxMDY1NDQwNTQxNDUwMjdAMTQwMjQxMzQ5MDY4OQ==
https://www.researchgate.net/publication/233845152_Bubbles_Drops_and_Particles?el=1_x_8&enrichId=rgreq-e4300068c37c53cc17bd152d276047d2-XXX&enrichSource=Y292ZXJQYWdlOzIyODQ1MzIwNTtBUzoxMDY1NDQwNTQxNDUwMjdAMTQwMjQxMzQ5MDY4OQ==
https://www.researchgate.net/publication/234467296_Radiation_Heat_Transfer?el=1_x_8&enrichId=rgreq-e4300068c37c53cc17bd152d276047d2-XXX&enrichSource=Y292ZXJQYWdlOzIyODQ1MzIwNTtBUzoxMDY1NDQwNTQxNDUwMjdAMTQwMjQxMzQ5MDY4OQ==
https://www.researchgate.net/publication/234467296_Radiation_Heat_Transfer?el=1_x_8&enrichId=rgreq-e4300068c37c53cc17bd152d276047d2-XXX&enrichSource=Y292ZXJQYWdlOzIyODQ1MzIwNTtBUzoxMDY1NDQwNTQxNDUwMjdAMTQwMjQxMzQ5MDY4OQ==
https://www.researchgate.net/publication/234228377_Summary_of_Thermal_Properties_for_Casting_Alloys_and_Mold_Materials?el=1_x_8&enrichId=rgreq-e4300068c37c53cc17bd152d276047d2-XXX&enrichSource=Y292ZXJQYWdlOzIyODQ1MzIwNTtBUzoxMDY1NDQwNTQxNDUwMjdAMTQwMjQxMzQ5MDY4OQ==
https://www.researchgate.net/publication/234228377_Summary_of_Thermal_Properties_for_Casting_Alloys_and_Mold_Materials?el=1_x_8&enrichId=rgreq-e4300068c37c53cc17bd152d276047d2-XXX&enrichSource=Y292ZXJQYWdlOzIyODQ1MzIwNTtBUzoxMDY1NDQwNTQxNDUwMjdAMTQwMjQxMzQ5MDY4OQ==
https://www.researchgate.net/publication/234228377_Summary_of_Thermal_Properties_for_Casting_Alloys_and_Mold_Materials?el=1_x_8&enrichId=rgreq-e4300068c37c53cc17bd152d276047d2-XXX&enrichSource=Y292ZXJQYWdlOzIyODQ1MzIwNTtBUzoxMDY1NDQwNTQxNDUwMjdAMTQwMjQxMzQ5MDY4OQ==
https://www.researchgate.net/publication/229808565_An_Improved_Algorithm_for_Heat_Conduction_Problems_with_Phase_Change?el=1_x_8&enrichId=rgreq-e4300068c37c53cc17bd152d276047d2-XXX&enrichSource=Y292ZXJQYWdlOzIyODQ1MzIwNTtBUzoxMDY1NDQwNTQxNDUwMjdAMTQwMjQxMzQ5MDY4OQ==https://www.researchgate.net/publication/229808565_An_Improved_Algorithm_for_Heat_Conduction_Problems_with_Phase_Change?el=1_x_8&enrichId=rgreq-e4300068c37c53cc17bd152d276047d2-XXX&enrichSource=Y292ZXJQYWdlOzIyODQ1MzIwNTtBUzoxMDY1NDQwNTQxNDUwMjdAMTQwMjQxMzQ5MDY4OQ==
https://www.researchgate.net/publication/229808565_An_Improved_Algorithm_for_Heat_Conduction_Problems_with_Phase_Change?el=1_x_8&enrichId=rgreq-e4300068c37c53cc17bd152d276047d2-XXX&enrichSource=Y292ZXJQYWdlOzIyODQ1MzIwNTtBUzoxMDY1NDQwNTQxNDUwMjdAMTQwMjQxMzQ5MDY4OQ==
https://www.researchgate.net/publication/225249320_Mathematical_modeling_of_porosity_formation_in_solidification?el=1_x_8&enrichId=rgreq-e4300068c37c53cc17bd152d276047d2-XXX&enrichSource=Y292ZXJQYWdlOzIyODQ1MzIwNTtBUzoxMDY1NDQwNTQxNDUwMjdAMTQwMjQxMzQ5MDY4OQ==
https://www.researchgate.net/publication/225249320_Mathematical_modeling_of_porosity_formation_in_solidification?el=1_x_8&enrichId=rgreq-e4300068c37c53cc17bd152d276047d2-XXX&enrichSource=Y292ZXJQYWdlOzIyODQ1MzIwNTtBUzoxMDY1NDQwNTQxNDUwMjdAMTQwMjQxMzQ5MDY4OQ==
https://www.researchgate.net/publication/229747879_An_efficient_algorithm_for_analysis_of_nonlinear_heat_transfer_with_phase_changes?el=1_x_8&enrichId=rgreq-e4300068c37c53cc17bd152d276047d2-XXX&enrichSource=Y292ZXJQYWdlOzIyODQ1MzIwNTtBUzoxMDY1NDQwNTQxNDUwMjdAMTQwMjQxMzQ5MDY4OQ==
https://www.researchgate.net/publication/229747879_An_efficient_algorithm_for_analysis_of_nonlinear_heat_transfer_with_phase_changes?el=1_x_8&enrichId=rgreq-e4300068c37c53cc17bd152d276047d2-XXX&enrichSource=Y292ZXJQYWdlOzIyODQ1MzIwNTtBUzoxMDY1NDQwNTQxNDUwMjdAMTQwMjQxMzQ5MDY4OQ==
https://www.researchgate.net/publication/229747879_An_efficient_algorithm_for_analysis_of_nonlinear_heat_transfer_with_phase_changes?el=1_x_8&enrichId=rgreq-e4300068c37c53cc17bd152d276047d2-XXX&enrichSource=Y292ZXJQYWdlOzIyODQ1MzIwNTtBUzoxMDY1NDQwNTQxNDUwMjdAMTQwMjQxMzQ5MDY4OQ==
https://www.researchgate.net/publication/284672671_Effects_of_solidification_parameters_on_the_feeding_efficiency_of_A356_aluminum_alloy?el=1_x_8&enrichId=rgreq-e4300068c37c53cc17bd152d276047d2-XXX&enrichSource=Y292ZXJQYWdlOzIyODQ1MzIwNTtBUzoxMDY1NDQwNTQxNDUwMjdAMTQwMjQxMzQ5MDY4OQ==
https://www.researchgate.net/publication/284672671_Effects_of_solidification_parameters_on_the_feeding_efficiency_of_A356_aluminum_alloy?el=1_x_8&enrichId=rgreq-e4300068c37c53cc17bd152d276047d2-XXX&enrichSource=Y292ZXJQYWdlOzIyODQ1MzIwNTtBUzoxMDY1NDQwNTQxNDUwMjdAMTQwMjQxMzQ5MDY4OQ==
https://www.researchgate.net/publication/284672671_Effects_of_solidification_parameters_on_the_feeding_efficiency_of_A356_aluminum_alloy?el=1_x_8&enrichId=rgreq-e4300068c37c53cc17bd152d276047d2-XXX&enrichSource=Y292ZXJQYWdlOzIyODQ1MzIwNTtBUzoxMDY1NDQwNTQxNDUwMjdAMTQwMjQxMzQ5MDY4OQ==
https://www.researchgate.net/publication/290104372_Finite_element_simulation_of_solidification_problems?el=1_x_8&enrichId=rgreq-e4300068c37c53cc17bd152d276047d2-XXX&enrichSource=Y292ZXJQYWdlOzIyODQ1MzIwNTtBUzoxMDY1NDQwNTQxNDUwMjdAMTQwMjQxMzQ5MDY4OQ==
https://www.researchgate.net/publication/290104372_Finite_element_simulation_of_solidification_problems?el=1_x_8&enrichId=rgreq-e4300068c37c53cc17bd152d276047d2-XXX&enrichSource=Y292ZXJQYWdlOzIyODQ1MzIwNTtBUzoxMDY1NDQwNTQxNDUwMjdAMTQwMjQxMzQ5MDY4OQ==
https://www.researchgate.net/publication/279893660_APPLICATION_OF_A_COMPUTER_SIMULATION_SYSTEM_TO_ALUMINUM_PERMANENT_MOLD_CASTINGS?el=1_x_8&enrichId=rgreq-e4300068c37c53cc17bd152d276047d2-XXX&enrichSource=Y292ZXJQYWdlOzIyODQ1MzIwNTtBUzoxMDY1NDQwNTQxNDUwMjdAMTQwMjQxMzQ5MDY4OQ==
https://www.researchgate.net/publication/279893660_APPLICATION_OF_A_COMPUTER_SIMULATION_SYSTEM_TO_ALUMINUM_PERMANENT_MOLD_CASTINGS?el=1_x_8&enrichId=rgreq-e4300068c37c53cc17bd152d276047d2-XXX&enrichSource=Y292ZXJQYWdlOzIyODQ1MzIwNTtBUzoxMDY1NDQwNTQxNDUwMjdAMTQwMjQxMzQ5MDY4OQ==
https://www.researchgate.net/publication/279893660_APPLICATION_OF_A_COMPUTER_SIMULATION_SYSTEM_TO_ALUMINUM_PERMANENT_MOLD_CASTINGS?el=1_x_8&enrichId=rgreq-e4300068c37c53cc17bd152d276047d2-XXX&enrichSource=Y292ZXJQYWdlOzIyODQ1MzIwNTtBUzoxMDY1NDQwNTQxNDUwMjdAMTQwMjQxMzQ5MDY4OQ==
https://www.researchgate.net/publication/284859680_Numerical_Heat_Transfer_and_Fluid_Flow?el=1_x_8&enrichId=rgreq-e4300068c37c53cc17bd152d276047d2-XXX&enrichSource=Y292ZXJQYWdlOzIyODQ1MzIwNTtBUzoxMDY1NDQwNTQxNDUwMjdAMTQwMjQxMzQ5MDY4OQ==
https://www.researchgate.net/publication/284859680_Numerical_Heat_Transfer_and_Fluid_Flow?el=1_x_8&enrichId=rgreq-e4300068c37c53cc17bd152d276047d2-XXX&enrichSource=Y292ZXJQYWdlOzIyODQ1MzIwNTtBUzoxMDY1NDQwNTQxNDUwMjdAMTQwMjQxMzQ5MDY4OQ==