DEVELOPMENT OF A COMPUTER-AIDED METHOD
FOR DESIGNING WELDING MATERIALS
V. L. Mazurovsky, M. I. Zinigrad, A. M. Zinigrad
College of Judea and Samaria, Ariel, Israel
ABSTRACT. Further development of the method for the computer-aided design of welding
materials described by Mazurovsky, Zinigrad, and Zinigrad [1] is presented. A brief analysis
of the method and a survey of the mathematical models on which it is based are given.
METHODOLOGY OF THE MATERIALS DESIGN
We understand design as a process of developing the package of technical
documentation for the new product manufacturing – starting from the technical specification
formulation and proceeding with its realization.
Design is complex system built as hierarchy and sequence of operations having
respective links, priorities, tasks and intermediate solutions.
The optimal way to realize such a system (while automating the process) calls, for our
opinion, for the following:
1. System approach (with the design process as the object of analysis)
2. Mathematical modeling (allowing automating the process of forming
intermediate solutions and final solution)
SYSTEM APPROACH
System approach is only a means to structure a problem, to establish links and the order
of priorities, to structure data, etc., using structural analysis. System approach as a multipurpose method uses abstract notions, which in our (as in any particular) case acquire a
specific practical application:
- subject domain – specific fabrication process for a specific customer;
- subject domain element - an object or a process (belonging to the subject domain and
having specific features, functions and links with other objects and processes) selected
during the structural analysis. In our application, those will be the following:
- technological process of welding (hardfacing) itself;
- welding equipment;
- tools;
- environment, etc.
- design object - a subject domain element, whose design (development) is an objective of
the task being structured. In our application, these are new welding materials.
A brief review of the major stages of structural analysis of the welding materials design
problems is presented below:
1. Definition of the design stages (stage of the technical specification formulation; stage
of the technical specification realization).
2. Structuring the stage of the technical specification formulation
2.1. Determining the structure of the design object
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2.2. Determining the structure of the subject domain.
2.3. Determining of the input parameters for the design:
2.3.1. Characteristics of the design object elements;
2.3.2. Characteristics of the environment.
2.4. Determining the output parameters: characteristics of the design object.
2.5.Establishing functional relationship between the design object and the subject domain
elements (direct and reverse connections).
2.6.Establishing connections between the subject domain and the design tool (expert
system).
2.7.Determining the operational algorithm structure and the subject domain representation
method for the design tool.
3. Structuring the stage of technical specification realization
3.1. Analysis of the technical specification. Formulating the task (specification) for
CAMD;
3.2. Forming design operations and procedures as well as priorities and links;
The design tool (CAMD system) provides the designer with the solution of the task
formulated (in our case: development of the welding material which provides for obtaining
welds with required properties – as defined by the customer).
MATHEMATICAL MODELING
The basis for the technical specification realization according to the approach proposed is
the CAMD system, based on the software package.
This software was developed on the base of the mathematical models of the technological
process of welding and the process of non-equilibrium weld/deposit metal crystallization. The
above models provide for the possibility of calculation of the composition of welding
material, which will ensure obtaining of the weld metal with required composition, structure
and properties.
MODELING PHASE INTERACTION
The method of the mathematical modeling of the phase interaction during welding and
some examples of its implementations are presented, for instance, in [2].
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 one of
the authors of the present work [3]. It is used to solve 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 the basis of this method it is possible to take into
account the complex interactions between all components, i.e. their interactions with each
other [3]. 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 authors of the work have
the large experience in the field of experimental obtaining of the physicochemical constants
[4 -8].
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The method described provided good results in the modeling of the bucket refining of
steel
[9, 01]. We developed a general scheme for the mathematical modeling of processes, 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 large 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,
composition, 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-limiting steps of the overall heterogeneous reaction.
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 describe 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 for the kinetic analysis of diffusion-controlled
reactions that we previously developed [3]. The theoretical basis of the method consists of
two assumptions:
1) under diffusion-controlled conditions the concentration ratio on the
phase boundary for each reaction 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 oxidation of elements in a metallic melt can be represented by the reaction:
n
1
[ Ei ]  ( FeO)  ( Ein Om )  Fe,
(1)
m
m
In this equation Ei are the elements dissolved in the liquid metal pool (Mn, Si, W, Mo, V,
etc.), and EinOm are their oxides in the slag phase. The problem 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 reaction 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 V Ei of reactions of type (1) for all the
metal components with taking into consideration their mutual influence:
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x m  K im
VEi 
EinOm 
Ei
,

Ein Om 
x

VEli Ei  VElinOm
m
(2)
K im
Here x is the ratio between the concentration of ferrous oxide (FeO) in the slag and the
concentration of iron in the metal [Fe] at the phase boundary; VEli and VElinOm are the limiting
diffusion rates of the components; [Ei] and (EinOm) are the initial concentrations of the
elements and their oxides in the metal and the slag, respectively; Ki is the equilibrium
constant of the reaction involving [Ei]; and n and m are the stoichiometric coefficients.
In other words, V Ei 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 determine 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 V Ei depend
significantly on the temperature, composition, hydrodynamic conditions, and some other
factors, the correct determination of the technological parameters of a welding process would
be of great value.
The concentration of element i in the weld metal in the case, for example, of fluxcore arc welding, can be written in the form [2]
[ Ei ] 
Vd  [ Ei ]d    Vbm  [ Ei ]bm    VEi  M Ei  Ap   100
mp
,
(3)
where Ap is the area of the interface between the metal and the slag, and mp is the mass of the
weld pool at the time .
The system of equations (2, 3) along with the equations deriving from the
stoichiometry of the reaction (1), comprises a mathematical model, which describes the
interaction between the phases in real welding (in this case FCAW) process. The model
connects the composition of the weld metal with the composition of the welding consumables
thus allowing calculating the composition of the welding consumable providing for the
obtaining of the weld metal with required composition.
MODELING NON-EQUILIBRIUM CRYSTALLIZATION PROCESS
The model of non-equilibrium weld crystallization process proposed by the authors [11],
constitutes mathematical description of the process of formation of the strengthening phases
and calculation of chrome and nickel equivalents thus connecting the content of the
strengthening phases and structure of the matrix with the composition of the metal (for weld
metals over a broad range of levels of alloying).
The Schaeffler diagram has been modified taking into account the following factors:
- nonequilibrium crystallization;
- the formation of strengthening phases;
- mutual influence of the alloying elements.
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The model includes the parametric dependencies connecting the weldability and
mechanical properties of the weld with its structure and composition.
DESIGN PROCEDURE
Based on the structural analysis and mathematical modeling, the authors have
developed a design method comprising a sequence of design stages (with specific instructions
and rules for each stage): from data package formulation to the solution development phase.
Structure of the design process with direct and reverse connections between the
stages, functional dependencies, and procedures of forming of input and output parameters
are presented in the flow-chart of the design process (See figure 0).
As seen from the figure 0, the proposed method comprises a close-circuit system with a
comprehensive coverage of reverse connections, thus providing the following:
1. structuring the problem, defined according to the actual application (as defined by the
customer);
2. forming data packages and technical specification
3. forming instructions and rules based on the above, presentation thereof as a task
definition for the CAMD system;
4. solving the task in a dialogue mode between the designer (expert) and the CAMD
system;
5. formulating the solution as:
a) formula of the welding material needed to obtain the weld metal required;
b) predicting the composition, structure and properties of the weld;
c) welding/ hardfacing parameters.
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Проектиров
Designer
щик
Data analysis
and formation of
data packages,
rules and
instructions
Characteristics of the
joint/hardfaced
element
Customer
Operating
conditions
including
environment
characteristics
Joint/hardfaced
element
Equipment
characteristics
Operating
environment
Results of
the design
object
operation
(weld/deposit
metal)
Design object
properties
Design object
functions
Customer
facilities
Task formulation
Cutomer’s
requirements
to the
weld/deposit
Design object
(welding
consumable)
Intellectual
interface
Testing of
the
weld/deposit
properties
CAMD
Figure 1: General flow-chart of the design process
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DEVELOPMENT OF THE METHOD
Formulating the technical specification and stating the design problem are the main stages
that determine the design quality. On the other hand, the faithfulness of the mathematical
models determines the “accuracy” of the design tool used. These two factors determine the
following new areas for developing the methodology:
1. Formalizing the subject domain of the design process for the purpose of obtaining the
optimal input parameters. Establishing the links between the subject domain, the
result of the design operations, and the design object.
2. Improving the level of faithfulness of the basic mathematical models.
Formalizing the subject domain reduces to creating strictly scientific representations of
the processes taking place in a given region and their effect on the result of the action of
the design subject (weld metal). In other words, there is a need for systematically
constructing physical and mathematical models, as well as models that describe the
changes in the weld metal itself. Ultimately it is important for us to obtain a picture of the
events taking place in the weld metal under the action of the external environment (the
subject domain) with structural and phase transformations. These include recrystallization
processes, cold-hardening phenomena, elastic and plastic deformation, microscopic
cracks and macroscopic fractures, and adsorption and corrosion processes (the formation
and destruction of oxide films). Such knowledge can provide a basis for formulating the
requirements for a specific type of weld metal that must function under specific
conditions, in contrast to what has been done hitherto, i.e., developing broad-purpose
welding materials, rather than welding materials for a specific task. This leads to
particular cases of rapid failure of hard-facing layers, since the service features of the part
and the effects of the environment are not taken into account. For this reason, we have
proposed the principle of individuality in planning special-purpose weld materials. This
is the fundamental principle guiding the development of our new method for designing
weld materials.
In addition, we are carrying out systematic studies to improve the level of faithfulness
of the mathematical models underlying thee design tool—the expert system.
Mathematical representation of phase-structure regions of a modified Schaeffler diagram
[11] allowed us to abandon the graphical determination of the required phase-structure
composition of a weld metal, which introduces significant errors. This task is formulated
in the form of simple mathematical equations in Table 1. This greatly simplifies the
search for the optimal structures of the weld metal determined from analysis of the
interaction of the environment and the weld metal, as noted above.
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Table 1. Formulation of the method for determining the phase-structure composition of a
weld metal
Determination of the
phase-structure region
Condition
0 ≤ Nieq< -2.45Creq +
7.42
Nieq ≥ -2.45Creq + 7.42 ;
Nieq ≥ 1.13Creq – 8.1;
Nieq < -0.8Creq + 19
Nieq ≥ 0 ;
Nieq ≥ 0.35Creq – 4.0 ;
Nieq < 1.13Creq – 8.1;
Nieq < -0.8Creq + 19
Account of the weld metal phasestructure composition
Region
F+M
Martensite
M+F
Nieq ≥ -0.8Creq + 19 ;
Nieq ≥ 0.35Creq – 4.0 ;
Nieq < -0.8Creq + 25.4;
Nieq < 1.13Creq – 8.1
M+A+F
0 ≤ Nieq< 0.35Creq –4.0
Nieq ≥ -0.8Creq + 25.4;
Nieq ≥ 1.13Creq – 8.1
Nieq ≥ -0.8Creq + 19 ;
Nieq ≥ 1.13Creq – 8.1;
Nieq < -0.8Creq + 25.4
Ferrite
Austenite
A+M
Note
QM = 100.75ln( Nieq + 2.45Creq ) –
99.324 ; QF = 100 - QM
QM = 100
If Rq ≤ 6.4 then QF = 10.142Rq +
85.071,
otherwise
QF = -13.972Rq2 –112.22 Rq –
125.38;
QM = 100 – QF
If Rq ≤ 6.4 then QF = 10.142Rq +
85.071,
otherwise
QF = -13.972Rq2 –112.22 Rq –
125.38;
QM = kz( 0.313QZ3 – 18.3-934QZ2 +
359.25QZ – 2037.3 );
QA = 100 – QF - QM
QF = 100
QA = 100
QM = 0.313QZ3 – 18.3-934QZ2 +
359.25QZ – 2037.3 ;
QA = 100 – QM
Rq = ( Nieq + 0.4455Creq )
/ ( 1 – 0.1908Creq )
Rq = ( Nieq + 0.4455Creq ) /
( 1 – 0.1908Creq );
kz = ( 100 – QF ) / 100;
QZ = Nieq + 0.8Creq
QZ = Nieq + 0.8Creq
CONCLUSIONS
A brief survey of a new method for developing welding materials has been given. The
principal factors determining the quality and reliability of the results of design work
employing this method have been indicated. The main areas for further development of
this method have been determined.
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