# Study of Microstructure and Properties of 316L with Selective Laser Melting Based on Multivariate Interaction Influence

Authors: Jianfeng Sun; Lu Shen; Weiqiang Wang; Zhu Liu; Huaming Chen; Jieli Duan
Journal: Advances in Materials Science and Engineering
 (2020)

---

## Abstract

The selective laser melting technique is widely used in aerospace and biomedical industries, and the performance of formed 316L parts is significantly subject to the forming angle. As the selective laser melting 316L parts are constrained by multiple performance indexes, the study involves multivariate interaction influenced on the forming parameters such as the angle with thexz plane, the angle with the xy plane, laser power, scan speed, powder thickness, and hatching space on the indexes like tensile strength, density, and surface roughness with linear regression equations based on multiobjective optimization to obtain the best process parameters. The study results of microstructure performance of the formed 316L parts show that the angle with the xz plane has significant effect on the experiment indexes, while the layer thickness has the greatest effect on the indexes. After stretching, the molten pools are obviously elongated and the microstructure of the formed 316L parts is composed of equiaxed crystals and columnar crystals with a grain width of 0.28–0.4 nm. The secondary growth of the dendrites is not obvious, and the crystallinity of the selective laser melting 316L parts is not as good as the standard parts, with the microstructure showing directional solidification due to grain refinement and microscopic distortion of crystals. As the fracture has dimples, it is a ductile fracture and typical plastic fracture. The hardness near the fracture is higher than that of the substrate, whilst the indexes regarding the selective laser melting parts are higher than the ASTM-A182 and ASTM-F3184-16 standards. Since the theoretical model built in this study has less error, the findings have practical engineering application value.


---

## Body

## 1. Introduction

The selective laser melting technique is a newly developed powder bed fusion additive manufacturing technique. The principle is that the metal powder is fused by laser and solidified to form a molten pool, and then multistacked by layer to produce a three-dimensional part [1]. As for a small number of customized parts, the technique has several advantages, such as short time consumption, fast response, and high efficiency [2]. In recent years, additive manufacturing has made great breakthroughs in various industries, especially in aerospace and biomedical fields [3, 4], showing broad application prospects.The selective laser melting process parameters have a great effect on the mechanical properties, surface quality, and friction performance of the formed parts. Some studies have shown that the laser power and scan speed have the most significant effect on the density of the sample [2, 5–8], and the scan speed, layer thickness, and manufacturing direction have a certain effect on the surface roughness and dimensional accuracy of the formed parts [9]. The lower the laser power, the lower the density and hardness of the sample, and the less the fusion at the boundary of the molten pool [10]. When the forming direction is inclined from 45° to 90°, the strength and fatigue resistance decrease and the elongation at break increases by more than 50% [11]. Wang et al. [12] studied the effect of the selective laser melting scanning strategy on residual stress and surface quality of the formed parts. The results show that the 316L stainless steel parts can achieve 99.37% of density with the scanning strategy of helical segmentation to effectively control the residual stress of the SLM 316L stainless steel parts. Dilip et al. [13] studied the effect of heat treatment on the microstructure and properties of the SLM HY100 steel. The results show that the microstructure of the parts after heat treatment is finer and more uniform with the mechanical properties being improved. Amato et al. [14] of the University of Tennessee in the United States studied the SLM Inconel 718 cylindrical parts. The results show that the Vickers hardness of untreated, HIP-treated, and heat-treated parts is 3.9 GPa, 5.7 GPa, and 4.6 GPa, respectively. Wei et al. [15] studied the microstructure and properties of stainless steel nanohydroxyapatite medical composites with selective laser melting technique. The results show that the tensile strength, elastic modulus, and hardness of the SS/NHA prototype obtained under the optimum process conditions are higher than the human bone, which provides the possibility to prepare the SS/NHA porous scaffold with AP mechanical properties of the weight-bearing bone.Selective laser melting direction is one of the important factors affecting the performance of the formed parts [16, 17]. At present, most of the forming parameters are obtained without considering the forming direction (the angle with the xy plane is default as 90°), but practically, the changes in the angle with the xy plane and the angle with the xz plane bring significant variation of density, surface roughness (step effect), and mechanical properties of the formed parts [18–20]. In the laser forming process, the thermal gradient and the cooling rate of the formed part change with the forming angle and a complex dynamic fluid flow is generated in the molten pool. These complex phenomena affect crystal growth and orientation [21], resulting in material sputtering and microstructure defects, mainly manifested by micropores, high residual stress, and large surface roughness [12, 22, 23]. These defects cause premature failure under fatigue loading. At present, there are many studies on the forming parameters of the 316L stainless steel with selective laser melting, mainly focusing on the effect of the single factor on the performance of the single formed part [24, 25], rather than the effect of multifactors on multiple indexes. The study on the interaction effect of multiple forming directions on the density, surface roughness, and tensile strength of the formed parts has not been reported [26].In this study, tensile parts with various forming angles were prepared by selective laser melting for the test of density, surface roughness, and mechanical properties of the parts, analysis of microstructure and fracture morphology of the parts with various forming angles, and exploration of the microstructure properties and forming mechanism in different areas and the effect on tensile mechanical properties, providing a theoretical basis for the control of microstructure and mechanical properties of the selective laser melting parts.


## 2. Experimental Materials and Methods

### 2.1. Experimental Equipment and Materials

In the experiment, the following products of Guangzhou Riton Laser Co., Ltd. were selected: the D280 AM machine with an accuracy of ±0.02 mm, laser wavelength of 1.064μm, focused spot diameter of 20–80 μm, and layer thickness of 20–80 μm for forming parts; WD-E stretching tester with a pressure sensor of 0–20 kN for the tensile test; KERN analytical balance ABJ 320-4NM with a range of 320 g and accuracy of 0.0001 g for quality measurement; TIME3220T roughness meter with a measurement platform size of 400 mm × 250 mm × 70 mm, lift height of 300 ±1 mm, x-direction fine tune of ±12.5 mm, y-direction fine tune of ±12.5 mm, rotating coarse tune of 360°, and fine tune of ±5° for detecting surface roughness; MQX1200-40 atmosphere box furnace with a maximum temperature of 1200° and temperature control accuracy of ±1° for heat treatment; XQ-1 metallographic specimen mounting press and YMPZ-1 automatic metallographic specimen grinding and polishing machine for metallographic preparation; EVO18 ZEISS scanning electron microscope with a magnification of 5–1,000,000x and acceleration voltage of 0.2–30 kV for microstructure observation; and SmartLab (9) X-ray diffractometer (XRD) with an X-ray generator of fine focusing 9 kW knob, X-ray generator filament of 0.4 mm × 8 mm, and goniometer minimum step size of 1/10000° for phase analysis.316L stainless steel powder (MTI S01C) is selected from Guangzhou Material Technology Innovation Co., Ltd. with the chemical composition parameters shown in Table1, and the microstructure of powder is shown in Figure 1. The powder diameter is D10: 23.48 μm, D50: 31.13 μm, and D90: 42.26 μm.Table 1
Chemical composition table of 316L stainless steel powder.
Composition (wt.%)
C
Cr
Fe
Mn
Mo
Ni
Si
P
N
S
0.01%
17.66%
Bal.
0.05%
2.40%
12.86%
0.74%
—
0.06%
0.0007%Figure 1
Powder of 316L.


### 2.2. Experimental Design

The response surface method is to study the influence of multiple factors on indicators based on both mathematics and statistics. The least square method is used to obtain the regression equation by second-order polynomial fitting, and the most suitable model is selected according to the significance test. The true functional relationship between the responseY and the independent variables ξ1, ξ2, …, ξk in the response surface method can be expressed as(1)Y=fξ1,ξ2,…,ξk+ε,where f is unknown, ξ is another variable not included in f, and ε is the error term.For second-order response surfaces, the following polynomial is used:(2)Y=b0+∑i=1kbixi+∑biixii2+∑i∑jbijxixj+ε,i≤j,where b0 is the intercept, bi, bii, and bij are the regression coefficients, and xi, xii, and xij are the horizontally encoding variables.The experimental design model of response surface method mainly includes central composite test design, BOX design, and secondary saturated D-optimal design. This study involves six factors and three levels in the BOX for experimental design.The response surface method was used to optimize the process parameters of 316L stainless steel with selective laser melting. The laser powerA, scan speed B, hatching space C, layer thickness D, the angle with the xy plane F (shown in Figure 2), and the angle with the xz plane E (shown in Figure 3) were selected. The horizontal values of each factor are shown in Table 2. The tensile specimen specifications are calculated according to ISO 6892-1: 2009, ASTM E8/8M. In this study, 316L stainless steel samples were formed with D280 (shown in Figure 4), the density of the sample Y2 was measured by the Archimedes drainage method, the surface roughness of the sample Y1 was measured with the roughness meter, and the tensile limit Y3 and the elongation rate Y4 were measured on the tensile test bench. The Archimedes principle formulas are as follows:(3)ρ2=m1m3/ρ1−m2−m1/ρ0,thenρ=ρ2/ρ3,where m1 is the mass (g) of the formed part in the air before sealing wax; m2 is the mass (g) of the formed part in the air after sealing wax; m3 is the mass (g) of the formed part in the water after sealing wax; ρ is the density (%) of the sample; ρ0 is the density of the wax, which is 0.880 g/cm3; ρ1 is the density of the distilled water, which is 1 g/cm3; ρ2 is the density (g/cm3) of the formed part; and ρ3 is the theoretical density of 316L stainless steel material, which is 7.98 g/cm3;Figure 2
Angle with thexy plane.Figure 3
Angle with thexz plane.Table 2
Factor coding and experimental level.
Code
A (W)
B (mm/s)
C (mm)
D (mm)
E (°)
F (°)
1
160
900
0.09
0.04
90
90
0
150
800
0.08
0.03
45
45
−1
140
700
0.07
0.02
0
0Figure 4
Physical image of the tensile specimen after heat treatment.To ensure the adaptability and accuracy of the model, it is necessary to evaluate the predictability. The coefficient of determinationR2 and the adjusted coefficient of determination Radj2 are often used to evaluate the approximation of the regression model [27]. The predicted coefficient of determination Rprep2 is adopted to evaluate the predictability of the regression model with the following formula:(4)R2=SSRSST=SSR−SSESST=1−∑i=1ny^−yi2∑i=1nyi−y¯2,where SST is the sum of squares; SSR is the sum of squared regression; SSE is the sum of squared residuals; y^ is the predicted value of the response surface; yi is the true value of the response at the ith observation; y¯ is the mean of the response; and n is the number of alignment runs or observations designed for the experiment. R2 is a fully fitted metric value, usually requiring a value above 0.9.Adjusted coefficient of determinationRadj2 is obtained by(5)Radj2=1−SSE/n−pSST/n−1=1−n−1n−p1−R2,where p is the number of regression coefficients in the model and Radj2 refers to the degree of correlation between all independent variables and dependent variables.Adjusted coefficient of determinationRprep2 is obtained by(6)Rpred2=1−VSST=1−∑i=1ny^i−yi2∑i=1nyi−y¯2,where V is the sum of the squares of the predicted errors; y^i is the predicted value of the response at the ith time; and Rprep2 represents the predictability based on the original regression model fitted to the data. In general, for a model with acceptable accuracy, the values of Rprep2 and R2 should be less than or equal to 0.3.


## 2.1. Experimental Equipment and Materials

In the experiment, the following products of Guangzhou Riton Laser Co., Ltd. were selected: the D280 AM machine with an accuracy of ±0.02 mm, laser wavelength of 1.064μm, focused spot diameter of 20–80 μm, and layer thickness of 20–80 μm for forming parts; WD-E stretching tester with a pressure sensor of 0–20 kN for the tensile test; KERN analytical balance ABJ 320-4NM with a range of 320 g and accuracy of 0.0001 g for quality measurement; TIME3220T roughness meter with a measurement platform size of 400 mm × 250 mm × 70 mm, lift height of 300 ±1 mm, x-direction fine tune of ±12.5 mm, y-direction fine tune of ±12.5 mm, rotating coarse tune of 360°, and fine tune of ±5° for detecting surface roughness; MQX1200-40 atmosphere box furnace with a maximum temperature of 1200° and temperature control accuracy of ±1° for heat treatment; XQ-1 metallographic specimen mounting press and YMPZ-1 automatic metallographic specimen grinding and polishing machine for metallographic preparation; EVO18 ZEISS scanning electron microscope with a magnification of 5–1,000,000x and acceleration voltage of 0.2–30 kV for microstructure observation; and SmartLab (9) X-ray diffractometer (XRD) with an X-ray generator of fine focusing 9 kW knob, X-ray generator filament of 0.4 mm × 8 mm, and goniometer minimum step size of 1/10000° for phase analysis.316L stainless steel powder (MTI S01C) is selected from Guangzhou Material Technology Innovation Co., Ltd. with the chemical composition parameters shown in Table1, and the microstructure of powder is shown in Figure 1. The powder diameter is D10: 23.48 μm, D50: 31.13 μm, and D90: 42.26 μm.Table 1
Chemical composition table of 316L stainless steel powder.
Composition (wt.%)
C
Cr
Fe
Mn
Mo
Ni
Si
P
N
S
0.01%
17.66%
Bal.
0.05%
2.40%
12.86%
0.74%
—
0.06%
0.0007%Figure 1
Powder of 316L.


## 2.2. Experimental Design

The response surface method is to study the influence of multiple factors on indicators based on both mathematics and statistics. The least square method is used to obtain the regression equation by second-order polynomial fitting, and the most suitable model is selected according to the significance test. The true functional relationship between the responseY and the independent variables ξ1, ξ2, …, ξk in the response surface method can be expressed as(1)Y=fξ1,ξ2,…,ξk+ε,where f is unknown, ξ is another variable not included in f, and ε is the error term.For second-order response surfaces, the following polynomial is used:(2)Y=b0+∑i=1kbixi+∑biixii2+∑i∑jbijxixj+ε,i≤j,where b0 is the intercept, bi, bii, and bij are the regression coefficients, and xi, xii, and xij are the horizontally encoding variables.The experimental design model of response surface method mainly includes central composite test design, BOX design, and secondary saturated D-optimal design. This study involves six factors and three levels in the BOX for experimental design.The response surface method was used to optimize the process parameters of 316L stainless steel with selective laser melting. The laser powerA, scan speed B, hatching space C, layer thickness D, the angle with the xy plane F (shown in Figure 2), and the angle with the xz plane E (shown in Figure 3) were selected. The horizontal values of each factor are shown in Table 2. The tensile specimen specifications are calculated according to ISO 6892-1: 2009, ASTM E8/8M. In this study, 316L stainless steel samples were formed with D280 (shown in Figure 4), the density of the sample Y2 was measured by the Archimedes drainage method, the surface roughness of the sample Y1 was measured with the roughness meter, and the tensile limit Y3 and the elongation rate Y4 were measured on the tensile test bench. The Archimedes principle formulas are as follows:(3)ρ2=m1m3/ρ1−m2−m1/ρ0,thenρ=ρ2/ρ3,where m1 is the mass (g) of the formed part in the air before sealing wax; m2 is the mass (g) of the formed part in the air after sealing wax; m3 is the mass (g) of the formed part in the water after sealing wax; ρ is the density (%) of the sample; ρ0 is the density of the wax, which is 0.880 g/cm3; ρ1 is the density of the distilled water, which is 1 g/cm3; ρ2 is the density (g/cm3) of the formed part; and ρ3 is the theoretical density of 316L stainless steel material, which is 7.98 g/cm3;Figure 2
Angle with thexy plane.Figure 3
Angle with thexz plane.Table 2
Factor coding and experimental level.
Code
A (W)
B (mm/s)
C (mm)
D (mm)
E (°)
F (°)
1
160
900
0.09
0.04
90
90
0
150
800
0.08
0.03
45
45
−1
140
700
0.07
0.02
0
0Figure 4
Physical image of the tensile specimen after heat treatment.To ensure the adaptability and accuracy of the model, it is necessary to evaluate the predictability. The coefficient of determinationR2 and the adjusted coefficient of determination Radj2 are often used to evaluate the approximation of the regression model [27]. The predicted coefficient of determination Rprep2 is adopted to evaluate the predictability of the regression model with the following formula:(4)R2=SSRSST=SSR−SSESST=1−∑i=1ny^−yi2∑i=1nyi−y¯2,where SST is the sum of squares; SSR is the sum of squared regression; SSE is the sum of squared residuals; y^ is the predicted value of the response surface; yi is the true value of the response at the ith observation; y¯ is the mean of the response; and n is the number of alignment runs or observations designed for the experiment. R2 is a fully fitted metric value, usually requiring a value above 0.9.Adjusted coefficient of determinationRadj2 is obtained by(5)Radj2=1−SSE/n−pSST/n−1=1−n−1n−p1−R2,where p is the number of regression coefficients in the model and Radj2 refers to the degree of correlation between all independent variables and dependent variables.Adjusted coefficient of determinationRprep2 is obtained by(6)Rpred2=1−VSST=1−∑i=1ny^i−yi2∑i=1nyi−y¯2,where V is the sum of the squares of the predicted errors; y^i is the predicted value of the response at the ith time; and Rprep2 represents the predictability based on the original regression model fitted to the data. In general, for a model with acceptable accuracy, the values of Rprep2 and R2 should be less than or equal to 0.3.


## 3. Experimental Results and Discussion

### 3.1. Analysis of Response Surface Method

Experimental analysis was performed using Design-Expert. The experimental results are shown in Table3.Table 3
Experimental results.
Exp. no.
Laser power (W)
Scanning speed (mm/s)
Scanning interval (mm)
Layer thickness (mm)
Angle with thexz plane
Angle with thexy plane
Surface roughness (μm)
Relative density (%)
Tensile strength (MPa)
Elongation rate (%)
1
140
700
0.08
0.02
45
45
4.69
87.92
543.69
23.22
2
160
700
0.08
0.02
45
45
6.46
89.59
497.90
45.00
3
140
900
0.08
0.02
45
45
4.62
96.28
507.16
38.40
4
160
900
0.08
0.02
45
45
6.99
89.19
590.96
37.62
5
140
700
0.08
0.04
45
45
8.30
86.31
171.31
2.69
6
160
700
0.08
0.04
45
45
8.87
86.25
449.16
33.63
7
140
900
0.08
0.04
45
45
8.43
75.80
52.87
1.39
8
160
900
0.08
0.04
45
45
11.25
80.07
202.25
3.21
9
150
700
0.07
0.03
0
45
13.43
85.95
313.03
6.18
10
150
900
0.07
0.03
0
45
9.53
82.10
129.84
3.11
11
150
700
0.09
0.03
0
45
9.07
82.17
211.51
3.76
12
150
900
0.09
0.03
0
45
12.44
73.83
138.42
4.42
13
150
700
0.07
0.03
90
45
11.29
86.09
217.35
3.87
14
150
900
0.07
0.03
90
45
12.06
85.89
169.67
5.71
15
150
700
0.09
0.03
90
45
13.50
82.67
116.81
3.79
16
150
900
0.09
0.03
90
45
11.00
73.41
103.16
1.12
17
150
800
0.07
0.02
45
0
10.42
89.49
553.97
29.83
18
150
800
0.09
0.02
45
0
9.72
86.52
536.03
29.28
19
150
800
0.07
0.04
45
0
25.53
73.78
340.04
16.54
20
150
800
0.09
0.04
45
0
18.02
66.18
293.15
9.73
21
150
800
0.07
0.02
45
90
6.45
88.29
457.36
48.52
22
150
800
0.09
0.02
45
90
7.90
92.08
484.48
46.72
23
150
800
0.07
0.04
45
90
5.04
89.11
233.40
6.24
24
150
800
0.09
0.04
45
90
5.64
79.47
221.49
5.11
25
140
800
0.08
0.02
0
45
7.16
90.17
546.57
51.08
26
160
800
0.08
0.02
0
45
6.03
82.10
565.66
33.21
27
140
800
0.08
0.04
0
45
12.21
83.16
72.06
2.33
28
160
800
0.08
0.04
0
45
11.51
87.64
179.40
6.48
29
140
800
0.08
0.02
90
45
5.86
93.39
540.82
23.34
30
160
800
0.08
0.02
90
45
5.97
95.04
517.92
45.01
31
140
800
0.08
0.04
90
45
11.02
73.50
90.66
2.87
32
160
800
0.08
0.04
90
45
10.03
77.03
234.72
19.33
33
150
700
0.08
0.03
0
0
20.17
90.18
419.23
19.90
34
150
900
0.08
0.03
0
0
23.38
86.38
237.74
1.67
35
150
700
0.08
0.03
90
0
17.70
79.39
550.22
16.28
36
150
900
0.08
0.03
90
0
15.21
80.95
404.71
16.19
37
150
700
0.08
0.03
0
90
5.66
90.36
365.37
13.68
38
150
900
0.08
0.03
0
90
5.38
82.70
292.86
4.97
39
150
700
0.08
0.03
90
90
4.36
90.41
330.01
11.12
40
150
900
0.08
0.03
90
90
5.38
87.71
324.01
7.74
41
140
800
0.07
0.03
45
0
16.60
79.59
421.77
21.52
42
160
800
0.07
0.03
45
0
11.52
87.11
536.21
26.19
43
140
800
0.09
0.03
45
0
14.60
79.28
512.41
20.90
44
160
800
0.09
0.03
45
0
19.87
68.65
366.55
13.09
45
140
800
0.07
0.03
45
90
4.71
88.49
327.83
8.79
46
160
800
0.07
0.03
45
90
4.76
89.06
386.66
19.23
47
140
800
0.09
0.03
45
90
4.21
85.47
266.28
2.62
48
160
800
0.09
0.03
45
90
5.59
72.59
386.67
8.83
49
150
800
0.08
0.03
45
45
9.33
89.24
181.02
8.29
50
150
800
0.08
0.03
45
45
8.87
86.38
246.68
6.62
51
150
800
0.08
0.03
45
45
10.52
79.02
195.18
6.57
52
150
800
0.08
0.03
45
45
12.64
81.20
191.50
1.59
53
150
800
0.08
0.03
45
45
10.33
82.59
152.35
3.19
54
150
800
0.08
0.03
45
45
8.95
85.10
194.44
1.69


#### 3.1.1. Analysis of Variance

The data in Table3 were treated using multivariate regression fitting to obtain the regression equations of the response surface roughness Y1, density Y2, tensile strength Y3, and elongation Y4, respectively, expressed by the laser power A, scan speed B, hatching space C, layer thickness D, the angle with the xz plane E, and the angle with xy plane F:(7)Y1=10.1+6.93×10−3B+2.23D−5.65F−3.38DF−1.67A2+1.33F2,Y2=83.92−1.791B−3.44C−5.07D+2.84F−3.94AC−3.08BD−2.25CD+2.659EF−3.458C2,Y3=193.53+5.859A−42.997B−158.41D−45.65F+40.27AD+52.73BD+84.72A2+74.16D2+156.42F2,Y4=4.65+3.82A−2.39B−14.2D−6.459AB+6.481AE−4.94BD−6.38DF+4.726A2+13.57D2+6.605F2.The response value and variance analysis are shown in Tables4–7. The p values of the four models are all less than 0.01, indicating that the selected factors in the equations are extremely significant, and p values of lack of fit are all greater than 0.05, which is not significant. For the surface roughness of the sample, the coefficient of determination R2 is 0.9158, the adjusted coefficient of determination Radj2 is 0.8283, and the predicted coefficient of determination Rprep2 is 0.5898, representing a difference of 0.326 between the coefficient of determination R2 and the predicted coefficient of determination Rprep2. For the density of the sample, the coefficient of determination R2 is 0.8961, the adjusted coefficient of determination Radj2 is 0.7881, and the predicted coefficient of determination Rprep2 is 0.5716, representing a difference of 0.3245 between the coefficient of determination R2 and the predicted coefficient of determination Rprep2. For the tensile strength, the coefficient of determination R2 is 0.937, the adjusted coefficient of determination Radj2 is 0.8715, and the predicted coefficient of determination Rprep2 is 0.6842, representing a difference of 0.2528 between the coefficient of determination R2 and the predicted coefficient of determination Rprep2. For the elongation of the sample, the coefficient of determination R2 is 0.9359, the adjusted coefficient of determination Radj2 is 0.8693, and the predicted coefficient of determination Rprep2 is 0.679, representing a difference of 0.2569 between the coefficient of determination R2 and the predicted coefficient of determination Rprep2. All the above indicates that the response surfaces of the four models have good predictability for the experimental results.Table 4
Analysis of variance of surface roughness.
Source
Sum of squares
DF
Mean square
F value
p value prob > F
Model
1172.94
27
43.44
10.47
<0.0001
A
1.71
1
1.71
0.41
0.5263
B
1.153× 10−3
1
1.153× 10−3
2.778× 10−4
0.9868
C
2.044× 10−3
1
2.044× 10−3
4.927× 10−4
0.9825
D
119.63
1
119.63
28.83
<0.0001
E
4.67
1
4.67
1.13
0.2983
F
767.11
1
767.11
184.88
<0.0001
AB
1.02
1
1.02
0.24
0.6248
AC
17.07
1
17.07
4.11
0.0529
AD
0.13
1
0.13
0.031
0.8620
AE
0.11
1
0.11
0.027
0.8698
AF
0.19
1
0.19
0.045
0.8331
BC
2.00
1
2.00
0.48
0.4934
BD
0.53
1
0.53
0.13
0.7236
BE
3.59
1
3.59
0.86
0.3610
BF
0.49
1
0.49
0.12
0.7334
CD
7.34
1
7.34
1.77
0.1949
CE
0.84
1
0.84
0.20
0.6556
CF
1.12
1
1.12
0.27
0.6076
DE
0.22
1
0.22
0.052
0.8217
DF
91.57
1
91.57
22.07
<0.0001
EF
16.06
1
16.06
3.87
0.0599
Residual
107.88
26
4.15
Lack of fit
97.78
21
4.66
2.31
0.1801
Pure error
10.10
5
2.02
Cor total
1280.82
53Table 5
Analysis of variance of density.
Source
Sum of squares
DF
Mean square
F value
p value prob > F
Model
2035.96
27
75.41
8.30
<0.0001
A
9.45
1
9.45
1.04
0.3171
B
77.01
1
77.01
8.48
0.0073
C
284.59
1
284.59
31.33
<0.0001
D
617.80
1
617.80
68.01
<0.0001
E
5.29
1
5.29
0.58
0.4524
F
193.92
1
193.92
21.35
<0.0001
AB
2.46
1
2.46
0.27
0.6071
AC
124.75
1
124.75
13.73
0.0010
AD
36.18
1
36.18
3.98
0.0565
AE
9.62
1
9.62
1.06
0.3130
AF
10.56
1
10.56
1.16
0.2907
BC
22.97
1
22.97
2.53
0.1239
BD
75.91
1
75.91
8.36
0.0077
BE
10.67
1
10.67
1.17
0.2884
BF
8.24
1
8.24
0.91
0.3497
CD
40.77
1
40.77
4.49
0.0438
CE
1.84
1
1.84
0.20
0.6560
CF
1.00
1
1.00
0.11
0.7425
DE
166.10
1
166.10
18.29
0.0002
DF
73.58
1
73.58
8.10
0.0085
EF
56.59
1
56.59
6.23
0.0192
Residual
236.18
26
9.08
Lack of fit
167.32
21
7.97
0.58
0.8281
Pure error
68.86
5
13.77
Cor total
2272.13
53Table 6
Analysis of variance of tensile strength.
Source
Sum of squares
DF
Mean square
F value
p value prob > F
Model
1.227× 106
27
45454.48
14.31
<0.0001
A
30861.77
1
30861.77
9.72
0.0044
B
44371.38
1
44371.38
13.97
0.0009
C
8444.14
1
8444.14
2.66
0.1150
D
6.023× 105
1
6.023× 105
189.67
<0.0001
E
686.54
1
686.54
0.22
0.6458
F
50015.45
1
50015.45
15.75
0.0005
AB
0.16
1
0.16
4.947× 10−5
0.9944
AC
4936.40
1
4936.40
1.55
0.2236
AD
25955.86
1
25955.86
8.17
0.0083
AE
3.46
1
3.46
1.089× 10−3
0.9739
AF
5545.85
1
5545.85
1.75
0.1978
BC
2596.73
1
2596.73
0.82
0.3741
BD
22248.05
1
22248.05
7.01
0.0136
BE
5530.04
1
5530.04
1.74
0.1985
BF
7718.38
1
7718.38
2.43
0.1311
CD
577.70
1
577.70
0.18
0.6732
CE
686.80
1
686.80
0.22
0.6458
CF
594.23
1
594.23
0.19
0.6689
DE
2029.53
1
2029.53
0.64
0.4313
DF
113.57
1
113.57
0.036
0.8515
EF
11412.79
1
11412.79
3.59
0.0692
Residual
82562.08
26
3175.46
Lack of fit
77877.06
21
3708.43
3.96
0.0663
Pure error
4685.02
5
937.00
Cor total
1.310× 106
53Table 7
Analysis of variance of elongation.
Source
Sum of squares
DF
Mean square
F value
p value prob > F
Model
10386.66
27
384.69
14.05
<0.0001
A
350.33
1
350.33
12.80
0.0014
B
138.03
1
138.03
5.04
0.0335
C
89.58
1
89.58
3.27
0.0820
D
4864.16
1
4864.16
177.70
<0.0001
E
1.30
1
1.30
0.048
0.8289
F
58.73
1
58.73
2.15
0.1550
AB
333.82
1
333.82
12.20
0.0017
AC
34.91
1
34.91
1.28
0.2691
AD
51.06
1
51.06
1.87
0.1837
AE
336.05
1
336.05
12.28
0.0017
AF
49.00
1
49.00
1.79
0.1925
BC
0.076
1
0.076
2.762× 10−3
0.9585
BD
195.25
1
195.25
7.13
0.0129
BE
39.24
1
39.24
1.43
0.2420
BF
4.86
1
4.86
0.18
0.6771
CD
3.90
1
3.90
0.14
0.7087
CE
1.58
1
1.58
0.058
0.8120
CF
0.16
1
0.16
5.684× 10−3
0.9405
DE
107.43
1
107.43
3.92
0.0582
DF
325.69
1
325.69
11.90
0.0019
EF
14.25
1
14.25
0.52
0.4770
Residual
711.70
26
27.37
Lack of fit
670.62
21
31.93
3.89
0.0687
Pure error
41.08
5
8.22
Cor total
11098.36
53The relationships between the actual values of surface roughness, density, tensile strength, and elongation and the predicted values of the regression models are shown in Figure5. As shown in Figure 5, the actual values are basically distributed on the predicted curves and the actual values are consistent with the trend of the predicted values, showing linear distribution. In general, the models verify the experimental data accurately, so the models can predict and analyze the effect of various factors on the indexes.Figure 5
Scatter plot: predicted values of (a) surface roughness, (b) density, (c) tensile strength, and (d) elongation.
(a)
(b)
(c)
(d)Within the horizontal range of the selected factors, the weight of effect on the surface roughness according to the F value of each factor is the angle with thexy plane > layer thickness > the angle with the xz plane > laser power>hatching space > scan speed; the weight of effect on the density is layer thickness > hatching space > the angle with the xy plane > scan speed > laser power > the angle with the xz plane; the weight of effect on tensile strength is layer thickness > the angle with the xy plane > scan speed > laser power > hatching space > the angle with the xz plane; and the weight of effect on elongation is layer thickness > laser power > scan speed > hatching space > the angle with the xy plane > the angle with the xz plane.


#### 3.1.2. Analysis of Multivariate Interactive Influence

When laser power, scan speed, hatching space, and the angle with thexz plane are constant, it can be seen from Figure 6 that when the angle with the xy plane is 0°, the surface roughness increases as the layer thickness increases, reaches the peak as the layer thickness further increases, and then decreases as the layer thickness continues to increase; when the layer thickness is constant, the surface roughness decreases as the angle with the xy plane increases.Figure 6
Effect of layer thickness and the angle with thexy plane on surface roughness.As shown in Figure7(a), when both laser power and scan speed increase, the density first increases and then decreases. When the laser power is 160 W and the hatching space is 0.07 mm, the density reaches the peak; when the hatching space ranges from 0.07 to 0.08 mm, the density increases as the laser power increases; and when the hatching space ranges from 0.08 to 0.09 mm, the density decreases as the laser power increases. As shown in Figure 7(b), when the layer thickness is constant, the density decreases as the scan speed increases; and when the scan speed is constant, the density increases as the layer thickness increases. As shown in Figure 7(c), when the layer thickness is 0.02 mm, the density increases first and then decreases as the hatching space increases; and when the scan speed is 0.09 mm/s, the density decreases at the fastest rate as the layer thickness increases. As shown in Figure 7(d), when the angle with the xy plane is constant, the density decreases as the layer thickness increases; when the angle with the xy plane is 0°, the density decreases at the fastest rate; when the layer thickness is constant, the density increases as the angle with the xy plane increases, and when the layer thickness is 0.04 mm, the density increases at the fastest rate as the angle with the xy plane increases. As shown in Figure 7(e), when the layer thickness is 0.02 mm, the density increases as the angle with the xz plane increases, reaching the maximum value, but the trend of density changes as the layer thickness further increases, and when layer thickness is above 0.02 mm, the density decreases as the angle with the xz plane increases. As shown in Figure 7(f), when the angle with the xy plane ranges from 0° to 50°, the density decreases as the angle with the xz plane increases, and when the angle with the xy plane ranges from 50° to 90°, the density increases as the angle with the xz plane increases.Figure 7
Effect of laser power, scan speed, scan spacing, layer thickness, angle with thexz plane, and angle with the xy plane on density. (a) Effect of interaction of laser power and scan spacing on density. (b) Effect of interaction of scan speed and layer thickness on density. (c) Effect of interaction of scan spacing and layer thickness on density. (d) Effect of interaction of angle with the xy plane and layer thickness on density. (e) Effect of interaction of angle with the xz plane and layer thickness on density. (f) Effect of interaction of angle with the xy plane and angle with the xz plane on density.
(a)
(b)
(c)
(d)
(e)
(f)As shown in Figure8(a), when the laser power is constant, the tensile strength decreases as the layer thickness increases; when the laser power is 140 W, the tensile strength decreases at the fastest rate; when the laser power is 160 W, the tensile strength decreases at the slowest rate; and when the layer thickness is constant, the tensile strength increases as the laser power increases. As shown in Figure 8(b), when the layer thickness is constant, the tensile strength decreases as the scan speed increases; when the layer thickness is 0.04 mm, the tensile strength decreases at the fastest rate; when the scan speed is constant, the tensile strength decreases as the layer thickness increases; and when the scan speed is 900 mm/s, the tensile strength decreases at the fastest rate.Figure 8
Effect of laser power, scan speed, and layer thickness on tensile strength. (a) Effect of interaction of laser power and layer thickness on tensile strength. (b) Effect of interaction of scan speed and layer thickness on tensile strength.
(a)
(b)As shown in Figure9(a), when the scan speed ranges from 700 to 760 mm/s, the elongation increases as the laser power increases; when the scan speed ranges from 760 to 900 mm/s, the elongation first decreases and then increases as the laser power increases; when the laser power ranges from 140 to 148 W, the elongation increases as the scan speed increases; when the laser power ranges from 148 to 160 W, the elongation decreases first and then increases as the scan speed increases; and at the minimum scan speed and the maximum laser power, the elongation reaches the maximum value. As shown in Figure 9(b), when the angle with the xz plane ranges from 0° to 50°, the elongation decreases first and then increases as the laser power increases; when the angle with the xz plane ranges from 50° to 90°, the elongation increases as the laser power increases; when the laser power ranges from 140 to 150 W, the elongation decreases as the angle with the xz plane increases; and when the laser power ranges from 150 to 160 W, the elongation increases as the angle with xz plane increases, reaching the maximum value together with the angle with the xz plane, laser power, and elongation. As shown in Figure 9(c), when the scan speed ranges from 700 to 800 mm/s, the elongation decreases first and then increases as the layer thickness increases; when the scan speed ranges from 800 to 900 mm/s, the elongation decreases as the layer thickness increases; when the layer thickness ranges from 0.02 to 0.03 mm, the elongation does not change significantly as the scan speed increases; and when the layer thickness ranges from 0.03 to 0.04 mm, the elongation decreases as the scan speed increases, and the maximum elongation is obtained from the minimum layer thickness and maximum scan speed. As shown in Figure 9(d), when the angle with the xy plane is constant, the elongation decreases rapidly first and then increases slowly as the layer thickness increases; when the layer thickness ranges from 0.02 to 0.023 mm, the elongation increases as the angle with the xy plane increases; and when the layer thickness ranges from 0.024 to 0.04 mm, the elongation decreases first and then increases as the angle with the xy plane increases.Figure 9
Effect of laser power, scan speed, scan spacing, layer thickness, angle withxz plane, and angle with xy plane on elongation. (a) Effect of interaction of scan speed and laser power on elongation. (b) Effect of interaction of angle with the xz plane and laser power on elongation. (c) Effect of interaction of scan speed and layer thickness on elongation. (d) Effect of interaction of angle with the xy plane and layer thickness on elongation.
(a)
(b)
(c)
(d)


#### 3.1.3. Optimization of Process Parameters

Based on the above experiments, the predicted and actual optimization results are shown in Table8 and formula (8). The error between the predicted and actual values of the surface roughness under optimized conditions is 4.6%, the error between the predicted and actual values of the density is 1%, the error between the predicted and actual values of the tensile strength is 19.5%, and the error between the predicted and actual values of the elongation is 18.9%. All errors are within the reasonable range, indicating that the results are reliable. The tensile strength and elongation of the formed parts with the optimal parameters are higher than that specified in ASTM-A182 and ASTM-F3184-16.(8)140≤A≤160,700≤B≤900,0.07≤C≤0.09,0.02≤D≤0.04,0≤E≤90,0≤F≤9,y1=f1A,B,C,D,E,F,minY1,maxY2,maxY3,maxY4.Table 8
Predicted and actual results under optimized conditions.
Exp. no.
Laser power (W)
Scanning speed (mm/s)
Scanning interval (mm)
Layer thickness (mm)
Angle with thexz plane
Angle with thexy plane
Surface roughness (μm)
Relative density (%)
Tensile strength (MPa)
Elongation rate (%)
Predicted values
160
836
0.07
0.02
83.3
89.7
4.1
97.27
609.5
55.9
Actual value
160
836
0.07
0.02
83.3
89.7
4.3
96.3
510
47
Relative error
4.6%
1%
19.5%
18.9%


### 3.2. Microstructure and Fracture Morphology Analysis

#### 3.2.1. Microstructure Analysis

As shown in Figure10(a), the microstructure of the selective laser melting sample before stretching is mainly composed of a plurality of oval molten pools, each of which has an aspect ratio of 0.5–0.65. This study suggests that there is certain unevenness in the powder size, a difference in laser energy absorption, and a Gaussian distribution of laser energy, which helps shape the oval molten pools due to different energy densities in various areas. Figure 10(b) shows the shape of the molten pools after stretching. Compared with Figure 10(a), the molten pools of the parts are obviously elongated after stretching with an aspect ratio of 2-1.5, or 2–4 times of that before stretching. Figures 10(c) and 10(d) show the microstructure before stretching. It can be seen from Figures 10(c) and 10(d) that the inside of the molten pool is mainly composed of equiaxed crystals and columnar crystals. The grain sizes are fine with a width of 0.28–0.4 nm, of which, the secondary arm of the columnar crystal is not developed and the morphology of the dendrites is not significant, with obvious planar crystals at the junction of the layers. The columnar crystals in the microstructure show apparent epitaxial growth characteristics because the laser melting process is at a high temperature gradient and solidification rate, while forming material and substrate temperature are lower, generally lower than the forming temperature by several orders of magnitude, resulting in heat transfer from the processing layer to the formed layer from top to bottom. The solidification direction inside the molten pool is from the bottom to the top of the molten pool, with solidification conditions in the growth range of equiaxed crystals and columnar crystals. Due to the rapid condensation of the laser, the bottom of the molten pool is closest to the formed layer with fastest solidification. The crystal grains at the bottom of the molten pool are solidified without growing, so equiaxed crystals appear at the bottom and boundary of the molten pool in the form of relatively fine grains, showing a planar crystal with white and bright layers of microstructure.Figure 10
Microstructure. (a) Molten pool before stretching. (b) Molten pool after stretching. (c) Microstructure in molten pool. (d) Partial enlargement of microstructure in molten pool.
(a)
(b)
(c)
(d)


#### 3.2.2. Hardness Analysis

The microhardness of the experiment is shown in Figure11. The distance closest to the fracture is set as 0, and three points are selected at each distance to obtain the average. As shown in Figure 11, the microhardness of the sample increases first and then decreases with the increase in the distance. The average microhardness at 2.5 mm from the fracture is 28.73 HRC, and the average microhardness at 20 mm from the fracture is 25.23 HRC, which is 87% of the hardness at the fracture. The microhardness at the fracture is significantly higher than the substrate because the fracture has a large number of dislocations, and dislocation multiplication and increased surface energy help improve the hardness.Figure 11
Microhardness. (a) Hardness curve. (b) Hardness physical image.
(a)
(b)


#### 3.2.3. XRD Analysis

The XRD of the sample formed by optimizing the parameters is shown in Figure12. Compared with the standard map, the diffraction peak intensity of the crystal planes increases at γ-Fe (111), and the diffraction peak intensity of the crystal planes decreases at γ-Fe (200) and γ-Fe (220), showing that the γ-Fe crystallinity is not as good as the standard map. When the diffraction angle ranges from 40° to 45°, a significant diffraction peak broadening occurs. The diffraction peak broadening is determined by two physical factors, grain refinement and crystal microscopic distortion.Figure 12
XRD.


#### 3.2.4. Fracture Analysis

The fracture morphology is shown in Figure13. As shown in Figure 13(a), there are a large number of clear dimples whose shapes have obvious tearing, called elongated dimples, and the specimen fracture is a typical plastic fracture. Figure 13(b) shows fracture cracks passing through the grains, which is known as a transgranular fracture, and there are many dimples in the fracture, which is a ductile fracture. The specimen fracture is mainly caused by a large amount of dislocation multiplication under tensile stress with increased grain boundary energy, and a great quantity of impurities in the material are broken to form a plenty of micropores. The micropores further grow under external force to generate cracks until the final failure.Figure 13
Fracture morphology. (a) Dimple morphology. (b) Crack.
(a)
(b)


## 3.1. Analysis of Response Surface Method

Experimental analysis was performed using Design-Expert. The experimental results are shown in Table3.Table 3
Experimental results.
Exp. no.
Laser power (W)
Scanning speed (mm/s)
Scanning interval (mm)
Layer thickness (mm)
Angle with thexz plane
Angle with thexy plane
Surface roughness (μm)
Relative density (%)
Tensile strength (MPa)
Elongation rate (%)
1
140
700
0.08
0.02
45
45
4.69
87.92
543.69
23.22
2
160
700
0.08
0.02
45
45
6.46
89.59
497.90
45.00
3
140
900
0.08
0.02
45
45
4.62
96.28
507.16
38.40
4
160
900
0.08
0.02
45
45
6.99
89.19
590.96
37.62
5
140
700
0.08
0.04
45
45
8.30
86.31
171.31
2.69
6
160
700
0.08
0.04
45
45
8.87
86.25
449.16
33.63
7
140
900
0.08
0.04
45
45
8.43
75.80
52.87
1.39
8
160
900
0.08
0.04
45
45
11.25
80.07
202.25
3.21
9
150
700
0.07
0.03
0
45
13.43
85.95
313.03
6.18
10
150
900
0.07
0.03
0
45
9.53
82.10
129.84
3.11
11
150
700
0.09
0.03
0
45
9.07
82.17
211.51
3.76
12
150
900
0.09
0.03
0
45
12.44
73.83
138.42
4.42
13
150
700
0.07
0.03
90
45
11.29
86.09
217.35
3.87
14
150
900
0.07
0.03
90
45
12.06
85.89
169.67
5.71
15
150
700
0.09
0.03
90
45
13.50
82.67
116.81
3.79
16
150
900
0.09
0.03
90
45
11.00
73.41
103.16
1.12
17
150
800
0.07
0.02
45
0
10.42
89.49
553.97
29.83
18
150
800
0.09
0.02
45
0
9.72
86.52
536.03
29.28
19
150
800
0.07
0.04
45
0
25.53
73.78
340.04
16.54
20
150
800
0.09
0.04
45
0
18.02
66.18
293.15
9.73
21
150
800
0.07
0.02
45
90
6.45
88.29
457.36
48.52
22
150
800
0.09
0.02
45
90
7.90
92.08
484.48
46.72
23
150
800
0.07
0.04
45
90
5.04
89.11
233.40
6.24
24
150
800
0.09
0.04
45
90
5.64
79.47
221.49
5.11
25
140
800
0.08
0.02
0
45
7.16
90.17
546.57
51.08
26
160
800
0.08
0.02
0
45
6.03
82.10
565.66
33.21
27
140
800
0.08
0.04
0
45
12.21
83.16
72.06
2.33
28
160
800
0.08
0.04
0
45
11.51
87.64
179.40
6.48
29
140
800
0.08
0.02
90
45
5.86
93.39
540.82
23.34
30
160
800
0.08
0.02
90
45
5.97
95.04
517.92
45.01
31
140
800
0.08
0.04
90
45
11.02
73.50
90.66
2.87
32
160
800
0.08
0.04
90
45
10.03
77.03
234.72
19.33
33
150
700
0.08
0.03
0
0
20.17
90.18
419.23
19.90
34
150
900
0.08
0.03
0
0
23.38
86.38
237.74
1.67
35
150
700
0.08
0.03
90
0
17.70
79.39
550.22
16.28
36
150
900
0.08
0.03
90
0
15.21
80.95
404.71
16.19
37
150
700
0.08
0.03
0
90
5.66
90.36
365.37
13.68
38
150
900
0.08
0.03
0
90
5.38
82.70
292.86
4.97
39
150
700
0.08
0.03
90
90
4.36
90.41
330.01
11.12
40
150
900
0.08
0.03
90
90
5.38
87.71
324.01
7.74
41
140
800
0.07
0.03
45
0
16.60
79.59
421.77
21.52
42
160
800
0.07
0.03
45
0
11.52
87.11
536.21
26.19
43
140
800
0.09
0.03
45
0
14.60
79.28
512.41
20.90
44
160
800
0.09
0.03
45
0
19.87
68.65
366.55
13.09
45
140
800
0.07
0.03
45
90
4.71
88.49
327.83
8.79
46
160
800
0.07
0.03
45
90
4.76
89.06
386.66
19.23
47
140
800
0.09
0.03
45
90
4.21
85.47
266.28
2.62
48
160
800
0.09
0.03
45
90
5.59
72.59
386.67
8.83
49
150
800
0.08
0.03
45
45
9.33
89.24
181.02
8.29
50
150
800
0.08
0.03
45
45
8.87
86.38
246.68
6.62
51
150
800
0.08
0.03
45
45
10.52
79.02
195.18
6.57
52
150
800
0.08
0.03
45
45
12.64
81.20
191.50
1.59
53
150
800
0.08
0.03
45
45
10.33
82.59
152.35
3.19
54
150
800
0.08
0.03
45
45
8.95
85.10
194.44
1.69


### 3.1.1. Analysis of Variance

The data in Table3 were treated using multivariate regression fitting to obtain the regression equations of the response surface roughness Y1, density Y2, tensile strength Y3, and elongation Y4, respectively, expressed by the laser power A, scan speed B, hatching space C, layer thickness D, the angle with the xz plane E, and the angle with xy plane F:(7)Y1=10.1+6.93×10−3B+2.23D−5.65F−3.38DF−1.67A2+1.33F2,Y2=83.92−1.791B−3.44C−5.07D+2.84F−3.94AC−3.08BD−2.25CD+2.659EF−3.458C2,Y3=193.53+5.859A−42.997B−158.41D−45.65F+40.27AD+52.73BD+84.72A2+74.16D2+156.42F2,Y4=4.65+3.82A−2.39B−14.2D−6.459AB+6.481AE−4.94BD−6.38DF+4.726A2+13.57D2+6.605F2.The response value and variance analysis are shown in Tables4–7. The p values of the four models are all less than 0.01, indicating that the selected factors in the equations are extremely significant, and p values of lack of fit are all greater than 0.05, which is not significant. For the surface roughness of the sample, the coefficient of determination R2 is 0.9158, the adjusted coefficient of determination Radj2 is 0.8283, and the predicted coefficient of determination Rprep2 is 0.5898, representing a difference of 0.326 between the coefficient of determination R2 and the predicted coefficient of determination Rprep2. For the density of the sample, the coefficient of determination R2 is 0.8961, the adjusted coefficient of determination Radj2 is 0.7881, and the predicted coefficient of determination Rprep2 is 0.5716, representing a difference of 0.3245 between the coefficient of determination R2 and the predicted coefficient of determination Rprep2. For the tensile strength, the coefficient of determination R2 is 0.937, the adjusted coefficient of determination Radj2 is 0.8715, and the predicted coefficient of determination Rprep2 is 0.6842, representing a difference of 0.2528 between the coefficient of determination R2 and the predicted coefficient of determination Rprep2. For the elongation of the sample, the coefficient of determination R2 is 0.9359, the adjusted coefficient of determination Radj2 is 0.8693, and the predicted coefficient of determination Rprep2 is 0.679, representing a difference of 0.2569 between the coefficient of determination R2 and the predicted coefficient of determination Rprep2. All the above indicates that the response surfaces of the four models have good predictability for the experimental results.Table 4
Analysis of variance of surface roughness.
Source
Sum of squares
DF
Mean square
F value
p value prob > F
Model
1172.94
27
43.44
10.47
<0.0001
A
1.71
1
1.71
0.41
0.5263
B
1.153× 10−3
1
1.153× 10−3
2.778× 10−4
0.9868
C
2.044× 10−3
1
2.044× 10−3
4.927× 10−4
0.9825
D
119.63
1
119.63
28.83
<0.0001
E
4.67
1
4.67
1.13
0.2983
F
767.11
1
767.11
184.88
<0.0001
AB
1.02
1
1.02
0.24
0.6248
AC
17.07
1
17.07
4.11
0.0529
AD
0.13
1
0.13
0.031
0.8620
AE
0.11
1
0.11
0.027
0.8698
AF
0.19
1
0.19
0.045
0.8331
BC
2.00
1
2.00
0.48
0.4934
BD
0.53
1
0.53
0.13
0.7236
BE
3.59
1
3.59
0.86
0.3610
BF
0.49
1
0.49
0.12
0.7334
CD
7.34
1
7.34
1.77
0.1949
CE
0.84
1
0.84
0.20
0.6556
CF
1.12
1
1.12
0.27
0.6076
DE
0.22
1
0.22
0.052
0.8217
DF
91.57
1
91.57
22.07
<0.0001
EF
16.06
1
16.06
3.87
0.0599
Residual
107.88
26
4.15
Lack of fit
97.78
21
4.66
2.31
0.1801
Pure error
10.10
5
2.02
Cor total
1280.82
53Table 5
Analysis of variance of density.
Source
Sum of squares
DF
Mean square
F value
p value prob > F
Model
2035.96
27
75.41
8.30
<0.0001
A
9.45
1
9.45
1.04
0.3171
B
77.01
1
77.01
8.48
0.0073
C
284.59
1
284.59
31.33
<0.0001
D
617.80
1
617.80
68.01
<0.0001
E
5.29
1
5.29
0.58
0.4524
F
193.92
1
193.92
21.35
<0.0001
AB
2.46
1
2.46
0.27
0.6071
AC
124.75
1
124.75
13.73
0.0010
AD
36.18
1
36.18
3.98
0.0565
AE
9.62
1
9.62
1.06
0.3130
AF
10.56
1
10.56
1.16
0.2907
BC
22.97
1
22.97
2.53
0.1239
BD
75.91
1
75.91
8.36
0.0077
BE
10.67
1
10.67
1.17
0.2884
BF
8.24
1
8.24
0.91
0.3497
CD
40.77
1
40.77
4.49
0.0438
CE
1.84
1
1.84
0.20
0.6560
CF
1.00
1
1.00
0.11
0.7425
DE
166.10
1
166.10
18.29
0.0002
DF
73.58
1
73.58
8.10
0.0085
EF
56.59
1
56.59
6.23
0.0192
Residual
236.18
26
9.08
Lack of fit
167.32
21
7.97
0.58
0.8281
Pure error
68.86
5
13.77
Cor total
2272.13
53Table 6
Analysis of variance of tensile strength.
Source
Sum of squares
DF
Mean square
F value
p value prob > F
Model
1.227× 106
27
45454.48
14.31
<0.0001
A
30861.77
1
30861.77
9.72
0.0044
B
44371.38
1
44371.38
13.97
0.0009
C
8444.14
1
8444.14
2.66
0.1150
D
6.023× 105
1
6.023× 105
189.67
<0.0001
E
686.54
1
686.54
0.22
0.6458
F
50015.45
1
50015.45
15.75
0.0005
AB
0.16
1
0.16
4.947× 10−5
0.9944
AC
4936.40
1
4936.40
1.55
0.2236
AD
25955.86
1
25955.86
8.17
0.0083
AE
3.46
1
3.46
1.089× 10−3
0.9739
AF
5545.85
1
5545.85
1.75
0.1978
BC
2596.73
1
2596.73
0.82
0.3741
BD
22248.05
1
22248.05
7.01
0.0136
BE
5530.04
1
5530.04
1.74
0.1985
BF
7718.38
1
7718.38
2.43
0.1311
CD
577.70
1
577.70
0.18
0.6732
CE
686.80
1
686.80
0.22
0.6458
CF
594.23
1
594.23
0.19
0.6689
DE
2029.53
1
2029.53
0.64
0.4313
DF
113.57
1
113.57
0.036
0.8515
EF
11412.79
1
11412.79
3.59
0.0692
Residual
82562.08
26
3175.46
Lack of fit
77877.06
21
3708.43
3.96
0.0663
Pure error
4685.02
5
937.00
Cor total
1.310× 106
53Table 7
Analysis of variance of elongation.
Source
Sum of squares
DF
Mean square
F value
p value prob > F
Model
10386.66
27
384.69
14.05
<0.0001
A
350.33
1
350.33
12.80
0.0014
B
138.03
1
138.03
5.04
0.0335
C
89.58
1
89.58
3.27
0.0820
D
4864.16
1
4864.16
177.70
<0.0001
E
1.30
1
1.30
0.048
0.8289
F
58.73
1
58.73
2.15
0.1550
AB
333.82
1
333.82
12.20
0.0017
AC
34.91
1
34.91
1.28
0.2691
AD
51.06
1
51.06
1.87
0.1837
AE
336.05
1
336.05
12.28
0.0017
AF
49.00
1
49.00
1.79
0.1925
BC
0.076
1
0.076
2.762× 10−3
0.9585
BD
195.25
1
195.25
7.13
0.0129
BE
39.24
1
39.24
1.43
0.2420
BF
4.86
1
4.86
0.18
0.6771
CD
3.90
1
3.90
0.14
0.7087
CE
1.58
1
1.58
0.058
0.8120
CF
0.16
1
0.16
5.684× 10−3
0.9405
DE
107.43
1
107.43
3.92
0.0582
DF
325.69
1
325.69
11.90
0.0019
EF
14.25
1
14.25
0.52
0.4770
Residual
711.70
26
27.37
Lack of fit
670.62
21
31.93
3.89
0.0687
Pure error
41.08
5
8.22
Cor total
11098.36
53The relationships between the actual values of surface roughness, density, tensile strength, and elongation and the predicted values of the regression models are shown in Figure5. As shown in Figure 5, the actual values are basically distributed on the predicted curves and the actual values are consistent with the trend of the predicted values, showing linear distribution. In general, the models verify the experimental data accurately, so the models can predict and analyze the effect of various factors on the indexes.Figure 5
Scatter plot: predicted values of (a) surface roughness, (b) density, (c) tensile strength, and (d) elongation.
(a)
(b)
(c)
(d)Within the horizontal range of the selected factors, the weight of effect on the surface roughness according to the F value of each factor is the angle with thexy plane > layer thickness > the angle with the xz plane > laser power>hatching space > scan speed; the weight of effect on the density is layer thickness > hatching space > the angle with the xy plane > scan speed > laser power > the angle with the xz plane; the weight of effect on tensile strength is layer thickness > the angle with the xy plane > scan speed > laser power > hatching space > the angle with the xz plane; and the weight of effect on elongation is layer thickness > laser power > scan speed > hatching space > the angle with the xy plane > the angle with the xz plane.


### 3.1.2. Analysis of Multivariate Interactive Influence

When laser power, scan speed, hatching space, and the angle with thexz plane are constant, it can be seen from Figure 6 that when the angle with the xy plane is 0°, the surface roughness increases as the layer thickness increases, reaches the peak as the layer thickness further increases, and then decreases as the layer thickness continues to increase; when the layer thickness is constant, the surface roughness decreases as the angle with the xy plane increases.Figure 6
Effect of layer thickness and the angle with thexy plane on surface roughness.As shown in Figure7(a), when both laser power and scan speed increase, the density first increases and then decreases. When the laser power is 160 W and the hatching space is 0.07 mm, the density reaches the peak; when the hatching space ranges from 0.07 to 0.08 mm, the density increases as the laser power increases; and when the hatching space ranges from 0.08 to 0.09 mm, the density decreases as the laser power increases. As shown in Figure 7(b), when the layer thickness is constant, the density decreases as the scan speed increases; and when the scan speed is constant, the density increases as the layer thickness increases. As shown in Figure 7(c), when the layer thickness is 0.02 mm, the density increases first and then decreases as the hatching space increases; and when the scan speed is 0.09 mm/s, the density decreases at the fastest rate as the layer thickness increases. As shown in Figure 7(d), when the angle with the xy plane is constant, the density decreases as the layer thickness increases; when the angle with the xy plane is 0°, the density decreases at the fastest rate; when the layer thickness is constant, the density increases as the angle with the xy plane increases, and when the layer thickness is 0.04 mm, the density increases at the fastest rate as the angle with the xy plane increases. As shown in Figure 7(e), when the layer thickness is 0.02 mm, the density increases as the angle with the xz plane increases, reaching the maximum value, but the trend of density changes as the layer thickness further increases, and when layer thickness is above 0.02 mm, the density decreases as the angle with the xz plane increases. As shown in Figure 7(f), when the angle with the xy plane ranges from 0° to 50°, the density decreases as the angle with the xz plane increases, and when the angle with the xy plane ranges from 50° to 90°, the density increases as the angle with the xz plane increases.Figure 7
Effect of laser power, scan speed, scan spacing, layer thickness, angle with thexz plane, and angle with the xy plane on density. (a) Effect of interaction of laser power and scan spacing on density. (b) Effect of interaction of scan speed and layer thickness on density. (c) Effect of interaction of scan spacing and layer thickness on density. (d) Effect of interaction of angle with the xy plane and layer thickness on density. (e) Effect of interaction of angle with the xz plane and layer thickness on density. (f) Effect of interaction of angle with the xy plane and angle with the xz plane on density.
(a)
(b)
(c)
(d)
(e)
(f)As shown in Figure8(a), when the laser power is constant, the tensile strength decreases as the layer thickness increases; when the laser power is 140 W, the tensile strength decreases at the fastest rate; when the laser power is 160 W, the tensile strength decreases at the slowest rate; and when the layer thickness is constant, the tensile strength increases as the laser power increases. As shown in Figure 8(b), when the layer thickness is constant, the tensile strength decreases as the scan speed increases; when the layer thickness is 0.04 mm, the tensile strength decreases at the fastest rate; when the scan speed is constant, the tensile strength decreases as the layer thickness increases; and when the scan speed is 900 mm/s, the tensile strength decreases at the fastest rate.Figure 8
Effect of laser power, scan speed, and layer thickness on tensile strength. (a) Effect of interaction of laser power and layer thickness on tensile strength. (b) Effect of interaction of scan speed and layer thickness on tensile strength.
(a)
(b)As shown in Figure9(a), when the scan speed ranges from 700 to 760 mm/s, the elongation increases as the laser power increases; when the scan speed ranges from 760 to 900 mm/s, the elongation first decreases and then increases as the laser power increases; when the laser power ranges from 140 to 148 W, the elongation increases as the scan speed increases; when the laser power ranges from 148 to 160 W, the elongation decreases first and then increases as the scan speed increases; and at the minimum scan speed and the maximum laser power, the elongation reaches the maximum value. As shown in Figure 9(b), when the angle with the xz plane ranges from 0° to 50°, the elongation decreases first and then increases as the laser power increases; when the angle with the xz plane ranges from 50° to 90°, the elongation increases as the laser power increases; when the laser power ranges from 140 to 150 W, the elongation decreases as the angle with the xz plane increases; and when the laser power ranges from 150 to 160 W, the elongation increases as the angle with xz plane increases, reaching the maximum value together with the angle with the xz plane, laser power, and elongation. As shown in Figure 9(c), when the scan speed ranges from 700 to 800 mm/s, the elongation decreases first and then increases as the layer thickness increases; when the scan speed ranges from 800 to 900 mm/s, the elongation decreases as the layer thickness increases; when the layer thickness ranges from 0.02 to 0.03 mm, the elongation does not change significantly as the scan speed increases; and when the layer thickness ranges from 0.03 to 0.04 mm, the elongation decreases as the scan speed increases, and the maximum elongation is obtained from the minimum layer thickness and maximum scan speed. As shown in Figure 9(d), when the angle with the xy plane is constant, the elongation decreases rapidly first and then increases slowly as the layer thickness increases; when the layer thickness ranges from 0.02 to 0.023 mm, the elongation increases as the angle with the xy plane increases; and when the layer thickness ranges from 0.024 to 0.04 mm, the elongation decreases first and then increases as the angle with the xy plane increases.Figure 9
Effect of laser power, scan speed, scan spacing, layer thickness, angle withxz plane, and angle with xy plane on elongation. (a) Effect of interaction of scan speed and laser power on elongation. (b) Effect of interaction of angle with the xz plane and laser power on elongation. (c) Effect of interaction of scan speed and layer thickness on elongation. (d) Effect of interaction of angle with the xy plane and layer thickness on elongation.
(a)
(b)
(c)
(d)


### 3.1.3. Optimization of Process Parameters

Based on the above experiments, the predicted and actual optimization results are shown in Table8 and formula (8). The error between the predicted and actual values of the surface roughness under optimized conditions is 4.6%, the error between the predicted and actual values of the density is 1%, the error between the predicted and actual values of the tensile strength is 19.5%, and the error between the predicted and actual values of the elongation is 18.9%. All errors are within the reasonable range, indicating that the results are reliable. The tensile strength and elongation of the formed parts with the optimal parameters are higher than that specified in ASTM-A182 and ASTM-F3184-16.(8)140≤A≤160,700≤B≤900,0.07≤C≤0.09,0.02≤D≤0.04,0≤E≤90,0≤F≤9,y1=f1A,B,C,D,E,F,minY1,maxY2,maxY3,maxY4.Table 8
Predicted and actual results under optimized conditions.
Exp. no.
Laser power (W)
Scanning speed (mm/s)
Scanning interval (mm)
Layer thickness (mm)
Angle with thexz plane
Angle with thexy plane
Surface roughness (μm)
Relative density (%)
Tensile strength (MPa)
Elongation rate (%)
Predicted values
160
836
0.07
0.02
83.3
89.7
4.1
97.27
609.5
55.9
Actual value
160
836
0.07
0.02
83.3
89.7
4.3
96.3
510
47
Relative error
4.6%
1%
19.5%
18.9%


## 3.1.1. Analysis of Variance

The data in Table3 were treated using multivariate regression fitting to obtain the regression equations of the response surface roughness Y1, density Y2, tensile strength Y3, and elongation Y4, respectively, expressed by the laser power A, scan speed B, hatching space C, layer thickness D, the angle with the xz plane E, and the angle with xy plane F:(7)Y1=10.1+6.93×10−3B+2.23D−5.65F−3.38DF−1.67A2+1.33F2,Y2=83.92−1.791B−3.44C−5.07D+2.84F−3.94AC−3.08BD−2.25CD+2.659EF−3.458C2,Y3=193.53+5.859A−42.997B−158.41D−45.65F+40.27AD+52.73BD+84.72A2+74.16D2+156.42F2,Y4=4.65+3.82A−2.39B−14.2D−6.459AB+6.481AE−4.94BD−6.38DF+4.726A2+13.57D2+6.605F2.The response value and variance analysis are shown in Tables4–7. The p values of the four models are all less than 0.01, indicating that the selected factors in the equations are extremely significant, and p values of lack of fit are all greater than 0.05, which is not significant. For the surface roughness of the sample, the coefficient of determination R2 is 0.9158, the adjusted coefficient of determination Radj2 is 0.8283, and the predicted coefficient of determination Rprep2 is 0.5898, representing a difference of 0.326 between the coefficient of determination R2 and the predicted coefficient of determination Rprep2. For the density of the sample, the coefficient of determination R2 is 0.8961, the adjusted coefficient of determination Radj2 is 0.7881, and the predicted coefficient of determination Rprep2 is 0.5716, representing a difference of 0.3245 between the coefficient of determination R2 and the predicted coefficient of determination Rprep2. For the tensile strength, the coefficient of determination R2 is 0.937, the adjusted coefficient of determination Radj2 is 0.8715, and the predicted coefficient of determination Rprep2 is 0.6842, representing a difference of 0.2528 between the coefficient of determination R2 and the predicted coefficient of determination Rprep2. For the elongation of the sample, the coefficient of determination R2 is 0.9359, the adjusted coefficient of determination Radj2 is 0.8693, and the predicted coefficient of determination Rprep2 is 0.679, representing a difference of 0.2569 between the coefficient of determination R2 and the predicted coefficient of determination Rprep2. All the above indicates that the response surfaces of the four models have good predictability for the experimental results.Table 4
Analysis of variance of surface roughness.
Source
Sum of squares
DF
Mean square
F value
p value prob > F
Model
1172.94
27
43.44
10.47
<0.0001
A
1.71
1
1.71
0.41
0.5263
B
1.153× 10−3
1
1.153× 10−3
2.778× 10−4
0.9868
C
2.044× 10−3
1
2.044× 10−3
4.927× 10−4
0.9825
D
119.63
1
119.63
28.83
<0.0001
E
4.67
1
4.67
1.13
0.2983
F
767.11
1
767.11
184.88
<0.0001
AB
1.02
1
1.02
0.24
0.6248
AC
17.07
1
17.07
4.11
0.0529
AD
0.13
1
0.13
0.031
0.8620
AE
0.11
1
0.11
0.027
0.8698
AF
0.19
1
0.19
0.045
0.8331
BC
2.00
1
2.00
0.48
0.4934
BD
0.53
1
0.53
0.13
0.7236
BE
3.59
1
3.59
0.86
0.3610
BF
0.49
1
0.49
0.12
0.7334
CD
7.34
1
7.34
1.77
0.1949
CE
0.84
1
0.84
0.20
0.6556
CF
1.12
1
1.12
0.27
0.6076
DE
0.22
1
0.22
0.052
0.8217
DF
91.57
1
91.57
22.07
<0.0001
EF
16.06
1
16.06
3.87
0.0599
Residual
107.88
26
4.15
Lack of fit
97.78
21
4.66
2.31
0.1801
Pure error
10.10
5
2.02
Cor total
1280.82
53Table 5
Analysis of variance of density.
Source
Sum of squares
DF
Mean square
F value
p value prob > F
Model
2035.96
27
75.41
8.30
<0.0001
A
9.45
1
9.45
1.04
0.3171
B
77.01
1
77.01
8.48
0.0073
C
284.59
1
284.59
31.33
<0.0001
D
617.80
1
617.80
68.01
<0.0001
E
5.29
1
5.29
0.58
0.4524
F
193.92
1
193.92
21.35
<0.0001
AB
2.46
1
2.46
0.27
0.6071
AC
124.75
1
124.75
13.73
0.0010
AD
36.18
1
36.18
3.98
0.0565
AE
9.62
1
9.62
1.06
0.3130
AF
10.56
1
10.56
1.16
0.2907
BC
22.97
1
22.97
2.53
0.1239
BD
75.91
1
75.91
8.36
0.0077
BE
10.67
1
10.67
1.17
0.2884
BF
8.24
1
8.24
0.91
0.3497
CD
40.77
1
40.77
4.49
0.0438
CE
1.84
1
1.84
0.20
0.6560
CF
1.00
1
1.00
0.11
0.7425
DE
166.10
1
166.10
18.29
0.0002
DF
73.58
1
73.58
8.10
0.0085
EF
56.59
1
56.59
6.23
0.0192
Residual
236.18
26
9.08
Lack of fit
167.32
21
7.97
0.58
0.8281
Pure error
68.86
5
13.77
Cor total
2272.13
53Table 6
Analysis of variance of tensile strength.
Source
Sum of squares
DF
Mean square
F value
p value prob > F
Model
1.227× 106
27
45454.48
14.31
<0.0001
A
30861.77
1
30861.77
9.72
0.0044
B
44371.38
1
44371.38
13.97
0.0009
C
8444.14
1
8444.14
2.66
0.1150
D
6.023× 105
1
6.023× 105
189.67
<0.0001
E
686.54
1
686.54
0.22
0.6458
F
50015.45
1
50015.45
15.75
0.0005
AB
0.16
1
0.16
4.947× 10−5
0.9944
AC
4936.40
1
4936.40
1.55
0.2236
AD
25955.86
1
25955.86
8.17
0.0083
AE
3.46
1
3.46
1.089× 10−3
0.9739
AF
5545.85
1
5545.85
1.75
0.1978
BC
2596.73
1
2596.73
0.82
0.3741
BD
22248.05
1
22248.05
7.01
0.0136
BE
5530.04
1
5530.04
1.74
0.1985
BF
7718.38
1
7718.38
2.43
0.1311
CD
577.70
1
577.70
0.18
0.6732
CE
686.80
1
686.80
0.22
0.6458
CF
594.23
1
594.23
0.19
0.6689
DE
2029.53
1
2029.53
0.64
0.4313
DF
113.57
1
113.57
0.036
0.8515
EF
11412.79
1
11412.79
3.59
0.0692
Residual
82562.08
26
3175.46
Lack of fit
77877.06
21
3708.43
3.96
0.0663
Pure error
4685.02
5
937.00
Cor total
1.310× 106
53Table 7
Analysis of variance of elongation.
Source
Sum of squares
DF
Mean square
F value
p value prob > F
Model
10386.66
27
384.69
14.05
<0.0001
A
350.33
1
350.33
12.80
0.0014
B
138.03
1
138.03
5.04
0.0335
C
89.58
1
89.58
3.27
0.0820
D
4864.16
1
4864.16
177.70
<0.0001
E
1.30
1
1.30
0.048
0.8289
F
58.73
1
58.73
2.15
0.1550
AB
333.82
1
333.82
12.20
0.0017
AC
34.91
1
34.91
1.28
0.2691
AD
51.06
1
51.06
1.87
0.1837
AE
336.05
1
336.05
12.28
0.0017
AF
49.00
1
49.00
1.79
0.1925
BC
0.076
1
0.076
2.762× 10−3
0.9585
BD
195.25
1
195.25
7.13
0.0129
BE
39.24
1
39.24
1.43
0.2420
BF
4.86
1
4.86
0.18
0.6771
CD
3.90
1
3.90
0.14
0.7087
CE
1.58
1
1.58
0.058
0.8120
CF
0.16
1
0.16
5.684× 10−3
0.9405
DE
107.43
1
107.43
3.92
0.0582
DF
325.69
1
325.69
11.90
0.0019
EF
14.25
1
14.25
0.52
0.4770
Residual
711.70
26
27.37
Lack of fit
670.62
21
31.93
3.89
0.0687
Pure error
41.08
5
8.22
Cor total
11098.36
53The relationships between the actual values of surface roughness, density, tensile strength, and elongation and the predicted values of the regression models are shown in Figure5. As shown in Figure 5, the actual values are basically distributed on the predicted curves and the actual values are consistent with the trend of the predicted values, showing linear distribution. In general, the models verify the experimental data accurately, so the models can predict and analyze the effect of various factors on the indexes.Figure 5
Scatter plot: predicted values of (a) surface roughness, (b) density, (c) tensile strength, and (d) elongation.
(a)
(b)
(c)
(d)Within the horizontal range of the selected factors, the weight of effect on the surface roughness according to the F value of each factor is the angle with thexy plane > layer thickness > the angle with the xz plane > laser power>hatching space > scan speed; the weight of effect on the density is layer thickness > hatching space > the angle with the xy plane > scan speed > laser power > the angle with the xz plane; the weight of effect on tensile strength is layer thickness > the angle with the xy plane > scan speed > laser power > hatching space > the angle with the xz plane; and the weight of effect on elongation is layer thickness > laser power > scan speed > hatching space > the angle with the xy plane > the angle with the xz plane.


## 3.1.2. Analysis of Multivariate Interactive Influence

When laser power, scan speed, hatching space, and the angle with thexz plane are constant, it can be seen from Figure 6 that when the angle with the xy plane is 0°, the surface roughness increases as the layer thickness increases, reaches the peak as the layer thickness further increases, and then decreases as the layer thickness continues to increase; when the layer thickness is constant, the surface roughness decreases as the angle with the xy plane increases.Figure 6
Effect of layer thickness and the angle with thexy plane on surface roughness.As shown in Figure7(a), when both laser power and scan speed increase, the density first increases and then decreases. When the laser power is 160 W and the hatching space is 0.07 mm, the density reaches the peak; when the hatching space ranges from 0.07 to 0.08 mm, the density increases as the laser power increases; and when the hatching space ranges from 0.08 to 0.09 mm, the density decreases as the laser power increases. As shown in Figure 7(b), when the layer thickness is constant, the density decreases as the scan speed increases; and when the scan speed is constant, the density increases as the layer thickness increases. As shown in Figure 7(c), when the layer thickness is 0.02 mm, the density increases first and then decreases as the hatching space increases; and when the scan speed is 0.09 mm/s, the density decreases at the fastest rate as the layer thickness increases. As shown in Figure 7(d), when the angle with the xy plane is constant, the density decreases as the layer thickness increases; when the angle with the xy plane is 0°, the density decreases at the fastest rate; when the layer thickness is constant, the density increases as the angle with the xy plane increases, and when the layer thickness is 0.04 mm, the density increases at the fastest rate as the angle with the xy plane increases. As shown in Figure 7(e), when the layer thickness is 0.02 mm, the density increases as the angle with the xz plane increases, reaching the maximum value, but the trend of density changes as the layer thickness further increases, and when layer thickness is above 0.02 mm, the density decreases as the angle with the xz plane increases. As shown in Figure 7(f), when the angle with the xy plane ranges from 0° to 50°, the density decreases as the angle with the xz plane increases, and when the angle with the xy plane ranges from 50° to 90°, the density increases as the angle with the xz plane increases.Figure 7
Effect of laser power, scan speed, scan spacing, layer thickness, angle with thexz plane, and angle with the xy plane on density. (a) Effect of interaction of laser power and scan spacing on density. (b) Effect of interaction of scan speed and layer thickness on density. (c) Effect of interaction of scan spacing and layer thickness on density. (d) Effect of interaction of angle with the xy plane and layer thickness on density. (e) Effect of interaction of angle with the xz plane and layer thickness on density. (f) Effect of interaction of angle with the xy plane and angle with the xz plane on density.
(a)
(b)
(c)
(d)
(e)
(f)As shown in Figure8(a), when the laser power is constant, the tensile strength decreases as the layer thickness increases; when the laser power is 140 W, the tensile strength decreases at the fastest rate; when the laser power is 160 W, the tensile strength decreases at the slowest rate; and when the layer thickness is constant, the tensile strength increases as the laser power increases. As shown in Figure 8(b), when the layer thickness is constant, the tensile strength decreases as the scan speed increases; when the layer thickness is 0.04 mm, the tensile strength decreases at the fastest rate; when the scan speed is constant, the tensile strength decreases as the layer thickness increases; and when the scan speed is 900 mm/s, the tensile strength decreases at the fastest rate.Figure 8
Effect of laser power, scan speed, and layer thickness on tensile strength. (a) Effect of interaction of laser power and layer thickness on tensile strength. (b) Effect of interaction of scan speed and layer thickness on tensile strength.
(a)
(b)As shown in Figure9(a), when the scan speed ranges from 700 to 760 mm/s, the elongation increases as the laser power increases; when the scan speed ranges from 760 to 900 mm/s, the elongation first decreases and then increases as the laser power increases; when the laser power ranges from 140 to 148 W, the elongation increases as the scan speed increases; when the laser power ranges from 148 to 160 W, the elongation decreases first and then increases as the scan speed increases; and at the minimum scan speed and the maximum laser power, the elongation reaches the maximum value. As shown in Figure 9(b), when the angle with the xz plane ranges from 0° to 50°, the elongation decreases first and then increases as the laser power increases; when the angle with the xz plane ranges from 50° to 90°, the elongation increases as the laser power increases; when the laser power ranges from 140 to 150 W, the elongation decreases as the angle with the xz plane increases; and when the laser power ranges from 150 to 160 W, the elongation increases as the angle with xz plane increases, reaching the maximum value together with the angle with the xz plane, laser power, and elongation. As shown in Figure 9(c), when the scan speed ranges from 700 to 800 mm/s, the elongation decreases first and then increases as the layer thickness increases; when the scan speed ranges from 800 to 900 mm/s, the elongation decreases as the layer thickness increases; when the layer thickness ranges from 0.02 to 0.03 mm, the elongation does not change significantly as the scan speed increases; and when the layer thickness ranges from 0.03 to 0.04 mm, the elongation decreases as the scan speed increases, and the maximum elongation is obtained from the minimum layer thickness and maximum scan speed. As shown in Figure 9(d), when the angle with the xy plane is constant, the elongation decreases rapidly first and then increases slowly as the layer thickness increases; when the layer thickness ranges from 0.02 to 0.023 mm, the elongation increases as the angle with the xy plane increases; and when the layer thickness ranges from 0.024 to 0.04 mm, the elongation decreases first and then increases as the angle with the xy plane increases.Figure 9
Effect of laser power, scan speed, scan spacing, layer thickness, angle withxz plane, and angle with xy plane on elongation. (a) Effect of interaction of scan speed and laser power on elongation. (b) Effect of interaction of angle with the xz plane and laser power on elongation. (c) Effect of interaction of scan speed and layer thickness on elongation. (d) Effect of interaction of angle with the xy plane and layer thickness on elongation.
(a)
(b)
(c)
(d)


## 3.1.3. Optimization of Process Parameters

Based on the above experiments, the predicted and actual optimization results are shown in Table8 and formula (8). The error between the predicted and actual values of the surface roughness under optimized conditions is 4.6%, the error between the predicted and actual values of the density is 1%, the error between the predicted and actual values of the tensile strength is 19.5%, and the error between the predicted and actual values of the elongation is 18.9%. All errors are within the reasonable range, indicating that the results are reliable. The tensile strength and elongation of the formed parts with the optimal parameters are higher than that specified in ASTM-A182 and ASTM-F3184-16.(8)140≤A≤160,700≤B≤900,0.07≤C≤0.09,0.02≤D≤0.04,0≤E≤90,0≤F≤9,y1=f1A,B,C,D,E,F,minY1,maxY2,maxY3,maxY4.Table 8
Predicted and actual results under optimized conditions.
Exp. no.
Laser power (W)
Scanning speed (mm/s)
Scanning interval (mm)
Layer thickness (mm)
Angle with thexz plane
Angle with thexy plane
Surface roughness (μm)
Relative density (%)
Tensile strength (MPa)
Elongation rate (%)
Predicted values
160
836
0.07
0.02
83.3
89.7
4.1
97.27
609.5
55.9
Actual value
160
836
0.07
0.02
83.3
89.7
4.3
96.3
510
47
Relative error
4.6%
1%
19.5%
18.9%


## 3.2. Microstructure and Fracture Morphology Analysis

### 3.2.1. Microstructure Analysis

As shown in Figure10(a), the microstructure of the selective laser melting sample before stretching is mainly composed of a plurality of oval molten pools, each of which has an aspect ratio of 0.5–0.65. This study suggests that there is certain unevenness in the powder size, a difference in laser energy absorption, and a Gaussian distribution of laser energy, which helps shape the oval molten pools due to different energy densities in various areas. Figure 10(b) shows the shape of the molten pools after stretching. Compared with Figure 10(a), the molten pools of the parts are obviously elongated after stretching with an aspect ratio of 2-1.5, or 2–4 times of that before stretching. Figures 10(c) and 10(d) show the microstructure before stretching. It can be seen from Figures 10(c) and 10(d) that the inside of the molten pool is mainly composed of equiaxed crystals and columnar crystals. The grain sizes are fine with a width of 0.28–0.4 nm, of which, the secondary arm of the columnar crystal is not developed and the morphology of the dendrites is not significant, with obvious planar crystals at the junction of the layers. The columnar crystals in the microstructure show apparent epitaxial growth characteristics because the laser melting process is at a high temperature gradient and solidification rate, while forming material and substrate temperature are lower, generally lower than the forming temperature by several orders of magnitude, resulting in heat transfer from the processing layer to the formed layer from top to bottom. The solidification direction inside the molten pool is from the bottom to the top of the molten pool, with solidification conditions in the growth range of equiaxed crystals and columnar crystals. Due to the rapid condensation of the laser, the bottom of the molten pool is closest to the formed layer with fastest solidification. The crystal grains at the bottom of the molten pool are solidified without growing, so equiaxed crystals appear at the bottom and boundary of the molten pool in the form of relatively fine grains, showing a planar crystal with white and bright layers of microstructure.Figure 10
Microstructure. (a) Molten pool before stretching. (b) Molten pool after stretching. (c) Microstructure in molten pool. (d) Partial enlargement of microstructure in molten pool.
(a)
(b)
(c)
(d)


### 3.2.2. Hardness Analysis

The microhardness of the experiment is shown in Figure11. The distance closest to the fracture is set as 0, and three points are selected at each distance to obtain the average. As shown in Figure 11, the microhardness of the sample increases first and then decreases with the increase in the distance. The average microhardness at 2.5 mm from the fracture is 28.73 HRC, and the average microhardness at 20 mm from the fracture is 25.23 HRC, which is 87% of the hardness at the fracture. The microhardness at the fracture is significantly higher than the substrate because the fracture has a large number of dislocations, and dislocation multiplication and increased surface energy help improve the hardness.Figure 11
Microhardness. (a) Hardness curve. (b) Hardness physical image.
(a)
(b)


### 3.2.3. XRD Analysis

The XRD of the sample formed by optimizing the parameters is shown in Figure12. Compared with the standard map, the diffraction peak intensity of the crystal planes increases at γ-Fe (111), and the diffraction peak intensity of the crystal planes decreases at γ-Fe (200) and γ-Fe (220), showing that the γ-Fe crystallinity is not as good as the standard map. When the diffraction angle ranges from 40° to 45°, a significant diffraction peak broadening occurs. The diffraction peak broadening is determined by two physical factors, grain refinement and crystal microscopic distortion.Figure 12
XRD.


### 3.2.4. Fracture Analysis

The fracture morphology is shown in Figure13. As shown in Figure 13(a), there are a large number of clear dimples whose shapes have obvious tearing, called elongated dimples, and the specimen fracture is a typical plastic fracture. Figure 13(b) shows fracture cracks passing through the grains, which is known as a transgranular fracture, and there are many dimples in the fracture, which is a ductile fracture. The specimen fracture is mainly caused by a large amount of dislocation multiplication under tensile stress with increased grain boundary energy, and a great quantity of impurities in the material are broken to form a plenty of micropores. The micropores further grow under external force to generate cracks until the final failure.Figure 13
Fracture morphology. (a) Dimple morphology. (b) Crack.
(a)
(b)


## 3.2.1. Microstructure Analysis

As shown in Figure10(a), the microstructure of the selective laser melting sample before stretching is mainly composed of a plurality of oval molten pools, each of which has an aspect ratio of 0.5–0.65. This study suggests that there is certain unevenness in the powder size, a difference in laser energy absorption, and a Gaussian distribution of laser energy, which helps shape the oval molten pools due to different energy densities in various areas. Figure 10(b) shows the shape of the molten pools after stretching. Compared with Figure 10(a), the molten pools of the parts are obviously elongated after stretching with an aspect ratio of 2-1.5, or 2–4 times of that before stretching. Figures 10(c) and 10(d) show the microstructure before stretching. It can be seen from Figures 10(c) and 10(d) that the inside of the molten pool is mainly composed of equiaxed crystals and columnar crystals. The grain sizes are fine with a width of 0.28–0.4 nm, of which, the secondary arm of the columnar crystal is not developed and the morphology of the dendrites is not significant, with obvious planar crystals at the junction of the layers. The columnar crystals in the microstructure show apparent epitaxial growth characteristics because the laser melting process is at a high temperature gradient and solidification rate, while forming material and substrate temperature are lower, generally lower than the forming temperature by several orders of magnitude, resulting in heat transfer from the processing layer to the formed layer from top to bottom. The solidification direction inside the molten pool is from the bottom to the top of the molten pool, with solidification conditions in the growth range of equiaxed crystals and columnar crystals. Due to the rapid condensation of the laser, the bottom of the molten pool is closest to the formed layer with fastest solidification. The crystal grains at the bottom of the molten pool are solidified without growing, so equiaxed crystals appear at the bottom and boundary of the molten pool in the form of relatively fine grains, showing a planar crystal with white and bright layers of microstructure.Figure 10
Microstructure. (a) Molten pool before stretching. (b) Molten pool after stretching. (c) Microstructure in molten pool. (d) Partial enlargement of microstructure in molten pool.
(a)
(b)
(c)
(d)


## 3.2.2. Hardness Analysis

The microhardness of the experiment is shown in Figure11. The distance closest to the fracture is set as 0, and three points are selected at each distance to obtain the average. As shown in Figure 11, the microhardness of the sample increases first and then decreases with the increase in the distance. The average microhardness at 2.5 mm from the fracture is 28.73 HRC, and the average microhardness at 20 mm from the fracture is 25.23 HRC, which is 87% of the hardness at the fracture. The microhardness at the fracture is significantly higher than the substrate because the fracture has a large number of dislocations, and dislocation multiplication and increased surface energy help improve the hardness.Figure 11
Microhardness. (a) Hardness curve. (b) Hardness physical image.
(a)
(b)


## 3.2.3. XRD Analysis

The XRD of the sample formed by optimizing the parameters is shown in Figure12. Compared with the standard map, the diffraction peak intensity of the crystal planes increases at γ-Fe (111), and the diffraction peak intensity of the crystal planes decreases at γ-Fe (200) and γ-Fe (220), showing that the γ-Fe crystallinity is not as good as the standard map. When the diffraction angle ranges from 40° to 45°, a significant diffraction peak broadening occurs. The diffraction peak broadening is determined by two physical factors, grain refinement and crystal microscopic distortion.Figure 12
XRD.


## 3.2.4. Fracture Analysis

The fracture morphology is shown in Figure13. As shown in Figure 13(a), there are a large number of clear dimples whose shapes have obvious tearing, called elongated dimples, and the specimen fracture is a typical plastic fracture. Figure 13(b) shows fracture cracks passing through the grains, which is known as a transgranular fracture, and there are many dimples in the fracture, which is a ductile fracture. The specimen fracture is mainly caused by a large amount of dislocation multiplication under tensile stress with increased grain boundary energy, and a great quantity of impurities in the material are broken to form a plenty of micropores. The micropores further grow under external force to generate cracks until the final failure.Figure 13
Fracture morphology. (a) Dimple morphology. (b) Crack.
(a)
(b)


## 4. Conclusion

(1)
The angle with thexz plane has a significant effect on the experiment indexes. The comprehensive factor that has the greatest effect on the experiment indexes is the layer thickness. The biggest effect on the surface roughness is from the angle with the xy plane.
(2)
The optimal forming parameters are laser power of 160 W, scan speed of 836 mm/s, hatching space of 0.07 mm, layer thickness of 0.02 mm, the angle with thexz plane of 83.3°, and the angle with the xy plane of 89.7°. The errors between the predicted values and the actual values of the surface roughness, the density, the tensile strength, and the elongation under optimized conditions are 4.6%, 1%, 19.5%, and 18.9%, respectively, and the errors are within a reasonable range, indicating that the model has practical engineering value.
(3)
After stretching, the molten pools of the parts are obviously elongated with the aspect ratio increasing from 0.5–0.65 to 1.5–2, up by 130%–300%. The microstructure of the formed parts is composed of equiaxed crystals and columnar crystals with a grain width of 0.28–0.4 nm. The secondary growth of dendrites is not obvious, with the microstructure showing directional solidification. XRD analysis shows that the crystallinity of the selective laser melting parts is not as good as that of the standard sample, with grain refinement and microscopic distortion of crystals.
(4)
There are many dimples in the fracture which is ductile fracture and typical plastic fractures, and the hardness near the fracture is greatly higher, or 1.14 times that of the substrate. The indexes regarding the selective laser melting parts are better than the ASTM-A182 and ASTM-F3184-16 standards.



---

*Source: 8404052-2020-01-20.xml*