Modeling flux chemistry for submerged arc weldments of high-strength low-alloy steel

Abstract

Chemical and mechanical properties of the welded joint are greatly affected by flux composition. The resulting chemical compositions of C, Si, Mn, P and S in the weld metal have been studied using formulated fluxes. The constrained mixture design, extreme vertices design, has been used to formulate fluxes to study the effect of flux constituents. Regression models were developed for weld metal content in terms of individual flux constituents and their binary mixtures for submerged arc welding of high-strength low-alloy steel. From the results, it is found that CaF₂ is the most significant flux constituent and Al₂O₃ is the second most significant constituent among individual mixtures. CaO–MgO and CaO–Al₂O₃ binary mixtures are the most effective to change weld metal content. Regression mathematical models have been checked for adequacy using t-test and analysis of variance (F-test). Flux mixtures’ composition has been provided for optimum chemical composition of weld metal.

Keywords

High-strength low-alloy extreme vertices design synergism anti-synergism X-ray diffraction weld metal content binary mixtures

Introduction

Submerged arc welding (SAW) is the primarily used welding processes due to its inherent qualities like high quality, deep penetration, smooth finish, capability to weld thicker sections and prevention of atmospheric contamination of weld pool.^1–3 Mechanical properties of weld metal^4,5 depend on weld metal chemistry and microstructure which further depends on flux composition, basicity index (BI) and welding parameters. If welding parameters are kept same, weld metal chemistry is solely dependent on the flux composition and flux BI. A number of researchers have tried to study weld metal content due to change in flux composition. Some researchers tried to find absolute element content of the weld metal whereas others found change in element content with respect to base metal/filler metal due to slag–metal reactions,^6,7 whereas still others investigated the change in element transfer due to welding parameters or flux constituents.^4,8,9

Kanjilal et al.⁴ in their work concluded that SAW is mainly affected by the factors: the transfer of elements to or from the slag, dilution of weld pool by the base plate and environmental contamination. The interaction effects are predominant than the individual effect of input factors. Among the welding parameters, polarity was found to be most important for all responses, namely, weld metal chemical composition and mechanical properties.

Pandey et al.⁸ studied the effect of welding parameters and flux BI on the weld chemistry. It was proposed in the study that element transfer depends on welding parameters and flux BI, but it could not be correlated with BI. The authors suggested that the final weld chemistry is the outcome of slag–metal reaction which depends on the flux composition and/or the flux BI which may be carried in further study.

The study of Chai and Eagar⁶ also indicates that weld metal chemistry is mainly dependent on flux composition, whereas welding parameters have insignificant effect. The study also showed that weld bead geometry is dependent on weld parameters only: welding current, voltage, travel speed, electrode diameter and electrode polarity and independent on flux composition.

The slag–metal reactions have been studied by Mitra and Eagar⁷ to predict the transfer of Cr, Si, Mn, P, S, C, Ni and Mo between the slag and the weld pool for weld bead in SAW of alloy steels. It was concluded from the study that the transfer of chromium is strongly dependent on the type of flux used; lower BI of the flux and high chromium content of the electrode enhances the chromium content of weld metal. It was also observed that the manganese content of the weld metal depends mainly on the amount of MnO in the flux and manganese content of the electrode. Lime-based fluxes produced weld metal with a lower phosphorous content than that produced by using the flux containing MnO.

Burck et al.¹⁰ evaluated the effects of CaF₂, CaO and FeO additions on weld metal chemistry on AIS11010, 1020 and 4340 steel base plates. The effective application of the SAW process for joining high-strength low-alloy (HSLA) steels depends heavily upon understanding the behavior of the flux. Understanding the elemental transfer mechanisms between the flux and the weld metal can be attained by studying the influence of each chemical additive on the flux behavior.

Ramirez¹¹ indicated that more work may be done in the developments of welding processes and consumables to produce weld metals with mechanical properties equivalent to the base metal in steel technology. However, to achieve this, better understanding of chemistry and microstructure property relationships in hollow structural section (HSS) weld metals is needed.

It was observed in the earlier work that very little work has been done in high-strength low-alloy (HSLA) welded joint and no studies indicated the optimization of weld metal chemistry to match base metal.

In this study, individual flux constituents and their binary mixtures have been studied with an aim to obtain regression equations for weld metal content by varying flux composition in CaO–MgO–CaF₂–Al₂O₃ flux system using statistical mixture design for SAW of HSLA steel.

Experimentation

Experiments were conducted by using 21 formulated fluxes to study the effect of flux constituents on the weld metal element. The agglomerated fluxes were formulated by using eight flux constituents: varying four flux constituents, CaO, Al₂O₃, CaF₂ and MgO, and keeping SiO₂, TiO₂, MnO and bentonite as constant as given in Table 1. Extreme vertices design suggested by McLean and Anderson for constrained mixtures design is used for designing flux composition^12
–14. Same design of experiment (DOE) technique was also used previously by Jindal et al.¹⁵ with same limits of flux constituents and same design table. The method suggests constrained mixture design for a mixture of q components having lower and upper limits on some or all the components and may be represented mathematically as

0 \leq a_{i} \leq x_{i} \leq b_{i} \leq 100

(1)

and

\sum_{i = 1}^{q} x_{i} = 100

(2)

where $i = 1, 2, 3 \dots, q$ and $a_{i} and b_{i}$ are the constraints on the $x_{i}$ imposed by the experimenter.

Table 1.

Design matrix for flux formulation.

Type of point	Flux no.	Varied mixture components				Basicity index
		CaO (%wt)	Al₂O₃ (%wt)	CaF₂ (%wt)	MgO (%wt)	Basicity index
Vertex	1	35.0	8.0	10.0	25.0	3.7
Vertex	2	10.0	8.0	40.0	20.0	3.7
Vertex	3	10.0	40.0	10.0	18.0	1.1
Vertex	4	20.0	8.0	10.0	40.0	3.7
Vertex	5	10.0	8.0	20.0	40.0	3.7
Vertex	6	10.0	18.0	10.0	40.0	2.5
Vertex	7	20.0	8.0	40.0	10.0	3.7
Vertex	8	35.0	8.0	25.0	10.0	3.7
Vertex	9	18.0	40.0	10.0	10.0	1.1
Vertex	10	35.0	23.0	10.0	10.0	2.1
Vertex	11	10.0	40.0	18.0	10.0	1.1
Vertex	12	10.0	18.0	40.0	10.0	2.5
Centroid	13	10.0	22.0	23.0	23.0	2.2
Centroid	14	21.7	8.0	24.2	24.2	3.7
Centroid	15	21.3	22.8	10.0	23.8	2.1
Centroid	16	21.3	22.8	23.8	10.0	2.1
Centroid	17	35.0	13.0	15.0	15.0	3.0
Centroid	18	12.7	40.0	12.7	12.7	1.1
Centroid	19	13.3	11.3	40.0	13.3	3.2
Centroid	20	13.3	11.3	13.3	40.0	3.2
Centroid	21	18.6	18.9	20.3	20.3	2.4

Upper and lower limits of the various flux constituents are decided on the basis of the phase diagrams of CaO–Al₂O₃–MgO system and performing trial experiments. The phase diagrams of CaO–Al₂O₃–MgO system were studied to obtain the weight percentage range of each component based on its solidification range and equilibrium solid solubility of one component in another. The phase diagram for CaO–Al₂O₃–MgO ternary system is shown Figure 1.¹⁷ The primary requirement while deciding the percentage composition of various flux ingredients is that their melting temperature should be lower than that of base metals as the flux should melt first before the base metals to be melted and should remain in the molten state even after the solidification of weldment so as to avoid the atmospheric contamination.¹⁸ Slag detachment, weld bead continuity and arc stability were observed during the trial experiments.

Figure 1.

Phase diagram for CaO–Al₂0₃–MgO ternary system showing different equilibrium temperatures.¹⁶

Upper and lower limits of the various flux constituents are given below

10 \leq CaO (x_{1}) \leq 35

8 \leq A l_{2} O_{3} (x_{2}) \leq 40

10 \leq Ca F_{2} (x_{3}) \leq 40

10 \leq MgO (x_{4}) \leq 40

(3)

\sum_{i = 1}^{4} x_{i} = 78

(4)

The mixture design consists of 12 vertices, four centroids of hexagonal faces and four centroids of triangular faces and one overall body centroid of truncated tetrahedron. In the first step, 12 vertices of polyhedron were selected from 4.2⁴⁻¹ = 32 combinations (=q.2^q−1) out of four components satisfying lower and upper bounds and total proportion of the mixture giving 12 vertices of truncated tetrahedron (Points 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 and 12) in three-dimensional (3D) space (refer Figure 2). Then two-dimensional faces were found by grouping the vertices of the truncated tetrahedron into groups of three or more vertices where each vertex has the same value x_i for one of the components. So eight such combinations, four hexagonal faces and four triangular faces, were selected forming the faces of truncated tetrahedron. Then centroids of hexagonal and triangular faces were taken as design points. Hence, a of total 21 experiments were performed; experiment numbers 1–12 represent 12 vertices, experiment numbers 13–20 represent eight centroids and experiment number 21 represents one overall centroid (refer Table 1).

Figure 2.

Graphical demonstration of flux mixture design by truncated tetrahedron in 3D space.

The output response characteristics are given in the form of second-order regression model as

y = \sum_{i}^{q} b_{i} x_{i} + \sum_{i < j} \sum^{q} b_{ij} x_{i} x_{j}

(5)

where y is the output response variable, and $b_{i}$ and $b_{ij}$ are least square model regression coefficients. Terms $b_{i} x_{i}$ and $b_{ij} x_{i} x_{j}$ in the regression model represent individual effect and interaction effect of the mixture components. If output response variable y is increasing with regression coefficient $b_{ij}$ positively, then the excess is called the synergism of the binary mixture; opposite to that if output response variable y is decreasing with regression coefficient $b_{ij}$ positively, then the decrease is called the anti-synergism of the binary mixture and vice versa.¹³ So positive and negative values of regression coefficient, $b_{ij}$ define synergistic and anti-synergistic effects of the binary mixtures, respectively.¹⁶

Preparation of fluxes

For preparation of fluxes, constituting elements were weighed separately on digital weighing balance (accuracy 1 mg) according to weight percentage, as per Table 1, and then mixed thoroughly in a container with sodium silicate binder (20% weight) for about 30 min to get homogenous semi-solid mass. Sodium silicate is added for better arc stability and binding the individual ingredients together.^19,20 Then solid mass was dried in air for 24 h and then baked in the muffle furnace at 750°C for nearly 1 h.²¹ After cooling, these fluxes were crushed and sieved and then kept in air-tight bags.

Welding of plates

For welding, the edges of HSLA plates were prepared by making a V-groove of 60°. Twenty-one weld samples were made taking two HSLA steel (API 5L X65) plates, each of size 250 × 150 mm and thickness 18 mm. Fixtures were made to get butt weld on the base plates on SAW setup (ADOR Tornado SAW M-800) at MMU, Mullana (Ambala). All the experiments were conducted using 3.2-mm-diameter wire electrode (EH-14) by taking optimum welding parameters: welding current 410 A, arc voltage 30.4 V and weld speed 21.2 m/h with direct current electrode positive (DCEP) in constant voltage mode. The optimum welding parameters were selected on the basis of trial runs and performing optimization experiments using response surface methodology (RSM) technique by varying the parameters: current range 349–651 A, voltage range 24–32 V and travel speed range 17–33 m/h keeping nozzle-to-tip distance constant at 25 mm with formulated flux number 11 (BI = 1.1). Composition of the flux has significant effect on chemical and mechanical properties of the weldments, but the effect of flux constituents on weld bead geometry has not been reported in earlier literature. The study of Chai and Eagar⁶ also indicates that weld metal chemistry is primarily dependent on weld metal flux composition and independent of operating parameters. Weld parameters are optimized on the basis of area of penetration, weld bead form factor and dilution.¹⁵

Analysis of weld samples

Chemical composition of base metal, filler metal (electrode wire) (Table 2) and all weld samples (Table 3) was determined by electron probe micro analysis (EPMA). Chemical analysis through EPMA was carried out on JEOL Electron Probe Microanalyzer (JXA-8230) at National Metallurgical Laboratory, Jamshedpur, at an accelerating voltage of 15 kV at a resolution of 1000× compositional and secondary images of two weld samples (sample numbers 5 and 21) are shown in Figure 3. Weld element content was determined by taking the average of three randomly selected points as shown in Figure 3. X-ray diffraction (XRD) analysis of all the slag samples was carried out to analyze the elemental pickup by slag during welding.

Table 2.

Chemical composition of base metal and electrode.

Chemical composition	C	Si	Mn	P	S	Ti	Nb	V
Base metal (API 5L X65)	0.214	0.17	1.74	0.01	0.01	0.193	0.484	0.105
Electrode wire (EH-14)	0.201	0.1	1.8	0.03	0.03	0.002	0.007	0.002

Table 3.

Various weld metal properties weld metal content (%).

Sample no.	Mixture components (%wt)				Weld metal content (%)
	CaO	Al₂O₃	CaF₂	MgO	C	Si	Mn	P	S
1	35.0	8.0	10.0	25.0	0.0543	0.2426	1.0847	0.0237	0.0087
2	10.0	8.0	40.0	20.0	0.0311	0.1477	1.1230	0.0147	0.0080
3	10.0	40.0	10.0	18.0	0.0360	0.1436	1.2533	0.0083	0.0236
4	20.0	8.0	10.0	40.0	0.0952	0.1954	1.1377	0.0257	0.0225
5	10.0	8.0	20.0	40.0	0.0562	0.1985	1.1977	0.0123	0.0063
6	10.0	18.0	10.0	40.0	0.0643	0.1090	1.8080	0.0067	0.0122
7	20.0	8.0	40.0	10.0	0.0653	0.1266	1.3710	0.0197	0.0237
8	35.0	8.0	25.0	10.0	0.0420	0.1775	1.3267	0.0203	0.0017
9	18.0	40.0	10.0	10.0	0.0589	0.1383	1.0540	0.0217	0.0247
10	35.0	23.0	10.0	10.0	0.0561	0.1157	1.4186	0.0063	0.0273
11	10.0	40.0	18.0	10.0	0.0248	0.2026	1.3077	0.0233	0.0060
12	10.0	18.0	40.0	10.0	0.0295	0.1264	1.3370	0.0117	0.0073
13	10.0	22.0	23.0	23.0	0.0181	0.1527	1.2073	0.0136	0.0026
14	21.7	8.0	24.2	24.2	0.0429	0.1966	1.1673	0.0200	0.0100
15	21.3	22.8	10.0	23.8	0.0587	0.1441	1.1520	0.0083	0.0214
16	21.3	22.8	23.8	10.0	0.0303	0.1440	1.3420	0.0183	0.0123
17	35.0	13.0	15.0	15.0	0.0439	0.1748	1.2590	0.0227	0.0125
18	12.7	40.0	12.7	12.7	0.0502	0.1293	1.2330	0.0193	0.0222
19	13.3	11.3	40.0	13.3	0.0312	0.1280	1.3270	0.0103	0.0119
20	13.3	11.3	13.3	40.0	0.0548	0.1709	1.2500	0.0123	0.0120
21	18.6	18.9	20.3	20.3	0.0317	0.1373	1.2657	0.0150	0.0209

Figure 3.

EPMA analysis images: (a) compositional, (b) point selection and (c) secondary images for sample no. 5. (d) Compositional, (e) point selection and (f) secondary images for sample no. 21.

Results

The results of weld metal element content are represented in Table 3.

Development of regression models for weld metal element content

Using the observed values of chemical properties from experimentation, least square regression equations have been developed in terms of percentage composition of individual components (CaO, Al₂O₃, CaF₂ and MgO). Second-order quadratic regression models are formed in terms of predictors of individual effect of mixtures components (CaO, Al₂O₃, CaF₂ and MgO) and interaction effect of binary mixtures (CaO·Al₂O₃, CaO·CaF₂, CaO·MgO, Al₂O₃·CaF₂, Al₂O₃·MgO, CaF₂·MgO).

\begin{matrix} C (WM) & = - 0.00142 CaO + 0.00181 A l_{2} O_{3} \\ + 0.00277 Ca F_{2} + 0.00349 MgO \\ + 0.00006 CaO \cdot A l_{2} O_{3} + 0.00002 CaO \cdot Ca F_{2} \\ + 0.00002 CaO \cdot MgO - 0.00012 A l_{2} O_{3} \cdot Ca F_{2} \\ - 0.00009 A l_{2} O_{3} \cdot MgO - 0.00014 Ca F_{2} \cdot MgO \end{matrix}

(6)

\begin{matrix} Si (WM) & = + 0.00484 CaO + 0.00645 A l_{2} O_{3} \\ - 0.00225 Ca F_{2} + 0.00107 MgO \\ - 0.00026 CaO \cdot A l_{2} O_{3} + 0.00001 CaO \cdot Ca F_{2} \\ + 0.00008 CaO \cdot MgO + 0.00007 A l_{2} O_{3} \cdot Ca F_{2} \\ - 0.00019 A l_{2} O_{3} \cdot MgO + 0.00016 Ca F_{2} \cdot MgO \end{matrix}

(7)

\begin{matrix} Mn (WM) & = + 0.03856 CaO - 0.00047 A l_{2} O_{3} \\ + 0.02478 Ca F_{2} + 0.04196 MgO \\ - 0.00016 CaO \cdot A l_{2} O_{3} - 0.00026 CaO \cdot Ca F_{2} \\ - 0.00148 CaO \cdot MgO + 0.00034 A l_{2} O_{3} \cdot Ca F_{2} \\ + 0.00049 A l_{2} O_{3} \cdot MgO - 0.00108 Ca F_{2} \cdot MgO \end{matrix}

(8)

\begin{matrix} P (WM) & = - 0.00037 CaO + 0.00110 A l_{2} O_{3} \\ - 0.00037 Ca F_{2} + 0.00021 MgO \\ - 0.00002 CaO \cdot A l_{2} O_{3} + 0.00003 CaO \cdot Ca F_{2} \\ + 0.00003 CaO \cdot MgO + 0.00000 A l_{2} O_{3} \cdot Ca F_{2} \\ - 0.00005 A l_{2} O_{3} \cdot MgO + 0.00001 Ca F_{2} \cdot MgO \end{matrix}

(9)

\begin{matrix} S (WM) & = - 0.00172 CaO + 0.00025 A l_{2} O_{3} \\ + 0.00113 Ca F_{2} + 0.00016 MgO \\ + 0.00007 CaO \cdot A l_{2} O_{3} + 0.00002 CaO \cdot Ca F_{2} \\ + 0.00005 CaO \cdot MgO - 0.00005 A l_{2} O_{3} \cdot Ca F_{2} \\ + 0.00000 A l_{2} O_{3} \cdot MgO - 0.00004 Ca F_{2} \cdot MgO \end{matrix}

(10)

Analysis of mathematical models

Prediction equations (6), (7), (8), (9) and (10) have been checked for adequacy using t-test and analysis of variance (ANOVA) (F-test). Individual regression coefficients ( $b_{i}$ , $b_{j}$ and $b_{ij}$ ) have been checked by comparing t₀ value with tabulated t-value (at 95% significance level for dof_error)^12,13 given in Appendix 1. Whole mixture model has been checked separately for linear and quadratic least square models as well as for full model tested by calculating F-value and p-value at 95% of significance level. R² values for all the equations have been calculated and are more than 80% except for manganese showing that the predicted values are in close agreement with the experimental values of weld metal composition as seen from Figure 4. Summary of regression equations indicating individual and interaction effects of binary mixtures on the chemical composition for weld metal is given in Table 4.

Figure 4.

Predicted values versus actual/observed values of chemical composition for weld metal: (a) C, (b) Si, (c) Mn, (d) P and (e) S.

Table 4.

Summary indicating the effect of different types of mixtures on the weld metal content.

Type of effect	Term	C	Si	Mn	P	S
Individual effect	CaO	–	Increase	Increase	–	Decrease
	Al₂O₃	Increase	Increase	–	Increase	–
	CaF₂	Increase	Decrease	Increase	–	Increase
	MgO	Increase	–	Increase	–	–
Binary mixture effect	CaO.Al₂O₃	Synergistic	Anti-synergistic	–	–	Synergistic
	CaO.CaF₂	–	–	–	–	–
	CaO.MgO	–	–	Anti-synergistic	–	Synergistic
	Al₂O₃.CaF₂	Anti-synergistic	–	–	–	Anti-synergistic
	Al₂O₃.MgO	Anti-synergistic	Anti-synergistic	–	Anti-synergistic	–
	CaF₂.MgO	Anti-synergistic	Synergistic	Anti-synergistic	–	Anti-synergistic

Discussion

Effect of different mixtures on the weld metal element is indicated in Table 4 and Appendix 1 Tables 7 and 8. Table 4 shows type of effect (synergistic/anti-synergistic) of different mixtures on the chemical composition, and t-table (Appendix 1) shows the significance of various flux mixtures according to t-value of corresponding term (flux mixture).

Effect of flux constituents on carbon content

Weld metal has lower carbon content than base metal and electrode wire as shown by results, which is in accordance with the previous literature.⁷ All individual flux mixtures affect weld metal carbon, but only CaO has insignificant decreasing effect as CaO oxidizes carbon to its oxides during slag–metal reactions. In the high-temperature environment near the welding plasma, CaO decomposes to release oxygen. The oxygen released from flux reacts with carbon of base metal and filler metal to form its oxides thereby reducing weld metal carbon.

Binary mixture CaO·Al₂O₃ has synergistic effect, whereas binary mixtures of Al₂O₃ with CaF₂ and MgO have anti-synergistic effect on C. The binary mixture CaF₂·MgO also has significant anti-synergistic effect on weld metal carbon.

Effect of flux constituents on silicon content

From the results, it seems that weld metal silicon content does not have any relationship with initial Si content of flux (SiO₂ content is constant), mainly dependent on slag–metal reactions and almost independent of Si content of base metal and filler metal.²² Increase in Si content occurs in most of the experiments as shown in Table 3.

Si content increased in weld samples as SiO₂ present in the flux dissociates to Si and O₂ as per equation (11)

Si O_{2} \to Si + O_{2}

(11)

Among individual flux mixtures, CaO and Al₂O₃ tend to increase Si content whereas CaF₂ tends to decrease weld metal silicon. Among the binary mixtures, CaF₂·MgO have synergistic effect on silicon content as in agreement with the previous literature,⁹ whereas CaO·Al₂O₃ and Al₂O₃·MgO have anti-synergistic effect on Si content (refer Table 4).

MgO has insignificant increasing effect on Si content which may be due to dissociation of MgO to Mg, in turn Si will form SiO₂ which will react with Mg in the weld pool to form MgO again. So Si content is expected to increase due to MgO.

Binary mixture CaO–MgO has insignificant anti-synergistic effect on silicon content which may be due to reduction in SiO₂ to complex silicates also verified in XRD analysis of slags in section “Discussion of XRD analysis.” Binary mixture CaF₂.MgO increases density of the molten metal which retards the transfer of Si across the slag–metal interface.

Effect of flux constituents on manganese content

In general, manganese transfer depends on manganese content of electrode and flux composition.⁷ Mn content in all samples is decreased except sample no. 6 which shows gain of Mn content. Individual flux ingredients tend to increase Mn content except Al₂O₃ which tend to decrease manganese content insignificantly. Binary mixtures CaO–MgO and CaF₂·MgO have anti-synergistic effect on Mn.

Increase in Mn in weld metal may be due to the electrochemical reaction occurring at the base metal (cathode in reverse polarity). During this reduction reaction, Mg dissociates from MgO. Manganese will form MnO with oxygen in the molten metal and Mg will react with this MnO to form MgO again which increases Mn content of weld metal. Addition of MgO to CaO and CaF₂ increases density and decreases conductivity of the molten metal which increases the resistance to Mn movement at the slag–metal interface thereby decreasing Mn content of weld metal and Mn vaporizes from electrode/base metal.

Effect of flux constituents on phosphorus content

Phosphorus is assumed to be an impurity which increases the strength of low-alloy steels and increases crack tendency during welding at the same time and so should be kept minimum. Sample numbers 1, 4 and 11 show gain of P content in weld metal; all the other samples show loss of P. Individual flux ingredient Al₂O₃ tends to increase P content and binary mixture Al₂O₃·MgO has anti-synergistic effect on phosphorus.

CaO and CaF₂ have insignificant decreasing effect on P content as phosphorus is oxidized to its oxides thereby decreasing its content. Substitution of flux ingredient by CaO and CaF₂ lowers activity coefficient of phosphorous pentoxide, $γ_{P_{2} O_{5}}$ in the slag promoting the reaction given by equation (12) and thereby decreasing phosphorus content⁶

4 P + 5 O_{2} = 2 (P_{2} O_{5})

(12)

Effect of flux constituents on sulfur content

Sample numbers 3, 4, 7, 10, 18 and 21 show gain of S content in weld metal; all the other samples show loss of sulfur. Only CaO among individual flux ingredients has significant decreasing effect on S as seen from equation (10) and the table (t coefficients in Appendix 1); binary mixtures CaO·Al₂O₃ and CaO–MgO have synergistic effect on S, whereas Al₂O₃·CaF₂ and CaF₂·MgO have anti-synergistic effect on S content.²³ Negative delta sulfur value was obtained in the work by Dallam et al.²³ in the CaF₂–CaO–SiO₂ flux system in HSLA steel weldments. Lime fluxes are well known to remove impurities during welding processes. CaO combines with sulfur of weld metal to form CaS and release O₂ as per reaction (equation (13)), thereby lowering sulfur content from weld metal. The result is in agreement with the results by Chai and Eagar⁶ but contrary to results by Kanjilal et al.⁹

CaO + S = CaS + \frac{1}{2} O_{2}

(13)

MnO from flux also reacts with weld metal S forming MnS and releasing O₂, thereby decreasing S content in all other samples having lesser CaO.

Discussion of XRD analysis

XRD analysis of all slag samples was taken after welding. For the XRD measurements, the slag specimens were analyzed using 2θ diffraction mode ranging from 10° to 120°. The XRD patterns of slag numbers 1, 10, 16 and 19 are shown in Figure 5.

Figure 5.

XRD analysis of some slag samples.

The different crystalline compounds are formed in the slags which are in agreement with the previous literature^24–26 such as Gehlenite (calcium magnesium aluminum silicate, Ca₂(Mg_0.25Al_0.75)(Si_1.25Al_0.75O₇)), melilite (calcium magnesium aluminum silicate, Ca₂(Mg_0.5Al_0.5)(Si_1.5Al_0.5O₇)), merwinite (calcium magnesium silicate, Ca₃Mg(SiO₄)₂), joesmithite (calcium lead aluminum iron magnesium beryllium silicate hydroxide, Ca_5.2Pb_.8Al_.3Fe_4.8Mg_4.9Be₄Si₁₂O₄₄(OH)₄), gismondine (calcium aluminum silicate hydrate, CaAl₂Si₂O₈·4H₂O), garronite (sodium calcium aluminum silicate hydrate, Na_.8Ca_2.82(Al₆Si₁₀O₃₂)(H₂O)_12.08), ungarettiite (sodium potassium calcium magnesium manganese silicate, (Na_0.80K_0.15)(Na_1.97Ca_0.03)(Mn_0.93Mg_0.07)(Mn_1.78Mg_0.22). Mn₂(Si₈O₂₂)O₂) and margarosanite (lead calcium manganese silicate, Pb(Ca Mn)₂(SiO₃)₃).

It may be seen from the PDF index names and chemical formula of the above compounds that silicates and silicate hydroxide have been observed in most of the high basicity slags and lesser in low basicity slags. Silicates are formed due to oxidation of different elements such as Mn, Al and Mg in the presence of Si, whereas silicate hydroxides have been formed due to oxidation of elements and moisture pickup from atmosphere. Sodium element is being observed in about all the slag compounds which may be due to sodium silicate binder added during the agglomeration process in the formulation of fluxes.

Contour surface plots for various properties

Contour plots indicating predicted values of chemical properties are shown in Figure 6. Different regions on contour surface²⁷ show variation in weld metal content, so every contour curve marked on the surface gives constant value of element content in weld metal and each dotted point on plot indicates one of the flux mixture combination. Figure 6 shows contour plots for C, Si, Mn, P and S for different proportions of flux components CaO, CaF₂ and Al₂O₃ with constant MgO = 10% content.

Figure 6.

Contour plots for (a) C, (b) Si, (c) Mn, (d) P and (e) S at different proportions of flux components CaO, CaF₂ and Al₂O₃ with constant MgO = 10% content.

Optimization of chemical composition and mechanical properties

In the multi-response optimization, attempt has been made to optimize the chemical composition of the weld metal equivalent to that of base metal.¹⁰ Simultaneous optimization of these output responses has been done using composite desirability optimization method suggested by Derringer and Suich.²⁸ This method makes use of an objective function D(x), called desirability function which transforms an estimated response into a value called composite desirability. Composite desirability is the weighted geometric mean of individual desirability for the responses. The factor settings with maximum total desirability are considered to be the optimal parameter combinations.²⁹

The composite desirability is given by³⁰

D = {[d_{1}^{w_{1}} \cdot d_{2}^{w_{2}} \dots d_{n}^{w_{n}}]}^{\frac{1}{(w_{1} + w_{2} \dots + w_{n})}}

(14)

D = {[Π_{i}^{n} d_{i}^{w_{i}}]}^{\frac{1}{(\sum_{i}^{n} w_{i})}}

(15)

where n is the number of responses, $d_{i}$ is the desirability of particular response and $w_{i}$ = weights satisfying 0 < $w_{i}$ < 1 and $(w_{1} + w_{2} \dots + w_{n}) = 1$ .

Three optimum solutions with equal weights for all responses were determined at different levels of desirability as presented in Table 5.

Table 5.

Optimum flux mixtures for chemical composition.

No.	CaO	Al₂O₃	CaF₂	MgO	C	Si	Mn	P	S	Desirability
1	10.63	13.08	14.29	40	0.058	0.153	1.440	0.010	0.010	0.731
2	35	14.5	18.5	10	0.041	0.156	1.408	0.017	0.010	0.587
3	35	15.57	12.77	14.66	0.046	0.164	1.280	0.015	0.014	0.558

Confirmatory experiments

Model validation was performed by randomly selecting some flux mixtures to ensure the repeatability and reliability of the predicted values (Table 6). Five flux mixtures were taken to produce weld samples. From the experimental values and predicted values, percentage error for each response was calculated and it has been observed that error is nearly 5% in almost all the samples.

Table 6.

Percentage error of predicted values and experimental values.

Flux constituents				Predicted values					Experimental values					Error (%)
CaO	Al₂O₃	CaF₂	MgO	C	Si	Mn	P	S	C	Si	Mn	P	S	C	Si	Mn	P	S
20.0	8.0	10.0	40.0	0.0886	0.2019	1.184	0.0209	0.0205	0.0825	0.223	1.2521	0.0198	0.02205	6.9	10.5	5.7	5.3	7.6
35.0	8.0	25.0	10.0	0.044	0.1782	1.4318	0.01835	0.00625	0.042	0.1695	1.5702	0.0190	0.00574	4.5	4.9	9.7	3.3	8.2
21.7	8.0	24.2	24.2	0.044	0.2003	1.0355	0.02104	0.01167	0.0481	0.219	1.112	0.0225	0.01099	9.4	9.4	7.4	6.9	5.8
12.7	40.0	12.7	12.7	0.0417	0.1519	1.202	0.01305	0.0195	0.0376	0.1421	1.0984	0.0123	0.0187	9.7	6.5	8.6	6.1	4.1
13.3	11.3	13.3	40.0	0.0678	0.1654	1.3554	0.01198	0.01328	0.0719	0.1575	1.2875	0.013	0.01432	6.0	4.8	5.0	8.6	7.8

$Percentage error = \frac{Actual Value - Predicted Value}{Predicted Value} \times 100$

Conclusion

The mathematical models have been developed for the weld metal element content in terms of flux constituents.

Individual flux mixtures Al₂O₃, CaF₂ and MgO tend to increase, whereas binary mixtures Al₂O₃·CaF₂, Al₂O₃·MgO, CaF₂·MgO tend to decrease carbon content.

Weld metal carbon content is decreased mainly due to decomposition of CaO in the flux mixture at high temperature.

Weld metal silicon content is independent of the initial Si content of flux but is solely dependent on slag–metal reactions.

Individual flux mixtures CaO, CaF₂ and MgO tend to increase, whereas binary mixtures CaO·MgO and Al₂O₃MgO tend to decrease manganese content.

The electrochemical reaction occurring at the cathode base metal is responsible for the increase in manganese weld metal.

Both CaO and CaF₂ tend to decrease weld metal phosphorus, whereas only CaO tends to decrease weld metal sulfur.

CaF₂ is the most significant flux constituent and Al₂O₃ is the second most significant constituent among individual mixtures.

CaF₂–MgO is the most significant and CaO–Al₂O₃ is the second most significant binary mixture affecting weld metal content.

Footnotes

Appendix 1

Table 8.

Analysis of regression models using ANOVA (F-test).

	Model	DOF	SS	MS	F-value	p-value	R²
C	Regression	9	0.005796	0.000644	12.94029	0.0001	91.37%
	Linear Mixture	3	0.001835	0.000612	12.2877	0.0008
	CaO·Al₂O₃	1	0.000223	0.000223	4.487475	0.0577
	CaO·CaF₂	1	0.000019	0.000019	0.390539	0.5448
	CaO·MgO	1	0.000025	0.000025	0.51079	0.4897
	Al₂O₃·CaF₂	1	0.001257	0.001257	25.25028	0.0004
	Al₂O₃·MgO	1	0.000746	0.000746	14.98545	0.0026
	CaF₂·MgO	1	0.001691	0.001691	33.97496	0.0001
	Residual error	11	0.000547	0.000050
	Total	20	0.006344
Si	Regression	9	0.022019	0.002447	14.03192	0.0001	91.99%
	Linear mixture	3	0.011708	0.003903	22.38317	0.0001
	CaO·Al₂O₃	1	0.004187	0.004187	24.01504	0.0005
	CaOCaF₂	1	0.000003	0.000003	0.019088	0.8926
	CaO·MgO	1	0.000422	0.000422	2.421971	0.1479
	Al₂O₃·CaF₂	1	0.000454	0.000454	2.602517	0.135
	Al₂O₃·MgO	1	0.003140	0.003140	18.00692	0.0014
	CaF₂·MgO	1	0.002105	0.002105	12.07223	0.0052
	Residual error	11	0.001918	0.000174
	Total	20	0.023937
Mn	Regression	9	0.365645	0.0406273	3.452165	0.0285	73.85
	Linear mixture	3	0.095128	0.0317094	2.694404	0.0973
	CaO·Al₂O₃	1	0.001688	0.0016881	0.143443	0.7121
	CaO·CaF₂	1	0.004182	0.0041823	0.355376	0.5632
	CaO·MgO	1	0.132352	0.1323520	11.24617	0.0064
	Al₂O₃·CaF₂	1	0.010419	0.0104193	0.885345	0.3669
	Al₂O₃·MgO	1	0.021537	0.0215370	1.830034	0.2033
	CaF₂·MgO	1	0.100338	0.1003383	8.52591	0.0139
	Residual error	11	0.129455	0.0117686
	Total	20	0.4951
P	Regression	9	0.000588	0.000065	4.914693	0.008	80.08
	Linear mixture	3	0.000250	0.000083	6.276915	0.0097
	CaO·Al₂O₃	1	0.000022	0.000022	1.634948	0.2273
	CaO·CaF₂	1	0.000060	0.000060	4.530042	0.0567
	CaO·MgO	1	0.000062	0.000062	4.667305	0.0537
	Al₂O₃·CaF₂	1	0.000002	0.000002	0.126405	0.7289
	Al₂O₃·MgO	1	0.000189	0.000189	14.23432	0.0031
	CaF₂·MgO	1	0.000003	0.000003	0.20848	0.6568
	Residual error	11	0.000146	0.000013
	Total	20	0.000734
S	Regression	9	0.001026	0.000114	5.255659	0.0061	81.13%
	Linear mixture	3	0.000193	0.000064	2.967138	0.0788
	CaO·Al₂O₃	1	0.000313	0.000313	14.40938	0.003
	CaO·CaF₂	1	0.000024	0.000024	1.100714	0.3166
	CaO·MgO	1	0.000126	0.000126	5.802099	0.0347
	Al₂O₃·CaF₂	1	0.000256	0.000256	11.79911	0.0056
	Al₂O₃·MgO	1	0.000000	0.000000	0.017515	0.8971
	CaF₂·MgO	1	0.000114	0.000114	5.2707	0.0423
	Residual error	11	0.000239	0.000022
	Total	20	0.001265

DOF: degree of freedom; SS: sum of squares; MS: mean sum of squares.

Declaration of conflicting interests

The authors declare that there is no conflict of interest.

Funding

This research received no specific grant from any funding agency in the public, commercial, or not-for-profit sectors.

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