Prediction for Dilution Rate of AlCoCrFeNi Coatings by Laser Cladding Based on a BP Neural Network

Abstract

The dilution rate has a significant impact on the composition and microstructure of the coatings, and the dilution rate and process parameters have a complex coupling relationship. In this study, three process parameters, namely laser power, powder feeding rate, and scanning speed, were selected as variables to design the orthogonal experiment. The dilution rate and hardness data were obtained from AlCoCrFeNi coatings based on orthogonal experiments. Then, a BP neural network was used to establish a prediction model of the process parameters on the dilution rate. The established BP neural network exhibited good prediction of the dilution rate of AlCoCrFeNi coatings, and the average relative error between the predicted value and the experimental value was only 5.89%. Subsequently, the AlCoCrFeNi coating was fabricated with the optimal process parameters. The results show that the coating was well-formed without defects, such as cracks and pores. The microhardness of the AlCoCrFeNi coating prepared with the optimal process parameters was 521.6 HV_0.3. The elements were uniformly distributed in the microstructure, and the grain size was about 20–60 μm. The microstructure of the AlCoCrFeNi coating was only composed of the BCC phase without the existence of the FCC phase and intermetallic compounds.

1. Introduction

Laser cladding is an important surface modification technology that uses a high-energy laser beam to melt and deposit powder or wire on a substrate surface to form a single-layer or multi-layer coating. The coatings are firmly combined with the substrate by metallurgical bonding, which can significantly improve the wear resistance, corrosion resistance, and oxidation resistance of the substrate surface [1,2]. In addition, it also has the advantages of fast forming speed, low heat input, and low dilution rate [3,4,5,6].

High-entropy alloys (HEAs) are also called multi-principal element alloys. Their composition is composed of several main metallic elements. As a structural and functional material, it has unique properties and arouses widespread interest [7,8]. The AlCoCrFeNi alloy is a typical high-entropy alloy with an equal atomic ratio, and it possesses excellent mechanical properties, because its microstructure is mainly composed of the BCC phase [9]. The related work of preparing AlCoCrFeNi coatings by laser cladding technology has been extensively studied. The hardness of AlCoCrFeNi coatings prepared by laser cladding is significantly higher than that of as-cast AlCoCrFeNi, and the grain size is also significantly reduced [10,11,12,13]. The microstructure of the AlCoCrFeNi coatings mainly contains the BCC phase and a very small amount of the FCC phase. It is difficult for dislocations to slip in the BCC phase, which is also the main reason for the high strength of AlCoCrFeNi high-entropy alloys [9].

The dilution rate refers to the change of the cladding alloy composition caused by the mixing of molten matrix in the process of laser cladding. The composition of the coating changes under a high dilution rate, resulting in a decrease in the mechanical properties of the coating. However, under a too-small dilution rate, the bond between the substrate and the coating is poor. Therefore, the dilution rate is one of the most important process control parameters and the key to obtaining a high-quality coating.

The high entropy coating prepared by laser cladding usually has a high dilution rate of about 49.3% [14,15]. The hardness of the AlCoCrFeNi alloy can reach up to 500 HV. The substrate used in this study is soft; its hardness is only 240 HV. At a high dilution rate, a large amount of molten substrate enters into the AlCoCrFeNi coating, resulting in a sharp decrease of hardness. Moreover, the elements from the molten substrate have an important influence on the microstructure of the AlCoCrFeNi high-entropy alloy coatings. The excessive Fe and Cr elements from the substrate material promote the generation of the FCC phase with low strength and hardness [14], resulting in a decrease of strength and hardness. Therefore, it is of great significance to predict and control the dilution rate of the AlCoCrFeNi high-entropy alloy coating.

The dilution rate is mainly affected by process parameters, among which the most important process parameters are laser power, scanning speed, and powder feeding rate. In actual production, the relationship between dilution rate and process parameters is a complex non-linear relationship, and there are many influencing factors [13,16]. Traditional experimental methods are applied to explore the accurate relationship between process parameters and dilution rate, which consumes a lot of time and labor.

In solving complex nonlinear problems, neural networks have excellent nonlinear processing capabilities. Neural networks provide an effective method to construct the relationship between process parameters and the dilution rate of the cladding layer [17]. Some researchers employed the back propagation neural network (BPNN) to predict process parameters and cladding forming quality [18,19]. Deng et al. [20] adopted quantum-behaved particle swarm optimization and a BP neural network to build a model of the process parameters and microhardness of the Ti(C, N) cladding layer. The model has strong predictive ability, and the relative error can reach 9.12%. Guo et al. [21] used a BP neural network to optimize and predict the process parameters of laser cladding a Co-based alloy, and the average relative error between the predicted value and the experimental value was less than 10%.

In this paper, 18 groups of process parameters were designed by the orthogonal experiment method, and the corresponding AlCoCrFeNi coatings were prepared. Then, the effects of laser power, powder feeding rate, and scanning speed on the dilution rate of AlCoCrFeNi high-entropy alloy coatings were analyzed preliminarily. According to the obtained dilution rate data, the BP neural network was conducted to establish the prediction model of the process parameters and the dilution rate. Finally, the microstructure of the coating prepared with the optimal process parameters was analyzed.

2. Experimental Procedures and Methods

2.1. Experimental Materials

AlCoCrFeNi high entropy alloy powder is a spherical powder prepared by a gas atomization process, and the powder particle size is 45–105 μm. The specific morphology is shown in Figure 1, and the content of each element is shown in

Table 1. Chemical composition of AlCoCrFeNi powder by XRF.

Element	Al	Co	Cr	Fe	Ni
Concentration (%)	9.8171	23.1098	20.5944	22.8544	23.5598
Atomic ratio (at.%)	18.5431	19.9760	20.1981	20.8136	20.4691

.

The material of substrate was 40CrNiMo alloy steel, with a size of 12 × 60 × 100 mm³. Before laser cladding, the surface of substrate was ground and polished, then it was scrubbed with alcohol and acetone to remove the oil on the surface.

2.2. Design of Orthogonal Experiment

The laser cladding was conducted using a continuous fiber laser machine (IPG, YLS-6000-S2, IPG Photonics, Oxford, MA, USA); the laser wavelength was 1070 nm, the maximum power was 6 kW, the laser focal length was 460 mm, and the square spot was 5 × 5 mm². The coaxial powder feeding method was adopted to transport the powder to the position near the focus of the beam under the argon carrier flow.

The orthogonal experiment selected the laser power (P), scanning speed (V), and powder feeding rate (R) as experimental factors, as shown in

Table 2. Experimental factors and levels.

Levels	Factors
	P/(kW)	R/(g/min)	V/(mm/s)
Level 1	2.00	15.00	6.00
Level 2	2.50	10.00	4.00
Level 3	1.50	–	2.00

. Each factor of laser power (P) and scanning speed (V) contained 3 levels, and the powder feeding rate contained 2 levels. The parameters of the 18 times L₁₈ (3³ × 2¹) orthogonal experiment are shown in

Table 3. Geometry sizes and laser cladding process parameters.

Sample	P (kW)	R (g/min)	V (mm/s)	H (mm)	W (mm)	h (mm)	η (%)	Hv (HV0.3)
S-1	1.50	15.00	4.00	1.09	6.03	0.36	25	491.87
S-2	2.00	15.00	4.00	1.20	6.57	0.42	26	516.50
S-3	2.50	15.00	4.00	1.38	7.43	0.68	33	503.80
S-4	1.50	15.00	2.00	2.20	5.26	0.30	12	499.75
S-5	2.00	15.00	2.00	2.40	6.68	0.45	16	521.60
S-6	2.50	15.00	2.00	2.10	7.08	0.69	25	558.87
S-7	1.50	15.00	6.00	0.49	6.27	0.44	47	259.00
S-8	2.00	15.00	6.00	0.79	7.11	0.32	29	320.97
S-9	2.50	15.00	6.00	1.02	7.78	0.55	35	363.07
S-10	1.50	10.00	4.00	0.88	8.43	0.79	47	333.27
S-11	2.00	10.00	4.00	0.92	6.45	0.45	33	305.43
S-12	2.50	10.00	4.00	0.81	6.91	0.48	37	264.47
S-13	1.50	10.00	2.00	1.48	6.40	0.31	17	467.4
S-14	2.00	10.00	2.00	1.61	7.67	0.42	21	441.97
S-15	2.50	10.00	2.00	1.58	8.10	0.49	24	413.97
S-16	1.50	10.00	6.00	0.41	7.47	0.39	49	351.53
S-17	2.00	10.00	6.00	0.68	8.34	0.72	51	407.63
S-18	2.50	10.00	6.00	0.72	9.38	0.82	53	256.23

. A cross-sectional view of the cladding layer is shown in Figure 2; h is the depth of the fusion zone, H is the height of the cladding layer, and W is the width of the cladding layer. The dilution rate (η) is expressed by the percentage of the substrate alloy molten into the cladding layer, and the calculation equation is η = h/(H + h).

2.3. Microhardness Measurement

The microhardness can be used as an important reference index for the wear resistance of coatings, as well as a simple index for evaluating the quality of the coatings. Therefore, the microhardness of the coatings was also measured in this study. The microhardness was measured using a MICRO MET-5103 digital microhardness tester (Baihe, Shanghai, China); the test load was 300 g, and the indenter loading time was 15 s. Coatings were measured for five points at different positions in the upper middle area; the maximum and minimum values were removed, and the average of the remaining 3 values were taken as the microhardness value of the coatings.

The cross section of prepared coatings was ground and polished. In order to clearly distinguish the boundary between the coating and the substrate, aqua regia (HNO₃:HCl = 1:3) was used for etching, and the etching time was 30 s. The cross section corroded was observed under a stereo microscope; then, the geometric dimensions of each part of the coating were measured.

2.4. Microstructure Characterization

The phase qualitative analysis of the coatings was carried out by X-ray polycrystalline diffractometer (XRD, Bruker D8 Advance, Bruker, Madison, WI, USA), and the specific parameters were the following: Cu target X-ray, tube voltage 40 kV, tube current 40 mA, scanning speed 4°/min, scanning range 20–90°, and step size 0.02°.

The polished coating samples were etched for 6 s, and then, the morphology and microstructure were observed by a scanning electron microscope (ZEISS Gemini SEM 300, Carl Zeiss, Oberkohen, Germany). The composition of coating samples was examined by the attached energy dispersive spectroscopy (EDS, Carl Zeiss, Oberkohen, Germany). In order to prepare electron backscatter diffraction (EBSD, Carl Zeiss, Oberkohen, Germany) samples, the polished metallographic samples were placed in a perchlorate alcohol solution; then, the surface stress layer was removed by electrolytic polishing.

2.5. Design of BP Neural Network

A back-propagation neural network (BPNN version x) is an error back-propagation neural network model with a strong nonlinear approximation ability. In this study, a three-layer structure of BP neural network was established to build the relationship between the dilution rate and process parameters. The structure of BPNN is shown in Figure 3, including 1 input layer, 1 hidden layer, and 1 output layer. The input layer has 3 neurons (X₁, X₂, X₃), corresponding to the laser power (P), the powder feeding rate (R), and the scanning speed (V), respectively. The P, R, and V are the input parameters used to train the BP neural network. The output layer only has a neuron Y, which is the dilution rate (η). The η is the output parameter used to train the BP neural network. The hidden layer contains 6 neurons, the number of which can be determined according to empirical formulas. The activation function (transfer function) employs the Tan-Sigmoid function. The training process of the BP neural network is as follows:

Step 1: Input data and output data is an m × n two-dimensional array, defined as (x_ij)_m×n. The input data and output data are normalized to the interval [–1,1] according to Formula (1).

$$X_{\mathrm{i}\mathrm{j}}=2\ast \frac{x_i{}_j-x_{j\min }}{x_j{}_{\max }-x_{j\min }}-1$$

(1)

(X_ij)_m×n is the normalized m × n matrix, x_jmax and x_jmin are the maximum and minimum values of the jth column of the (x_ij)_m×n matrix, respectively.

Step 2: The input layer neurons transmit the normalized data to the neurons of the hidden layer, or it transmits the value calculated by the neurons of the previous hidden layer to the next neurons of the hidden layer. The input of the lth layer neurons can be expressed by Formula (2):

$$U_j^l=\{\begin{array}{l}{X}_{\mathrm{j}}={{(X}_{1\mathrm{j}}{,X}_{2\mathrm{j}},\dots X_{3\mathrm{j}})}^{\mathrm{T}},l=0\\ f\left({\displaystyle \sum _{i=1}^h{w}_{ij}^l}{U}_i^{l-1}+{\theta }_j^l\right),l=1,2,3\cdot \cdot \cdot P\end{array}$$

(2)

where X_j is the jth column vector of the above two-dimensional matrix (X_ij)_m×n, and w^l_ij is the connection weight of the neuron (i) in the (l−1) layer and the neuron (j) in the l layer. $U_i^{l-1}$ is the input of neuron (i) in the layer (l−1); ${\theta }_j^l$ is the threshold value of neuron (j) in the layer l, and the tansig function is adopted as the transfer function.

Step 3: The output neurons in the output layer (U_k) can be calculated by the following Formula (3):

$$U_k={\displaystyle \sum _{j=1}^h{U}_j^P}{w}_{jk}^{P+1}+{\theta }_k^{P+1},k=1,2,3\dots n_0$$

(3)

where $w_{jk}^{P+1}$ is the connection weight of neuron (j) in the p layer and neuron (k) in the (p+1) layer, and ${\theta }_k^{P+1}$ is the threshold value of the (p+1) layer neuron (k).

Step 4: The error of network training is evaluated by the Mean Square Error (MSE), which is calculated by Formula (4). The weight correction of each layer is calculated by the derivation rule of the differential chain in the following Formula (5):

$$\mathrm{MSE}=\frac{1}{N_{\mathrm{s}}}{\displaystyle \sum _{k=1}^{N_s}\left[\frac{1}{2}{{\displaystyle \sum _{k\in \left\{C\right\}}(d_k-U_k)}}^2\right]}$$

(4)

$$\mathsf{\Delta }{w}_{ij}^l=-\lambda \frac{\partial \mathrm{MSE}}{\partial y_k}\frac{\partial y_k}{\partial U_j^l}\frac{\partial U_j^l}{w_{ij}^l}$$

(5)

where d_k is the experimental response, N_s is the total number of samples, {C} is the output data set, and λ is the learning rate usually in the interval [0,1].

3. Results and Discussion

The ultra-depth-of-field 3D microscope was used to observe the morphology of the single-track coatings, and the results are shown in Figure 4. The interface between coatings and the substrate presents a good metallurgical bond, and there was no crack in the coatings. The data, such as the geometry sizes, dilution rate, and hardness of the coatings, are shown in Table 3.

3.1. The Effect of Process Parameters on the Dilution Rate

The influence of laser cladding process parameters on the geometry and dilution rate of the coatings is shown in Figure 5. It could be found that when the powder feeding rate (R) and scanning speed (V) remained unchanged, as the laser power increased, the melting width, depth, and dilution rate of the coatings showed an increasing trend. However, the laser power (P) and scanning speed (V) remained unchanged; when the powder feeding rate increased from 10 g/min to 15 g/min, the melting width decreased, as shown in Figure 5a,b.

The depth rises with the increment of laser power, and the greater the powder feeding rate, the smaller the coating depth, as shown in Figure 5c,d. For coaxial powder feeding laser cladding, the substrate is heated by the laser energy that passes through the powder particle cloud [22]. The more powder particles in the laser beam, the stronger the shielding effect on the laser beam, resulting in forming of a smaller clad depth. When the powder feeding rate is 15 g/min, the scanning speed has the least influence on the clad depth, and the laser power has the greatest influence on the clad depth.

According to Figure 5e,f, the laser power has a minor effect on melting height, whereas scanning speed and powder feeding rate have a greater influence on coating height. At a powder feeding rate of 10 g/min, when the power increases from 2000 W to 2500 W, the height of coatings shows a slight downward trend, which indicates that the powder has been sufficiently melted at the power of 2000 W.

The variation in the dilution rate (η) is depicted in Figure 5g,h. As the laser power increases, the dilution rate rises correspondingly. Under the same laser power and scanning speed, the increase in powder feeding rate can significantly reduce the dilution rate of the coatings. It can be seen from Figure 5g that the scanning speed has the greatest influence on the dilution rate. A lower scanning speed can increase the amount of powder in the molten pool unit area, increasing the coatings height. In addition, the lower scanning speed has more heating time so that the powder can be melted more fully.

Moreover, there is an interesting phenomenon that the dilution rate can influence the microhardness of AlCoCrFeNi coatings. When the dilution rate is greater than the 40%, the microhardness is about 330 HV_0.3, such as in S-11 and S-16 samples. The microhardness is obviously lower than that of the sample with a dilution ratio of less than 25%.

The sample with the smallest dilution rate was S-4; the dilution rate was 12%; the microhardness value was 499.75 HV_0.3; and the process parameters were a laser power of 1500 W, scanning speed of 2 mm/s, and powder feeding rate of 15 g/min. For the S-5 sample, the dilution rate was 16%, but the microhardness value was 521.6 HV_0.3, and the coating height was 2.4 mm, which was higher than the 2.2 mm height of the S-4 sample. Obviously, the AlCoCrFeNi powder can be melted more abundantly under the power of 2000 W, so the overall mechanical properties were better than those of the S-4 sample.

The optimal process parameters were not directly given by the BP neural network. In this study, the dilution rate was the most important reference index. However, the laser cladding also needed to consider the hardness. If considering only the pursuit of low dilution rate, the coating may have defects, such as peeling and incomplete melting. Therefore, the optimal process parameter was the combination of hardness and dilution rate. The process parameters used for the S-5 sample, with a dilution rate of 16% and hardness of 521.6 HV_0.3, were optimal. The optimal process parameters were as follows: the laser power: 2 kW, the scanning speed: 2 mm/s, and the power feeding rate: 15 g/min.

3.2. Analysis of Performance of BP Model

The feedforwardnet function in the neural network training tool of MATLAB (MATLAB R2018b) was used to build and train a BP neural network. Due to the geometric size and the dilution rate data of samples, S-7 and S-10 were relatively abnormal; these two groups of data were eliminated, and a total of 16 groups of data were used for the establishment and training of the BP neural network. Twelve groups of data were randomly selected as the training data for the BP neural network. The sample data used for test and validation consisted of 4 groups, namely samples S-9, S-11, S-12, and S-15.

It can be seen from Figure 6 that the training of the BP neural network underwent 8 epochs, and it reached the best training performance at the 5th epoch, with a mean square error of 0.05%.

Table 4. Dilution rate of prediction.

No.	Sample	Experimental η (%)	Predicted η (%)
1	S-1	25	24.26575
2	S-2	26	26.06222
3	S-3	33	32.87267
4	S-4	12	11.67059
5	S-5	16	16.06459
6	S-6	25	25.05431
7	S-8	29	28.77535
8	S-9 (test)	35	32.99414
9	S-11 (test)	33	30.54423
10	S-12 (test)	37	38.58375
11	S-13	17	17.01862
12	S-14	21	21.08211
13	S-15 (test)	24	22.52957
14	S-16	49	48.90431
15	S-17	51	50.79725
16	S-18	53	52.09692

and Figure 7a show that the predicted value of the dilution rate in the training data was very close to the experimental value. As shown in Figure 7b, during the training process, the maximum value of the relative error between the predicted value and the training value was 1.70%, which proves that the BP neural network training effect was good. The predicted values of the test and validation samples were 32.99414, 30.54423, 38.58375, and 22.53957. Compared with the experimental values, the relative errors were 5.73%, 7.44%, 4.28%, and 6.13%, and the average relative error was 5.89%. It can be seen from the relative error of the test data that the BP neural network established in this paper had excellent predictive performance after training.

3.3. Microstructure of the AlCoCrFeNi HEA Coating

The AlCoCrFeNi HEA coating was fabricated by the optimal process parameters, and then, its microstructure was observed. The XRD diffraction pattern of the AlCoCrFeNi coating is shown in Figure 8. It could be found that the phase of the coating was mainly the BCC phase, and the BCC phase was divided into disordered phase A2 and ordered phase B2. The disordered A2 phase is generally an Fe–Cr-rich phase, and the ordered B2 phase is generally an Al–Ni-rich phase [23]. Due to the fact that three crystal structures of these two phases are a cubic orientation and the lattice parameters are similar, the formed X-ray diffraction was coherent. Therefore, most of the diffraction peaks on the XRD pattern overlapped, and it was difficult to distinguish [24,25,26]. However, there was a small diffraction peak near 31°, corresponding to the (100) plane of the B2 phase, which confirmed the existence of the ordered phase B2 [27,28].

Clear grain boundaries could be observed at the cross-section of the AlCoCrFeNi coating corroded by aqua regia, as shown in Figure 9. The elements distributed homogeneously, and the microstructure uniformly consisted of a simple BCC solid solution phase, as shown in Figure 9a. The crystal grains were equiaxed with a size of about 20–60 μm. The high magnification of the microstructure is shown in Figure 9b; there was no precipitation of intermetallic compounds with an abnormal color contrast. There are two kinds of equiaxed grains with different contrasts in Figure 9a. However, according to EDS analysis, the two kinds of grains have very similar chemical compositions. This result is also consistent with the results obtained from other studies [11]. EDS point analysis was performed on the microstructure of the coatings in Figure 9b, and the results are shown in

Table 5. EDS point of the AlCoCrFeNi coating (S-5 sample) (at.%).

Points	Al	Co	Cr	Fe	Ni	N
A	38.41	6.02	9.87	13.50	6.97	25.23
B	14.98	19.66	17.32	30.40	17.64	0

. At the region marked B in Figure 9b, the Fe element content was the highest, which was 30.40 at.%; and the Al element content was the lowest, which was 14.98 at.%. This is due to a small part of the molten substrate material entering into the molten pool, increasing the content of the Fe element in the region B.

The black granular microstructure (marked A) had the highest content of Al and N elements, which were 38.41 at.% and 25.23 at.%, which indicates that the particles were the AlN phase. This kind of microstructure has also been found in the related research of AlCoCrFeNi high-entropy alloy, and it was confirmed that the structure was AlN particles, and the N element came from the impurities contained in the material [29]. Due to the small size and low content of the particles, they were not detected in XRD detection.

Figure 10 is the EDS element mapping of the AlCoCrFeNi coatings. The Al element aggregated at the black particles, resulting in the increasement of Al element concentration. This also explains why the Al element content in the other area of coatings was less. Except for the aggregation of partial Al elements, the other four elements were uniformly distributed, and no segregation phenomenon occurred, which also proves that the microstructure was composed of uniform solid solution.

Figure 11a is an IPF diagram of AlCoCrFeNi coatings. The high-angle boundaries are shown with the black line; the misorientation angle exceeds 10°. There were many different orientations of grains in the microstructure of coatings. It could be found that the AlCoCrFeNi coating possessed a texture index in the three pole figures (PFs), with an intensity range of 0–6.92, especially with a maximum texture index in the {100} PF up to 6.92, as depicted in Figure 11d.

The microstructure of the AlCoCrFeNi coating was composed of the BCC phase and almost contained no FCC phase, as shown in Figure 11b. This result is also consistent with the previous XRD and SEM analysis results. However, a small part of the substrate melted into the molten pool during the laser cladding, resulting in the Fe element content in the coatings exceeding 20 at.%. The microstructure of the coatings did not change and was still composed of the BCC solid solution phase. The dilution rate corresponding to the laser cladding process parameters did not cause the formation of the FCC phase.

4. Conclusions

In this study, a BP neural network was used to establish a prediction model of the laser cladding process parameters on the dilution rate, based on data obtained from an orthogonal experiment of AlCoCrFeNi high-entropy alloy coatings. The following conclusions could be drawn:

(1)

The training performance of the established BP neural network was outstanding, and the maximum relative error between the training value and the predicted value was 1.70%. The prediction performance was excellent, with an average relative error of only 5.89% between the predicted value and the experimental value.

(2)

The optimal process parameters were as follows: laser power of 2000 W, a scanning speed of 2 mm/s, and a powder feeding rate of 15 g/min. The dilution rate was 16%, and the microhardness value was 521.6 HV_0.3.

(3)

The grains of the coatings under this process parameter were equiaxed, with uniform composition distribution, and no serious composition segregation occurred. The microstructure of coatings was still composed of the BCC phase solid solution. The FCC phase does not form in the microstructure due to the excessive Fe element content. These results also prove that the dilution rate under the process parameters does not have a major impact on the microstructure and properties of the AlCoCrFeNi coatings.