PREDICTING WELD STRUCTURE
USING MODIFIED SCHAEFFLER CONSTITUTION DIAGRAM
V. Mazurovsky[1], M.Zinigrad[2], A. Zinigrad[3]
Abstract
A mathematical model providing for predicting weld structure based on modified Schaeffler diagram has been developed. The objective and the scope of diagram modification are described.
Introduction
Schaeffler diagram is an important tool to predict Cr-Ni austenite, austenite-ferrite or austenite-martensite weld with carbon content of up to 0.12%. However, it does not allow for determining the composition and volume of carbide phase. Furthermore, if carbon content in weld is over 0.12% (like, for example, in the case of hardfacing), the forecast agreement with actual data is markedly reduced due to an intense consumption of carbon and carbide-forming elements by the process of carbide formation. In addition, an accurate prediction can be complicated either by a lower content (or absence) of Cr and Ni in the weld, or by a higher content of Mn (above 4%). Firstly, it could be attributed to the fact that the carbide formation process in weld is not taken into consideration (as mentioned above), and secondly, it is caused by using constant empiric coefficients in the equations determining Cr and Ni equivalents (Ref.1). The third problem relating to microstructure prediction based on the Schaeffler diagram lies in the difficulty of determining the volume of a specific phase in multiphase zones. Therefore, the Schaeffler diagram should be modified to provide a more accurate prediction of weld structure as follows:
- taking into consideration of the carbide formation process;
- implementation of variable coefficients in Cr and Ni equivalents equations (the coefficients should depend on the concentration and mutual influence of alloying components, and on the carbide formation process in the weld);
- incorporating of phase percentage lines for interphase zones (i.e., the zones which contain two or more phases, as performed by Schaeffler for austentite-ferrite zone).
It should be mentioned that various attempts were undertaken in order to improve the efficiency and accuracy of the metal structure prediction based on constitution diagram. As far as we know, no one of them provided a comprehensive solution for the above problems. For instance, relatively new WRC-1992 Diagram and its modified versions (Ref. 2,3) do not allow for predicting micro-structure of metals other than austenite-ferrite ones with carbon content not higher than 0.12%. On the other hand, those researchers who proposed to modify the Schaeffler Diagram (for example, Ref. 4) did not take into account the above-mentioned problems, e.g. carbide formation.
Carbide formation process
As mentioned above, if carbon concentration is over 0.12%, the volume of carbon and carbide-forming elements consumed for carbide formation can markedly increase. This process is disregarded in the Schaeffler diagram. The authors believe that it could be a reason for the disagreement between the matrix microstructure prediction results based on the Schaeffler diagram and the actual data for steels with high carbon content.
To pay a due regard to the carbide formation process, the authors use a new notion of carbide-forming ability of an element (CFA). It can be described by the following equation:
(1)
- absolute CFA of i-th element;
- atomic radius of i-th element, Ǻ;
- number of d-electrons at the outermost electron shell of i-th element.
Analysis of this equation (1) shows that CFA grows according to the following sequence:
Fe, Mn, Cr, Mo, W, Nb, V, Ta, Ti, Zr, Hf. However, in real alloys, CFA of a specific element depends on its concentration and some other factors. Therefore, for practical purposes, CFA of an element can be expressed as:
(2)
- actual CFA of i-th element;
- coefficient which takes into account the above factors.
Determination of coefficient is the most complicated challenge. The authors developed an appropriate method, which allows them to determine . The method cannot be published at the present stage.
The quantity of carbon required to form carbides from the carbide-forming i-th element will be as follows, %wt:
(3)
С% - carbon concentration in weld, % wt.
The quantity of carbon dissolved in the matrix is as follows, % wt:
(4)
n - a number of carbide-forming elements in weld.
The quantity of i-th element consumed to form -type j-th carbide:
(5)
- probability of formation of j-th carbide;
g, x - stoichiometric coefficients in the j-th carbide chemical formula;
- atomic weight of a carbide-forming i-th element;
- atomic weight of carbon.
The total quantity of i-th element consumed to form carbides, % wt:
(6)
k - the number of types of the carbides formed from a carbide-forming i-th element.
Now we can determine the quantity of the carbide-forming element dissolved in the matrix.
(7)
Therefore, the and values obtained while taking into account the carbide formation process can be used to determine Cr and Ni equivalents.
At the same time, now we are able to calculate the amount of matrix-strengthening carbide phases. The amount of carbide phase formed by i-th element is determined by the following formula:
(8)
- amount of carbide phase formed by i-th element, %wt;
and - see (3) and (6) accordingly.
The total amount of carbide phase in weld will be as follows:
(9)
At the same time, we must take into account the consumption of alloying elements to boride and nitride formation. If Ni content in alloys is over 5%, the phase formation shall also be taken into account. However, these issues cannot be described in the framework of this paper.
Adjustment of coefficients in Cr and Ni equivalent equations
By analyzing the structures of more than 50 types of deposit weld metal, the authors determined coefficient variation empirical dependencies for the equations defining Cr () and Ni () equivalents in the Schaeffler diagram (Ref.1). When modified, these equations are as follows:
(10)
(11)
l - number of ferrite-forming elements;
- concentration of ferrite-forming i-th element in the matrix, %wt;
- function determining empirical coefficient for ferrite-forming i-th element;
z - number of austentite-forming elements;
- concentration of austentite-forming i-th element in the matrix, %wt;
- function determining empirical ratio for austentite-forming i-th element;
- complex factors defined for the ferrite- and austentite-forming elements based on the structure analysis, as described above.
Phase proportions in multi-phase zone of the Schaeffler diagram
Phase proportions in multi-phase zone of the Schaeffler diagram were found by means of the structure analysis applied to determine the coefficients in equations (10), (11), and taking into account carbide formation process (9). Accordingly, percentage lines for the amount of the second (third) phase were incorporated in the appropriate zones of the diagram. For three-phase zones, algorithms to determine each phase content were developed. The modified Schaeffler diagram is shown in Fig. 1. The boundaries of austentite-martensite and ferrite-martensite (perlite) zones are slightly displaced upwards, as confirmed by numerous calculations and the analysis described.
Fig 1. – Modified Schaeffler diagram taking into consideration the effect of carbide formation.
Computer implementation of the model
Equations (1) - (11) and the mathematical description of the Schaeffler diagram served as a base of the mathematical model developed by the authors. The model is being implemented for solving two tasks, namely:
a) direct task, i.e., microstructure forecast according to the chemical composition of the weld;
b) reverse task, i.e., determination of the chemical composition of weld according to the microstructure required.
The reverse task is of course the most complicated challenge.
Currently, a pilot version of software based on the above mathematical model has been developed.
Model approbation
The above-mentioned software was approved by determining over 50 compositions of welds with a known matrix composition (microstructure) and strengthening phase volume. The obtained data proved a good agreement with the experimental data. The deviation did not exceed 15-20%.
Conclusions
The Schaeffler diagram was modified as follows:
а) consumption of elements to carbide formation was taken into account;
b) functional dependencies were applied to determine empirical coefficients in Nieq and Creq equations;
с) phase proportions in multiphase zones of the diagram were found.
The mathematical equations derived were used as a basis of a mathematical model to determine the microstructure of weld and strengthening phases. Computer implementation and approbation of the mathematical model were performed. The obtained results proved a good agreement between the calculated and actual data.
References
1. Schaeffler, A.L. 1949. Constitution diagram for stainless steel weld metal. Metal Progress 56(11):680 - 680B.
2. Kotecki, D.J., and Siewert, T.A. 1992. WRC-1992 constitution diagram for stainless steel weld metals: a modification of the WRC diagram. Welding Journal 71 (5): 171-s to 178-s.
3. Kotecki, D.J. 2000. Forecasting weld microstructure. Advanced materials and processes, 157 (6): 74 – 77.
4. Beres, L. 1998. Proposed modification to Schaeffler diagram for chrome equivalents and carbon for more accurate prediction of martensite content. Welding Journal, 77 (7): 273-s to 276-s
5. Olson, D.L. 1985. Prediction of austenitic weld metal micristructure and properties. Welding Journal 64 (10): 281-s to 295-s
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[1] CWC Ltd., Ariel, Israel
[2] College of Judea and Samaria, Ariel, Israel
[3] CWC Ltd., Ariel, Israel