140
Development of new welding materials and technologies
based on computer simulation
M. Zinigrad
College of Judea & Samaria, Ariel, Israel
Abstract
The mathematical modeling of real welding technologies based on a physicochemical
analysis of the interact
ion between the phases (metal, slag, and gas) is employed in the
present work. The model is based on the fundamental equations of the thermodynamics and
kinetics of high

temperature metallurgical reactions and factors which take into account the
thermal an
d hydrodynamics conditions of the real process.
Such an approach permits optimization of the composition of the materials and the
technology of the process already in the planning stage with minimal expenditures of time
and materials.
The model is used t
o develop fundamentally new compositions for electrode coatings and
flux

cored electrodes (including those based on the use of industrial waste products and
recycled materials).
The performance and adequacy of the model was tested using special technologi
cal
experiments and as the research goes on the software is modified. The data base of the
model includes the relevant experimental and theoretical data concerning the complex
interaction of various alloying components.
The proposed model is used to devel
op the following welding materials:
new self

shielded flux

cored wire for high

quality high

speed welding
of assemblies made from galvanized sheet steel;
new coated electrodes for surfacing of turbine blades by materials
based on Ni

Al alloys.
Introduct
ion
The cybernetics of industrial chemical processes, which is a relatively new area of science,
has become widespread. Cybernetic methods are also finding increasingly greater
application in the analysis of physicochemical processes in metallurgy, weldin
g,
technologies for depositing coatings, etc. Cybernetic methods are used to study complex
systems characterized by a large number of elements (subsystems) and interactions between
them. The main method used to study such systems is computer modeling. The
use of
mathematical models decreases the amount of time and the amount of labor needed for an
investigation, as well as makes it possible to carry out experiments which cannot be
performed or can be performed only with great difficulty on a real object.
T
he development of computer technology and its accessibility have made it possible to solve
problems for which there were previously no known methods of solution or these methods
were so tedious that they proved to be unsuitable for practical application.
It has become possible to mathematically model complex physicochemical processes in
metallurgical systems [1

22] both in reference to processes involving the smelting and
refining of steels and alloys [1

4, 6, 10, 11, 14

19,46, 47] and for the analysis we
lding
technologies [5, 7

9, 20

23, 37, 48

59].
141
The complexity of these processes stems from the simultaneous occurrence of a
considerable number of physical and chemical processes involving liquid, solid, and gas
phases, as well as the high temperatures, t
he complex character of the hydrodynamic and
heat fluxes, and the nonstationary nature of the processes. This complexity is manifested in
the large number of parameters determining the course of the processes and the fact that the
variation of a few parame
ters causes the variation of many others. Therefore, such complex
objects are studied by constructing models, i.e., simplifying systems, which reflect the most
significant aspects of the object under consideration.
Physical modeling. i.e., the representat
ion of experimental data in the form of dependences
of dimensionless variables (similarity criteria), which are composed of various physical
quantities and linear dimensions, is convenient for comparatively simple systems.
Interesting results were obtained
, for example, from the physical modeling of slag foaming
[24]. "Cold" and "hot'' models, the bubble sizes, and such important characteristics as the
viscosity and the adhesive force of oxide melts were investigated. In such cases, the focus is
generally p
laced on physical or physicochemical characteristics of the phases which are
subject to direct measurement.
Such a method is poorly suited to complex systems and processes described by systems of
equations.
In the case of mathematical modeling, the proces
s is studied on a mathematical model using
a computer, and not on a physical object. The input parameters of the mathematical model
are fed into the computer, and the computer supplies the output parameters calculated in the
process. The first stage in the
mathematical modeling of physicochemical systems is
generally the construction of thermodynamic models [10, 11, 14

17, 25

36]. This stage is
very important both for ascertaining the fundamental possibility of the combined occurrence
of particular chemical
processes and for listing the most important thermodynamic
characteristics. The investigation of the activities of the components in binary and more
complex, i.e.. ternary, systems and the creation of a database of thermodynamic
characteristics was the su
bject, for example, of [10, 35]. If the rates of the chemical reactions
are sufficiently high, the composition of the reactant mixture at the outlet of the chemical
reactor should be fairly close to the equilibrium composition and can be found by
thermodyn
amic methods. There are several approaches to the creation of thermodynamic
models. They include the employment of polymer theory to model complex multicomponent
systems [15], modeling for the purpose of constructing phase diagrams [11, 25, 28, 31, 32,
36]
. the construction of statistical

thermodynamic models [13, 14, 17

19, 26, 27, 29], the
determination of the enthalpy and other thermal characteristics [16, 30], the modeling of
melting processes and structure

building processes [36]. Very interesting and
important
results were obtained from the investigation of the microstructure and properties of
deposited weld metals [48, 49, 51

53] and susceptibility to cracking and extent of hot
cracking [50]. The results of these investigations will be very useful for
us

for
determination of the influence of weld metal composition (which will be obtained from our
model computations) on the structure and properties.
When there are no or only few theoretical data on the process being modeled, the
mathematical descript
ion can take the form of a system of empirical equations obtained from
a statistical study of the real process. As correlation between the input and output parameters
of the object is established as a result of such a study [14, 33]. Naturally, the employm
ent of
statistical models is restricted by the width of the range of variation of the parameters
studied.
142
In
recent years mathematical modeling has been applied not only to the investigation of
theoretical aspects of physicochemical processes, but also to
the analysis of real
technologies.
The areas of the prediction and optimization of the composition and properties of materials
obtained in different technological processes are especially promising [2, 3, 4

9, 36, 56, 57].
Some of the results were obtain
ed from the modeling of the process of the formation of a
weld pool [5], from modeling of weld metal transformations [58,59], and from the modeling
of processes involving the segregation of nonmetallic inclusions in steel [4], the interaction
of particles
during welding [9], and diffusion

controlled kinetics [2, 3, 6, 7, 54

57].
Important results were obtained from the studies of the physical and chemical parameters of
welding processes [54] and development of kinetic model of alloy transfer [55, 57].
By
determining the chemical composition of the weld metal researchers have developed the
kinetic model [56, 57]. Basing on this model the authors described the transfer of alloying
elements between the slag and the metal during arc welding. The model takes in
to
consideration the practical weld process parameters such as voltage, current, travel speed,
and weld preparation geometry. The model was tested experimentally [57] for transfer Mn,
Si, Cr, P, Ni, Cu, and Mo.
In our opinion the problem of modeling compl
ex objects with consideration of the kinetics
of the chemical processes occurring them is more complicated. This applies both to
diffusion processes [56] and especially to the analysis of the kinetics of complicated
heterogeneous reactions [12].
An adequa
te description of real chemical processes requires the construction of a
mathematical model which takes into account the diffusion of all the components in the
complex multicomponent system, the kinetics and mechanism of the individual chemical
reactions,
the special features of their simultaneous occurrence, and the influence of heat
transfer and the hydrodynamics, as well as the influence of the engineering parameters and
other factors. There is presently a large amount of experimental and theoretical dat
a, which
make it possible to solve such problems.
This paper presents the results of the development of mathematical models of such a type on
the basis of the method developed by us [43] for the kinetic analysis of reactions in
multicomponent systems.
T
he modeling method description
Weld/deposited metal with required properties is usually obtained (in welding, surfacing,
plasma surfacing, etc.) with the use of various welding materials: coated electrodes for
manual welding and surfacing, solid and flux

cored electrodes for semi automated and
automated welding and surfacing, fluxes, powders, etc. These materials are employed in all
branches of modern industry for welding, hardening the surfaces of items, and corrosion
protection, as well as for restoring
worn items.
The main problem which the technologies cited solve is the production of metal (welds,
coatings, etc.) with a required composition and properties. At the present time, these
problems are generally solved empirically, i.e.. either by means of t
echnological
experiments or by the statistical treatment of existing experimental data.
Such an approach requires great expenditures of time and resources and the consumption of
considerable amounts of expensive materials. In addition, the results of such
investigations
have a random character and are far from optimal.
143
A fundamentally different approach was employed in the present research: the mathematical
model of the physicochemical processes developed and the computer program written on its
basis makes
it possible to "run" a large number of variants within a short time without
considerable expenses and to select the optimal variant, which provides products with the
required composition and properties.
Such a result cannot be obtained even after the pe
rformance of hundreds of technological
experiments.
The use of such a program permits investigations of the possibility of replacing expensive
metallic components by metal

and oxide

containing industrial waste products, something
which is practically impo
ssible to do under the empirical approach.
In most welding materials are generally used expensive components such as ferroboron,
ferrochrome, ferromolibdenum, ferrotitanium, ferrotungsten, ferrovanadium, ferrosilicon,
etc., and pure metallic and oxide pow
ders.
The cost of these components is usually greater then the cost of other raw materials such as
electrode rods (in case of manual arc welding) or steel sheath (in case of flux core welding
processes).
The mathematical model of the processes involved in
the physicochemical interaction of the
phases is based on the method for the kinetic analysis of the interaction of multicomponent
metallic and oxide melts previously developed with participation of the author of the present
project [43]. It is used to so
lve the most complex problems in modeling, viz., consideration
of the rates of transfer of all the elements through the phase boundaries, as well as
consideration of the mutual influence of all the chemical reactions taking place on these
boundaries. On th
e basis of this method it is possible to take into account the complex
interactions between all components, i.e. their interactions with each other [43]. At present
in the physicochemical literature there are a lot of data on the thermodynamic and kinetic
parameters of high temperature processes involving different metals, oxides and gases and
physical properties of these phases which are necessary for computation. The missing data is
obtained in the present paper. The author of the work has the large exper
ience in the field of
experimental obtaining of the physicochemical constants [38

43].
The method described provided good results in the modeling of the bucket refining of steel
[44, 45]. We developed a general scheme for the mathematical modeling of pro
cesses,
whose investigation will be the subject of the present work, and we have compiled the
database needed to create the model (which includes thermodynamic, kinetic, and diffusion
constants, as well as a large body of technological data).
A fairly la
rge amount of experimental data on the kinetics of chemical reactions on a metal

slag interface has been obtained. Both general laws and individual steps of processes have
been investigated while taking into account the influence of the temperature, compo
sition,
mixing rate, and other factors.
In most technological processes involved in the production of metals and alloys, the
principal reactions determining the final composition of the products take place on the
boundary of the metal with the slag. They
are primarily redox reactions involving alloying
elements and harmful impurities, as well as vaporization, gas

adsorption, and other
processes. When the kinetics are analyzed, special attention is focused on revealing the
nature of the individual rate

li
miting steps of the overall heterogeneous reaction.
144
We note that the analysis of the kinetics and mechanism of individually occurring reactions
does not present any special difficulties at the present time and that, as a rule, its results
faithfully descr
ibe the real processes. A kinetic analysis of the interaction of
multicomponent metallic and slag melts with consideration of the mutual influence of
reactions taking place in parallel is considerably more complicated.
Let us briefly describe the method f
or the kinetic analysis of diffusion

controlled reactions
that we previously developed [43]. The theoretical basis of the method consists of two
assumptions:
1)
under diffusion

controlled conditions the concentration ratio on the
phase boundary for each rea
ction is close to the equilibrium value;
2)
the rate of transfer of the reactants to the phase boundary or away
from it is proportional to the difference between their concentrations
in the bulk and on the boundary of the metallic and oxide melts.
The oxidat
ion of elements in a metallic melt can be represented by the reaction:
,
)
(
1
)
(
]
[
Fe
O
E
m
FeO
E
m
n
m
i
i
n
(1)
In this equation E
i
are the elements dissolved in the liquid metal pool (Mn, Si, W, Mo, V,
etc.), and
E
in
O
m
are their oxides in the slag phase. The proble
m reduces to calculating the
rates of reactions of type (1). We note that the problem of determining the rate of such a
reaction for each element individually does not create special difficulties today. However,
such an approach, i.e., analyzing each rea
ction individually, does not correspond to the
situation in an industrial welding process. In the real case the mutual influence of the metal
and slag components, as well as the mutual influence of all the heterogeneous reactions
occurring in this complex
system, are observed.
Our approach permits the determination of the rates
i
E
V
of reactions of type (1) for all the
metal components with taking into consideration their mutual influence:
,
l
m
O
in
E
m
in
i
m
i
l
i
E
m
i
m
in
m
i
m
i
E
V
O
E
E
K
V
x
E
O
E
K
x
V
(2)
Here
x
is the ra
tio between the concentration of ferrous oxide (FeO) in the slag and the
concentration of iron in the metal [Fe] at the phase boundary;
l
E
i
V
and
l
O
E
m
in
V
are the limiting
diffusion rates of the components; [
E
i
] and (
E
in
O
m
)
are the initial concentrations of the
elements and their oxides in the metal and the slag, respectively;
K
i
is the equilibrium
constant of the reaction involving [
E
i
]; and n and m are the stoichiometric coefficients.
In other words,
i
E
V
is the rate of passage of any element from the slag to the metal (or in the
opposite direction), and the further problem reduces to calculating the concentration of that
element as a function of time. After solving this problem, we become able to determi
ne
both the time

variant composition of the liquid metal pool and the final composition of the
weld metal. Since the rates of passage of elements through the phase boundary
i
E
V
depend
significantly on the temperature, composition, hydrodyna
mic conditions, and some other
145
factors, the correct determination of the technological parameters of a welding process
would be of great value.
Mathematical modeling of the real technological processes
The scheme of the technological process analyzed is
presented in Fig. 1.
Direction of welding
Electrode
bare
Electrode coating
Drop
Slag film
Weld arc
3
b
2
1
a
4
c
d
6
7
5
Molten metal pool
Molten slag pool
Molten weld pool
Slag
W
eld metal
Base metal
Fig.1 Interaction of phases in manual (“stick”) arc

睥汤l湧 灲潣e獳
146
The scheme shows the interaction of phases with regard to these assumption. On the
scheme figures denote the direction of material transfer, and letters denote the interaction of
phases:
1

melting of the electrode bare and formation of a drop;
2

melting of the electrode coating and formation of slag film over the drop;
3

transfer of the drop metal (which has reacted with slag film at the stage of
transfer) to the metal pool;
4

transfer of
the slag film (which has reacted with the drop metal at the stage of
transfer) to the slag pool;
5

melting of base metal;
6

crystallization of the slag pool;
7

crystallization of the metal pool;
a,b

redox reaction at slag

metal boundary in a welding drop;
c,d

redox reaction at slag

metal boundary in a welding pool.
It is expedient to consider the shaping of the composition in two stages of the process: the
drop stage and the pool stage.
The final composition of the drop in general case is determined by the c
oncentrations in
each of the powdered components in the flux of the flux

cored wire or in the electrode
coating
l
pd
i
E
]
[
and, accordingly, by the melting rates of these components
l
pd
V
, the
concentration of each element in the
metal in the metal sheath or in the electrode bare [
E
i
]
b
and its melting rate
V
b
, as well as by the rates of passage of the elements through the
interface
i
E
V
of the drop (3) and the slag film (4) on its surface, which can be calculated
in
accordance with the methods described above. The values of
l
pd
V
and
V
b
are found from
empirical relations as functions of the technological parameters of the process.
Thus, the concentration of the
i

th element in the drop at any moment i
n time
d
i
E
]
[
, can
be calculated from the equation (3):
,
100
]
[
]
[
]
[
1
d
d
E
E
L
l
l
pd
i
l
pd
b
i
b
d
i
m
A
M
V
E
V
E
V
E
i
i
(3)
where
A
d
is the surface area of the liquid drop,
l
labels the type of powder,
L
is the number
of types,
i
E
M
is the molecular weight of the el
ement, and
d
m
is the mass of the metal drop
at the time
.
The final drop composition thus calculated [
E
i
]
d
is used to calculate the concentration of the
i

th element in the weld pool at any time
. The composition of the pool and theref
ore the
composition of the weld metal are determined by the concentrations of the elements in the
liquid drop [
E
i
]
d
and accordingly by the rate of descent of the drops into the liquid pool
V
d
,
the concentration of each element in the base metal [
E
i
]
bm
, the
melting rate of the base metal,
and, as in the case of the drop stage, by the rate of passage of each element through the
interface between the metal (5) and slag (6) pools.
In accordance with the foregoing, the expression for calculating the concentratio
n of element
i
in the weld metal can be written in the form
147
,
100
]
[
]
[
]
[
p
p
E
E
bm
i
bm
d
i
d
i
m
A
M
V
E
V
E
V
E
i
i
(4)
where
A
p
is the area of the interface between the metal and the slag, and
m
p
is the mass of
the weld pool at the time
.
The system of equations (2

4) comprises a math
ematical model, which describes the
interaction between the phases in an industrial flux

core welding (surfacing) process.
Optimization of the composition of a flux

core wire for galvanized steel welding
The industrial process analyzed in this part of t
he work has a number of significant features,
which often complicate its practical realization. Although the welding of galvanized steel
parts has been employed for a relatively long time and has been described in fairly great
detail in various technologi
cal textbooks and standards [60], there are numerous
technological problems that make it difficult to obtain a high

quality joint, especially in the
case of high welding speeds [61, 62]. The research in [61] concerned the tailored blank
welding of mild st
eel sheet and galvanized steel sheet using a CO
2
laser beam. The Taguchi
method was employed to obtain the optimum conditions for employing tailored blank laser
welding in practical manufacturing processes.
Serious problems due to defect formation were d
iscovered in the MAG welding of
galvanized steel in [62]. The effects of the welding parameters and wire composition on gas
pocket generation were studied in the case of the MAG welding of galvanized steel sheet.
Lap joint and vertical

down position make
the number of gas pockets larger in comparison
with others. An increase in the welding current and speed or in the Ar content in the
shielding gas also promotes gas pocket generation. A special metal

cored wire for the CO
2
welding of galvanized steel sh
eet has been developed as a result of research, and the wire is
currently used in car manufacturing. The appearance of such defects is associated, in
particular, with the vaporization of zinc, which takes place with a high rate along with the
redox process
es.
As far as we know, the employment of flux

cored wires without additional gas shielding for
such purposes does not yield good results at welding speeds exceeding 0.50
–
0.75 m/min.
On the other hand, intensification of the automobile production proces
s under current
conditions calls for increasing the welding speed while maintaining the necessary level of
quality of the welded joint.
Therefore, we should examine the possibility of using mathematical modeling to develop a
self

shielded flux

cored wire
for welding galvanized sheet steel.
In addition to the processes of type (1) in an ordinary analysis, we also take into account the
oxidation and vaporization of zinc:
[ Zn ] + ( FeO ) → ( ZnO ) + Fe
(5)
[ Zn ] → { Zn }
(6)
where [Zn] and {Zn} denot
e zinc in the metallic and gaseous states, respectively.
A computer program for PC computers has been written using the model developed.
148
This program can be used to determine the composition of a flux

co.red wire that ensures
the formation of a weld with
required properties. In this case, the output parameter is the
new formula of the flux

cored wire.
The required weld composition can clearly be obtained with different combinations of
components in the flux. The database contains the chemical compositions
of various
components, which should be utilized in selecting the optimal flux composition.
The program has to establish the flux composition that provides the required weld metal
composition and to select the most inexpensive variant among them. The tech
nological
characteristics of the electrode should be optimized as well.
The program also includes a special module, which provides an evaluation and optimization
of the mechanical properties of the weld metal having the composition obtained.
This obviously
requires a large number of iterations to perform calculations with all possible
component ratios.
In the case at hand the approximate time for the calculations and optimization was 15 to 20
min. A series of welding experiments was carried out to adjust t
he composition to the real
technological conditions. The result is a new formula for an electrode that provides an
assigned joint composition.
After performing calculations of the chemical composition of
the wire from assigned values of the chemical compo
sition of the weld metal, samples of the
flux

cored wire were prepared. They were produced from a steel ribbon, as well as
powdered materials containing metallic alloying, deoxidizing, slag

forming and gas

forming
components that impart self

shielding prop
erties to the wire.
Wires with diameters from 1.8 to 1.65 mm were manufactured using laboratory equipment.
Galvanized sheet metal coupons with a thickness of 2.4 mm were welded. The thickness of
the zinc layer was 8∙10

6
m.
Samples of the weld metal fro
m butt joints were taken for chemical analysis.
In addition, lap and fillet joints were made.
The formation of the weld, the metal spattering during the transfer of metal from the
electrode to the weld pool, the removability of the slag from the weld sur
face, the porosity
of the welds, and the mechanical properties of the welded joints were evaluated.
The results of these tests were used to adjust the composition of the wire with respect to the
components responsible for the various properties.
Then new
samples were prepared, and the entire calculation and testing cycle was repeated.
As a result, we developed a flux

cored wire that ensures uniformity of the strength of the
welded joints at a high welding speed (up to 1.25 m/min).
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