Optimisation of Elemental Transfer Efficiency in Fe-C-Cr-Ti-Cu Hardfacing by Self-Shielded Flux-Cored Wire: A Synergistic Taguchi–ANOVA–FD–PCA–GRA Approach

Abstract

The objective of this article is to optimise the deposition modes and the content of exothermic additions (EAs) in the core filler in Fe-C-Cr-Ti with Cu additions hardfacing. To achieve this, JMatPro Release 7.0, Sente Software Ltd., 2016 material characterisation software was used to simulate and calculate the equilibrium phase structure and composition of the Fe-C-Cr-Ti-Cu alloy during the welding thermal cycle. A synergistic approach combining the Taguchi–Analysis of Variance (ANOVA)–Factorial design (FD) method with the standard hybrid Taguchi–ANOVA–Principal Component Analysis (PCA)–Grey Relational Analysis (GRA) is used and justified to optimise factors and develop mathematical models for parameters in the L9 orthogonal experimental design. The study examines how the transfers of deoxidisers depend on the content of exothermic additions in the cored wire filler (EA) and the contact tip-to-work distance (CTWD), while the behaviour of carbide formers is influenced by wire feed speed (WFS) and present arc voltage at the power source (U_set). The research specifically investigates the Fe-C-Cr-Ti-Cu system and the role of copper in stabilising austenite. Findings show that high Cu concentrations (7 wt.%) enhance hardenability by 13%, effectively suppressing pearlite transformation and expanding the bainite region. The desired chemical composition of the deposited metal is determined by the distribution of selected factors, as measured by the transfer coefficients of each element.

1. Introduction

In 2024, the global market volume of welding products was estimated to exceed USD 15 billion [1,2]. Welding consumables and technologies are a key driver of global growth in the welding market [3,4]. These technologies play a significant role in numerous industrial sectors, including the chemical industry, construction [5], the oil and gas industry, railway engineering [6,7,8], and automotive manufacturing [9,10]. Surfacing processes are widely used for both surface hardening and the restoration of worn components [11]. In the former case, cost reduction is achieved by using inexpensive, technologically advanced substrate materials such as structural steels [12,13]. In the latter case, the service life of components is extended. This is done through localised restoration of worn geometries. At the same time, high wear resistance is ensured [14]. In engineering practice, several surface strengthening technologies are employed. These include processes in the solution state, such as sol–gel, electrochemical deposition, and chemical solution deposition [15]; the gaseous state, such as ion beam-assisted deposition (IBAD), chemical vapour deposition (CVD), and physical vapour deposition (PVD) [16]; and the molten or semi-molten state, such as arc welding [17,18], plasma technologies [19,20,21,22], thermal spraying [23,24,25], and laser or electron beam processing [26,27,28]. However, hardfacing processes remain the most widely used due to their cost-effectiveness, technological simplicity, and broad industrial accessibility [29]. Using hardfacing technologies significantly reduces the cost of final products by enabling the use of large components made from inexpensive structural materials. Meanwhile, surface layers with enhanced tribological properties are formed only in zones subject to severe operating conditions. The most commonly used arc hardfacing techniques include shielded metal arc welding (SMAW) [30,31], gas tungsten arc welding (GTAW [32,33,34] or TIG [35,36]), gas metal arc welding (GMAW) [37,38,39,40], submerged arc welding (SAW) [41,42,43,44], manual metal arc welding (MMAW) [45,46], and flux-cored arc welding (FCAW) [47,48,49,50,51]. In recent decades, self-shielded flux-cored arc welding (FCAW-S) has gained prevalence in industry due to its high productivity, technological flexibility, and ability to produce hardfacing layers with customisable operational properties [52,53,54,55,56,57]. This approach effectively resists various types of wear [58], including abrasive [59,60], corrosive [61,62,63], impact-abrasive [64,65], abrasive-corrosive [66,67], and thermal softening [11]. Shape retention of wear-resistant parts allowed to preserve the performance and reliability of machine units [68,69,70], reduce dynamic stresses [71,72,73], and increase the operational lifespan of facilities and structures [74,75]

The properties of the deposited metal are determined by the chemical composition of the hardfacing layer. This layer is formed as a result of complex physicochemical processes occurring in the welding arc, the molten pool and during metal solidification [76,77]. The deposition conditions, which define the welding thermal cycle, also play a crucial role [78,79,80]. Carbide-forming elements are commonly used as primary alloying elements. These include chromium [81,82], titanium [83,84], vanadium [85], tungsten [86], and boron [87,88,89], among others. These elements form hard phases in the microstructure of the deposited metal in the form of carbides, carbonitrides, carboborides, and similar compounds. The transition of alloying elements from the powdered filler and the metallic sheath of the wire into the deposited metal is of particular importance [90,91,92,93].

Self-shielded flux-cored wires are complex multicomponent systems due to the presence of slag-forming, gas-forming, and deoxidising components in their composition, which significantly complicates the kinetics of the involved reactions [2,94]. The hardfacing process consists of two main stages: the formation of a molten metal droplet and a flux column, followed by the transfer of electrode material into the weld pool [95]. In the first stage, a molten metal droplet forms alongside the development of a flux column, which is a protrusion of the filler material [96,97,98]. In the second stage, the molten metal droplet is transferred into the weld pool. Depending on the hardfacing parameters (welding current, arc voltage, and contact tip-to-work distance) and the characteristics of the flux-cored wire (wire design, filler composition, and filling coefficient [98,99,100,101]), the molten metal droplet may form in one of two sub-modes (Figure 1): Type A (asymmetric) and Type B (central).

Upon forming, the flux column may either melt and mix with the molten metal droplet or collapse into the weld pool when it reaches a critical length or mass [92,95]. The melting of the flux column is caused by heat transfer from direct contact with the molten droplet (liquid metal of the wire sheath), Joule heating, as well as convective heat from the arc and the weld pool. This accounts for up to 15–30% of the total core filler volume [95]. On the other hand, flux column collapse is linked to forces like arc pressure and plasma shear forces. In these conditions, the flux column often separates from the metallic part several milliseconds before the metal droplets [98]. Large agglomerates subsequently fall onto the surface of the weld pool and are displaced by convective and gas-dynamic flows towards the trailing, crystallising region of the pool. There is insufficient time for them to dissolve in the liquid alloy [102]. Consequently, alloying elements from the flux-cored wire filler are transferred into the deposited metal via two pathways: through the molten metal droplet or through fragments of the flux column entering the weld pool directly. According to [102], the former mechanism is preferable as it results in a higher proportion of the alloying elements being dissolved by diffusion in the molten metal. The transfer of elements at the droplet stage can be described by the interaction between the molten metal and an annular layer of the charge with a thickness Δ, located adjacent to the wire sheath (Figure 2). This is based on the effective layer model proposed by Erokhin et al. [90]. The completeness of this interaction is characterised by the element transfer coefficient, which depends mathematically on the inner wire radius r₁ and the current density j. It has been established that an increase in current density leads to a systematic decrease in the effective layer thickness, Δ. Thus, the formation of a flux column during non-uniform electrode melting has a detrimental effect on the transfer of elements from the flux-cored wire filler into the deposited metal. It also contributes to the contamination of the hardfacing layer with non-metallic inclusions.

The most important challenges in modern welding technologies are the use of materials and processes that save energy, reducing and recycling waste, and optimising resources. The focus here is particularly on the environmental benefits and economic efficiency of the process [56,103]. Incorporating exothermic additions into the filler of flux-cored wires has been shown to enhance the energy efficiency and productivity of hardfacing processes [104,105,106], reduce droplet size [107] and improve the quality of the deposited metal [108,109,110,111,112]. However, the presence of an exothermic addition can significantly impact the uniformity of melting of both the metallic sheath and the flux-cored wire filler [92]. Depending on the hardfacing parameters and the thermophysical properties of the exothermic addition, the exothermic reaction may occur in one of two regions of the process: (1) in the electrode extension section due to Joule heating [113], or (2) within the arc column and flux column under the influence of arc heat [114,115] (see Figure 3). In the first case, introducing the exothermic addition results in uniform melting of both the core filler and the metallic sheath. In the second case, the intense heat released by the exothermic reaction can cause significant overheating of the droplets during transfer or neck rupture during short-circuit transfer [115]. This can substantially affect the behaviour of conventional metal droplet transfer.

In the first case, the metallic sheath and the core filler melt uniformly; however, the deposited metal may become more susceptible to atmospheric contamination due to the premature decomposition of gas-forming components. In the second case, the filler material may become excessively overheated due to intense additional chemical heat release. This can result in metal expulsion. This, in turn, contributes to increased burn-off losses and spattering. Trembach et al. [115] investigated the influence of the amount of EA introduced into the flux-cored wire filler and the hardfacing parameters on melting characteristics and weld bead morphology. As shown in

Table 1. Melting characteristics [115].

№ Exp	Melt-off Rate MOR, [kg·hr−1]	Deposition Rate DR, [kg·hr−1]	Spattering Factor SF [%]	Deposition Efficiency De [%]
1	4.43	3.88	9.68	87.55%
2	4.83	4.28	8.45	88.70%
3	5.04	4.52	10.12	89.68%
4	5.38	4.79	10.15	89.09%
5	5.73	5.07	11.12	88.53%
6	4.85	4.51	6.02	93.02%
7	5.52	5.16	5.35	93.54%
8	4.37	3.98	7.9	91.00%
9	5.04	4.83	3.52	95.76%

, the deposition rate was found to be most influenced by the wire feed speed, in combination with the amount of exothermic addition. Conversely, the spattering factor and deposition efficiency were primarily affected by the exothermic addition content and the contact tip-to-work distance. This indicated a significant contribution of the chemical reaction to the overall energy balance during the melting of flux-cored wire.

Investigating the transition of elements from core-filler materials into the deposited metal is still a challenging area of investigation. Without a clear understanding of the mechanisms influencing the behaviour of elements during hardfacing and their assimilation by the deposited metal, it is not possible to select the composition of flux-cored wire rationally. Therefore, studying element transition during hardfacing with self-shielded flux-cored wires is important from both scientific and technological perspectives. There are no published studies investigating the influence of surfacing conditions on the uptake of alloying elements by the deposited metal when surfacing with flux-cored wires containing an exothermic CuO-Al core filler. Research on the effect of reduced copper from EA on the microstructure, phase composition, and mechanical properties of deposited metal in the Fe-Cr-Ti-Cu system is also limited. The present work has two aims. First, it aims to conduct a comprehensive investigation into the element transition characteristics during hardfacing with self-shielded flux-cored wires. Secondly, the influence of technological parameters on the chemical composition and properties of the deposited metal is to be investigated.

2. Materials and Methods

2.1. Statistical Evaluation

The experimental methodology employed in this study was based on the approach described in references [110,115]. This combined approach [116,117,118] and standard hybrid method [119,120,121] were applied to an orthogonal four-factor, three-level experimental design. The combined approach identifies the most significant factors and eliminates insignificant variables through ANOVA. A factorial experimental design can be used to develop mathematical models that describe the target-dependent variables. In contrast, the hybrid Taguchi–Principal Component Analysis (PCA)–Grey Relational Analysis (GRA) method is employed to optimise the variables under investigation in processes characterised by multiple interdependent quality responses. PCA reduces data dimensionality by transforming correlated response variables into a smaller set of uncorrelated principal components while preserving dominant sources of variability [122,123].

2.1.1. Taguchi’s Design of Experiment

As the main experimental design, an orthogonal array based on the Taguchi method was employed. Four factors were investigated: the EA, CTWD, WFS, and U_set. The values of each variable were selected based on preliminary tests, conducted to establish the optimal valuesfor the variables. The EA content was varied at three levels of 20, 30, and 40 wt.%, while the CTWD was set to 35, 40, and 45 mm. The wire feed speed was adjusted to 1.50, 2.07, and 2.73 m·min⁻¹, and the set voltage values were 28, 31, and 34 V. The selection of experimental ranges was fundamentally grounded in the thermodynamic behaviour of self-shielding flux-cored wires with exothermic additions (EA). The EA content (20–40 wt.%) was optimised to balance internal chemical heat generation with the stability of the gas-slag protection [107,112,114], while the increased CTWD (35–45 mm) was specifically chosen to utilise Joule–Lenz heating. According to the calculation methodology proposed by Kassov et al. [124], this increased distance ensures sufficient preheating of the core to initiate the exothermic reaction before the arc zone [114]. The ranges for wire feed speed (1.50–2.73 m·min⁻¹) and arc voltage (28–34 V) were further refined to maintain a stable metal transfer mode, ensuring that the rate of the internal core reaction harmonises with the melting rate of the metallic sheath to prevent porosity and excessive spatter [104,108,110]. The nine experiments were conducted according to

Table 2. Design matrix of the experiment of full factor analysis using the orthogonal array L9 by the method.

№ Exp.	Fact Mean
	EA, [wt.%]	CTWD, [mm]	WFS, [m·min−1]	Uset, [V]
1	18	35	1.63	28
2	18	40	1.85	31
3	18	45	2.07	34
4	28	35	1.85	34
5	28	40	2.07	28
6	28	45	1.63	31
7	38	35	2.07	31
8	38	40	1.63	34
9	38	45	1.85	28

, and each experiment was repeated three times.

The content of the exothermic addition and the parameter variables of the hardfacing modes were optimised using the STATISTICA software Version 6.0 (Statsoft Inc., Tulsa, OK, USA, 2006).

2.1.2. Grey Relational Analysis

To facilitate the GRA process, raw data were normalised to calculate both the GRC and GRG values. Initially, a grey relational matrix was established by scaling the performance metrics to a normalised interval [0, 1]. This systematic approach was implemented for each of the three quality criteria. In accordance with the methodologies suggested by previous studies [115,123], the specific performance indicators summarised in Table 2 were evaluated using the following mathematical expressions [115,123]:

$$X_i^{*}={\displaystyle \frac{X_{i\max }-X_i}{X_{i\max }-X_i\min }} (\mathrm{smaller} \mathrm{is} \mathrm{better}),$$

(1)

$$X_i^{*}={\displaystyle \frac{X_i-X_{i\min }}{X_{i\max }-X_i\min }} (\mathrm{larger} \mathrm{is} \mathrm{better}),$$

(2)

where i = 1, …, m and k = 1, …, n; m = 9 is the number of experimental runs and n = 4 is the number of process factors. The term $X_i^0$ represents the original or reference sequence; $X_i^0\min$ and $X_i^0\max$ represents the minimum and maximum values in the original sequence; $X_i^{*}$ represents the sequence produced after data processing.

The GRC after data processing was calculated with the particular deviation calculations as given in Equations (3) and (4) [115,123]:

$${\Delta }_{oi}\left(k\right)=\left|X_i^{*}-X_i\right|,$$

(3)

$${\xi }_i\left(k\right)={\displaystyle \frac{{\Delta }_{\min }+\psi ·{\Delta }_{\max }}{{\Delta }_{oi}(k)+\psi ·{\Delta }_{\max }}},$$

(4)

where ${\Delta }_{oi}\left(k\right)$ is the deviation sequence of the original reference sequence of $X_i^{*}$ and compatibility sequence $X_i$; $\psi$ is the distinguishing coefficient and is usually taken as 0.5 when equal weightage is given to the process parameters.

Evaluated on a scale between 0 and 1, the GRG serves as a quantitative measure of the relational proximity between the reference and comparative sequences. Elevated GRG values reflect a stronger correspondence among the integrated process factors, which designates the most favourable operating conditions [115,123]:

$${\gamma }_i\left(GRC\right)={\displaystyle \frac{1}{n}}{\displaystyle \sum _{k=1}^n{\xi }_i\left(k\right)},$$

(5)

where $\gamma$_i(GRG) is the i-th experiment and n represents the number of performance characteristics.

The higher value of the grey relational grade shows that the corresponding experimental results are closer to the optimum value or normalised value.

2.1.3. Principal Component Analysis

To analyse the variance and covariance of the investigated performance parameters, Principal Component Analysis (PCA) [76] was utilised. This method facilitates the linear integration of variables to identify underlying patterns in the dataset. In accordance with the frameworks described by [115,123], the computational phases of the PCA approach are structured as follows [115,123]:

$$X_i=\begin{array}{cccc}{X}_1\left(1\right)& X_1\left(2\right)& \dots & X_1\left(n\right)\\ X_2\left(1\right)& X_1\left(2\right)& \dots & X_1\left(n\right)\\ \dots & \dots & \dots & \dots .\\ X_m\left(1\right)& X_1\left(2\right)& \dots & X{m}_1\left(n\right)\end{array},$$

(6)

where $X_i\left(j\right)$, i = 1 to m, j = 1 to n. Here in this study, $X$ represents the GRC of each performance characteristic.

The computation of the correlation coefficient array is computed using the following equation [115,123]:

$$R_i\left(k\right)=\left({\displaystyle \frac{\mathrm{cov}\left(X_i\left(j\right),X_i\left(\mathcal{l}\right)\right)}{{\sigma }_{Xi}\left(j\right)·{\sigma }_{Xi}\left(\mathcal{l}\right)}}\right),$$

(7)

where $\mathrm{cov}\left(X_i\left(j\right),X_i\left(\mathcal{l}\right)\right)$ is the covariance sequence of $X_i\left(j\right)$ and $X_i\left(\mathcal{l}\right)$, and ${\sigma }_{Xi}\left(j\right)$, ${\sigma }_{Xi}\left(\mathcal{l}\right)$ are the standard deviations of the sequence $X_i\left(j\right)$ and $X_i\left(\mathcal{l}\right)$ respectively.

Then, the eigenvectors and eigenvalues are determined by using a coefficient correlation array with the help of the equation shown below [115,123]:

$$\left(R_i\left(k\right)-{\lambda }_k·\mathcal{l}\right)·v_k=0,$$

(8)

Where $R_i\left(k\right)$ is the correlation coefficient matrix form $R_i\left(k\right)$, ${\lambda }_k$ is the k-th eigenvalue, ${\displaystyle {\sum }_{k=1}^n{\lambda }_k=n}$, k = 1, 2…, n and V_i,k = [ak1, ak2, …, akn] is the eigenvector corresponding to the eigenvalue ${\lambda }_k$.

The principal component of each response value can be determined as follows [115,123]:

$$Y_{mk}={\displaystyle \sum _{i=1}^n{X}_m}\left(i\right)·v_{ik}.$$

(9)

The grey relational grade for each response can be calculated using the following equation [123]:

$${\gamma }_i\left(GRC\right)={\displaystyle \frac{1}{n}}{\displaystyle \sum _{k=1}^n{\xi }_i\left(k\right)}.$$

(10)

2.2. Filler Materials

For this study, three self-shielded flux-cored wire specimens with a diameter of 4 mm were manufactured. The fabrication process involved multiple drawing passes through calibrated dies with a gradual reduction in the outlet diameter. A low-carbon steel strip made of St 24 steel (DIN 1614.1) in the annealed condition was used as the material for the metal sheath, with dimensions of 20 mm in width and 0.5 mm in thickness.

The main filler consisted of gas- and slag-forming components (fluorite, rutile, and calcium carbonate, at 12%, 7%, and 4% by weight, respectively), which protected the molten metal from atmospheric contamination and aided its purification. In addition, alloying, deoxidisers elements and EA components were incorporated into the filler to control chemical composition and enhance process efficiency. The exothermic addition was prepared with the following composition: Graphite (4.5 wt.%); Metallic chromium (14.5 wt.%); Ferromanganese (6 wt.%); Ferrosilicon (4 wt.%); Ferrovanadium (4 wt.%); Titanium powder (5 wt.%); Iron powder (balance). The detailed composition of the exothermic additive is presented in

Table 3. Composition of core filler FCAW-SS, wt.%.

The Name of the Component	Content of the Components in Core Filler of FCAW-S, [wt.%]
	FCAW-P3-E1-1	FCAW-P3-E1-2	FCAW-P3-E1-3
Oxide of copper powder GOST 16539-79	15	23.3	32.5
Aluminium powder PA1 GOST 6058-73	3	4.7	6.5

. The oxidiser-to-reductant ratio was selected according to stoichiometric proportions. The coefficients of wire filling (C_WF) for the experimental flux-cored wires were 0.342, 0.345 and 0.348.

2.3. Hardfacing Procedure

The hardfacing was applied to the steel plates using the single-pass roller method. These plates were made of low-carbon steel (S235J2+N steel, manufactured in accordance with EN 10025-2 were sourced from the Azovstal Iron and Steel Works, Mariupol, Ukraine) measuring 10 × 100 × 200 mm. The hardfacing process was conducted using an A-874 automatic welding system (Paton Electric Welding Institute, Kyiv, Ukraine). This unit, designed for mechanised arc welding and hardfacing, provided precise control over electrode wire feed (2.0–5.0 mm) and travel speeds (15–120 m/h). This was equipped with a power source featuring a rigid volt-ampere characteristic under reverse polarity. The travel speed was set to TS = 18 m/h and remained constant throughout. The selection of the travel speed parameter was made based on experience. It was also based on preliminary research [108].

2.4. Calculation of the Elements’ Transfer Coefficients and the Recovery Coefficient

In this case, the element transfer coefficient (η(E)) and element recovery factor (RF(E)) of the alloying elements determine the outcome of the individual reactions that occur at various stages of filler material melting and weld pool formation [92].

The assimilation coefficients of the i-th element TF(E) and the element recovery coefficients (RF) were calculated using improved equations that account for losses of filler metal, deposition efficiency, and spatter losses [91,92]:

$$\eta \left(E\right)={\displaystyle \frac{M{e}_d·De}{C_{WF}·K_{WF}·\left(100-SF\right)}},$$

(11)

$$RF\left(E\right)={\displaystyle \frac{M{e}_d·De}{C_{WF}·K_{WF}·\left(100-SF\right)}},$$

(12)

where Me_d is the content of alloying element in deposited metal, wt.%; $C_{WF}$ is the coefficient wire filling of the FCAW-S; $K_{WF}$ is the concentration of component in the flux core FCAW–S, wt.%; K(E) is the concentration of alloying element in the content of component of the core filler, wt.%; De is deposition efficiency, %; SF is spattering factor, %.

The total transition coefficient of alloying elements (η(SS)) was determined. The method used was as follows [91]:

$$\eta (SS)={\displaystyle \sum _1^p\left(\eta (E)·C_o\right)}+{\displaystyle \sum _1^o\left(RF(E)·C_o\right)},$$

(13)

where C_i, C_j are the corresponding proportions of the components in the filler p, and the o are components of the oxides that are reduced.

3. Results

3.1. Elemental Composition of the Deposited Metal

Chemical composition analysis of the experimental FCAW–S weld metal was performed using a Spectrolab LAVFC01A optical emission spectrometer (SPECTRO Analytical Instruments GmbH, Kleve, Germany). The findings of this investigation are presented in

Table 4. Chemical composition of samples of applied metal steel of the Fe-C-Cr-Ti-Cu system in three layers.

Item No.		Content of Alloying Element in Metal Deposit, wt.%
	C	Cr	Cu	Si	Mn	Ti	V	Al	N	P	S
P3-E1-1	0.51	2.49	3.1	0.79	1.08	0.43	0.39	0.23	0.042	0.022	0.024
P3-E1-2	0.58	3.06	3.4	0.69	1.28	0.4	0.43	0.25	0.043	0.021	0.024
P3-E1-3	0.61	2.76	3.4	0.72	1.18	0.45	0.43	0.27	0.043	0.019	0.021
P3-E1-4	0.71	3.9	5.7	1.05	1.88	0.72	0.37	0.17	0.044	0.022	0.024
P3-E1-5	0.86	4.04	6.05	1.01	1.98	0.61	0.37	0.19	0.043	0.022	0.024
P3-E1-6	0.57	3.55	6.7	1.04	1.79	0.83	0.3	0.24	0.045	0.017	0.019
P3-E1-7	0.5	2.36	7.5	1.15	1.41	0.61	0.22	0.28	0.045	0.017	0.019
P3-E1-8	0.52	2.7	8.6	1.13	1.71	0.83	0.26	0.25	0.043	0.018	0.020
P3-E1-9	0.77	3.1	6.8	1	1.82	0.59	0.34	0.39	0.044	0.018	0.019

.

The chemical composition of the investigated alloys varied within the following ranges: C = 0.50–0.86 wt.%, Mn = 1.04–1.88 wt.%, Cr = 2.49–4.04 wt.% and Cu = 3.1–8.8 wt.%. In addition, minor alloying additions of V and Ti were present. The results showed that the copper content of the deposited metal clearly depended on the total amount of exothermic addition introduced into the core filler of the flux-cored wire. The deposited metal samples produced using FCAW-S with filler material P3-E1-1 (samples P3-E1-1, P3-E1-2 and P3-E1-3) contained a relatively low and stable copper content of 3.1–3.4 wt.%. By contrast, the deposited metal obtained using P3-E1-2 filler material exhibited a wider copper concentration range of 5.7–6.7 wt.%. The greatest variation in copper content was observed in deposits produced using filler materials containing the highest proportion of EA (40 wt.% of the core filler), which corresponded to P3-E1-3. In this case, the copper content ranged from 6.8 to 7.5 wt.%, which indicates that copper transfer is more sensitive to the content of the exothermic addition in the wire.

3.2. Element Transfer Coefficient

3.2.1. Experiment Results for Element Transfer Coefficient

The results obtained for the element transition coefficients for each experiment are shown in

Table 5. Experimental and calculated values of the element transfer coefficient.

№ Exp.	Carbon Transfer Coefficient				Chrome Transfer Coefficient
	η(C)(e)	η(C)(c)	Difference	Deviation	η(Cr)(e)	η(Cr)(c)	Difference	Deviation
1	0.375	0.411	−0.036	9.7%	0.638	0.664	−0.026	4.1%
2	0.433	0.483	−0.050	11.5%	0.785	0.739	0.047	5.9%
3	0.443	0.432	0.011	2.5%	0.686	0.707	−0.020	2.9%
4	0.532	0.501	0.031	5.8%	0.955	0.989	−0.035	3.7%
5	0.653	0.636	0.017	2.7%	0.989	0.976	0.013	1.4%
6	0.410	0.331	0.079	19.2%	0.850	0.829	0.021	2.5%
7	0.365	0.393	−0.029	7.9%	0.728	0.731	−0.003	0.4%
8	0.370	0.413	−0.042	11.4%	0.809	0.815	−0.006	0.7%
9	0.561	0.542	0.019	3.4%	0.918	0.909	0.008	0.9%
min	0.375				0.638
max	0.653				0.989
№ Exp.	Titanium Transfer Coefficient				Vanadium Transfer Coefficient
	η(Ti)(e)	η(Ti)(c)	Difference	Deviation	η(V)(e)	η(V)(c)	Difference	Deviation
1	0.358	0.363	−0.005	1.5%	0.797	0.848	−0.051	6.4%
2	0.333	0.352	−0.018	5.5%	0.880	0.843	0.037	4.2%
3	0.364	0.340	0.024	6.5%	0.853	0.839	0.014	1.7%
4	0.592	0.587	0.005	0.8%	0.747	0.672	0.075	10.0%
5	0.502	0.533	−0.032	6.3%	0.747	0.736	0.011	1.5%
6	0.668	0.641	0.027	4.0%	0.593	0.679	−0.086	14.6%
7	0.506	0.452	0.054	10.6%	0.597	0.742	−0.145	24.2%
8	0.669	0.644	0.025	3.7%	0.686	0.683	0.003	0.5%
9	0.470	0.548	−0.078	16.7%	0.886	0.744	0.141	16.0%
min	0.333				0.672
max	0.669				0.848
№ Exp.	Silicon Transfer Coefficient				Manganese Transfer Coefficient
	η(Si)(e)	η(Si)(c)	Difference	Deviation	η(Mn)(e)	η(Mn)(c)	Difference	Deviation
1	0.728	0.710	0.017	2.4%	0.575	0.583	−0.008	1.3%
2	0.630	0.665	−0.035	5.6%	0.699	0.684	0.015	2.2%
3	0.639	0.622	0.017	2.7%	0.618	0.625	−0.008	1.2%
4	0.973	0.966	0.007	0.7%	0.902	0.904	−0.002	0.2%
5	0.934	0.949	−0.015	1.6%	0.954	0.951	0.003	0.4%
6	0.942	0.935	0.007	0.8%	0.837	0.839	−0.002	0.2%
7	0.959	0.972	−0.014	1.4%	0.773	0.763	0.009	1.2%
8	0.915	0.887	0.027	3.0%	0.929	0.948	−0.019	2.0%
9	0.794	0.808	−0.014	1.7%	0.982	0.973	0.009	0.9%
min	0.630				0.575
max	0.973				0.982
№ Exp.	Aluminium Transfer Coefficient				Total Element Transition Coefficient
	η(Al)(e)	η(Al)(c)	Difference	Deviation	η(SS)(e)	η(SS)(c)	Difference	Deviation
1	0.211	0.214	−0.002	1.0%	0.449	0.453	−0.004	0.9%
2	0.230	0.218	0.012	5.2%	0.503	0.506	−0.003	0.5%
3	0.241	0.251	−0.010	4.1%	0.475	0.469	0.007	1.4%
4	0.103	0.106	−0.003	3.1%	0.705	0.693	0.012	1.6%
5	0.115	0.111	0.004	3.8%	0.734	0.746	−0.013	1.7%
6	0.142	0.143	−0.001	0.8%	0.710	0.709	0.001	0.1%
7	0.128	0.123	0.005	4.1%	0.683	0.690	−0.008	1.1%
8	0.111	0.128	−0.016	14.7%	0.759	0.743	0.015	2.0%
9	0.171	0.160	0.011	6.5%	0.698	0.706	−0.008	1.1%
min	0.103				0.449
max	0.241				0.759

. The results obtained for the copper recovery factor for each experiment are shown in

Table 6. Experimental and calculated values of the recovery factor.

№ Exp.	Copper Recovery Coefficient
	RE(Cu)(e)	RE(Cu)(c)	Difference	Deviation
1	0.713	0.704	0.009	1.3%
2	0.783	0.805	−0.022	2.8%
3	0.759	0.746	0.013	1.7%
4	0.863	0.874	−0.011	1.3%
5	0.916	0.919	−0.003	0.3%
6	0.993	0.979	0.014	1.4%
7	0.859	0.850	0.008	1.0%
8	0.957	0.959	−0.002	0.2%
9	0.747	0.753	−0.006	0.8%
min	0.713
max	0.993

The indices on the right side of the geometric parameter notation have the following meanings: (e)—experimental values; (c)—calculated values obtained by introducing the corresponding values of variables into the developed mathematical models.

.

3.2.2. Taguchi Method and ANOVA for Element Transfer Coefficient

The Taguchi method was used to obtain the experimental results for parameters of element transfer coefficient, as shown in Figure 4.

ANOVA was applied to determine the percentage contribution of the welding parameters to the melting characteristics. The results are presented in Figure 5.

The analysis revealed that the investigated variables had a similar influence on the transition coefficients of carbon and vanadium. Figure 5a1,a2 show that three variables had a significant impact on the transition coefficients of carbon and transition coefficients vanadium EA, WFS, and U_set. The influence of the CTWD was found to be within the noise level and therefore negligible. The optimal conditions for achieving maximum values of η(C) and η(V) were identified as WFS = 1.85 m·min⁻¹ and U_set = 28 V (Figure 4c,f). The optimal EA content value differed for these elements and was located at low to medium levels (Figure 4c,f). Figure 5 also shows that the EA had a significant effect on the η(SS) (Figure 4b). Figure 5a1 show a similar response of η(Al), η(Si), and η(Mn) to the variables under investigation. These elements acted as active deoxidisers and were strongly affected by the CTWD. The optimal exothermic addition content for aluminium, silicon, and manganese transitions was identified as EA = 30 wt.% (see Figure 4b,g,h), whereas the optimal CTWD corresponded to CTWD = 35 mm (see Figure 4b,g).

It was found that the wire feed speed had a significant effect on the transfer coefficients of carbon, vanadium, and chromium (see Figure 5a1,a2). This parameter contributed 35.65%, 32.45%, and 19.91% respectively Optimal WFS values were observed at a medium level of 1.85 m·min⁻¹ (Figure 4c,d,f). Additionally, a significant influence of wire feed speed on both the titanium transfer coefficient and the copper recovery factor was identified (see Figure 5a1,a2).

The voltage set on the power source, a parameter of the hardfacing process, influenced the transfer coefficients of carbon and vanadium (see Figure 5), as well as the copper recovery factor (see Figure 5a1). The optimal U_set values were ensured at the average level of U_set = 31 V (see Figure 4a,c). This was indicated by the high signal-to-noise ratio values (Figure 4a). However, the highest transfer coefficients of vanadium were achieved at a lower voltage level of U_set = 28 V (see Figure 4f).

3.2.3. Factorial Design Analysis of Element Transfer Coefficient

Regression models of melting characteristics are represented by Equations (14)–(22):

$$\begin{array}{l}{Y}_{(\eta (C))}=-0.03-0.00043\times E{A}^2+8.87282\times WFS-1.546\times WF{S}^2-\\ -0.87282\times U_{ser}+2.00244\times U_{set}^2+0.01155\times EA\times WFS-0.10454\times WFS\times U_{ser,}\end{array}$$

(14)

$$\begin{array}{l}{Y}_{(\eta (Cr)),}=1.5742-0.27364\times EA+0.0001\times E{A}^2-0.6198\times WF{S}^2-\\ +0.202626\times EA\times WFS+0.002\times E{A}^2\times WFS-0.00158\times E{A}^2\times WF{S}^2\end{array}$$

(15)

$$\begin{array}{l}{Y}_{(\eta (Th)),}=-1.31362+0.12283\times EA-0.00137\times E{A}^2+0.29629\times WFS-\\ -0.01947\times EA\times WFS\end{array}$$

(16)

$$\begin{array}{l}{Y}_{(\eta (V))}=1.589137-0.054945\times EA+0.000874\times E{A}^2+0.29629\times WF{S}^2-\\ -0.01947\times U_{set,}^2\end{array}$$

(17)

$$\begin{array}{l}{Y}_{(\eta (Si)),}=1.99114-0.08777\times EA+0.002114\times E{A}^2-0.067643\times CTWD+\\ +0.004779\times EA\times CTWD+0.000003\times EA\times CTW{D}^2-0.000096\times E{A}^2\times CTWD\end{array}$$

(18)

$$\begin{array}{l}{Y}_{(\eta (Mn)),}=-10.3725+0.4838\times EA-0.009\times E{A}^2+0.3737\times CTWD-\\ -0.0032\times CTW{D}^2-0.0099\times EA\times CTWD+0.0002\times E{A}^2\times CTWD\end{array}$$

(19)

$$\begin{array}{l}{Y}_{(\eta (Al)),}=1.4729-0.039338\times EA+0.000622\times E{A}^2-\\ -0.041132\times CTWD+0.000561\times CTW{D}^2\end{array}$$

(20)

$$\begin{array}{l}{Y}_{(RE(Cu))}=-9.23274+0.07505\times EA-0.00121\times E{A}^2+0.31305\times WF{S}^2+\\ +0.58559\times U_{set}+0.000561\times U_{wet}^2-0.03921\times EA\times WFS+0.00228\times EA\times U_{set,}\end{array}$$

(21)

$$\begin{array}{l}{Y}_{(\eta (SS)).}=-3.49774+0.07985\times EA-0.00121\times E{A}^2+\\ +0.58559\times CTWD+0.000561\times CTW{D}^2\end{array}$$

(22)

Table 7. Result of analysis of variance for the applied conditions on element transfer coefficients and recovery fact.

Criteria	Mathematical Model
	Yη(c)	Yη(cr)		Yη(Ti)	Yη(V)
Coefficient of Determination (R sqr)	0.99999	0.98226		0.90705	0.86763
Adjusted Sum of Squares (R Adj)	0.99995	0.92904		0.8141	0.73526
Model quality	Very good	Very good		Good	Good
Criteria	Mathematical Model
	Yη(Si)	Yη(Mn)	Yη(Al)	YRE(Cu)	Yη(SS)
Coefficient of Determination (R sqr)	0.9971	0.9951	0.97003	0.99912	0.99406
Adjusted Sum of Squares (R Adj)	0.9884	0.98039	0.94005	0.99299	0.98811
Model quality	Very good	Very good	Very good	Very good	Very good

displays the coefficients of determination (R²) and the adjusted sums of squares (R Adj) for each developed mathematical model. The quality of these models is rated as ‘very good,’ supported by the high values of the coefficients of determination and adjusted sums of squares.

The obtained data demonstrated that the developed mathematical models exhibited very good or good performance. This is also confirmed by the plots of observed versus predicted values constructed for the models (see Figure 6). The models’ predictive accuracy is indicated by the close proximity of the predicted data points to the diagonal red line. All models showed excellent quality, except for those describing the vanadium and titanium transfer coefficients (Figure 6e,f).

A Pareto chart (see Figure 7) was used to present the results, which were evaluated using analysis of variance (ANOVA).

Figure 7 presents Pareto charts illustrating the relative influence of the regression equation terms on copper recovery and elemental transfer coefficients in the weld bead. For all considered responses, the main effects dominated over interaction and quadratic terms, indicating that the elemental transfer was primarily governed by individual process parameters rather than their combined effects. The results obtained showed that the terms of the regression equation linked to the percentage of exothermic addition in the core filler had the greatest effect on the elemental transfer coefficients.

Figure 8 and Figure 9 show the response surfaces of the mathematical model illustrating the relationship between the transition element and the parameters of the hardfacing modes, as well as the content of the exothermic addition in the core filler.

3.3. Welding Thermal Cycle Parameters

During FCAW-S hardfacing, the thermal cycle of the weld was primarily governed by heat input, peak temperature, and cooling rate. These factors determined the evolution of the deposited metal and the degree to which it was diluted with the base material. These factors ultimately determined the microstructure of the deposited metal and its mechanical and service properties. Increased heat input and slower cooling rates usually resulted in grain coarsening and increased dilution. On the other hand, a reduction in heat input could lead to the formation of a finer microstructure and an increase in hardness [125]. The thermal cycle was described by three key parameters: heat input (HI), cooling rate (CR), and cooling time Δt_8/5. Heat input (HI) is the quantity of energy introduced from the arc per unit length of weld. The heat input was calculated by means of Equation (23) [114]:

$$HI={\displaystyle \frac{60\times {\eta }_{FCAW}\times U_{set}\times I}{1000\times TS}}$$

(23)

where HI is heat input, (kJ/mm); η_FCAW is the coefficient of efficiency of the process η_FCAW = 0.75.

The cooling rate (CR) and cooling time (Δt_8/5) were calculated using Equations (24) and (25) [112,114].

$$C{R}_{8.5}=\raisebox{1ex}{$\Delta T_{8/5}$}\!\left/ \!\raisebox{-1ex}{$\Delta t_{8/5}$}\right.,$$

(24)

$$\Delta t_{8.5}={\displaystyle \frac{E·}{2·\pi ·k}}·\left[{\displaystyle \frac{1}{500-T_0}}-{\displaystyle \frac{1}{800-T_0}}\right],$$

(25)

where ΔT_8/5 was the temperature variation within the selected range of 800 and 500 °C, E is welding energy (kJ·cm⁻¹), λ is material thermal conductivity λ = 42 J/(s·m·C) [114], and T₀ is the initial temperature of the plate T₀ = 25 °C.

3.3.1. Experiment Results for Welding Thermal Cycle Parameters

Table 8. Experimental and calculated values of welding thermal cycle parameters.

№ Exp.	Heat Input				Cooling Time
	HI(e)	HI(c)	Diff.	Dev. %	Δt8/5(e)		Δt8/5(c)		Diff.		Dev. %
1	1.237665	1.269883	−0.032218	2.60	5.755207		5.963896		−0.208689		3.63
2	1.259300	1.332659	−0.073359	5.83	5.855807		6.063564		−0.207757		3.55
3	1.778054	1.746563	0.031492	1.77	8.268044		8.196100		0.071944		0.87
4	1.418210	1.381530	0.036680	2.59	6.594749		6.490871		0.103878		1.58
5	1.547082	1.515590	0.031492	2.04	7.194009		7.122065		0.071944		1.00
6	1.601868	1.537432	0.064436	4.02	7.448766		7.031389		0.417378		5.60
7	1.568093	1.631077	−0.062983	4.02	7.291714		7.435601		−0.143887		1.97
8	1.772763	1.804981	−0.032218	1.82	8.243437		8.452125		−0.208689		2.53
9	1.320467	Hardness	0.036680	2.78	6.140238		6.036360		0.103878		1.69
№ Exp.	Cooling rate				Hardness
	CR(e)	CR(c)	Diff.	Dev. %	1	2	3	HV(e)	HV(c)	Diff.	Dev.%
1	52.12671	50.79853	1.32817	2.55	571	538	514	541.0	539.3	1.7	0.32
2	51.23119	48.52666	2.70454	5.28	648	677	514	613.0	594.3	18.7	3.06
3	36.28428	37.00087	−0.71659	1.97	546	546	514	535.3	547.4	−12.1	2.25
4	45.49074	46.84301	−1.35227	2.97	489	563	493	515.0	500.6	14.4	2.79
5	41.70137	42.41796	−0.71659	1.72	464	352	292	369.3	378.3	−9.0	2.44
6	40.27513	42.93147	−2.65635	6.60	390	497	724	537.0	556.6	−19.6	3.65
7	41.14259	39.70941	1.43318	3.48	565	550	593	569.3	568.5	0.9	0.15
8	36.39259	35.06441	1.32817	3.65	677	824	756	752.3	754.6	−2.3	0.31
9	48.85804	50.21031	−1.35227	2.77	401	401	420	407.3	400.0	7.3	1.79

shows the experimental results for the thermal cycle parameters and hardness of all alloys across nine experiments.

3.3.2. Taguchi Method and ANOVA for Welding Thermal Cycle Parameters

Figure 10 shows the main effects of the signal-to-noise (S/N) ratio for each of the parameters investigated. The ‘smaller-is-better’ criterion was applied to heat input and cooling time, while the ‘higher-is-better’ criterion was applied to cooling rate and hardness. The resulting plots demonstrate the robustness of the experimental design and the reliability of the obtained results. Red circles indicate the levels that achieve the best S/N ratios.

The optimal parameters and the results of the analysis of variance (ANOVA) are shown in Figure 11.

Analysis of the data presented in Figure 11a revealed that the two main factors influencing the parameters that define the welding thermal cycle were wire feed speed and voltage set on the power source. These two parameters accounted for 41.79% and 36.53% of the total variation, respectively. The influence of the other two parameters—namely, EA and CTWD—was minor and could be considered indirect, acting through their effect on the two dominant parameters. The optimal conditions differed for the three parameters of the welding thermal cycle (Figure 10a–c) and were achieved at a medium wire feed speed (WFS = 1.85 m·min⁻¹), a low voltage set on the power source (U_set = 28 V), as well as low values of exothermic addition in the core filler (EA = 20 wt.%) and a low contact tip to work distance (CTWD = 35 mm) (see Figure 10).

As shown in Figure 11b, the voltage set on the power source had the greatest influence on the hardness of the deposited metal, while the wire feed speed and the percentage of exothermic addition in the core filler had a smaller effect. These factors contributed 50.18%, 23.47%, and 18.81% respectively. The optimal voltage setting for hardness differed from that for the welding thermal cycle parameters and was observed at U_set = 34 V; EA = 20 wt.%; and WFS = 1.63 m·min⁻¹.

3.3.3. Factorial Design Analysis of Welding Thermal Cycle Parameters

Following the ANOVA-based elimination of insignificant variables, the regression models were established as follows:

$$\begin{array}{l}{Y}_{HI}=-95.4008+100.1886\times WFS-26.0396\times WF{S}^2+\\ +3.6992\times U_{ser}-3.8646\times WFS\times U_{ser}+1.-129\times WF{S}^2\times U_{ser,}\end{array}$$

(26)

$$\begin{array}{l}{Y}_t=-443.619+0.27364\times WFS-121.085\times WF{S}^2+17.202\times U_{ser}-\\ -18.715\times WFS\times U_{ser}+0.012\times WFS\times U_{set}^2-0.00158\times WF{S}^2\times U_{ser,}\end{array}$$

(27)

$$\begin{array}{l}{Y}_{CR}=2497.08-2497.84\times WFS+639.83\times WF{S}^2-95.49\times U_{ser}+\\ +98.66\times WFS\times U_{ser}-25.59\times WF{S}^2\times U_{ser,}\end{array}$$

(28)

$$\begin{array}{l}{Y}_{(\eta (V))}=-7115.16-1.6\times E{A}^2-237.42\times WFS+597.27\times U_{ser}-\\ -12.72\times U_{set}^2-9.54\times EA\times WF{S}^2+0.07\times E{A}^2\times U_{ser}+1.26\times WFS\times U_{set.}^2\end{array}$$

(29)

The parameters characterising the quality of the developed models are summarised in

Table 9. Result of analysis of variance for the applied conditions on welding thermal cycle parameters.

Criteria	Mathematical Model
	YHI	Yt	YCR	YTV
Coefficient of Determination (R sqr)	0.93948	0.97587	0.91451	0.99743;
Adjusted Sum of Squares (R Adj)	0.83862	0.90349	0.77203	0.97945
Model quality	Good	Very good	Good	Good

.

The regression models developed for all the investigated welding thermal cycle parameters were statistically significant and adequate, as confirmed by the ANOVA results (Table 9). The coefficients of determination (R²) are greater than 0.91 for all responses, showing a strong agreement with the experimental data. The mathematical models developed for heat input (HI) and cooling rate (CR) demonstrate stable approximation quality, with the highest model accuracy achieved for hardness (HV).

The predictive capability of the developed regression model was further verified by analysing the level of consistency between experimentally obtained data and model-estimated responses. The graphs in Figure 12 show the change in observed efficiency as a function of predicted efficiency for each of the mathematical models that were developed.

Figure 12a–d shows a close agreement between the experimental and predicted values for all dependent variables, indicating a high level of agreement with the line of equality. A uniform distribution of data points along the regression line is observed for HI and cooling time Δt₈/₅, indicating the absence of systematic model errors.

Figure 13 illustrates the outcome of the Pareto analysis, with the contribution of each parameter to the overall response expressed through the length of the standardised effect bars.

The plots that were obtained provide confirmation of the results of the ANOVA analysis for the welding thermal cycle parameters and hardness. The most significant effects were associated with the regression terms relating to wire feed speed and the voltage set on the power source. The Pareto chart (Figure 13d) shows that the linear effects of the welding process parameters, especially wire feed speed and arc voltage, had a significantly more pronounced influence on the hardness of the deposited metal. These effects were statistically significant. This indicated that the structural and mechanical properties of the welded joint were highly sensitive to variations in the thermal cycle.

Figure 14 and Figure 15 show the response surfaces of the mathematical model of the dependence of the hardfacing thermal cycle parameters on the parameters of the hardfacing modes.

3.4. Taguchi–Grey Relational Analysis Coupled with Principal Component Analysis

The normalised values and deviation sequence are shown in

Table 10. Normalised data of response characteristics.

№ Exp.	DRn	SFn	RE(Cu)n	HVn
1	0.000000	0.179293	0.000000	0.448303
2	0.312500	0.356061	0.250000	0.636292
3	0.500000	0.164141	0.164286	0.433420
4	0.710938	0.109848	0.535714	0.380418
5	0.929688	0.000000	0.725000	0.000000
6	0.492187	0.643939	1.000000	0.437859
7	1.000000	0.747475	0.521429	0.522193
8	0.078125	0.393939	0.871429	1.000000
9	0.742188	1.000000	0.121429	0.099217

.

The values of the principal-component loadings for each response were presented in

Table 11. PCA Components (Loadings).

Principal Component	MOR	DR	RE(Cu)	HV
PC1	0.794408	0.297909	0.085891	−0.522292
PC2	0.079026	0.094945	0.936443	0.328352
PC3	−0.152286	0.933592	−0.177093	0.271759
PC4	0.582649	−0.175047	−0.290405	0.738609

.

The computation of grey relation grades (GRGs) after introducing PCA and the weighted value of each performance characteristic.

Table 12. Grey relational grades.

№ Exp.	GRA	Rank
1	0.381411	9
2	0.461184	7
3	0.431601	8
4	0.491173	6
5	0.548312	5
6	0.630416	3
7	0.675005	1
8	0.650770	2
9	0.592357	4

showed the GRGs and rank.

The GRA results indicate that the optimal experimental runs are Exp. 7 (Rank 1), Exp. 8 (Rank 2), and Exp. 6 (Rank 3). Their GRGs are relatively close, with values of 0.675005, 0.650770, and 0.630416, respectively. Analysis of the experimental data for these runs revealed that Exp. 8 has a lower deposition rate (DR = 3.98 kg·h⁻¹) than Exp. 7 (DR = 5.16 kg·h⁻¹) and Exp. 6 (DR = 4.51 kg·h⁻¹). However, it demonstrates the highest hardness. Furthermore, the analysis showed that the P3-E1-7 weld metal specimen (Exp. 7) had a higher hardness than the P3-E1-6 specimen (569 HV vs. 537 HV). These findings confirm the effectiveness of the GRA approach for multi-objective optimisation. The optimal parameters identified are as follows: EA = 38 wt.%, CTWD = 35 mm, WFS = 2.07 m·min⁻¹, and U_set = 31 V.

3.5. The Microstructure of Welded Metal Samples Is Analysed

3.5.1. Theoretical Analysis and Phase Stability Simulation of Microstructure by JMatPro

A phase diagram simulating the phase ratio at a given temperature was created based on the chemical composition, using the simulation software JMatPro^® API v7.0 (Figure 16). The resulting phase diagram provides approximate information about the critical temperatures at which individual phase transformations occur.

The equilibrium phase diagrams calculated for the deposited metal samples are shown in Figure 16a–i.

For a better understanding of phase structural changes in alloys, phase changes and chemical element distribution were additionally analysed for one of the alloys (see Figure 17).

A wide solidification temperature range was observed for alloys with high carbon and copper content (P3-E1-5 and P3-E1-9). The lowest liquidus and solidus temperatures were exhibited by these alloys at the same time. For alloy P3-E1-5, the liquidus and solidus temperatures were Tₗ(5) = 1403.47 °C and Tₛ(5) = 1267.19 °C, respectively; for P3-E1-9, they were Tₗ(9) = 1410.8 °C and Tₛ(9) = 1290.09 °C. The presence of elevated copper content (in alloys P3-E1-6, P3-E1-7, and P3-E1-8) has two effects. Firstly, it reduces the solidus temperature. Secondly, it promotes the formation of Cu-rich phases. On the other hand, higher concentrations of carbide-forming elements have a slightly higher liquidus temperature-increasing effect (see

Table 13. JMatPro predictions on the melting range of each phase (°C).

Alloy	Tl	Ts	ΔT
P3-E1-1	1454.73	1367.42	87.31
P3-E1-2	1446.56	1351.39	95.17
P3-E1-3	1445.72	1352.49	93.23
P3-E1-4	1445.72	1352.49	93.23
P3-E1-5	1403.47	1267.19	136.28
P3-E1-6	1420.22	1330.26	89.96
P3-E1-7	1427.6	1334.5	93.1
P3-E1-8	1416.33	1325.5	90.83
P3-E1-9	1410.80	1290.09	120.71

Where T_l: liquidus, T_s: solidus.

).

The MN solid phase is a high-temperature phase that is similar to titanium carbonitride (Ti(N,C)). It slowly becomes richer in vanadium and carbon, approaching the composition TiN·(V,Cr)C. This phase is retained in the deposited metal after complete cooling because of the welding conditions (Figure 17d). Since this phase was high temperature, it had a shape similar to a regular rhombohedral shape. The final portions of the liquid metal enriched in alloying elements (see Figure 17b) are known to form sulfides during the cooling process, which precipitate in the form of the Ti4C2S2 phase (see Figure 17a). This is consistent with the Ti2CS phase (see Figure 17e). This observation is consistent with reported results for titanium-containing steels [126], since this phase is more stable than MnS. During solidification, a small amount of MnS is produced as a result of partial decomposition. However, MC-type carbides (Ti- and V-rich) are the first to precipitate, with their fraction remaining below 1 wt.%. Once solidified, the austenitic phase will be heavily enriched with elements such as Cu, Cr, Mn, etc. (see Figure 17c for details). At temperatures of around 1200 °C, a copper phase (Figure 17a) consisting predominantly of copper precipitates within the matrix. This phase forms as copper precipitates with a body-centred cubic (BCC) structure that is embedded in a BCC iron matrix [127]. An increase in hardness and static strength is attributed to the presence of finely dispersed Cu precipitates, resulting from dispersion strengthening [128]. However, owing to the non-equilibrium state of the deposited metal caused by the high cooling rate, the copper dissolved in the austenitic phase does not fully precipitate [112,129].

Following solidification, a stable austenitic matrix (γ-phase) is formed within the temperature range of 1050–850 °C. The addition of Cu and Mn makes the austenite stability region bigger at lower temperatures (see Figure 16f–h). On the other hand, high C and Cr contents (inalloys P3-E1-4 and P3-E1-5) restrict this region due to the high-temperature stability of the carbides. In the temperature range of 950–850 °C, M₇C₃ carbides gradually precipitate from the austenitic solid solution. In Cr-rich compositions, the process is followed at lower temperatures by the precipitation of M₂₃C₆ carbides at grain boundaries.

Table 14. Summarised critical temperature data for the analysed deposited metals were obtained with self-shielded flux-cored wires of different compositions and hardfacing modes.

N/ Specimen	Filler Material	Fs	Ps	Bs	Martencite
					Ms	Me
P3-E1-1	FCAW-P3-E1-1	767.1	516	764.1	301.6	181.5
P3-E1-2	FCAW-P3-E1-1	765.9	497.3	752.9	277.2	154.6
P3-E1-3	FCAW-P3-E1-1	767.3	497.6	753	272.0	148.8
P3-E1-4	FCAW-P3-E1-2	761.4	461.7	748	258.5	133.7
P3-E1-5	FCAW-P3-E1-2	754.8	454.2	734.9	227.5	98.9
P3-E1-6	FCAW-P3-E1-2	767.8	463.4	757.8	270.2	146.8
P3-E1-7	FCAW-P3-E1-3	775.4	477.2	767.1	269.2	145.7
P3-E1-8	FCAW-P3-E1-3	769.3	462.4	758.1	262.1	137.7
P3-E1-9	FCAW-P3-E1-3	766.9	457.4	748.3	224.8	95.8

Fs—start temperature of transformation of austenite into ferrite (more than 0.01% of volume); Ps—start temperature of transformation of austenite into pearlite (more than 0.01% of volume); Bs—start temperature of transformation of austenite into bainite (more than 0.01% of volume); Ms—temperature of the beginning of martensitic phase appearance from residual austenite (more than 0.01% of volume); Me—the temperature of the end of transformation of the residual austenitic phase to the martensitic phase (more than 90% of the volume).

shows the numerical values for the onset of austenite phase transformations into pearlite, bainite, and ferrite, as well as the onset of martensite formation and transformation into 90% martensite for each sample.

Figure 18a–i shows that the onset curves of the pearlitic transformation (Ps) shift towards longer times and lower temperatures when the total content of alloying elements such as Cr, Mn, and Cu increases. This behaviour indicates a reduction in diffusion-controlled processes and an increase in the hardenability of steels. The pearlitic transformation in steels with a carbon content of around 0.50–0.58 wt.% and moderate alloying occurs at higher temperatures and shorter cooling times. However, for steels with a high carbon content (≥0.77 wt.%) and a copper content of up to 8.8 wt.%, the pearlitic transformation region is significantly narrowed, and under rapid cooling conditions, pearlite formation is almost completely suppressed. This finding is consistent with that reported by Yi et al. [130].

For all investigated steels, the bainitic transformation region (Bs–Bf) is located within the range of intermediate temperatures and cooling times. For steels with increased carbon and copper content, earlier suppression of pearlite transformation and expansion of the temperature–time range of bainite and martensite formation were observed. An increase in copper content reduced the bainite transformation temperature. According to Table 14, alloy P3-E1-8, which has a high copper content of 8.6 wt.%, exhibits a significantly lower bainite transformation temperature than alloy P3-E1-1, which has a moderate copper content of 3.1 wt.%, despite having comparable levels of other alloying elements.

Analysis of the CCT diagrams reveals a significant and consistent combined impact of copper content and cooling rate on the microstructural evolution of the deposited metal. Copper stabilises undercooled austenite, a finding that is supported by previous studies [131]. In steels with an elevated copper content, the microstructure is dominated by fine bainite, with a limited fraction of martensite, even at moderate cooling rates of approximately CR = 43–45 °C·s⁻¹ (Figure 16e–g). At the highest cooling rates (Figure 18a,i), copper’s effect is evident in the reduction of the bainitic transformation temperature range and the increased formation of lower bainite and martensite from austenite [130].

Given the non-equilibrium nature of the cooling processes inherent in welding, thermodynamic simulations were performed to evaluate the evolution of the phase state under the influence of the specific thermal cycles [132]. The resulting calculated phase diagrams and the corresponding phase distribution within the deposited metal for the investigated samples are illustrated in Figure 19, reflecting the structural transformations as a function of the welding parameters.

Considering the conditions of the experiment (Figure 19a–i), namely cooling in air to a temperature of 200 °C, the phase composition of the sample matrix was determined at this temperature.

The results of thermodynamic modelling of phase transformations during the welding cycle showed that for all nine samples of deposited metal, an almost completely austenitic structure was formed in the temperature range above Ac₃. During subsequent accelerated cooling, diffusion transformations (ferrite–pearlite and bainite) were suppressed, and martensite became the main product of austenite decomposition, accounting for more than 80–90 wt.% of the final structure for all compositions.

It was established that an increase in the carbon content in the deposited metal was the determining factor in the formation of a high-martensitic structure after the welding cycle: an increase in C concentration led to a decrease in the start temperature of martensitic transformation and an increase in hardenability. However, an increase in Cu concentration led to an expansion of the temperature range of austenite existence and a slight decrease in the start temperature of martensitic transformation, which contributed to the formation of a more dispersed martensitic matrix. Thus, the matrix of the deposited metal will consist of martensite.

3.5.2. Study of the Microstructure of the Deposited Metal

To confirm the theoretical results obtained, a sample of P3-E1-1 and P3-E1-7 metal was examined, which was produced for the worst experiment Exp.1 and studied under the optimal conditions of the experiment Exp.7. The microstructure of the hardfacing layer was observed by scanning electron microscopy using a ZEISS EVO 40XVPmicroscope, with an INCA Energy X-ray microanalysis system.

The SEM image of the microstructure confirmed that it consists of a tempered martensite matrix with eutectic. The microstructure exhibited a eutectic constituent localised at the dendritic margins, forming a continuous mesh (Figure 20a1,b1). This constituent was identified as a composite of austenite solid solution and Cr₂₃C₇carbides. The microstructural analysis of the Fe-C-Cr-Ti-Cu system reveals that increasing the copper content from 3.1 wt.% in sample P3-E1-1 to 7.5 wt.% in sample P3-E1-7 significantly influences the phase transformation kinetics and final constituent morphology. Thermodynamic simulations using JMatPro indicate that higher copper concentrations stabilise the austenite phase, resulting in a depression of the martensite start (M_s) temperature from 301.6 °C to 269.2 °C and the martensite finish (M_e) temperature from 181.5 °C to 145.7 °C. Equilibrium phase diagrams confirm that while both alloys form a matrix of ferrite and martensite reinforced by M7C3 carbides and M(C,N) carbonitrides. SEM observations at 2000× magnification correlate these findings, showing that while P3-E1-1 maintains a refined martensitic–ferritic structure with dispersed carbides, the P3-E1-7 sample displays a more heterogeneous morphology with distinct copper-rich inclusions and a modified carbide distribution, which are critical factors in the synergistic optimisation of elemental transfer efficiency and hardfacing performance.

The microstructural evolution during the entire cooling process (crystallisation and subsequent cooling in the solid state) of the Fe-C-Cr-Ti-Cu alloy system was shown schematically in Figure 21.

3.6. Study of Exothermic Additions to the Chemical Composition of Slag

During the welding/surfacing process using self-shielded flux-cored wires, slag has a significant impact on their chemical composition [133]. Slag composition affects the gas content in the molten metal (such as nitrogen and oxygen) and inclusions dissolved during welding [134]. The introduction of an exothermic addition into the flux-cored wire filler changes the chemical composition of the slag. This is primarily due to the presence of an active reducing agent, Al powder. As a result of the exothermic reaction, a large amount of Al₂O₃ is formed, which changes the physicochemical properties of the slag. This is also confirmed by the results of studies by Li et al. [111]. This also caused a decrease in the basicity of the slag.

Table 15. The compositions of slag (wt.%).

№ Exp.	CaF2	TiO2	CaO	ZrO2	MgO	MnO	SiO2	Cr2O3	Al2O3	FeO	BI
1	22.66	23.48	4.84	5.42	0.35	7.13	5.05	16.62	12.92	1.53	0.94
2	24.41	25.72	5.21	5.84	0.38	5.45	7.40	10.62	13.59	1.39	0.95
3	23.15	23.89	4.94	5.54	0.36	6.55	6.84	14.71	12.71	1.31	0.92
4	28.09	24.37	6.00	6.72	0.43	2.38	0.62	2.68	27.33	1.38	1.17
5	28.36	26.44	6.05	6.78	0.44	1.12	1.53	0.66	27.22	1.39	1.13
6	26.58	21.61	5.67	6.36	0.41	3.74	1.25	8.35	24.73	1.30	1.11
7	22.77	21.16	4.86	6.54	0.39	3.83	0.87	10.39	28.70	0.49	0.88
8	24.46	19.87	5.22	7.02	0.42	1.29	1.92	7.82	31.44	0.52	0.89
9	24.79	23.69	5.29	7.12	0.43	0.33	4.70	3.42	29.70	0.53	0.84
min	22.66	19.87	4.84	5.42	0.35	0.33	0.62	0.66	12.71	0.49	0.84
max	28.36	26.44	6.05	7.12	0.44	7.13	7.40	16.62	31.44	1.53	1.17
Av	25.03	23.36	5.34	6.37	0.40	3.54	3.36	8.36	23.15	1.09

shows the composition of slag with different Al/Fe₂O₃ content and deposited under different deposition conditions.

The basic to acidic components ratio was known as the basicity index (BI) and was calculated by Equation (2) in mass% values [135,136].

$$BI={\displaystyle \frac{\left[\%Ca{F}_2+\%CaO+\%MgO+\%BaO+\%N{a}_{2}O+\%K_{2}O+\%L{i}_{2}O+0.5·\left(\%MnO+\%FeO\right)\right]}{\left[\%Si{O}_2+0.5·\left(\%A{l}_2{O}_3+\%Ti{O}_2+\%Zr{O}_2\right)\right]}},$$

(30)

The studied slag system can be classified as a multicomponent oxide–fluoride system: CaF₂-TiO₂-Al₂O₃-CaO-ZrO₂. Low MnO content (avg. 3.54%) indicates an exothermic reaction. BI varies in the range of 0.84–1.17, with an average value of 0.98. The slag is neutral or weakly basic. This ensures good bead formation and easy separability of the slag crust. In experiments four, five, and 6six an increase in BI (>1.1) is observed due to the high content of Al₂O₃ and CaF₂. Low content of iron oxides FeO (avg. 1.09%) indicates high deoxidation of the weld pool. In experiments one, two, and three, an increased content of Cr₂O₃ (up to 16.62%) is observed, which may indicate partial loss of chromium. With an increase in the EA content from 18 wt.% to 28 wt.%, the reducing capacity of the slag increased. The Al₂O₃ content increased from ~13% to ~26%. A further increase in EA does not lead to a significant increase in the Al₂O₃ content. The high Al₂O₃ content in experiments four to nine indicates the introduction of a higher percentage of the exothermic mixture.

According to Coetsee [136], the decrease in chromium and manganese oxidation is facilitated by increasing slag basicity (which decreases the activity of oxides). The research results showed that for the process performed with flux-cored wire, the FCAW-P3-E1-1 and FCAW-P3-E1-3 indexes (EA = 18 wt.% and EA = 38 wt.%), the average value of chromium transfer was η(Cr) = 0.703 and η(Cr) = 0.818, respectively (Figure 22). Whereas the processes performed with FCAW P3 E1 2 a basic slag, η(Cr) = 0.931 (Figure 22). The results also indicate that an increase in the Al₂O₃ content in the slag crusts had a positive effect on the transfer coefficients of silicon, manganese, and titanium, which is consistent with the results of the studies of Bang et al. [137]. Some decrease in the conversion factors when moving from flux-cored wire with medium to high EA content, characterised by an increase in Al₂O₃ content, can be associated an increase in viscosity and density [138]. This can lead to losses due to sticking of unmelted particles in the slag.

4. Discussion

The analysis showed a significant influence of the amount of CuO-Al exothermic addition on the transition of alloying elements. At the same time, according to the influence of welding parameters, the transition coefficients of elements could be grouped into three groups: deoxidisers (aluminium, silicon and manganese), carbide-forming elements with carbon (chromium, vanadium, titanium and carbon), and the reducible element of the exothermic addition. For the transition of elements in the deoxidiser group, along with the strong influence of EA, the second most important parameter was the CTWD. High transition values η(Al), η(Si) and η(Mn) were achieved at low contact tip-to-work distance values CTWD = 35 mm and medium or high EA content 30–40 wt.%.

The transition of carbide-forming elements such as carbon and vanadium was most influenced by parameters related to the melting of the filler material, namely the wire feed speed (WFS) and the voltage set on the power source (U_set), which determined the power of the welding arc. The percentage of exothermic addition in the core filler and the associated contact tip-to-work distance determined the amount of heat generated by the chemical reaction. The optimal values at which the highest values of η(C) and η(V) were achieved: WFS = 1.85 m·min⁻¹ (medium level), U_set = 28 V (low level), EA = 30 wt.% (medium level). Low voltage values could be explained by air suction [139] and an increase in the length of the electrode extension section [106]. The positive effect of the exothermic addition was associated with improved uniformity of flux-cored wire melting. At the same time, diffusion dissolution of graphite into droplets of molten metal at the electrode tip was observed. This was also confirmed by the results of studies by Zhudra et al. [102]. In the case of a significant effect of uneven melting of the filler and metal shell, undissolved graphite particles may enter the weld pool. Low carbon transfer was caused by graphite entering the weld pool in an unmelted state due to the collapse of the flux column. Graphite granules that did not have time to react completely at the droplet and weld pool stages floated up (due to their low specific weight) and were transferred into the slag [102]. Carbon losses, when the filler had a high exothermic addition content, may be caused by its oxidation as a result of the carbothermic reaction 2CuO + C→2Cu + CO₂↑ [92,140]. In addition, the melting of the core filler and its transition into a drop of molten metal, followed by heating at the droplet stage, promoted the dissolution and transition into the liquid metal solution of carbide-forming elements such as Cr, V, and Ti. This prevented their burnout due to interaction with the air. Burnout will also be facilitated by an increase in voltage, i.e., the associated arc length.

When melting in the charge, carbon binds with carbide-forming elements (chromium, vanadium, etc.) to form refractory compounds [92]. In a bound state, it is transferred into a molten metal droplet, thus preventing the burnout of elements such as V. Meanwhile, titanium Ti will bind into titanium nitride at high temperatures, as confirmed by thermodynamic calculations. The significant influence of welding current and arc voltage on the transition of C and Cr was also reported in the study by Garg et al. [141]. However, the determining variable influencing the overall transition coefficient of alloying elements was EA. This indicated a positive influence.

The analysis of the influence of variables on the parameters of the welding thermal cycle and hardness showed a dependence on WFS and U_set. This could be explained by their influence on the arc power. It was known that when welding/surfacing with self-shielded flux-cored wires, the welding current was primarily determined by the wire feed speed [124]. The influence of EA was not so noticeable, but the early occurrence of exothermic reactions could lead to a decrease in welding current caused by the melting of the core filler [114]. Thus, the amount of exothermic addition introduced had a significant effect on the transition of elements, as well as a slight effect on the parameters of the welding thermal cycle. The analysis showed that the microstructure will depend on the composition of the deposited metal. Changes in the chemical composition of the deposited metal and the cooling rate had a significant effect on the microstructure, phase composition, and mechanical properties of the deposited metal. An increase in the content of Cr and Cu significantly shifted the curves of the start of pearlite formation towards longer durations and lower temperatures. The latter indicated an increase in hardenability [130,142]. At high copper content (6–8 wt.%), an increase in carbon content from 0.55 wt.% to 0.77 wt.% led to complete suppression of pearlite formation. Copper acted as a potent stabiliser of supercooled austenite [131]. Higher Cu concentrations led to a distinct depression of the bainite start temperature. Specifically, alloy P3-E1-8 (8.6 wt.% Cu) demonstrated a significantly lower transformation temperature compared to alloy P3-E1-1 (3.1 wt.% Cu), confirming the role of copper in refining the transformation products. The main alloying elements that determined the microstructure of the matrix and the content of the strengthening phase in the form of carbides were carbon and chromium [143]. Cr₇C₃ carbides were formed at Cr/C ≥ 2, and Cr₂₃C₆ carbides were formed at Cr/C ≥ 5. The results of our studies showed that the formation of Cr₂₃C₆ carbides in Fe-C-Cr-Ti-Cu alloys was observed at Cr/C ratios ≥ 4.7. The formation of orthogonal carbide Cr₇C₃ was preferable to that of orthogonal carbide Cr₂₃C₆, which had a lower calculated microhardness (HV = 13.5 GPa versus HV = 10.1 GPa [144]).

Analysis of the obtained hardness values showed (Table 8) that the highest hardness was exhibited by alloys P3-E1-8 and P3-E1-2 (752.3 HV and 613 HV, respectively). Their microstructure corresponded to martensitic. These alloys contained C = 0.52–0.57 wt.% and had a Cr/C ratio of 5.19–5.27. For alloys P3-E1-1, P3-E1-3, P3-E1-6, and P3-E1-7 with a tempered martensite structure, their hardness ranged from HV = 535 to 569. The lowest hardness was observed in alloys with indices P3-E1-4, P3-E1-5 and P3-E1-9, whose microstructure corresponded to the troostite structure with a hardness in the range of 400–500. The latter alloys had a high carbon content (C > 0.71) and chromium content (Cr = 3.9).

In view of the considerable interest in researching the influence of filler composition [145,146], methods for studying and controlling deposited metal [147,148], and increasing productivity [124], the proposed research methodology could be useful for optimising processes [149,150,151], developing and testing new materials and mechanical properties, modern technologies [152,153], and life cycle analysis [154,155,156].

5. Conclusions

The obtained results can be used to optimise surfacing parameters, improve the compositions of flux-cored wires, and predict the properties of the deposited layers. The statistical and experimental analysis of the surfacing process parameters yielded the following conclusions regarding the transfer coefficients of alloying elements:

• Based on their response to welding parameters, the alloying elements could be categorised into three distinct groups: deoxidisers (Al, Si, and Mn), carbide-forming elements (Cr, V, Ti, and C), and the recovery element from the exothermic addition (Cu).
• The transfer coefficients such deoxidisers asη(Al), η(Si), and η(Mn) were primarily governed by the percentage of exothermic addition (EA) and the contact tip-to-work distance (CTWD). High values of their conversion coefficients are achieved at EA = 28 wt.% and CTWD = 35 mm.
• The transfer coefficients η(C) and η(V) were highly sensitive to parameters affecting the filler material melting and arc power—specifically wire feed speed (WFS) and voltage (U_set). Optimal transition for η(C) and η(V) was observed at WFS = 1.85 m·min⁻¹ (medium level), U_set = 28 V (low level), and EA = 28 wt.%.
• Maximum recovery was achieved at low contact tip-to-work distance (CTWD = 35 mm) and medium-to-high EA content (EA = 38 wt.%,).
• It was established that copper had a pronounced stabilising effect on supercooled austenite in Fe–C–Cr–Cu steels, shifting the ‘nose’ of pearlite transformation to longer times and lower temperatures. This, in turn, expanded the time–temperature range for bainite transformation. Copper at high concentrations (≥7 wt.%) further stabilised austenite and promoted increased hardenability.
• High-copper Fe–C–Cr–Cu steels, with increasing carbon and chromium content, exhibited a narrower austenite region. Increased copper content contributed to the expansion of the austenite stability range and shifted the γ-phase region toward lower temperatures.
• The highest hardness values (613–752.3 HV) were achieved in alloys with a martensitic microstructure, characterised by C = 0.52–0.57 wt.% and a Cr/C > 5.2. Alloys with higher carbon (C > 0.71) and lower chromium (Cr/C = 4–4.7) exhibited a troostite structure with lower hardness (400–500 HV).
• The study successfully implemented an advanced synergistic Taguchi–ANOVA–FD–PCA–GRA approach, a combined Taguchi-ANOVA-based approach with a hybrid Taguchi–GRA–PCA methodology for an orthogonal four-factor, three-level experimental design. This integrated approach facilitated the systematic identification and exclusion of insignificant variables through ANOVA to develop mathematical models using FD while effectively addressing multi-objective optimisation challenges.
• Optimal values of the studied variables were obtained for the multi-objective problem using the hybrid Taguchi–GRA–PCA methodology. The optimal parameters identified are as follows: EA = 38 wt.%, CTWD = 35 mm, WFS = 2.07 m min⁻¹, and U_set = 31 V, which ensures high process productivity, minimal spatter, high hardness, and alloying element transition.