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Statistical modelling and optimization of microhardness transition through depth of laser surface hardened AISI 1045 carbon steel
Optics and Laser Technology 124 (2020) 105976
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Statistical modelling and optimization of microhardness transition through depth of laser surface hardened AISI 1045 carbon steel
T
⁎
Changrong Chena, , Xianbin Zengb, Qianting Wangb, Guofu Liana, Xu Huanga, Yan Wangc a
School of Mechanical and Automotive Engineering, Fujian University of Technology, Fuzhou 350118, China College of Materials Science and Engineering, Fujian University of Technology, Fuzhou 350118, China c School of Computing, Engineering and Mathematics, University of Brighton, Brighton BN2 4AT, United Kingdom b
H I GH L IG H T S
transition is defined as the division of micro-hardness over layer depth. • Hardness responses are statistically modelled with sound accuracy and generalization. • Three of three variables on microhardness are studied by metallographic analysis. • Effects of AISI 1045 steel has a threefold increase after laser surface hardening. • Hardness • Microhardness gradient is monotonic surfaces without local maximum in design space.
A R T I C LE I N FO
A B S T R A C T
Keywords: Laser surface hardening Response surface methodology Hardened layer Microhardness property Metallographic analysis
The mechanical properties of laser surface hardened material are closely related to the hardened layer. Respective study of geometrical dimension and microhardness would only result in insufficient understanding of the hardened layer. In this paper, a central composite design (CCD) is proposed, based on response surface methodology (RSM), to investigate the influences of processing parameters including laser power (LP), scanning speed (SS) and defocusing distance (DD) on the geometrical dimensions, microhardness and microhardness transition of laser surface hardened AISI 1045 carbon steel. Two-tailed Pearson correlation of selected responses was firstly undertaken to screen out unrelated ones. Second order response surface models were then developed and tested for three responses: hardened width (HW), microhardness of hardened area (MH) and hardness gradient (HG). Scanning electron microscopy(SEM) was conducted to evaluate the evolution of microstructure with three process parameters. The results indicate that three response models are capable of interpreting the hardened width, microhardness and hardness gradient with satisfactory accuracy. It is observed that the HW is only linearly determined by LP and SS, while the hardness properties (MH and HG) are both affected by all the investigated parameters significantly. The hardness of base metal can be improved from 200HV to 660HV after laser surface hardening. Quadratic correlation can be obtained when the HG is transformed inversely. Validation experiment was finally conducted for testing the generalisation of fitted regression models. As the maximum relative prediction errors for three responses are respectively 4.18%, 2.25% and −4.36%, good generalisation has been accomplished by the developed models.
1. Introduction Laser surface hardening (LSH) heats up the materials superficially by laser irradiation and obtains desired structural transformation through materials’ self-quenching capabilities [1–4]. The microhardness of hardened area could reach the order of 675-750HV with surface roughness of 0.6–1.2 μm [5,6]. The process is popularly used for improving the wear resistance of tribological systems due to the ⁎
advantageous characteristics of no quenching medium, minimal distortion and high flexibility [1,3,7–9]. LSH is also desirably used to enhance regional properties of large volume tools, such as the cutting edges of stamping dies, closing areas of injection moulds and radii of deep drawing dies, where entire treatment of structures by conventional methods requires much larger equipment and more accurate deformation control [10–13]. Most of the research endeavours to obtain enough mechanical
Corresponding author. E-mail address: [email protected] (C. Chen).
https://doi.org/10.1016/j.optlastec.2019.105976 Received 14 April 2019; Received in revised form 6 October 2019; Accepted 23 November 2019 Available online 14 December 2019 0030-3992/ © 2019 Elsevier Ltd. All rights reserved.
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properties, usually hardness and wear resistance, in processed area. Zhang et al. [14] carried out LSH of low carbon steel to obtain tiny lathy martensite with increased hardness on steel surface. They also found that the treatment decreased the friction coefficient and improved the wear resistance. Babu et al. [15] used a Box-Behnken design to develop mathematical models between process parameters and wear resistance. They presented that laser surface hardened samples exhibit a lower wear rate and coefficient of friction compared to as-received samples. Sarkar et al. [16] laser surface hardened low carbon steel (0.05% and 0.07% carbon) of around 1 mm thickness with a high power fiber laser. They also observed increase in microhardness, tensile strength, reduction in percentage elongation and improvement in scratch resistance of the hardened surface. Syed et al. [17] treated a C-Mn low carbon automotive steel sheet and obtained significantly improved hardness, yield strength and ultimate tensile strength. Cao et al. [18] investigated the microstructure, wear and rolling contact fatigue of wheel and rail materials to optimize processing parameters of laser dispersed quenching. They obtained homogeneous martensite in the treated wheel/rail rollers, and the surface hardness increased significantly. Moradi and KaramiMoghadam [19] surveyed the effects of process variables on the hardened layer geometry, average micro-hardness and the ferrite phase percentage of laser surface hardened AISI 4130 carbon steel. The hardness has been increased to three times of the base material. Additionally, some researchers have been devoted to achieving designated hardened surface layers. Badkar et al. [20,21] applied response surface methodology (RSM) to model, optimize and analyse the influences of dominant laser-processing parameters on heat input and bead geometries of laser hardened surface quality of commercially pure titanium sheet of 1.6 mm in thickness using a 2 kW continuous wave Nd:YAG laser. Li et al. [2] compared the effects of LSH process parameters using two industrial lasers (high-power diode laser and CO2 laser) on structure, case depth, and microhardness of the AISI 1045 steel. They found that the depths of heat affected zone (HAZ) due to the former laser were almost equal in total HAZ, but varied through the HAZ for the second type. Sun et al. [22] used two shapes of laser beams to surface treat 42CrMo cast steel for uniform hardened layer. They observed that a wider and more uniform hardened layer could be obtained using the non-uniform intensity beam at relative higher scanning velocities and laser power. From the literature, one can find that mechanical properties, as straightforward performance criteria, are commonly considered as important process outputs. The geometries of hardened layer, on the other hand, are also useful results for much more complicated surface processing. However, these two aspects are commonly treated as irrelevant process responses and studied independently. Furthermore, the performance of treated layer is also determined by the transition boundary between hardened and untreated zone. Residual stresses of high magnitudes would be induced inside the hardened plate due to high thermal gradients and non-uniform plastic deformation [23]. While compressive stresses are detected near the surface, tensile counterparts are resulted in the deeper area [24]. This is primarily caused by the phase transformation of martensite from the thermal processing [25]. Taking into consideration the phase-property correlation, abrupt change of mechanical properties in processed components symbolizes fragile bondings and should be avoided. This paper investigates the microhardness and its gradient in depth to obtain the smoothest transition of laser surface hardened AISI 1045 carbon steel using response surface methodology. A central composite design (CCD) was proposed for three input process parameters: laser power, scanning speed and defocusing distance. A correlation study was then conducted to the collected response data and three responses including hardened width (HW), microhardness of hardened layer (MH) and hardness gradient (HG) were considered in the following regression analysis. The effects of process parameters on the responses were mathematically modelled using analysis of variance(ANOVA).
Table 1 Chemical composition of the AISI 1045 steel(wt%). C
Si
Mn
Cr
Ni
Cu
Fe
0.42–0.50
0.17–0.37
0.50–0.80
⩽0.25
⩽0.25
⩽0.25
Bal.
Microstructure evaluation of laser hardened zones was also performed using scanning electron microscopy(SEM) to understand the parameter effects. Validation of established models was finally carried out through the process optimization. 2. Experimental 2.1. Material and experimental set-up Laser surface hardening was conducted on the AISI 1045 steel substrate with dimensions of 50×25×10 in mm. The chemical composition is shown in Table 1. A laser cladding system was used for the surface hardening experiment in this research, as depicted in Fig. 1. A Lasermesh FDH0273 laser head with focus length of 300 mm is mounted at a FANUC M710iC/50 industrial robot to deliver laser beams generated by an IPG high power fiber laser YLS-3000. The shielding gas Argon is coaxially delivered onto the hardening surface at a pressure of 0.5 MPa to avoid surface oxidization at high temperature. The gas flow rate is kept constant by a flow valve for all the experimental runs. 2.2. Experimental procedure The substrate was cleaned with acetone to remove surface impurities before surfacing and processed at ambient environment without preheating for better accordance with industrial requirements. Experimental runs of hardening processing were conducted according to a Central Composite Design, proposed based on RSM, in a random manner. The investigated process parameters include laser power (LP), scanning speed (SS) and defocusing distance (DD). The parameter centre and span were selected for better modelling performance based on previous research. Five levels of all three variables were studied, as listed in Table 2. An alpha level of 1.682 was selected for the axial points and six replications were applied at the centre point only to investigate data accuracy, leading to an only 20-run experimental matrix. The variable values were round off for better control, as illustrated in Table 3. After laser hardening, the specimens were transversely sectioned by wire electrical discharge machining (Wire EDM), ground and polished for geometrical morphology and microstructure observation (using an ANDONSTAR portable Optical Microscope and a TM3030 Plus Scanning Electron Microscope) after 30s etching in 4% nitric acid alcohol. The cross-sectional profile characteristics of processed layer are defined as shown in Fig. 2 wherein the microhardness is measured at the cross points of three zones. The gradient of micro-hardness is calculated from the difference of averaged values between fusion zone (5 points) and unaffected area (2 points) divided by the hardened depth, as shown in Eq. (1). As the treatment of actual parts is normally conducted in multi-pass manner, the hardness gradient in transverse direction is not considered in this work.
∇Hv,d =
HvFZ − HvUZ d
(1)
The results were then appended in Table 3 as well. A two-tailed Pearson correlation matrix was proposed using IBM SPSS® Statistics 22 to investigate the correlations among these responses, as shown in Table 4. From the table, one can find that the width, depth and area of hardened layer are strongly correlated with each other. The microhardness of hardened layer, on the other hand, 2
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Fig. 1. Laser cladding system used for hardening processing.
by second order polynomials. The mathematical models correlating process variables to responses HW, MH and HG during laser surface hardening of AISI 1045 steel are depicted below:
Table 2 Laser hardening variables and levels. Variable
Notation
Unit
Laser Power Scanning Speed Defocusing Distance Hardened Width Hardened Depth Hardened Area Microhardness Hardness Gradient
LP SS DD
kW mm/s mm
w d A Hv ∇Hv,d
mm mm mm2 HV1 HV1/mm
Levels 0.300 3 −2
0.475 5 −0.8
0.750 8 1 Response Response Response Response Response
1.025 10 2.8
⎧ w = 0.899+ 2.547 × LP + 0.0409 × SS − 8.855 × 10−3 × DD ⎪ − 0.141 × LP × SS + 0.0237 × DD2 ⎪ ⎪ Hv = 334.693 + 0.588 × LP + 26.693 × SS + 23.393 × DD ⎪ − 44.054 × LP × DD ⎪ ⎪ + 2.233 × SS × DD − 316.033 × LP2 − 2.427 × SS2 ⎨ − 4.613 × DD2 ⎪ 1000 = 1.669 − 0.0261 × LP − 0.158 × SS + 0.113 × DD ⎪ ∇H − 110 ⎪ v,d − 0.306 × LP × SS ⎪ ⎪ + 0.343 × LP × DD − 0.0387 × SS × DD + 3.132 × LP 2 ⎪ + 0.0219 × SS 2 ⎩
1.200 12 4
1 2 3 4 5
has only about 42% probability relevant to three profile characteristics. The correlations of depth and area to width are demonstrated in Fig. 3. Both the depth and area of hardened layer are second order polynomials of width, as shown in Eq. (2), with adjusted R-squared values of 0.9309 and 0.9173. Therefore, only the width of hardened layer is considered as one profile characteristic for the mathematical modelling. The other characteristics, depth and area, can then be identified by Eq. (2). 2 ⎧ d = − 0.0166 + 0.0703w + 0.0943w 2 ⎨ = 1.444 − 1.523w + 0.590w ⎩A
(3) Tables 5–7 show the ANOVA results for three responses, respectively. As can be found that the p-values for selected regression models are all less than 0.01% and the lack of fit values are all greater than 0.05, which indicate that the selected models interpret the experimental data with more than 99.99% accuracy and lack of fitness is probably caused by random errors. Small PRESS (predicted residual error sum of squares) values in the tables suggest good capability of predicting new experimental results. The values of Adequate Precision are both much larger than 4, which also means high confidence in the model predictions. Table 8 illustrates the coefficients of determination for three response models. From the table, it is obvious that R2 and Adjusted R2 values are pretty close to 1 and the divergence of Predicted R2 from Adjusted R2 are less than 0.2. Additionally, it can also be evidenced by the little discrepancy between model predictions and experimental data depicted in Fig. 4. Therefore, the regression models have excellent goodness of fits and prediction capacity.
(2)
3. Results and discussion 3.1. Response surface models Multiple regression was carried out to fit the response data by analysing statistical significance test on model coefficients and lack-offits. All the three responses, Hardened Width (HW), Micro-hardness (MH) and Hardness gradient (HG, transformed inversely) are modelled 3
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Table 3 Central composition design and responses. Run
LP, kW
SS, mm/s
DD, mm
w, mm
d, mm
A, mm2
HvFZ , HV1
HvUZ , HV1
∇Hv,d , HV1/mm
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
0.75 0.75 0.475 0.475 1.025 1.025 0.474 1.025 0.75 0.75 0.475 1.025 0.75 0.75 0.75 0.3 0.75 0.75 1.2 0.75
8 8 5 10 10 5 5 5 8 8 10 10 8 8 8 8 3 12 8 8
1 1 2.8 −0.8 2.8 −0.8 −0.8 2.8 1 1 2.8 −0.8 1 −2 4 1 1 1 1 1
2.336 2.354 2.098 1.864 2.650 3.078 1.918 3.068 2.352 2.187 1.937 2.556 2.309 2.368 2.731 1.772 2.786 2.140 2.898 2.107
0.660 0.691 0.529 0.385 0.837 1.062 0.481 1.134 0.698 0.630 0.427 0.829 0.705 0.660 0.706 0.459 0.924 0.565 1.023 0.514
1.070 1.133 0.820 0.515 1.471 2.323 0.687 2.387 1.140 1.030 0.589 1.510 1.162 1.138 1.225 0.640 1.744 0.828 2.232 1.147
663.9 652.8 630.5 543.8 607.4 689.9 604.9 610.2 658.0 665.9 591.8 628.9 657.6 618.0 610.4 563.1 640.3 583.0 620.0 663.2
205.6 235.6 200.6 216.1 195.1 194.6 196.8 207.2 210.4 205.9 205.2 212.3 193.1 202.3 212.5 204.1 201.6 212.5 205.8 201.6
694.5 650.1 812.8 851.1 492.7 466.4 848.5 355.4 641.3 730.2 905.3 502.6 658.9 629.9 563.6 782.3 474.8 655.9 404.9 898.0
Table 5 Analysis of variance for width (w). Source
Sum of Squares
df
Mean Square
F Value
p-value Prob > F
Model LP SS DD (LP×SS) DD2 Residual Lack of Fit Pure Error Cor Total
2.78 2.23 0.38 0.065 0.076 0.084 0.14 0.091 0.053 2.92
5 1 1 1 1 1 14 9 5 19
0.56 2.23 0.38 0.065 0.076 0.084 0.010 0.010 0.011
53.86 215.73 37.04 6.32 7.37 8.13
< 0.0001 < 0.0001 < 0.0001 0.0248 0.0167 0.0128
Significant
0.96
0.5510
Not Sign.
Fig. 2. Hardness gradient demonstration.
3.2. Effects of process parameters on responses
Table 4 Pearson correlation of response variables.
Width Depth Area Microhardness
Width
Depth
Area
Microhardness
1 0.966 0.949 0.422
0.966 1 0.977 0.420
0.949 0.977 1 0.429
0.422 0.420 0.429 1
Fig. 5 shows the perturbation of three responses due to significant factors. It is obvious that all three responses, HW, MH and HG are influenced by three investigated process parameters. This can also be found from the model terms with small p-values(Prob>F ) listed in Table 5–7. Specifically, the hardened width is linearly determined by LP (positively) and SS (negatively), but non-linear with DD. The microhardness in hardened layer is non-linearly influenced by all three
Fig. 3. Correlation between depth, area and width of hardened layer. 4
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Table 6 Analysis of variance for microhardness (Hv ).
Table 8 Coefficients of model determination.
Source
Sum of Squares
df
Mean Square
F Value
p-value Prob > F
Model LP SS DD (LP× DD) (SS× DD) LP2 SS2 DD2 Residual Lack of Fit Pure Error Cor Total
25838.74 4998 5073.62 195.61 3807.73 821.36 7506.16 3976.39 3110.25 737.01 615.76 121.25 26575.74
8 1 1 1 1 1 1 1 1 11 6 5 19
3229.84 4998 5073.62 195.61 3807.73 821.36 7506.16 3976.39 3110.25 67 102.63 24.25
48.21 74.6 75.72 2.92 56.83 12.26 112.03 59.35 46.42
< 0.0001 < 0.0001 < 0.0001 0.1155 < 0.0001 0.005 < 0.0001 < 0.0001 < 0.0001
Significant
4.23
0.0674
Not Sign.
Response
R-Squared
Adjusted RSquared
Predicted RSquared
Adequate Precision
w Hv ∇Hv,d
0.9506 0.9723 0.9303
0.9329 0.9521 0.8796
0.8956 0.8703 0.7307
26.716 25.451 15.112
defocusing distance rotating about a relative high scanning speed to lower defocusing distance. 3.3. Metallographic analysis In the previous section, the influences of process parameters on the microhardness of hardened layer was analysed directly from the macroscopic response data. This section, on the other hand, is to reveal the effect mechanism from microscopic observation.
parameters with maximums in design space. The hardness gradient is negatively proportional to DD, but non-linearly affected by LP and SS. Apart from main effects, the width of hardened layer is also influenced by the interaction of LP and SS, as illustrated in Fig. 6. The gradient of width with respect to laser power becomes smaller as the scanning speed increases. Corresponding 3D response surface of hardened width to LP and SS is illustrated in Fig. 7. The 3D surface of width is a slightly curved plane inclined in the direction of increasing LP and decreasing SS. The microhardness, as shown in Table 6, is relevant to two interaction effects LP×DD and SS×DD. From Figs. 8 and 9, one can observe that the microhardness becomes wider and lower parabolas of LP and SS with maximums shifting from edges to centres of design space, as defocusing distance increases from −2 to 4. Figs. 10 and 11 depict the 3D response surfaces of layer microhardness to (LP, DD) and (SS, DD), respectively. The former surface indicates a sheer ascending from the front corner to back, while keeping much more flattened from left to right. The latter one, on the other hand, obtains similar increasing trends from four corners. The gradient of microhardness in hardened layer, as shown in Table 7, is affected by all three interactions, LP×SS, LP×DD and SS×DD. The detail interaction effects are demonstrated in Figs. 12, 14 and 16. As the velocity of scanning increases, the gradient shifts from a gently curved line to a more apparent parabola function of laser power, leading to a lower maximum in the design space. While as the defocusing distance increases, contrary variations are resulted with regard to LP and SS, respectively. Figs. 13, 15 and 17 depict the 3D response surfaces of the microhardness gradient in depth to (LP, SS), (LP, DD) and (SS, DD), respectively. The response surface of HG to LP and SS resembles part of conical surface, revolving about the low power and medium scanning speed position. The second surface appears like a deflected plane curved at the low power and in-substrate defocusing distance corner. The last surface presents like a curve at higher
3.3.1. Effect of laser power Fig. 18 illustrates the microstructure variation of hardened layer using different laser powers. It can be seen that the hardened layer is mainly composed of lathy or fine acicular martensite. As the laser power increases, referring to Fig. 18(a) and (b) the hardened layer is more uniformly and finely martensited into acicular form with reduced austenite. This is because the increased laser power provides more heat input into the substrate, leading to higher temperature gradient between hardened area and untreated zone. Therefore, the martensite transformation is more thoroughly completed with finer grains. However, the continued increase in laser power would prolong the molten pool to allow temperature rise in the substrate and thus decrease the thermal gradient. Therefore, the hardened surface is not completely transformed into martensite with large amount of austenite retained, as illustrated in Fig. 18(c). This explains why the microhardness of hardened layer is a convex parabolic function of laser power. 3.3.2. Effect of scanning speed The effect of scanning speed on the microstructure evolution can be seen from Fig. 19. Similarly, as the scanning speed is reduced, the hardened layer is more uniformly and finely martensited into acicular form with reduced austenite, as demonstrated in Fig. 19(b) and (c). This is because the decreased speed allows more laser energy being absorbed by the substrate, leading to higher degree supercooling of the hardened area. Therefore, the martensitation transformation is more thoroughly completed. However, the continued decrease in scanning speed would then reduce the degree of supercooling. The hardened zone would not completely transform into martensite and some amount of austenite is retained. The similar grain sizes of martensite in Fig. 19(a) and (b) can be attributed to the close resultant microhardness values, as illustrated
Table 7 Analysis of variance for microhardness gradient(∇Hv,d). Source Model LP SS DD (LP× SS) (LP× DD) (SS× DD) LP2 SS2 Residual Lack of Fit Pure Error Cor Total
Sum of Squares −5
1.018×10 7.408×10−6 8.551×10−7 2.838×10−7 3.598×10−7 2.312×10−7 2.462×10−7 7.434×10−7 3.301×10−7 7.627×10−7 4.987×10−7 2.640×10−7 1.095×10−5
df 8 1 1 1 1 1 1 1 1 11 6 5 19
Mean Square −6
1.273×10 7.408×10−6 8.551×10−7 2.838×10−7 3.598×10−7 2.312×10−7 2.462×10−7 7.434×10−7 3.301×10−7 6.934×10−8 8.311×10−8 5.280×10−8
5
F Value
p-value Prob > F
18.36 106.84 12.33 4.09 5.19 3.33 3.55 10.72 4.76
< 0.0001 < 0.0001 0.0049 0.0681 0.0437 0.0951 0.0862 0.0074 0.0517
Significant
1.57
0.3176
Not Sign.
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Fig. 4. Comparison of predicted and actual responses.
Fig. 5. Perturbation of responses due to significant factors. (A: laser power; B: scanning speed; C: defocusing distance).
Fig. 6. Interaction of LP and SS on width.
Fig. 7. 3D Response surface of width to LP and SS.
in Fig. 5(b). Therefore, the microhardness of hardened layer is also a convex function of scanning speed.
3.4. Model confirmation The aim of this LSH process is to maximize the HW and achieve target MH with minimum gradient through the layer depth. The desirability function approach (DFA) is used to deal with the multiple objectives by converting them into one dimensionless desirability function. The multiple responses are characterised by individual scalê i = 1, 2, free values between 0 and 1 using desirability functions (di ( yi ), …, m, where yi ̂ is the ith estimated response model and m is the number of responses). The transformation from yi ̂ to di can be achieved by Eqs. (4)–(6), i.e. the smaller the better(SB), the larger the better(LB), and the target the better(TB).
3.3.3. Effect of defocusing distance Fig. 20 illustrates the effect of defocusing depth on the microstructure variation. As the defocusing amount decreases, the hardened layer is more uniformly and finely martensited into acicular form. This is due to that the closer focusing increases the power density of laser spot and more laser energy is applied to unit substrate area, thereby leading to higher thermal gradient between melt and untreated zone. More proportion of austenite has been transformed into martensite, as illustrated in Fig. 20(b). That is why the microhardness of hardened layer is also a parabolic function of defocus depth as well. 6
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Fig. 8. Interaction of LP and DD on microhardness.
Fig. 12. Interaction of LP and SS on hardness gradient.
Fig. 9. Interaction of SS and DD on microhardness.
Fig. 13. 3D response surface of microhardness gradient to LP and SS.
Fig. 10. 3D response surface of microhardness to LP and DD.
Fig. 14. Interaction of LP and DD on hardness gradient.
Fig. 11. 3D Response surface of microhardness to SS and DD.
Fig. 15. 3D Response surface of microhardness gradient to LP and DD. 7
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TB:
yi ̂ < Li or yi ̂ > Ui
0,
⎧ ⎪ ⎪ ⎪ di (yi )̂ = ⎨ ⎪ ⎪ ⎪ ⎩
⎡ Ui − yUi ̂ ⎤ , ⎣ Ui − Ti ⎦ 1,
Li , Ui, TiL
TiU
yi ̂ − Li
r 1i
⎡ L ⎤ , ⎣ Ti − Li ⎦ r 2i
Li ⩽ yi ̂ < TiL TiU < yi ̂ ⩽ Ui TiL ⩽ yi ̂ ⩽ TiU
(6)
where and are the minimal, maximal acceptable values, the lower and upper targets of the ith response, respectively. si, r 1i and r2i are user-specified weights describing the shapes of desirability functions. The overall desirability, denoted by D, is the weighted geometric mean of all the transformed responses, given by
D = (∏ diwi )1/ ∑ wi
Fig. 16. Interaction of SS and DD on hardness gradient.
The multiple response surface optimisation model is then accomplished by maximising the overall desirability D. The multi-objective criterion is presented in Table 9 for process optimization. The first 10 optimal hardening conditions according to the criterion are summarized in Table 10. Optimum response combination would be accomplished at a maximum HW of about 3.349 mm, a MH of 660HV1, and a HG of about 353.6 HV1/mm. The corresponding intervals for three process parameters, LP, SS and DD, are [1.10, 1.20] kW, [3.00, 4.78] mm/s and [-0.43, 0.13] mm. Fig. 21 plots the overlay area of LP and SS with target responses settled as HW>3.0 mm, MH = 660HV1 and HG<400 HV1/mm. The shadow area in blue signifies the parameter space fulfilling the target. As can be seen from Fig. 21(a), the optimal parameter space is a circular segment at down right side. When DD is reduced from 0.6 to 0, −0.6 and −1.2, as shown in Fig. 21(b) to (d), the optimal parameter space moves right downwards with greater areas. The values of laser power and scanning speed become greater with broader range. Therefore, appropriate sets of input variables can be selected to achieve high quality laser surface hardened layers. For better experimental operation, the 6th process condition was selected for the confirmation of response models. Additionally, another extra trial was conducted to test the model generalization at parameter setting listed in Table 11. It can be observed that the predictions by response models are in good accordance with corresponding experimental data. The maximum relative errors of model predictions for three responses are 4.18%, 2.25% and −4.36%, respectively. Therefore, the established regression models are capable of predicting design space generally.
Fig. 17. 3D Response surface of microhardness gradient to SS and DD.
SB:
LB:
1, yi ̂ < Li ⎧ ⎪ Ui − yi ̂ si di (yi )̂ = ⎡ ⎤ , Li ⩽ yi ̂ ⩽ Ui ⎨ ⎣ Ui − Li ⎦ ⎪ 0, yi ̂ > Ui ⎩
(4)
0, yi ̂ < Li ⎧ ⎪ yi ̂ − Li si di (yi )̂ = ⎡ ⎤ , Li ⩽ yi ̂ ⩽ Ui ⎨ ⎣ Ui − Li ⎦ ⎪ 1, yi ̂ > Ui ⎩
(5)
(7)
4. Conclusions In this research, response surface methodology is utilized to understand the influences of LSH process parameters (including laser power, scanning speed and defocusing distance) on the cross-sectional geometry and hardness gradient of the hardened layer. Second-order
Fig. 18. Comparison of microstructure at different laser powers(SS = 8 mm/s,DD = 1 mm). 8
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Fig. 19. Comparison of microstructure at different scanning speeds(LP = 750 W,DD = 1 mm).
Fig. 20. Comparison of microstructure at different defocus depths(LP = 750 W,SS = 8 mm/s). Table 9 Optimization criteria applied in this study. Name
LP, kW
SS, mm/s
DD, mm
HW, mm
MH, HV1
HG, HV1/mm
Goal Lower Limit Upper Limit Importance
In range 0.3 1.2 5
In range 3 12 5
In range −2 4 5
maximize 1.772 3.078 5
target = 660 543.8 689.9 5
Minimize 355.4 905.3 5
Table 10 Optimal solutions obtained based on the criterion.
•
No.
LP
SS
DD
HW
MH
HG
Desirability
1 2 3 4 5 6 7 8 9 10
1.18 1.16 1.17 1.13 1.16 1.20 1.15 1.19 1.19 1.18
4.50 3.90 4.36 3.43 4.09 4.78 3.79 3.74 4.69 4.43
−0.03 −0.02 0.03 −0.08 0.02 −0.10 −0.01 −0.32 −0.06 −0.03
3.349 3.371 3.342 3.381 3.356 3.342 3.369 3.455 3.340 3.352
660.0 660.0 660.0 660.0 660.0 660.0 660.0 660.0 660.0 660.0
353.6 351.1 354.1 351.0 352.5 355.1 351.4 344.2 355.0 353.2
1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00
• Selected
Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
polynomial mathematical models for HW, MH and HG were developed using experimental observations. Based on the results, following conclusions can be drawn:
Acknowledgements The authors are grateful for the financial support from the National Natural Science Foundation of China (Grant No. 51575110), the Ministry of Industry and Information Technology (Grant No. 2016-75563), the Provincial Education and Research Program for Young and Middle-aged Teachers (Grant No. JAT170376) and Fujian University of Technology (Grant No. E0600276). The authors are thankful to the Public Service Platform for Technical Innovation of Machine Tool Industry in Fujian Province for the technical support.
• The profile characteristics (depth, width and area of hardened layer) •
of hardness gradient are quadratically determined; The effects of three process variables on the microhardness of hardened layer can be explained by the martensitation process via metallographic analysis; The microhardness of the base material can be improved to threefold (from 200HV1 to 660HV1) with a hardness gradient of 355.1HV1/mm.
are significantly correlated with each other. Depth and area of hardened zone can be considered as quadratic functions of the width; All three responses, w,Hv and ∇Hv,d are determined by three process variables. While the width of hardened layer is approximately linear with three variables, the microhardness and inverse transformation 9
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Fig. 21. Overlay plot with target formation quality of HW > 3 mm, MH = 660HV1 and HG < 400HV1/mm. [2] R.F. Li, Y.J. Jin, Z.G. Li, K. Qi, A comparative study of high-power diode laser and CO2 laser surface hardening of AISI 1045 steel, J. Mater. Eng. Perform. 23 (9) (2014) 3085–3091, https://doi.org/10.1007/s11665-014-1146-x. [3] H. Ki, S. So, S. Kim, Laser transformation hardening of carbon steel sheets using a heat sink, J. Mater. Process. Technol. 214 (11) (2014) 2693–2705, https://doi.org/ 10.1016/j.jmatprotec.2014.06.013. [4] W.M. Steen, Laser Material Processing, Springer, London, 2010. [5] A.V. Aborkin, V.E. Vaganov, A.N. Shlegel, I.M. Bukarev, Effect of laser hardening on die steel microhardness and surface quality, Metallurgist 59 (7–8) (2015) 619–625, https://doi.org/10.1007/s11015-015-0148-8. [6] M. Moradi, H. Arabi, S.J. Nasab, K.Y. Benyounis, A comparative study of laser surface hardening of AISI 410 and 420 martensitic stainless steels by using diode laser, Opt. Laser Technol. 111 (2019) 347–357, https://doi.org/10.1016/j. optlastec.2018.10.013. [7] L. Orazi, A. Fortunato, G. Cuccolini, G. Tani, An efficient model for laser surface hardening of hypo-eutectoid steels, Appl. Surf. Sci. 256 (6) (2010) 1913–1919. [8] G. Tani, A. Fortunato, A. Ascari, G. Campana, Laser surface hardening of martensitic stainless steel hollow parts, CIRP Ann. – Manuf. Technol. 59 (1) (2010) 207–210. [9] S.M. Shariff, T.K. Pal, G. Padmanabham, S.V. Joshi, Influence of chemical composition and prior microstructure on diode laser hardening of railroad steels, Surf. Coat. Technol. 228 (228) (2013) 14–26. [10] J. Zhou, Y. Fu, H. Xu, Y. Zhang, J. Yang, Y. Zhang, Investigation into the effects of laser surface hardening on CrWMn steel, in: X.P. Xu (ed.), Advances in Grinding and Abrasive Processes, vol. 259–2 of Key Engineering Materials. Huaqiao Univ; Kistler China Ltd; Jinshan Stone tools Technol Ltd. pp. 502–506, ISBN 1-87849-919-9; 2004. doi:https://doi.org/10.4028/www.scientific.net/KEM.259-260.502; 12th Grinding and Machining Conference, Kunming, PEOPLES R CHINA, NOV 28-30, 2003.
Table 11 Experimental results and model predictions of validation run. Run
LP (kW)
SS (mm/ s)
DD (mm)
1
1.200
5
0
2
0.935
6
−0.4
Predicted Actual Error (%) Predicted Actual Error (%)
HW (mm)
MH (HV1)
HG (HV1/ mm)
3.342 3.208 4.18 2.732 2.648 3.17
660 653.4 1.02 682.4 667.4 2.25
355.1 371.3 −4.36 526.6 525.4 0.23
Appendix A. Supplementary material Supplementary data associated with this article can be found, in the online version, at https://doi.org/10.1016/j.optlastec.2019.105976. References [1] L. Orazi, E. Liverani, A. Ascari, A. Fortunato, L. Tomesani, Laser surface hardening of large cylindrical components utilizing ring spot geometry, CIRP Ann.-Manuf. Technol. 63 (1) (2014) 233–236, https://doi.org/10.1016/j.cirp.2014.03.052.
10
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[11] S.Martinez, E. Ukar, A. Lamikiz, F. Liebana, Laser hardening prediction tool based on a solid state transformations numerical model, in: F. Chinesta, Y. Chastel, M. ElMansori (eds.) International conference on advances in materials and processing technologies, PTS one and two; vol. 1315 of AIP Conference Proceedings. Ctr Arts & Metiers ParisTech; MINES ParisTech; Centrale Nantes; ENI St Etienne; Univ Valenciennes; Oxford Diffract; Transvalor. ISBN 978-0-7354-0871-5; 2010, p. 1594+. International Conference on Advances in Materials and Processing Technologies, Ctr Arts & Metiers ParisTech, Paris, FRANCE, OCT 24-27, 2010. [12] J.Bouquet, D. Van Camp, O. Malek, P. Ten Haaf, K. Vanmeensel, B. Lauwers, Aiming for improved lifetime of die and mold components through an integrated laser hardening operation, combining machining and a selective heat treatment in one setup, in: R. Wertheim, S. Ihlefeldt, C. Hochmuth, M. Putz (eds.), 7TH HPC 2016 – CIRP conference on high performance cutting; vol. 46 of Procedia CIRP. CIRP; 2016, pp. 541–544. 2016, doi:https://doi.org/10.1016/j.procir.2016.04.018; 7th CIRP Conference on High Performance Cutting (HPC), Stadthalle Chemnitz, Chemnitz, GERMANY, MAY 31-JUN 02. [13] S. Martinez, A. Lamikiz, E. Ukar, A. Calleja, J.A. Arrizubieta, L.N. Lopez de Lacalle, Analysis of the regimes in the scanner-based laser hardening process, Opt. Lasers Eng. 90 (2017) 72–80, https://doi.org/10.1016/j.optlaseng.2016.10.005. [14] P.L. Zhang, H. Yan, P.Q. Xu, Z.S. Yu, C.G. Li, Q.H. Lu, Effect of laser surface hardening on the microstructure, hardness, wear resistance and softening of a low carbon steel, Lasers Eng. 28 (3–4) (2014) 135–149. [15] P.D. Babu, G. Buvanashekaran, K.R. Balasubramanian, The elevated temperature wear analysis of laser surface-hardened EN25 steel using response surface methodology, Tribol. Trans. 58 (4) (2015) 602–615, https://doi.org/10.1080/10402004. 2014.998356. [16] S. Sarkar, M. Gopinath, S.S. Chakraborty, B. Syed, A.K. Nath, Analysis of temperature and surface hardening of low carbon thin steel sheets using yb-fiber laser, Surf. Coat. Technol. 302 (2016) 344–358, https://doi.org/10.1016/j.surfcoat.2016. 06.045. [17] B. Syed, S.M. Shariff, G. Padmanabham, S. Lenka, B. Bhattacharya, S. Kundu, Influence of laser surface hardened layer on mechanical properties of re-engineered
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low carbon steel sheet, Mater. Sci. Eng. A-Struct. Mater. Propert. Microstruct. Process. 685 (2017) 168–177, https://doi.org/10.1016/j.msea.2016.12.124. X. Cao, L.B. Shi, Z.B. Cai, Q.Y. Liu, Z.R. Zhou, W.J. Wang, Investigation on the microstructure and damage characteristics of wheel and rail materials subject to laser dispersed quenching, Appl. Surf. Sci. 450 (2018). M. Moradi, M. KaramiMoghadam, High power diode laser surface hardening of AISI 4130; statistical modelling and optimization, Opt. Laser Technol. 111 (2019) 554–570, https://doi.org/10.1016/j.optlastec.2018.10.043. D.S. Badkar, K.S. Pandey, G. Buvanashekaran, Effects of laser phase transformation hardening parameters on heat input and hardened-bead profile quality of unalloyed titanium, Trans. Nonferr. Met. Soc. China 20 (6) (2010) 1078–1091. D.S. Badkar, K.S. Pandey, G. Buvanashekaran, Application of the central composite design in optimization of laser transformation hardening parameters of commercially pure titanium using nd:yag laser, Int. J. Adv. Manuf. Technol. 59 (1) (2012) 169–192, https://doi.org/10.1007/s00170-011-3492-2. P.P. Sun, S.X. Li, G. Yu, X.L. He, C.Y. Zheng, W.J. Ning, Laser surface hardening of 42CrMo cast steel for obtaining a wide and uniform hardened layer by shaped beams, Int. J. Adv. Manuf. Technol. 70 (5–8) (2014) 787–796, https://doi.org/10. 1007/s00170-013-5292-3. N. Nazemi, J. Urbanic, M. Alam, Hardness and residual stress modeling of powder injection laser cladding of P420 coating on AISI 1018 substrate, Int. J. Adv. Manuf. Technol. 93 (9–12) (2017) 3485–3503, https://doi.org/10.1007/s00170-0170760-9. N.S. Bailey, C. Katinas, Y.C. Shin, Laser direct deposition of AISI H13 tool steel powder with numerical modeling of solid phase transformation, hardness, and residual stresses, J. Mater. Process. Technol. 247 (2017) 223–233, https://doi.org/10. 1016/j.jmatprotec.2017.04.020. Y.S. Yang, S.J. Na, A study on residual stresses in laser surface hardening of a medium carbon steel, Surf. Coat. Technol. 38 (3) (1989) 311–324, https://doi.org/ 10.1016/0257-8972(89)90093-5 http://www.sciencedirect.com/science/article/ pii/0257897289900935.
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Statistical modelling and optimization of microhardness transition through depth of laser surface hardened AISI 1045 carbon steel
T
⁎
Changrong Chena, , Xianbin Zengb, Qianting Wangb, Guofu Liana, Xu Huanga, Yan Wangc a
School of Mechanical and Automotive Engineering, Fujian University of Technology, Fuzhou 350118, China College of Materials Science and Engineering, Fujian University of Technology, Fuzhou 350118, China c School of Computing, Engineering and Mathematics, University of Brighton, Brighton BN2 4AT, United Kingdom b
H I GH L IG H T S
transition is defined as the division of micro-hardness over layer depth. • Hardness responses are statistically modelled with sound accuracy and generalization. • Three of three variables on microhardness are studied by metallographic analysis. • Effects of AISI 1045 steel has a threefold increase after laser surface hardening. • Hardness • Microhardness gradient is monotonic surfaces without local maximum in design space.
A R T I C LE I N FO
A B S T R A C T
Keywords: Laser surface hardening Response surface methodology Hardened layer Microhardness property Metallographic analysis
The mechanical properties of laser surface hardened material are closely related to the hardened layer. Respective study of geometrical dimension and microhardness would only result in insufficient understanding of the hardened layer. In this paper, a central composite design (CCD) is proposed, based on response surface methodology (RSM), to investigate the influences of processing parameters including laser power (LP), scanning speed (SS) and defocusing distance (DD) on the geometrical dimensions, microhardness and microhardness transition of laser surface hardened AISI 1045 carbon steel. Two-tailed Pearson correlation of selected responses was firstly undertaken to screen out unrelated ones. Second order response surface models were then developed and tested for three responses: hardened width (HW), microhardness of hardened area (MH) and hardness gradient (HG). Scanning electron microscopy(SEM) was conducted to evaluate the evolution of microstructure with three process parameters. The results indicate that three response models are capable of interpreting the hardened width, microhardness and hardness gradient with satisfactory accuracy. It is observed that the HW is only linearly determined by LP and SS, while the hardness properties (MH and HG) are both affected by all the investigated parameters significantly. The hardness of base metal can be improved from 200HV to 660HV after laser surface hardening. Quadratic correlation can be obtained when the HG is transformed inversely. Validation experiment was finally conducted for testing the generalisation of fitted regression models. As the maximum relative prediction errors for three responses are respectively 4.18%, 2.25% and −4.36%, good generalisation has been accomplished by the developed models.
1. Introduction Laser surface hardening (LSH) heats up the materials superficially by laser irradiation and obtains desired structural transformation through materials’ self-quenching capabilities [1–4]. The microhardness of hardened area could reach the order of 675-750HV with surface roughness of 0.6–1.2 μm [5,6]. The process is popularly used for improving the wear resistance of tribological systems due to the ⁎
advantageous characteristics of no quenching medium, minimal distortion and high flexibility [1,3,7–9]. LSH is also desirably used to enhance regional properties of large volume tools, such as the cutting edges of stamping dies, closing areas of injection moulds and radii of deep drawing dies, where entire treatment of structures by conventional methods requires much larger equipment and more accurate deformation control [10–13]. Most of the research endeavours to obtain enough mechanical
Corresponding author. E-mail address: [email protected] (C. Chen).
https://doi.org/10.1016/j.optlastec.2019.105976 Received 14 April 2019; Received in revised form 6 October 2019; Accepted 23 November 2019 Available online 14 December 2019 0030-3992/ © 2019 Elsevier Ltd. All rights reserved.
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properties, usually hardness and wear resistance, in processed area. Zhang et al. [14] carried out LSH of low carbon steel to obtain tiny lathy martensite with increased hardness on steel surface. They also found that the treatment decreased the friction coefficient and improved the wear resistance. Babu et al. [15] used a Box-Behnken design to develop mathematical models between process parameters and wear resistance. They presented that laser surface hardened samples exhibit a lower wear rate and coefficient of friction compared to as-received samples. Sarkar et al. [16] laser surface hardened low carbon steel (0.05% and 0.07% carbon) of around 1 mm thickness with a high power fiber laser. They also observed increase in microhardness, tensile strength, reduction in percentage elongation and improvement in scratch resistance of the hardened surface. Syed et al. [17] treated a C-Mn low carbon automotive steel sheet and obtained significantly improved hardness, yield strength and ultimate tensile strength. Cao et al. [18] investigated the microstructure, wear and rolling contact fatigue of wheel and rail materials to optimize processing parameters of laser dispersed quenching. They obtained homogeneous martensite in the treated wheel/rail rollers, and the surface hardness increased significantly. Moradi and KaramiMoghadam [19] surveyed the effects of process variables on the hardened layer geometry, average micro-hardness and the ferrite phase percentage of laser surface hardened AISI 4130 carbon steel. The hardness has been increased to three times of the base material. Additionally, some researchers have been devoted to achieving designated hardened surface layers. Badkar et al. [20,21] applied response surface methodology (RSM) to model, optimize and analyse the influences of dominant laser-processing parameters on heat input and bead geometries of laser hardened surface quality of commercially pure titanium sheet of 1.6 mm in thickness using a 2 kW continuous wave Nd:YAG laser. Li et al. [2] compared the effects of LSH process parameters using two industrial lasers (high-power diode laser and CO2 laser) on structure, case depth, and microhardness of the AISI 1045 steel. They found that the depths of heat affected zone (HAZ) due to the former laser were almost equal in total HAZ, but varied through the HAZ for the second type. Sun et al. [22] used two shapes of laser beams to surface treat 42CrMo cast steel for uniform hardened layer. They observed that a wider and more uniform hardened layer could be obtained using the non-uniform intensity beam at relative higher scanning velocities and laser power. From the literature, one can find that mechanical properties, as straightforward performance criteria, are commonly considered as important process outputs. The geometries of hardened layer, on the other hand, are also useful results for much more complicated surface processing. However, these two aspects are commonly treated as irrelevant process responses and studied independently. Furthermore, the performance of treated layer is also determined by the transition boundary between hardened and untreated zone. Residual stresses of high magnitudes would be induced inside the hardened plate due to high thermal gradients and non-uniform plastic deformation [23]. While compressive stresses are detected near the surface, tensile counterparts are resulted in the deeper area [24]. This is primarily caused by the phase transformation of martensite from the thermal processing [25]. Taking into consideration the phase-property correlation, abrupt change of mechanical properties in processed components symbolizes fragile bondings and should be avoided. This paper investigates the microhardness and its gradient in depth to obtain the smoothest transition of laser surface hardened AISI 1045 carbon steel using response surface methodology. A central composite design (CCD) was proposed for three input process parameters: laser power, scanning speed and defocusing distance. A correlation study was then conducted to the collected response data and three responses including hardened width (HW), microhardness of hardened layer (MH) and hardness gradient (HG) were considered in the following regression analysis. The effects of process parameters on the responses were mathematically modelled using analysis of variance(ANOVA).
Table 1 Chemical composition of the AISI 1045 steel(wt%). C
Si
Mn
Cr
Ni
Cu
Fe
0.42–0.50
0.17–0.37
0.50–0.80
⩽0.25
⩽0.25
⩽0.25
Bal.
Microstructure evaluation of laser hardened zones was also performed using scanning electron microscopy(SEM) to understand the parameter effects. Validation of established models was finally carried out through the process optimization. 2. Experimental 2.1. Material and experimental set-up Laser surface hardening was conducted on the AISI 1045 steel substrate with dimensions of 50×25×10 in mm. The chemical composition is shown in Table 1. A laser cladding system was used for the surface hardening experiment in this research, as depicted in Fig. 1. A Lasermesh FDH0273 laser head with focus length of 300 mm is mounted at a FANUC M710iC/50 industrial robot to deliver laser beams generated by an IPG high power fiber laser YLS-3000. The shielding gas Argon is coaxially delivered onto the hardening surface at a pressure of 0.5 MPa to avoid surface oxidization at high temperature. The gas flow rate is kept constant by a flow valve for all the experimental runs. 2.2. Experimental procedure The substrate was cleaned with acetone to remove surface impurities before surfacing and processed at ambient environment without preheating for better accordance with industrial requirements. Experimental runs of hardening processing were conducted according to a Central Composite Design, proposed based on RSM, in a random manner. The investigated process parameters include laser power (LP), scanning speed (SS) and defocusing distance (DD). The parameter centre and span were selected for better modelling performance based on previous research. Five levels of all three variables were studied, as listed in Table 2. An alpha level of 1.682 was selected for the axial points and six replications were applied at the centre point only to investigate data accuracy, leading to an only 20-run experimental matrix. The variable values were round off for better control, as illustrated in Table 3. After laser hardening, the specimens were transversely sectioned by wire electrical discharge machining (Wire EDM), ground and polished for geometrical morphology and microstructure observation (using an ANDONSTAR portable Optical Microscope and a TM3030 Plus Scanning Electron Microscope) after 30s etching in 4% nitric acid alcohol. The cross-sectional profile characteristics of processed layer are defined as shown in Fig. 2 wherein the microhardness is measured at the cross points of three zones. The gradient of micro-hardness is calculated from the difference of averaged values between fusion zone (5 points) and unaffected area (2 points) divided by the hardened depth, as shown in Eq. (1). As the treatment of actual parts is normally conducted in multi-pass manner, the hardness gradient in transverse direction is not considered in this work.
∇Hv,d =
HvFZ − HvUZ d
(1)
The results were then appended in Table 3 as well. A two-tailed Pearson correlation matrix was proposed using IBM SPSS® Statistics 22 to investigate the correlations among these responses, as shown in Table 4. From the table, one can find that the width, depth and area of hardened layer are strongly correlated with each other. The microhardness of hardened layer, on the other hand, 2
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Fig. 1. Laser cladding system used for hardening processing.
by second order polynomials. The mathematical models correlating process variables to responses HW, MH and HG during laser surface hardening of AISI 1045 steel are depicted below:
Table 2 Laser hardening variables and levels. Variable
Notation
Unit
Laser Power Scanning Speed Defocusing Distance Hardened Width Hardened Depth Hardened Area Microhardness Hardness Gradient
LP SS DD
kW mm/s mm
w d A Hv ∇Hv,d
mm mm mm2 HV1 HV1/mm
Levels 0.300 3 −2
0.475 5 −0.8
0.750 8 1 Response Response Response Response Response
1.025 10 2.8
⎧ w = 0.899+ 2.547 × LP + 0.0409 × SS − 8.855 × 10−3 × DD ⎪ − 0.141 × LP × SS + 0.0237 × DD2 ⎪ ⎪ Hv = 334.693 + 0.588 × LP + 26.693 × SS + 23.393 × DD ⎪ − 44.054 × LP × DD ⎪ ⎪ + 2.233 × SS × DD − 316.033 × LP2 − 2.427 × SS2 ⎨ − 4.613 × DD2 ⎪ 1000 = 1.669 − 0.0261 × LP − 0.158 × SS + 0.113 × DD ⎪ ∇H − 110 ⎪ v,d − 0.306 × LP × SS ⎪ ⎪ + 0.343 × LP × DD − 0.0387 × SS × DD + 3.132 × LP 2 ⎪ + 0.0219 × SS 2 ⎩
1.200 12 4
1 2 3 4 5
has only about 42% probability relevant to three profile characteristics. The correlations of depth and area to width are demonstrated in Fig. 3. Both the depth and area of hardened layer are second order polynomials of width, as shown in Eq. (2), with adjusted R-squared values of 0.9309 and 0.9173. Therefore, only the width of hardened layer is considered as one profile characteristic for the mathematical modelling. The other characteristics, depth and area, can then be identified by Eq. (2). 2 ⎧ d = − 0.0166 + 0.0703w + 0.0943w 2 ⎨ = 1.444 − 1.523w + 0.590w ⎩A
(3) Tables 5–7 show the ANOVA results for three responses, respectively. As can be found that the p-values for selected regression models are all less than 0.01% and the lack of fit values are all greater than 0.05, which indicate that the selected models interpret the experimental data with more than 99.99% accuracy and lack of fitness is probably caused by random errors. Small PRESS (predicted residual error sum of squares) values in the tables suggest good capability of predicting new experimental results. The values of Adequate Precision are both much larger than 4, which also means high confidence in the model predictions. Table 8 illustrates the coefficients of determination for three response models. From the table, it is obvious that R2 and Adjusted R2 values are pretty close to 1 and the divergence of Predicted R2 from Adjusted R2 are less than 0.2. Additionally, it can also be evidenced by the little discrepancy between model predictions and experimental data depicted in Fig. 4. Therefore, the regression models have excellent goodness of fits and prediction capacity.
(2)
3. Results and discussion 3.1. Response surface models Multiple regression was carried out to fit the response data by analysing statistical significance test on model coefficients and lack-offits. All the three responses, Hardened Width (HW), Micro-hardness (MH) and Hardness gradient (HG, transformed inversely) are modelled 3
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Table 3 Central composition design and responses. Run
LP, kW
SS, mm/s
DD, mm
w, mm
d, mm
A, mm2
HvFZ , HV1
HvUZ , HV1
∇Hv,d , HV1/mm
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
0.75 0.75 0.475 0.475 1.025 1.025 0.474 1.025 0.75 0.75 0.475 1.025 0.75 0.75 0.75 0.3 0.75 0.75 1.2 0.75
8 8 5 10 10 5 5 5 8 8 10 10 8 8 8 8 3 12 8 8
1 1 2.8 −0.8 2.8 −0.8 −0.8 2.8 1 1 2.8 −0.8 1 −2 4 1 1 1 1 1
2.336 2.354 2.098 1.864 2.650 3.078 1.918 3.068 2.352 2.187 1.937 2.556 2.309 2.368 2.731 1.772 2.786 2.140 2.898 2.107
0.660 0.691 0.529 0.385 0.837 1.062 0.481 1.134 0.698 0.630 0.427 0.829 0.705 0.660 0.706 0.459 0.924 0.565 1.023 0.514
1.070 1.133 0.820 0.515 1.471 2.323 0.687 2.387 1.140 1.030 0.589 1.510 1.162 1.138 1.225 0.640 1.744 0.828 2.232 1.147
663.9 652.8 630.5 543.8 607.4 689.9 604.9 610.2 658.0 665.9 591.8 628.9 657.6 618.0 610.4 563.1 640.3 583.0 620.0 663.2
205.6 235.6 200.6 216.1 195.1 194.6 196.8 207.2 210.4 205.9 205.2 212.3 193.1 202.3 212.5 204.1 201.6 212.5 205.8 201.6
694.5 650.1 812.8 851.1 492.7 466.4 848.5 355.4 641.3 730.2 905.3 502.6 658.9 629.9 563.6 782.3 474.8 655.9 404.9 898.0
Table 5 Analysis of variance for width (w). Source
Sum of Squares
df
Mean Square
F Value
p-value Prob > F
Model LP SS DD (LP×SS) DD2 Residual Lack of Fit Pure Error Cor Total
2.78 2.23 0.38 0.065 0.076 0.084 0.14 0.091 0.053 2.92
5 1 1 1 1 1 14 9 5 19
0.56 2.23 0.38 0.065 0.076 0.084 0.010 0.010 0.011
53.86 215.73 37.04 6.32 7.37 8.13
< 0.0001 < 0.0001 < 0.0001 0.0248 0.0167 0.0128
Significant
0.96
0.5510
Not Sign.
Fig. 2. Hardness gradient demonstration.
3.2. Effects of process parameters on responses
Table 4 Pearson correlation of response variables.
Width Depth Area Microhardness
Width
Depth
Area
Microhardness
1 0.966 0.949 0.422
0.966 1 0.977 0.420
0.949 0.977 1 0.429
0.422 0.420 0.429 1
Fig. 5 shows the perturbation of three responses due to significant factors. It is obvious that all three responses, HW, MH and HG are influenced by three investigated process parameters. This can also be found from the model terms with small p-values(Prob>F ) listed in Table 5–7. Specifically, the hardened width is linearly determined by LP (positively) and SS (negatively), but non-linear with DD. The microhardness in hardened layer is non-linearly influenced by all three
Fig. 3. Correlation between depth, area and width of hardened layer. 4
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Table 6 Analysis of variance for microhardness (Hv ).
Table 8 Coefficients of model determination.
Source
Sum of Squares
df
Mean Square
F Value
p-value Prob > F
Model LP SS DD (LP× DD) (SS× DD) LP2 SS2 DD2 Residual Lack of Fit Pure Error Cor Total
25838.74 4998 5073.62 195.61 3807.73 821.36 7506.16 3976.39 3110.25 737.01 615.76 121.25 26575.74
8 1 1 1 1 1 1 1 1 11 6 5 19
3229.84 4998 5073.62 195.61 3807.73 821.36 7506.16 3976.39 3110.25 67 102.63 24.25
48.21 74.6 75.72 2.92 56.83 12.26 112.03 59.35 46.42
< 0.0001 < 0.0001 < 0.0001 0.1155 < 0.0001 0.005 < 0.0001 < 0.0001 < 0.0001
Significant
4.23
0.0674
Not Sign.
Response
R-Squared
Adjusted RSquared
Predicted RSquared
Adequate Precision
w Hv ∇Hv,d
0.9506 0.9723 0.9303
0.9329 0.9521 0.8796
0.8956 0.8703 0.7307
26.716 25.451 15.112
defocusing distance rotating about a relative high scanning speed to lower defocusing distance. 3.3. Metallographic analysis In the previous section, the influences of process parameters on the microhardness of hardened layer was analysed directly from the macroscopic response data. This section, on the other hand, is to reveal the effect mechanism from microscopic observation.
parameters with maximums in design space. The hardness gradient is negatively proportional to DD, but non-linearly affected by LP and SS. Apart from main effects, the width of hardened layer is also influenced by the interaction of LP and SS, as illustrated in Fig. 6. The gradient of width with respect to laser power becomes smaller as the scanning speed increases. Corresponding 3D response surface of hardened width to LP and SS is illustrated in Fig. 7. The 3D surface of width is a slightly curved plane inclined in the direction of increasing LP and decreasing SS. The microhardness, as shown in Table 6, is relevant to two interaction effects LP×DD and SS×DD. From Figs. 8 and 9, one can observe that the microhardness becomes wider and lower parabolas of LP and SS with maximums shifting from edges to centres of design space, as defocusing distance increases from −2 to 4. Figs. 10 and 11 depict the 3D response surfaces of layer microhardness to (LP, DD) and (SS, DD), respectively. The former surface indicates a sheer ascending from the front corner to back, while keeping much more flattened from left to right. The latter one, on the other hand, obtains similar increasing trends from four corners. The gradient of microhardness in hardened layer, as shown in Table 7, is affected by all three interactions, LP×SS, LP×DD and SS×DD. The detail interaction effects are demonstrated in Figs. 12, 14 and 16. As the velocity of scanning increases, the gradient shifts from a gently curved line to a more apparent parabola function of laser power, leading to a lower maximum in the design space. While as the defocusing distance increases, contrary variations are resulted with regard to LP and SS, respectively. Figs. 13, 15 and 17 depict the 3D response surfaces of the microhardness gradient in depth to (LP, SS), (LP, DD) and (SS, DD), respectively. The response surface of HG to LP and SS resembles part of conical surface, revolving about the low power and medium scanning speed position. The second surface appears like a deflected plane curved at the low power and in-substrate defocusing distance corner. The last surface presents like a curve at higher
3.3.1. Effect of laser power Fig. 18 illustrates the microstructure variation of hardened layer using different laser powers. It can be seen that the hardened layer is mainly composed of lathy or fine acicular martensite. As the laser power increases, referring to Fig. 18(a) and (b) the hardened layer is more uniformly and finely martensited into acicular form with reduced austenite. This is because the increased laser power provides more heat input into the substrate, leading to higher temperature gradient between hardened area and untreated zone. Therefore, the martensite transformation is more thoroughly completed with finer grains. However, the continued increase in laser power would prolong the molten pool to allow temperature rise in the substrate and thus decrease the thermal gradient. Therefore, the hardened surface is not completely transformed into martensite with large amount of austenite retained, as illustrated in Fig. 18(c). This explains why the microhardness of hardened layer is a convex parabolic function of laser power. 3.3.2. Effect of scanning speed The effect of scanning speed on the microstructure evolution can be seen from Fig. 19. Similarly, as the scanning speed is reduced, the hardened layer is more uniformly and finely martensited into acicular form with reduced austenite, as demonstrated in Fig. 19(b) and (c). This is because the decreased speed allows more laser energy being absorbed by the substrate, leading to higher degree supercooling of the hardened area. Therefore, the martensitation transformation is more thoroughly completed. However, the continued decrease in scanning speed would then reduce the degree of supercooling. The hardened zone would not completely transform into martensite and some amount of austenite is retained. The similar grain sizes of martensite in Fig. 19(a) and (b) can be attributed to the close resultant microhardness values, as illustrated
Table 7 Analysis of variance for microhardness gradient(∇Hv,d). Source Model LP SS DD (LP× SS) (LP× DD) (SS× DD) LP2 SS2 Residual Lack of Fit Pure Error Cor Total
Sum of Squares −5
1.018×10 7.408×10−6 8.551×10−7 2.838×10−7 3.598×10−7 2.312×10−7 2.462×10−7 7.434×10−7 3.301×10−7 7.627×10−7 4.987×10−7 2.640×10−7 1.095×10−5
df 8 1 1 1 1 1 1 1 1 11 6 5 19
Mean Square −6
1.273×10 7.408×10−6 8.551×10−7 2.838×10−7 3.598×10−7 2.312×10−7 2.462×10−7 7.434×10−7 3.301×10−7 6.934×10−8 8.311×10−8 5.280×10−8
5
F Value
p-value Prob > F
18.36 106.84 12.33 4.09 5.19 3.33 3.55 10.72 4.76
< 0.0001 < 0.0001 0.0049 0.0681 0.0437 0.0951 0.0862 0.0074 0.0517
Significant
1.57
0.3176
Not Sign.
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Fig. 4. Comparison of predicted and actual responses.
Fig. 5. Perturbation of responses due to significant factors. (A: laser power; B: scanning speed; C: defocusing distance).
Fig. 6. Interaction of LP and SS on width.
Fig. 7. 3D Response surface of width to LP and SS.
in Fig. 5(b). Therefore, the microhardness of hardened layer is also a convex function of scanning speed.
3.4. Model confirmation The aim of this LSH process is to maximize the HW and achieve target MH with minimum gradient through the layer depth. The desirability function approach (DFA) is used to deal with the multiple objectives by converting them into one dimensionless desirability function. The multiple responses are characterised by individual scalê i = 1, 2, free values between 0 and 1 using desirability functions (di ( yi ), …, m, where yi ̂ is the ith estimated response model and m is the number of responses). The transformation from yi ̂ to di can be achieved by Eqs. (4)–(6), i.e. the smaller the better(SB), the larger the better(LB), and the target the better(TB).
3.3.3. Effect of defocusing distance Fig. 20 illustrates the effect of defocusing depth on the microstructure variation. As the defocusing amount decreases, the hardened layer is more uniformly and finely martensited into acicular form. This is due to that the closer focusing increases the power density of laser spot and more laser energy is applied to unit substrate area, thereby leading to higher thermal gradient between melt and untreated zone. More proportion of austenite has been transformed into martensite, as illustrated in Fig. 20(b). That is why the microhardness of hardened layer is also a parabolic function of defocus depth as well. 6
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Fig. 8. Interaction of LP and DD on microhardness.
Fig. 12. Interaction of LP and SS on hardness gradient.
Fig. 9. Interaction of SS and DD on microhardness.
Fig. 13. 3D response surface of microhardness gradient to LP and SS.
Fig. 10. 3D response surface of microhardness to LP and DD.
Fig. 14. Interaction of LP and DD on hardness gradient.
Fig. 11. 3D Response surface of microhardness to SS and DD.
Fig. 15. 3D Response surface of microhardness gradient to LP and DD. 7
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TB:
yi ̂ < Li or yi ̂ > Ui
0,
⎧ ⎪ ⎪ ⎪ di (yi )̂ = ⎨ ⎪ ⎪ ⎪ ⎩
⎡ Ui − yUi ̂ ⎤ , ⎣ Ui − Ti ⎦ 1,
Li , Ui, TiL
TiU
yi ̂ − Li
r 1i
⎡ L ⎤ , ⎣ Ti − Li ⎦ r 2i
Li ⩽ yi ̂ < TiL TiU < yi ̂ ⩽ Ui TiL ⩽ yi ̂ ⩽ TiU
(6)
where and are the minimal, maximal acceptable values, the lower and upper targets of the ith response, respectively. si, r 1i and r2i are user-specified weights describing the shapes of desirability functions. The overall desirability, denoted by D, is the weighted geometric mean of all the transformed responses, given by
D = (∏ diwi )1/ ∑ wi
Fig. 16. Interaction of SS and DD on hardness gradient.
The multiple response surface optimisation model is then accomplished by maximising the overall desirability D. The multi-objective criterion is presented in Table 9 for process optimization. The first 10 optimal hardening conditions according to the criterion are summarized in Table 10. Optimum response combination would be accomplished at a maximum HW of about 3.349 mm, a MH of 660HV1, and a HG of about 353.6 HV1/mm. The corresponding intervals for three process parameters, LP, SS and DD, are [1.10, 1.20] kW, [3.00, 4.78] mm/s and [-0.43, 0.13] mm. Fig. 21 plots the overlay area of LP and SS with target responses settled as HW>3.0 mm, MH = 660HV1 and HG<400 HV1/mm. The shadow area in blue signifies the parameter space fulfilling the target. As can be seen from Fig. 21(a), the optimal parameter space is a circular segment at down right side. When DD is reduced from 0.6 to 0, −0.6 and −1.2, as shown in Fig. 21(b) to (d), the optimal parameter space moves right downwards with greater areas. The values of laser power and scanning speed become greater with broader range. Therefore, appropriate sets of input variables can be selected to achieve high quality laser surface hardened layers. For better experimental operation, the 6th process condition was selected for the confirmation of response models. Additionally, another extra trial was conducted to test the model generalization at parameter setting listed in Table 11. It can be observed that the predictions by response models are in good accordance with corresponding experimental data. The maximum relative errors of model predictions for three responses are 4.18%, 2.25% and −4.36%, respectively. Therefore, the established regression models are capable of predicting design space generally.
Fig. 17. 3D Response surface of microhardness gradient to SS and DD.
SB:
LB:
1, yi ̂ < Li ⎧ ⎪ Ui − yi ̂ si di (yi )̂ = ⎡ ⎤ , Li ⩽ yi ̂ ⩽ Ui ⎨ ⎣ Ui − Li ⎦ ⎪ 0, yi ̂ > Ui ⎩
(4)
0, yi ̂ < Li ⎧ ⎪ yi ̂ − Li si di (yi )̂ = ⎡ ⎤ , Li ⩽ yi ̂ ⩽ Ui ⎨ ⎣ Ui − Li ⎦ ⎪ 1, yi ̂ > Ui ⎩
(5)
(7)
4. Conclusions In this research, response surface methodology is utilized to understand the influences of LSH process parameters (including laser power, scanning speed and defocusing distance) on the cross-sectional geometry and hardness gradient of the hardened layer. Second-order
Fig. 18. Comparison of microstructure at different laser powers(SS = 8 mm/s,DD = 1 mm). 8
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Fig. 19. Comparison of microstructure at different scanning speeds(LP = 750 W,DD = 1 mm).
Fig. 20. Comparison of microstructure at different defocus depths(LP = 750 W,SS = 8 mm/s). Table 9 Optimization criteria applied in this study. Name
LP, kW
SS, mm/s
DD, mm
HW, mm
MH, HV1
HG, HV1/mm
Goal Lower Limit Upper Limit Importance
In range 0.3 1.2 5
In range 3 12 5
In range −2 4 5
maximize 1.772 3.078 5
target = 660 543.8 689.9 5
Minimize 355.4 905.3 5
Table 10 Optimal solutions obtained based on the criterion.
•
No.
LP
SS
DD
HW
MH
HG
Desirability
1 2 3 4 5 6 7 8 9 10
1.18 1.16 1.17 1.13 1.16 1.20 1.15 1.19 1.19 1.18
4.50 3.90 4.36 3.43 4.09 4.78 3.79 3.74 4.69 4.43
−0.03 −0.02 0.03 −0.08 0.02 −0.10 −0.01 −0.32 −0.06 −0.03
3.349 3.371 3.342 3.381 3.356 3.342 3.369 3.455 3.340 3.352
660.0 660.0 660.0 660.0 660.0 660.0 660.0 660.0 660.0 660.0
353.6 351.1 354.1 351.0 352.5 355.1 351.4 344.2 355.0 353.2
1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00
• Selected
Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
polynomial mathematical models for HW, MH and HG were developed using experimental observations. Based on the results, following conclusions can be drawn:
Acknowledgements The authors are grateful for the financial support from the National Natural Science Foundation of China (Grant No. 51575110), the Ministry of Industry and Information Technology (Grant No. 2016-75563), the Provincial Education and Research Program for Young and Middle-aged Teachers (Grant No. JAT170376) and Fujian University of Technology (Grant No. E0600276). The authors are thankful to the Public Service Platform for Technical Innovation of Machine Tool Industry in Fujian Province for the technical support.
• The profile characteristics (depth, width and area of hardened layer) •
of hardness gradient are quadratically determined; The effects of three process variables on the microhardness of hardened layer can be explained by the martensitation process via metallographic analysis; The microhardness of the base material can be improved to threefold (from 200HV1 to 660HV1) with a hardness gradient of 355.1HV1/mm.
are significantly correlated with each other. Depth and area of hardened zone can be considered as quadratic functions of the width; All three responses, w,Hv and ∇Hv,d are determined by three process variables. While the width of hardened layer is approximately linear with three variables, the microhardness and inverse transformation 9
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Fig. 21. Overlay plot with target formation quality of HW > 3 mm, MH = 660HV1 and HG < 400HV1/mm. [2] R.F. Li, Y.J. Jin, Z.G. Li, K. Qi, A comparative study of high-power diode laser and CO2 laser surface hardening of AISI 1045 steel, J. Mater. Eng. Perform. 23 (9) (2014) 3085–3091, https://doi.org/10.1007/s11665-014-1146-x. [3] H. Ki, S. So, S. Kim, Laser transformation hardening of carbon steel sheets using a heat sink, J. Mater. Process. Technol. 214 (11) (2014) 2693–2705, https://doi.org/ 10.1016/j.jmatprotec.2014.06.013. [4] W.M. Steen, Laser Material Processing, Springer, London, 2010. [5] A.V. Aborkin, V.E. Vaganov, A.N. Shlegel, I.M. Bukarev, Effect of laser hardening on die steel microhardness and surface quality, Metallurgist 59 (7–8) (2015) 619–625, https://doi.org/10.1007/s11015-015-0148-8. [6] M. Moradi, H. Arabi, S.J. Nasab, K.Y. Benyounis, A comparative study of laser surface hardening of AISI 410 and 420 martensitic stainless steels by using diode laser, Opt. Laser Technol. 111 (2019) 347–357, https://doi.org/10.1016/j. optlastec.2018.10.013. [7] L. Orazi, A. Fortunato, G. Cuccolini, G. Tani, An efficient model for laser surface hardening of hypo-eutectoid steels, Appl. Surf. Sci. 256 (6) (2010) 1913–1919. [8] G. Tani, A. Fortunato, A. Ascari, G. Campana, Laser surface hardening of martensitic stainless steel hollow parts, CIRP Ann. – Manuf. Technol. 59 (1) (2010) 207–210. [9] S.M. Shariff, T.K. Pal, G. Padmanabham, S.V. Joshi, Influence of chemical composition and prior microstructure on diode laser hardening of railroad steels, Surf. Coat. Technol. 228 (228) (2013) 14–26. [10] J. Zhou, Y. Fu, H. Xu, Y. Zhang, J. Yang, Y. Zhang, Investigation into the effects of laser surface hardening on CrWMn steel, in: X.P. Xu (ed.), Advances in Grinding and Abrasive Processes, vol. 259–2 of Key Engineering Materials. Huaqiao Univ; Kistler China Ltd; Jinshan Stone tools Technol Ltd. pp. 502–506, ISBN 1-87849-919-9; 2004. doi:https://doi.org/10.4028/www.scientific.net/KEM.259-260.502; 12th Grinding and Machining Conference, Kunming, PEOPLES R CHINA, NOV 28-30, 2003.
Table 11 Experimental results and model predictions of validation run. Run
LP (kW)
SS (mm/ s)
DD (mm)
1
1.200
5
0
2
0.935
6
−0.4
Predicted Actual Error (%) Predicted Actual Error (%)
HW (mm)
MH (HV1)
HG (HV1/ mm)
3.342 3.208 4.18 2.732 2.648 3.17
660 653.4 1.02 682.4 667.4 2.25
355.1 371.3 −4.36 526.6 525.4 0.23
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