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 [1].

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 [2]. 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 [2]. 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 [3 -7].

The method described provided good results in the modeling of the bucket refining of steel [8, 9]. 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 metalslag 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 [2]. 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:

In this equation E; 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, of reactions of type (1) for all the metal components with taking into consideration their mutual influence:

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; V, and V are the limiting diffusion rates of the components; [E;] and (EinOm) are the initial concentrations of the elements and their oxides in the metal and the slag, respectively; K; is the equilibrium constant of the reaction involving [E]; and n and m are the stoichiometric coefficients. In other words, VE, 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 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.

E

The concentration of element i in the weld metal in the case, for example, of flux-core arc welding, can be written in the form [1]

where A, is the area of the interface between the metal and the slag, and m, is the mass of the weld pool at the time t.

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 [10], 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 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 2).

As seen from the figure 2, 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.

CONCLUSIONS

The novel welding materials design method developed constitutes a comprehensive system allowing for the developing of custom welding consumables.

REFERENCES

1. Detroit, MI. 1999. Computer modeling of metallurgical technologies. Proc. Ninth International Conference “Computer Technology in Welding”, M. Zinigrad, V. Mazurovsky: 164-171, NIST Special Publication 949.

2. Boronenkov V.; Shanchurov S.; and Zinigrad M. 1979. Kinetics of the interaction of multicomponent metal with slay under diffusion conditions. Izvestiva Ac. Nauk USSR. Metal, 6: 21-s to 27-s.

3. Panphilova L.; Zinigrad M.; and Barmin L. 1978. Effect of surface concentration of oxygen in Me-S melts on the kinetics of its transfer through a sulfur-oxide melt interface. Journal Phys. Chem.: 5, 10, 2491-s to 2494-s.

4. Flyagin A.; Zinigrad M.; and Barmin L. 1979. Kinetics of ion exchange between an ironcarbon-aluminium melt and an oxide electrolyte. Electrochem.:, 5, 12, 1858-s to

1861-s.

5. Panphilova L.; Zinigrad M.; and Barmin L. 1981. Quick stage kinetics of oxygen ion discharge on the boundary of sulfide melts and liquid oxides. Electrochem.: 17, 9, 1346-s to 1349-s.

6. Zinigrad M.; Phephelov A.; Barmin L.; and Shalimov M. 1986. Kinetics of the interaction of a boron containing metal melt with an oxide electrolyte. Electrochem.: 22, 1, 74-s to 76-s.

7. Zinigrad M.; Okolzdajev A.; and Flyagin A. 1988. Limiting stage of anodic oxidation of tungsten at the boundary of metallic and oxide melts. Rasplavy: 2, 3, 46-s to 51-s. 8. Boronenkov V.; Zinigrad M.; and Shalimov M. 1983. Mathematical modeling of metal and slag- processes interaction in a ladle. IZV VUZ. Tcher. metallurg: 1, 36-4. 9. Sendai, Japan. 1992. Simulation of metal and slag interaction for optimization and development of technological processes, Proc. of the 4th Molten Slags and Fluxes International Conference. M. Zinigrad: 125.

10. Ariel, Israel. 2000. Predicting weld structure using modified Schaeffler constitution diagram. Proc. of the International Conference Mathematical Modeling and

Simulation of Metal Technologies. V. Mazurovsky, A. Zinigrad, and M. Zinigrad: 540-545. College of Judea & Samaria Press.

Finite Element Analysis of Creep Strength
Mis-matched Dissimilar Welded Joints

Chen Hui*, Chen Zigang"

* Department of Materials Engineering, Southwest Jiaotong University, Chengdu, China,

610031

** Dept. of Materials Science and Engineering, Dalian Railway Institute, Dalian, China, 116028

The finite element analysis (FEA) of mismatched welded joints with a 30° groove angle was performed to study the mechanical behavior of DMWJs (dissimilar metal welded joints). It is concluded that the distribution of stress triaxiality in the DMWJs is uneven, especially near the bond lines. The degree of creep strength mismatch has remarkable effect on the distribution. The higher the level of mismatch is, the more uneven the distribution is and the easier for premature failure to occur in the joint.

Key Words: dissimilar metal welded joints, finite element analysis, creep strength mismatch, stress and strain