Development of new welding materials on the base of mathematical modeling

of metallurgical processes

Part 1. Phase Interaction Analysis and Development of the Basic Model.

M. Zinigrad, V. Mazurovsky

Colledge of Judea and Samaria, Ariel, Israel

The development of new electrode coating compositions is the topical area in the

current research, especially when we consider such problems as the welding of

special-purpose steels and alloys, built-up layers with special properties, or specific

maintenance works. The brief review of currently existing calculation techniques for

electrode coating compositions demonstrates that they are based on the experimentally

deduced dependence which allows to calculate the chemical composition of built-up

metal (weld metal) using so called transition coefficients (Ref. 21) or assimilation

coefficients (Ref. 22) In some cases the attempt is made to take into consideration

some redox reactions in the welding zone (on molten metal-slag boundary in the

welding pool) (Ref. 21, 23). Usually, however, the composition of built-up metal is

calculated using the mixture method without taking into consideration physico-

chemical processes in the welding pool (Ref. ? ). This approach can be appropriate in

order to forecast the chemical composition of built-up metal or to calculate electrode

coating for the welding of low-alloy steel and carbon steel, but leads to erroneous

results for high-alloy steel and alloys or for built-up layers with special properties. In

the latter case the considerable amount of experimental work can be required in order

to develop the new composition of electrode coating which can take months or even

years.

During the last decade both the increasing potential and the availability of personal

computers opened new possibilities for the solution of the above-mentioned problems,

and along with it we can consider the computer modeling of physico-chemical

processes in the reaction zone connected with technological parameters of the welding

process. Computer modeling used now for industrial chemical processes study and for

the analysis of real technologies allows us to decrease the amount of time and the

amount of labor needed for the research, 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. The development of computer technology and its accessibility have

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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 the

practical application. Computer approach is especially valid for physicochemical

processes since their complexity 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, the 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 in the fact that the variation of a few parameters causes the variation

of many others. Such complex physicochemical objects are studied by constructing

models, i.e., simplifying systems, which reflect the most significant aspects of the

object under consideration.

Computer Modeling as an Up-to-date Approach to New Welding Materials

Development.

One of the most promising directions of physicochemical objects computer

modeling is the usage of these models for welding technologies analysis which is

represented in (Ref. 1-19). The first stage of these modeling is generally

thermodynamic models construction. 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. 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 thermodynamic methods. There are several

approaches to the creation of thermodynamic models. They include the employment of

polymer theory to model complex multicomponent systems, modeling for the purpose

of constructing phase diagrams, the construction of statistical thermodynamic models,

the determination of the enthalpy and other thermal characteristics, the modeling of

melting processes and structure-building processes.

When there are no or only few theoretical data on the process being modeled, the

mathematical description can take the form of a system of empirical equations obtained

from a statistical study of the real process.

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A correlation between the input and output parameters of the object is established as

a result of such a study. Naturally, the employment of statistical models is restricted by

the width of the range of variation of the parameters studied.

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 actual technologies.

The areas of the prediction and optimization of the composition and properties of

materials obtained in different technological processes are especially promising (Ref.

1-4, 17). Some of the results were obtained from the modeling of the process of the

formation of a weld pool (Ref. 1), from the modeling of weld metal transformations

(Ref. 18, 19), and from the modeling of processes involving the segregation of

nonmetallic inclusions in steel, the interaction of particles during welding (Ref. 4), and

diffusion-controlled kinetics (Ref. 2, 16, 17).

Important results were obtained from the studies of the physical and chemical parameters of welding processes (Ref. 16) and development of kinetic model of alloy transfer (Ref. 17).

By determining the chemical composition of the weld metal researchers have developed the kinetic model (Ref. 17) Basing on this model the authors described the transfer of alloying elements between the slag and the metal during flux-shielded welding. The model also takes into consideration the practical welding process parameters such as voltage, current, travel speed, and weld preparation geometry. The model was tested experimentally for transfer Mn, Si, Cr, P, Ni, Cu, and Mo. In our opinion the problem of modeling complex objects with consideration of the kinetics of the chemical processes occurring them is more complicated. This applies both to diffusion processes (Ref. 17) and especially to the analysis of the kinetics of complicated heterogeneous reactions.

A more complete, adequate description of actual 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,

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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 data, which make it possible to solve such problems.

The present research is also intended to be devoted to the development of

mathematical models of such a type on the basis of a new method for the kinetic

analysis of reactions in multicomponent systems.

The main problem which the technologies cited solve is the production of deposited

metal (welds, coatings, etc.) with a required composition and assigned properties. At

present time, these problems are generally solved empirically, i.e., either by means of

technological 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 researches have a random character and are far from optimal.

Peculiarities of Proposed Approach, Objects, and Stages of the Research

The approach employed in the present research fundamentally different from the

above mentioned ones. The mathematical model of the physicochemical processes

developed and the computer program written on its basis will make 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, in principle, even after the performance

of hundreds of technological experiments.

The use of such a program permits to investigate the possibility of replacing

expensive metallic components metal- and oxide-containing industrial waste products,

something which is practically impossible to do under the empirical approach.

In the most welding materials the expensive components are generally used. Such as ferroboron, ferrochrome, ferromolibdenum, ferrotitanium, ferrotungsten, ferrovanadium, ferrosilicon, etc., and pure metallic and oxide powders.

The cost of these components is usually greater then the cost of other raw materials such as electrode rods (in case of most manual welding) or steel band in case of flux cored welding processes.

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Therefore, the replacement of expensive components with industrial waste products saves considerable consumption of these expensive materials.

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The research is carried out in three stages: 1) mathematical description of the

process being studied, i.e., construction of the mathematical model; 2) development of

an algorithm for solving the problem, i.e., a procedure for determining the numerical

values of the output parameters; 3) establishment of the equivalence of the model to the

process being studied. Special attention was focused on the stage of constructing the

model, which was based on a thorough analysis of the physicochemical essence of the

phenomena being described and on constructing based on the model computer

program.

From these considerations the following problems of the work were defined:

- to develop a mathematical model of industrial welding processes on the basis of a

thermodynamic and kinetic analysis of the metallurgical processes, involving the metal,

slag, and gas;

- to use the model and the computer program, written on its basis, to optimize welding

technologies employing coated electrodes;

-to optimize the composition of electrode coatings which produce welded joints with

the preset composition;

- to develop a fundamentally new class of electrodes, which coating contain industrial

waste products instead of expensive components.

The object of modeling for the analysis of the physicochemical processes, taking

place during welding, is a system which includes the following phases: metal, oxide

melt (slag), gas, and solid phases, in which various chemical and physical processes

take place.

Phase Interaction Analysis

Metal-slag interaction in the process of arc welding exerts a substantial impact on

the chemical composition of built-up metal (weld metal) which ultimately determines

the working characteristics of weld metal or built-up layer. The consideration of this

interaction in the process of electrode coating development which can ensure the

preset composition of weld metal is based on the mathematical modeling of the

welding technological process, taking into account the following features of the

process:

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- metal-slag interaction at two consecutive stages - electrode (drop) and welding

pool - which differ in temperature, geometrical and hydrodynamic parameters;

- continual renewal of interacting phases (molten metal and slag) at each stage through

the melting and crystallization of base and adding materials;

- simultaneous occurrence of all reactions at each stage and their interplay.

Since it is impossible to built a model describing a process with the absolute

adequacy, we offer some assumptions and simplifications. Thus in the model under

consideration basing on the experimental data for the stationary welding conditions the

following assumptions were made:

- within the phases under consideration there are not any gradients of chemical

potential (the ideal mixing of phases);

- while considering the interaction between gas and slag phases we take into account

only the reactions with hydrogen and nitrogen;

- metal-slag reactions surfaces for each stage are kinetically homogeneous.

Figure 1 is a scheme showing the interaction of phases with regard to these

assumptions.

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Figure 1. Interaction of phases in MMA-welding process

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Drop

Slag film

Weld arc

Electrode rod

Direction of welding

Electrode coating

Molten metal pool

Molten slag pool

Slag

Weld metal

Base metal

3 b 2 1

a

4

5

cd67

On the scheme figures denote the direction of material transfer, and letters denote

the interaction of phases:

1 - melting of the electrode rod 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 slag pool;

7 - crystallization of 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.

Development of the Basic Model

The welding process has a stage-like character, and it goes without saying. It should

be only specified that the stage of electrode melting as well as the existence of the drop

are of considerable importance. At this stage we already observe that the reactions of

interaction between phases exert considerable effect on the changes in the chemical

composition of molten metal and slag incoming to the welding pool, for which pool

they provide the starting chemical composition of incoming electrode metal and slag.

Regardless of the process stage and phase type the material balance of elements can be

described by the following equation:

(1)

where:

- the input speed of i-th element incoming to the phase, g/s;

- the output speed of i -th element out of the phase, g/s;

- the concentration of i -th element in the incoming flux, wt %;

- the concentration of i -th element in the outgoing flux, wt %;

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- the rate of passage of the i -th element through a phase boundary of area at

j-th stage, mol / cm2 s;

- the area of the reaction surface at j -th stage, cm2;

- element’s molecular (atomic) mass, g/mol.

- the accumulated amount of an element in the phase volume under the

non-stationary conditions, and therefore in our case equals to zero;

Thus for each stage of the welding process we can compute the concentration of an

element (metal phase) or its oxide (slag phase).

The stage of electrode melting (the electrode drop)

Metal Phase

From (1) follow the material balance equation for the metal phase of the electrode

drop:

(2)

where:

- the speed of electrode melting, g/s;

- the element’s concentration in the electrode rod, wt %;

- the element’s concentration in the drop metal, wt %;

- the area of the drop’s reaction surface, cm2;

- the rate of passage of the i -th element through a phase boundary of slag film

– drop metal, mol / cm2 s;

- element’s molecular (atomic) mass, g/mol.

Then the concentration of the element in drop metal is defined as:

(3)

Slag Phase

By analogy with the preceding:

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(4)

where:

- oxide concentration in slag film, wt %;

- oxide concentration in electrode coating, wt %;

- the share of slag which did not interact at the drop stage,

where:

f - relative slag film mass;

Kc - relative coating mass.

- the speed of coating’s melting, g/s .

The Stage of the Pool

Metal Phase

From (1) follow the material balance equation for the metal phase of the welding

pool:

(5)

where:

- the concentration of i-th element in base metal, wt %;

- the concentration of i-th element in welding pool, wt %;

- the crystallization speed of metal pool, g/s;

- the melting speed of base metal, g/s;

- the area of pool’s reactive surface, cm2;

- the rate of passage of the i -th element through a phase boundary of slag pool

– metal pool, mol / cm2 s;

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Hence the concentration of i-th element in welding pool is:

(6)

Slag Phase

By analogy with the metal phase concentration of i-th oxide in welding pool is

(7)

From (3), (4), (6), (7) one can see that in order to compute the chemical composition

of phases we need to know rate of passage of the i -th reagent through a phase

boundary of slag – metal I Ri j ( where: Ri - reagent, i.e. Ei or EinOm and j - the stage of

the process ), which can be computed using the method of kinetic analysis (Ref. 20) for

the reactions at the molten metal-slag boundary, the latter being generalized as:

(8)

If stoichiometry coefficient n = 1, the rate of passage of the i –th element through a

phase boundary (Ref. 20):

, (9)

with n = 2

I Ei

2 42

, (10)

where

x K E

I

mim

i

Ei

[ ]lim

2

2

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( [Fe] and (FeO) are concentrations of iron and iron oxide

correspondingly on slag – metal boundary);

Ki - the coefficient, including:

- the reaction equilibrium constant (8) of the i –th element;

- activite’s coefficients i ;

- coefficients of recalculation of molar concentration into weight ones.

Limiting diffusion rates of the components in the metal and the slag (Ref. ):

(11)

where:

Ri - convection constant, s-0.5

Ri - the concentration of i-th element or oxide, wt %

Ri - reagent’s density, g/cm3;

DRi - reagent’s diffusion coefficient, cm2/s;

MRi - reagent’s molecular (atomic) mass, g/mol.

For the solution us task take into account the obvious stoichiometry correlationf

followed from the reaction (8):

(12)

The system of the above equations (3,4,6,7,10,12) presents the general

mathematical model of physico-chemical processes of the manual metal arc welding.

In actual practice the solution of this problem allows to compute the chemical

composition of built-up metal provided that we know the electrode formula and the

type of base metal. Rather often, however, we are faced with the inverse problem

when it is necessary to compute such an electrode formula that can give us the

required chemical composition of built-up metal in the process of welding (or

building-up) of specific metal (hereafter, “the opposite problem”).

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The computation is based on the above model. The initial stage of the solution (the

preliminary computation) determines the initial formula of an electrode. Using it as a

base one can easily compute the chemical composition of built-up metal and forecast

its properties. If the results of this computation do not satisfy the verification criteria,

then appropriate corrections are introduced into the initial formula whereupon it

becomes “the intermediate formula”. The computation is repeated, and the results are

again checked. This procedure is repeated until (after n iterations) the desirable results

are gained and the final formula of an electrode is obtained.

Conclusion

The mathematical model of welding technology process on the basis of the kinetic

analysis method [20] had been developed.

The model takes into consideration:

- stage-by-stage implementation of the welding process;

- continuous renovation of interacting phases;

- simultaneous running of all reactions and their mutual influence;

- physico-chemical properties of the interaction phases;

- hydrodynamic conditions of the welding process;

- interconnection between welding process parameters (welding conditions) and

kinetics of reactions.

The proposed method can be applied to the development of new compositions of

welding materials (electric coatings, flux cored wires, welding fluxes). The practical

implementation of this approach is considered in Part 2.

References:

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“Mashinostroenie”, 1973, 448 pages.

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3. Potapov N.N. “The Metallurgy of Welding. Welding and Welding Materials. The

Handbook in 3 Vols. Ed. by V.I.Volchenko. Vol.1”

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4. Ducharme R., Kapadia P., Dowden J., Williams K, Steen W., “An integrated

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