Materials Sciences and Applications, 2015, 6, 978-994
Published Online November 2015 in SciRes.
How to cite this paper: Billaud, G., El Ouafi, A. and Barka, N. (2015) ANN Based Model for Estimation of Transformation
Hardening of AISI 4340 Steel Plate Heat-Treated by Laser. Materials Sciences and Applications, 6, 978-994.
ANN Based Model for Estimation of
Transformation Hardening of
AISI 4340 Steel Plate
Heat-Treated by Laser
Guillaume Billaud, Abderazzak El Ouafi, Noureddine Barka
Mathematics, Computer Science and Engineering Department, University of Quebec at Rimouski, Rimouski,
Received 7 October 2015; accepted 15 November 2015; published 18 November 2015
Copyright © 2015 by authors and Scientific Research Publishing Inc.
This work is licensed under the Creative Commons Attribution International License (CC BY).
Quality assessment and prediction becomes one of the most critical requirements for improving
reliability, efficiency and safety of laser surface transformation hardening process (LSTHP). Accu-
rate and efficient model to perform non-destructive quality estimation is an essential part of the
assessment. This paper presents a structured and comprehensive approach developed to design
an effective artificial neural network (ANN) based model for quality estimation and prediction in
LSTHP using a commercial 3 kW Nd:Yag laser. The proposed approach examines laser hardening
parameters and conditions known to have an influence on performance characteristics of hard-
ened surface such as hardened bead width (HBW) and hardened depth (HD) and builds a quality
prediction model step by step. The modeling procedure begins by examining, through a structured
experimental investigations and exhaustive 3D finite element method simulation efforts, the rela-
tionships between laser hardening parameters and characteristics of hardened surface and their
sensitivity to the process conditions. Using these results and various statistical tools, different
quality prediction models are developed and evaluated. The results demonstrate that the ANN
based assessment and prediction proposed approach can effectively lead to a consistent model
able to accurately and reliably provide an appropriate prediction of hardened surface character-
istics under variable hardening parameters and conditions.
Laser Hardening Process, AISI 4340 Steel, Case Depth, Hardened Bead Width, Artificial Neural
Netwo rk
G. Billaud et al.
1. Introduction
In the industry, many steel components require a surface heat treatment in order to have the desired surface
qualities such as hardness and wear resistance. Among the available processes, laser hardening process (LHP) is
one of the most efficient, as it allows a very fast and localized metallurgical transformation. In addition, the
process generates a hard surface layer with low distortion [1]. Using high energy beam, the surface is rapidly
heated to reach the transition temperatures (microstructure changes) before being quenched by heat conduction
into the colder core of the material. Consequently, a martensitic layer is produced without affecting the core of
the material [2].
Despite its industrial advantages, pred icting hardness profiles with a good accuracy remains difficult. Indeed,
besides the process parameters (Power, scanning velocity and focus diameter), which can be properly set, the
process is affected by the non-line ar b ehavio r o f the r mo -physical and metallurgical properties of the material [1].
It makes the temperature distribution uneasy to predict by complicating the resolution of the governing heat-
flow equation. Experimental tests are also expensive in terms of time and resources, especially if one wants to
test many combinations of control parameters to have a better understanding of the process.
Among all the approaches that can be used to understand the process and ultimately to predict its performance,
3D simulation represents a powerful tool for combining multi-physics problems and taking into account the ma-
terial and complex geometries. In fact, the developed model includes the non-linear properties of the material
and the heat-flow equation is solved using the finite element method (FEM) [3] [4]. The FEM enables solving
the governing heat-flow equation that determines the temperature distribution for each time step during the
heating process. The hard ness is t hen appr oximated by the equations of Ashby and Eas t erling [5]. The advant age
of the simulation is that, although it might be long and tedious to implement, once it is completed and experi-
mentally verified in a few cases, one can test any combination of input parameters and quickly generate a large
number of data which can be used for further exploitation. Many studies have been conducted to optimize the
various laser process parameters (surface hardening, laser welding, laser cutting, etc.) through statistical meth-
ods such as the ANOVA method. It can be applied in many fields of engineering, including production proc-
esses and products for professional and consumer markets all over the world [6]. S-L Chen a nd D. She n [7] used
the Taguchi tools such as graphic designs of parameters and analysis of variance (ANOVA) to optimize the
hardened depth (HD) and the hardened bead width (HBW) in the case of the LHP. Bad kar and Pandey [8] used
the same tools to determine the relative importance of each parameter on the LHP. K.Y. Bentounis, A.G. Olabi
and M.S.J. Hashmi [9] conducted a similar study in the case of a laser welding process. Most recently, Sathiya et
al. [10] also used the Taguchi method to optimize the laser welding parameters. Given that experimental char-
acterization requires great efforts in terms of time and money, it is not easy to experiment all the combinations
of the input parameters. The Taguchi method reall y is an asset, as it is a partial factorial design that only requir es
some combinations of the input parameters in order to be performed and yet, it gives accurate statistical results
in the overall process.
Others studies are conducted using artificial neural networks (ANN) in order to improve the performance of
the laser processes [11]. Ciurana J. et al. [12] used ANNs to establish a model for laser micromachining of
hardened steel and to optimize the process parameters. Pan Q.Y et al. [13] performed a similar study by using a
neural network to model the non-linear relationship between laser processing parameters and corrosion resis-
tance of the surface of stainless steel during the process of laser surface re-melting, which loc ally improved the
corrosion resistance of the steel. Munteanu and Adriana [14] predicted the surface hardness of steel usi ng a ne u-
ral network in the case of an electron beam machining process which is similar to the LHP. F. Lambiase et al.
developed a prediction model of laser hardening by means of an ANN using experimental datasets and linear
interpolatio ns between those experimental measures to train the network. Ho wever, to obtain good and efficient
modeling results with ANN techniques, a large quantity of experimental data is advantageous and the observa-
tions should cover a sampling space as wide as possible in order to simplify the interpolation task.
Indeed, in any modelling experi ment, the results depend, to a large degree, on the method used to collect data.
In a lot of cases, full factorial experiments are conducted. This appro ach cannot be implemented when too many
factors are under consideration, because the number of repetitions required would be prohibitive in time and cost.
Regular fractional factorial designs cannot produce credible results when interactions among the factors exist.
By contrast, the use o f a testing strategy such as the orthogonal arrays (OAs) developed by Taguchi leads to an
efficient and ro bust fractional factorial desig n of experiments that can collec t all the statistically significant da ta
G. Billaud et al.
with a minimum number of repetitions. Accordingl y, OAs a re use d in th is st ud y fo r t he exp e ri ment al d e s ig n. On
the ot her hand, by using 3D FEM simulation tha t can provide results matching fairly well with the experimen-
tally observed variables, one can easily and quickly obtain additional data for any combination of input parame-
ters. The quantity of simulated data generated in a short time compared to experimental data would allow ex-
haustive statistical analysis including all levels of all input parameters. Moreover, with a large quantity of data
for training, a simple Multilayer Perceptron ANN can be appropriate for modeling.
The objective of this paper is to present a str uctured a nd compre hensive a ppro ach develop ed to de sign an ef-
fective artificial neural network (ANN) based model for quality estimation and prediction in LSTHP using a
commercial laser source. The proposed approach examines laser hardening parameters and conditions known to
have an influence on performance characteristics of hardened surface such as hardened bead width (HBW) and
hardened depth (HD) and builds a quality prediction model step by step. The modeling procedure begins by
examining, through a structured experimental investigations and exhaustive 3D FEM simulation efforts, the
relationships between laser hardening parameters and characteristics of hardened surface and their sensitivity
to the process conditions. Using these results and various statistical tools, different quality prediction models
are developed and evaluated. In order to carry out the models building procedure, an efficient modeling plan-
ning metho d c o mbini ng ne ur a l networks p ar a di gm, a multi-criter ia optimization and various statistical to ols is
2. 3D Model Implementation and Validation
2.1. Implementation
The 3D FEM model is developed on the commercial software to estimate the temperature profiles. These tem-
perature profiles are used to approximate the surface hardness profiles (surface hardness, HD, HBW ) . T he part is
a 50 mm × 30 mm × 5 mm parallelepiped (Figure 1).
In this stud y, the heat f lux used for the si mulation is con side re d as a Ga ussian bea m distribution type which is
given by Equation (1) [1],
( )
( )
[ ]
( )
{ }
00 0
exp2 2E ExxVtwyyw
=×−−+×+ −
where V is t he sc an ning velo cit y, and x0 and y0 are the beam center coordinates at t = 0 s. E (W/m2) represents a
Gaussia n heat flux moving according to the x-axis at the velocity V. E0 is defined by Equation (2),
( )
( )
1πE PRcw= −
where w i s the Gaussia n beam ra dius, P is the laser beam power, Rc is the reflectio n coefficient of the mater ial
surface [2].
The movin g isot her mal cont our s can b e o bse rved in Figure 2. B ecause of the Gaussian form of the beam, the
temperature is at its maximum (about 1110 K) at the center of the spot. The temperature decreases rapidly with
Figure 1 . Sample with its mesh implemented on COMSOL.
G. Billaud et al.
Figure 2 . Isothermal contours: (a) t = 0.4 s and (b) t = 2.5 s.
the depth because of heat conduction into the colder core of the material. The heated volume is small at the be-
ginning of the process (t = 0.4 s) and it gets larger as the time passes and the bea m moves (t = 2.5 s). As it can be
seen i n Figure 2, the small volume of the part that had reached the temperature of 1110 K at t = 0.4 s (see Fig-
ure 2(a)) cool downed to reach a temperature under 430 K at t = 2.5 s (see Figure 2(b)). It means that a very
fast quenching hap pened in t hat volume.
Once the temperature distribution is determined, the hardness profile is estimated using the equations of
Ashby and Easterling [5]. Those equations are implemented in MATLAB® to obtain the hardness at any point
belonging to the heated part and, conseque ntly, the hardness curve rep resent ing t he hardness versu s dep t h.
The 4340 steel properties are displayed in Table 1.
The specific heat and the thermal conductivity are temperature dependant and their dependency is taken into
account in our model .
G. Billaud et al.
Table 1. Metallurgical properties.
Property Symbol Unit Value
Reflecti o n coefficient Rc 0.6
Eutectoi d temperature Ac 1 K 996
Austenitization temperature Ac3 K 1053
Austeni te gra i n size (assumed) g µm 10
Activation energy of carbon diffusion in ferrite Q kJ/mol 80
Pre-exponent ial for dif fusion of carbon D0 m2/s 6 × 105
Gas constant R J/mol·K 8.314
Steel carbon conten t C 0.43%
Austenite carbon content Ce 0.8%
Ferrite carbon content Cf 0.01%
Critical value of carbon content Cc 0.05%
Volume fraction of pearlite colonies fi 0.5375
2.2. Metallurgical Equations
When the temperature in the material reaches the eutectoid temperature Ac1 in a small volume under the surface,
the steel microstructure, which is generally tempered martensite in the case of the steel AISI 4340, starts to
transform into austenite. The complete transformation from tempered martensite to austenite occurs when the
temperature reaches Ac3. In the case of laser hardening treatment, when the temperature drastically decreases
due to rapid heat diffusion into the colder core of the part, the austenite transforms into hard martensite. This is
what is called a heat cycle (Figure 3).
As see n on Figure 3, the peak temperature at the surface is above Ac3. Therefore, a complete transformation
into hard martensite happened at the surface. However, the peak temperature at 1.4 mm under the surface is un-
der Ac1. It means that no transformation happened a t this dep th.
The to ta l nu mber o f d iffus i ve j u mps t hat o c cur d uri n g the heat c ycl e a f fect s the e xtent o f the str uctura l c ha nge
and is given b y the kinetic strength I [1] [5],
[ ]
( )
{ }
exp dIQR Ttt= −×
where Q is the activation energy for the transformation and R is the gas constant. It is more convenient to ex-
press I as described in Equation (4).
Here Tp is the peak te mperature at the co nsidered depth and τ is the thermal time constant. The terms α and τ
are approximated by Equations (5) and (6),
( )
= ×
( )
( )
where T0 is the initial temperature.
The obtained austenite has the same carbon content as a perlite microstructure Ce = 0.8%. From there, the
carbon diffuses into the proeutectoid ferrite. When the temperature reaches Ac1, the volu me fraction of a ustenite
is fi ( which is also the minimum volume fraction of martensite), gi ven by Equa tio n (7),
() ()
0.8 0.8
if f
f CCCC=− −≈
where Cf is the negligible carbon content of the ferrite and C is the carbon content of the steel.
G. Billaud et al.
Figure 3 . Temperature evolution at different depths (850 W and 9 mm/s).
The maxi mum martensite fraction allowed by the trans formation te mperature time diagram (TTT diagram) is
( )
( )
1 3113
0 if
1 if
0 if
ip p
fmT Ac
fmfif TAcAcAcAcTAc
fmT Ac
= <
= +−−−<<
= <
Ashby and Easter ling supposed that all the material with a specific ca rbon propor tion above the critical value
Cc will transfor m into martensite. The volume fraction of the martensite is then given by Equation (9 ) [1] [5].
( )
( )
( )
() ()
{ }
2/3 0
exp 12πln 2
i iec
ffmfm ffgCCDI
= −−×−××
Here g is the mean grain size and D0 is the diffu sio n constant for the car bon in ferrite.
The hardness can then be calculated by a mixture rule (Equation (10)).
( )
m fp
H fHfH
=×+− ×
The value Hm and Hf+p are given by Maynier equations that take in account the cooling rate and the composi-
tion of the material [15].
2.3. Experimental Validation
The experimental procedure consists of a first heat treatment in a furnace with a water quenching followed by a
tempering at 640˚C for 1 hour . T he ai m is to r each a homogene ous hardness of 440 HV for all t he samples. Then,
a commercial 3 kW Nd:Yag laser power (IPG YLS-3000-ST2), combined with a 6 degrees of freedom articu-
lated robot (Figure 4) is used to perform laser heating. The plan-parallel sample is put on a metal plate under the
laser head. This type of laser generates a laser beam with a wavelength λ = 1064 µm. The p r o cess parameters are
the input power, the scanning velocity and the focus diameter. In this study, the laser beam has a straight-line
trajectory as seen in Figure 2. Finally, the resulting case d e pth is measured by micro indentation.
Experimental validations are conducted according the Table 2. The focus diameter is 1260 µm for the three
tests. The values are chosen so that the surface temperature reaches the austenite temperature Ac3 but does not
hit the melting temperature (about 145 0˚C).
A mic r o -hardness machine is used to characterize the hardness curve as a function of the depth. After the laser
treatment, the samples are prepared and polished to reach adequate surface finish. The hardness is then meas-
ured by using a micro -hardness machi ne. The validation i s conducted by micro indentation, with 100 µm steps
between consecutive Vickers marks on the surface along a vertical axis. The experimental results help to vali-
date and calibrate the model. In this sense, the obtained results confirm the concordance between the experi-
mental and simulated hardness curves. This suggests that even if the developed model is not able to accurately
Temperature (°C)
Time (s)
0 mm
0.7 mm
1.4 mm
2.1 mm
2.8 mm
G. Billaud et al.
Figure 4 . Experimental setup for model validation.
Table 2. Experimental matrix for validation.
Test Powe r (W) Scanning velocity (mm/s)
1 850 9
2 850 12
3 950 12
predict the hardness curve, it can determine the hardened depth with good accuracy. Figures 5-7 show a com-
parison between the simulated and measured hardness curve using Vickers hardness scale (VH) for the three
tests (Table 2). It is worth noting that the developed 3D model is unable to predict the over-tempered zone
where the hardness of the material becomes inferior to the initial hardness. However, hardened zone, transition
zone and unaffected zone are correctly predicted. As expected, the hardened depth (at the start of the transition
zone) increases as the power rises and/or the scanning velocity decreases. Table 3 shows the average absolute
and relative errors between measured and simulated hardness. The preliminary tests allow to conclude that, de-
spite the difference of more than 50 HV in terms of absolute error, the relative error is very small, not exceeding
10%. As sho wn in Figures 5-7, the si mulation is fairly accurate in both hardness prediction and case depth pre-
3. Calibration of the Model with Corrected Rc
The coefficient Rc can be estimated around 0.6 for steel [2]. However, this coefficient greatly varies according
to the surface temperature. Moreover, the surface temperature depends on the process parameters. In order to
correctly calibrate Rc, different combinations of process parameters are executed using laser heating cell and the
Rc is corrected so the results generated by the simulation match the experimental results for each set of input
parameters. Finally, Rc is approximated as a function of the process parameters using a linear regression tech-
nique. Tab le 4 shows the Rc values depending on the laser p ower, the scanning velocity and the focus radius of
the beam spot. The coefficient seems to increase as the power and/or the scanning velocity increases. Also, it
seems to decrease when the focus radius increases.
The regression equation (Equation (11)) proves that there is a linear relationship between Rc and the process
parameters. The correlation coefficient is 0.994, which confirms a good correlation.
Rc0.42050.000303 P0.003553 V0.000198Rad=+×+×−×
P is t he inp ut po wer i n W, V is the sca nni ng velo city i n mm/ s, and Ra d is t he foc us radi us in µ m. The d evel-
oped equation is incorporated in the simulation model. The HD and HBW can be estimated with good accuracy
as a function of the process parameters.
G. Billaud et al.
Figure 5 . Hardness curve for test 1 (850 W and 9 mm/s).
Figure 6 . Hardness curve for test 2 (850 W and 12 mm/s).
Figure 7 . Hardness curve for test 3 (950 W and 12 mm/s).
05001000 1500
Hardness (HV)
Depth (µm )
Simul ated ha rdnes s (HV)
Meas ured hardne ss ( HV)
05001000 1500
Hardness (HV)
Depth (µm )
Simul ated ha rdnes s (HV)
Meas ured hardne ss ( HV)
05001000 1500
Hardness (HV)
Depth (µm )
Simul ated ha rdnes s (HV)
Meas ure d har nes s ( HV )
G. Billaud et al.
Table 3. Average absolute and relative hardness errors resulting from the preliminary tests.
Test Absolute error (HV) Relative error (%)
1 43 8.8
2 30 5.2
3 24 4.0
Table 4. Corrected R c according to process p arameters.
Power P (W) Scanning veloci ty V (mm/s) Focus radius Rad (µm) Correc ted Rc
400 20 550 0.50
520 20 550 0.54
630 20 550 0.57
740 20 550 0.61
400 12 550 0.47
400 16 550 0.49
400 16 480 0.51
400 16 613 0.48
400 16 663 0.47
4. Shadowgraph Measurement
As this stud y is focused on the HD and HBW and not the hardness values themselves, the depth and width are
measured using optical method based on shadowgraph measurement. Figure 8 shows a micrographic picture o f
a part heat treated by laser with a power of 1000 W and a scanning velocity of 12 mm/s. The hardened region
with hard martensite appears very clearly after a chemical treatment and can even be observed with the naked
eye. Two sig ni ficant z o ne s c a n b e d istin g uis hed . T he fir s t one i s the melted re gion near the surface that received
a great amount of energy, enough to reach the melting point. The second region represents the hardened region
where the temperature exceeded the austenitization temperature (Ac3) without reaching the melting point and
where the micro str ucture chan ged into martensite upon self-quenching.
5. Statistical Study
In the p re sent study, the objective is to predict the HD and HBW with given process parameters provided by the
great number of data generated through simulation (assuming the input parameters are included in the range of
study). A statistical study is conducted through a design of experiment (DOE) to determine the relative signifi-
cance of each parameter and the interactions between them. The ANOVA method aims to study the effects of
parameters on the hardness. It gives the contribution of each parameter on the variation of the outputs (HD and
HBW). The process parameters and their design levels are displayed in Table 5. The levels are chosen so that
the surface transformation happens and the surface temperature does not hit the melting temperature regardless
of the combination of process parameters.
The simulatio n allowed us to quickly ob tain result s for all 64 (43) possible combinatio ns of factor level s, and
thus to generate a full factorial design.
Statistical studies such as analysis of variance, main effects studies and linear regression are conducted.
5.1. ANOVA for HD versus P, V and Rad
Table 6 presents the detailed statist ical analysis. An F-value above 11.77 implies that the parameter is very sig-
nificant. In this case, power (P), scanning velocity (V), focus radius (Rad) are all significant models terms. The
interaction terms are less important since their contributions are less than 0.4%. Also, it is clear that the power
G. Billaud et al.
Figure 8 . Micro graphic pictu r e illustrating the HBW and HD after ch emical etchi ng.
Table 5. Factors and levels used for the ANOVA study.
Fac to rs Factor Levels
Laser Power (P) [W] 410 520 613 740
Scannin g Velocit y (V) [mm/s] 12 16 18 20
Focus Radius (Rad) [µm] 480 550 613 663
Table 6. ANOVA for HD.
Source DF SS contribution MS F-value p-value
P 3 563906 48.4% 1879 69 499.71 0.000
V 3 568906 48.8% 189635 504.14 0.000
Rad 3 13281 1.1% 4427 11.77 0.000
P × V 9 4531 0.4% 503 1.34 0.264
P × Rad 9 2656 0.2% 295 0.78 0.632
V × Rad 9 2656 0.2% 295 0.78 0.632
Model 36 1155936 99.1% 383124
Error 27 10158 0.9% 376
Total 63 1166094
and the scanni ng veloci ty hav e the large st effec t on the res ponse val ue and that they are equival ent wit h contri-
butions around 48%. The three interaction terms can be considered negligible.
Figure 9 shows the effect of all parameters on the case depth (HD). The obtained results confirm that the HD
increases as beam power increases and/or as scanning velocity decreases. It also increases as the focus radius
decreases. The ANOVA method is conducted in order to assess the significance of each parameter. For each pa-
rameter studied, the variance ratio value, F, is compared to the values from standard F-tables for gi ven stati stical
levels of significance. In this way, it is concluded that within the invest igated processing ranges, the power, the
scanning velocity and the focus radius are significant for the case depth at 95% confidence. Since the interaction
terms have negligible contributio ns, they will not be conside red in the rest o f the study. Figure 10 shows the HD
calculated using the regression formula (Equation (12)) for all 64 combinations of process parameters and their
distribution around the bisector of the quadrant. If the formula is perfectly accurate, all the points should be on
the bisector. For the regression formula to be considered accurate, a maximum relative error of 10% is allowed
Har dene d be ad w idth ( HB W )
depth ( HD)
1 mm
G. Billaud et al.
Figure 9 . Effects of parameters o n case depth.
Figure 10. Comparison between simulated HD and HD calculated by regression formula (Equation (12)).
for all 64 sets of process parameters. A maximum relative error of 6.51% is observed, with a mean relative error
of 2.25% between the HD calculated with the regression formula and the one simulated by the software. The
coefficient of deter mination R2 is mainly used to measure the relationship between experimental data and meas-
ured data. A coefficient R2 = 99.13% indicates an accurate study.
HD1113.70.7557P31.70 V0.2036 Rad=+×−× −×
5.2. ANOVA for HBW versus P, V and Rad
Table 7 shows the detailed statistical analysis. An F-value above 70.68 implies that the parameter is very sig-
nificant. In this case, power (P), scanning velocity (V), focus radius (Rad) are all significant models terms. The
interaction terms are less important since their contributions are less than 0.7%. Also, it appears that the input
power and the scanning velocity have the largest effect on the response value with contributions around 37% -
43%. The three interaction terms can be considered negligible. The coefficient of determination R2 is mainly
used to measure the relationship between experimental data and measured data. Just like for the hardened depth,
the input laser power and the scanning velocity have the same degree of impact (and the opposite effect); the
other parameter (Rad) still have significance, and the interactions are negligible.
The fir st t hin g one c an no ti ce on Fig ure 11 is that the main effects plot for H BW is similar to the main effects
plot for the HD, with the noticeable exception of the focus radius, which has the opposite effect on the HBW
compared to the effect it has on the HD. Indeed, when the focus radius increases the HBW increases as well,
whereas the HD decreases (see Figure 9 and Fig ure 11). This is caused b y the Gaussia n distribution of the en-
ergy at the surface of the material, which results in a relationship between HD and HBW. Indeed, the fact that
the radius is greater while the power and the scanning velocity remain the same means that there will be less en-
ergy at the center of the focus.
410 520 630 740
12 14 16 18 20
600 700800 900100011001200
Calculated HD (µm)
Simulated hardened depth (µm)
Statistica lly calculate d HD (µm)
Simulate d HD (µm)
G. Billaud et al.
Table 7. Resu l ts of the ANOVA for HBW.
Source DF SS Contribution MS F-value p-va lue
P 3 1763125 37.4% 587,708 161.71 0.000
V 3 2023125 43% 674,375 185.56 0.000
Rad 3 770625 16.4% 256,875 70.68 0.000
P × V 9 13125 0.3% 1458 0.40 0.923
P × Rad 9 30625 0.7% 3403 0.94 0.511
V × Rad 9 10625 0.2% 1181 0.94 0.959
Mode l 36 4611250 98% 1525,000
Error 27 98125 2% 3634
Total 63 4709375
Figure 11. Main effects plot for hardened bead width.
As for the HBW , it appears that the interactions are negligib le with very low F-value. Ther efore they will no t
be include d in the re gres s i on e quation.
Figure 12 shows the HBW calculated using the regression formula (Equation (13)) for all 64 combinations of
process parameters and their distribution around the bisector of the quadrant. If the formula is perfectly accurate,
all the points should be on the bisector. A maximum relative error of 6.95% is observed, with a mean relative
error of 2.39% between the HBW calculated with the regression for mula and the one simulated by the software.
Bo t h value s are well under the maximum criteria of 10% and thus, t he fo rmula can be considered accurate.
Moreover, the coefficient of determination R2 = 97.92% testifies an accurate regression equation albeit not as
satisfying as it is for the HD.
HBW1782 1.3409 P57.68 V1.598 Rad=+×−× +×
In addition to the statistical stud y, and in order to provide a reliable alte rnative to standard ther mal techniques
that would be accurate and less time consuming, we conducted a study with an artificial neural network (ANN).
6. Neural Network Modeling
As compared to other techniques, a n ANN provides a more effective modeling capability, particularly when the
relationship between sensor-derived information and the characteristic(s) to be identified is non-linear. ANNs
can handle strong non-linearity, a large number of variables, and missing information. Based on their intrinsic
learning capabilities, ANNs can be used in a case where there is no exact knowledge concerning the nature of
the relationships between various variables. This is very useful in reducing experiment effor ts.
410 520 630 740
12 14 16 18 20
G. Billaud et al.
Figure 12. Comparison between simulated HBW and HBW calculated by
regression formula (Equation (13)).
A neural network is used to predict the hardened depth and hardened bead width. Neural networks are gener-
ally presented as systems of interconnected neurons, where the links between neurons are weighted. Figure 13
shows the general principle of an ANN model. The goal is to produce one or more outputs that reflect the
user-defined i nformation sto re d in the con nections d uring t ra i ning.
In this stud y, a Generalized Feed-Forward M ultilayer Pe rceptro n (GFF-M LP) neura l netwo rk mode l with one
hidd en layer co ntainin g 7 neuro ns is chosen. Whil e vario us ANN te chniques can be used in this ap proac h, gen-
eralized feed forward networks seem to be the most appropriate because of their simplicity and flexibility. Be-
fore selecting the variables and training the models, it is important to establish the network topology and opti-
mize the training performances. The idea is to approximate the relationship between the ne t work p ar a me te rs a nd
the complexity of the variables to be estimated. The selected network is that which achie ved the bes t res ults, the
[n|2n+1|3] network, where n is the number of inputs. The perceptron is characterized by a nonlinear sigmoid
function. This type of neural network is always fully connected, meaning each perceptron of each layer is con-
nected with all the perceptrons in the previous layer [16]. In a G FF-MLP network, connections between layers
can jump over one or more layers. In practice, these networks solve problems much more efficiently than MLP
networks [17].
Neural networks need to be trained with data sets in order to be able to interpolate for any given input pa-
rameters that fall within the training range. Neural networks cannot extrapolate, which means one cannot get re-
liable outputs if the input par ameters ar e not within the rang e of the training pa ra meters. In this stud y, the goal is
to obtain a neural network able to predict the case depth and hardened bead width for a given combination of
input parameters (within its training range). In all neural networks, during the training step, the input data are
normalized to the range of [1, 1]. The weights and biases of the network are initialized to small random values
to avoid a fast sat ur ation of the ac tivatio n function.
6.1. Maintaining the Integrity of the Specifications
For a commercial laser device, there are usuall y 3 c ontr ol p ara meters , the i nput po wer (P ), the sc anni ng vel ocit y
(V) and the focus radius (Rad). In this study, 4 levels for each of those parameters are chosen and are displayed
in Table 5. The levels are chosen to ensure minimal martensitic transformation and to avoid the melting point
(about 1450˚C) regardless of the combination of levels. With 3 parameters with 4 levels, the total number of
possible combinations is 64 (43). The simulation allo ws to quickly get all of the 64 combinations and produce a
full L64 matrix as in the preceding statistical studies.
In addition to the training data, a neural network also requires verification data (that are different from the
training data) in o rder to validate the training step. These verification d ata are disp layed in Table 8 . In this case,
the mean value of two consecutive levels are identified and used in simulation to generate data for verification.
This leads to a valid a tion design o f 33 possible.
The neural network is trained considering the mean square error (MSE) of the cross-validation as an
achievement indicator. The training of the neural network stops when the MSE stops decreasing. In order to
evaluate the effectiveness of the network, some criteria are used, the correlation coefficient and the root mean
square error, which would be respectively equal to 1 and 0 in the best case scenario with perfect accuracy.
1900 2100 23002500 2700 2900 31003300
Calculated HBW (µm)
Sim ul ated hardened bead wi dth (µm)
Statistically calculated HBW (µm)
largeur durcie en surface (µm)
G. Billaud et al.
Figure 13. Principle of the neural network.
Table 8 . Middle points.
Factors Factor Levels
Laser Power (P) [W] 465 575 685
Scanning Veloci ty (V) [mm/s] 14 17 19
Focus Radius (Rad) [µm] 515 581.5 638
6.2. Result and Inte rp reta t ion
Once the training step of the network is performed, the 27 combinations of verification data are applied as input
parameters. The outputs of the ANN model are compared with those obtained by simulation. Therefore, this
comparison is effective using various statistical indexes that characterize the prediction capability of the ANN
model. Two main criteria are used to evaluate the accuracy of the network: the absolute error and the relative
Figure 14 shows the a bso lute err or s for bo th HD and HB W for all 27 te st co mbinatio ns. The maxi mum ab so-
lute errors for HD and HBW are, respectively, 64 and 94 µm. This means that the absolute error is of less than
100 µm for the overall test data, for both HD and HBW. Given that the values of HD are between 700 µm and
1100 µm, and that the values of HBW are between 2400 µm and 3000 µm, the model exhibits a good potential
in terms of accuracy.
As can be seen in the Figure 15, the relative errors for both the HD and HBW are very low in every case. The
maximum relative errors for HD and HBW are, respectively, 8.01% and 3.62%. The mean relative errors for HD
and HBW are 2.40% and 1.63%, re s pect ively, which he i ghtens the accuracy of the ne ural ne twork.
Figure 16 and Figure 17 present, respectively, the results of the ANN models during the verification stage for
HD and HBW. In fact, the figures show the ANN model and those obtained by simulation. The data are mostly
located around the bisector of the 1st quadrant, which outlines the accuracy of the model. The two figures show
that the net work is well tr ained and is hig hly effic ient. T he net work is t here fore a reliab le way to p red ict the HD
and HBW for any combination of input parameters within the training range (between 480 W and 663 W for
power, 12 mm/s and 20 mm/s for scanning velocity, 480 mm and 663 mm for focus radius). The ANN models
don’t require any computation time to predict the outputs comparatively to the simulation. Note that the ANN
models can predict the desired o utputs in the studied variation range only and they cannot extrapolate outside.
Table 9 shows the comparison between the results generated by simulation and those generated by ANN
model during training stage and confirms the observations from Figure 14 and Figure 15.
Even if the ANN models have good performances in terms of robustness and accuracy, it is still important to
validate them usi ng experimental validatio n.
7. Experimental Validation of the Neural Net wo r k
The great number of data that can be generated by a 3D FEM allows to accurately train a neural network that
will be able to predict the HD and HBW, and thus, it avoids the need to produce expensive experimental data
that are often less numerous because of their cost.
Once the network accuracy is verified with data generated by a FEM si mulation, experimental validation tests
are conducted using a Nd:Yag laser and the shadowgraph measurement method.
Eight sets are randomly chosen among the 27 sets of verification data. The experimental matrix is displayed
in Table 10.
The input powers are between 465 W and 685 W, the scanning velocities are between 14 mm/s and 17 mm/s.
Finally, the focus radii are between 515 µm and 638 µm.
G. Billaud et al.
Figure 14. Absolute relative errors for HD and HBW.
Figure 15. Relative errors for HD and HBW.
Figure 1 6. Comparison between simulated HD and HD calculated by the
neural network.
Figure 17. Comparison between simulated HBW and HBW calculated by
the neura l ne t work .
absolute errors (µm)
absolute errors HD
absolute errors HBW
Relative error
Relative errors HD
Relative errors HBW
7008009001000 1100
Predicted HD by neural
network (µ m)
Simulated HD (µm)
2200 2400 2600 2800 3000
Predicted HBW by neural
network ( µm)
Simlated HBW (µm)
G. Billaud et al.
The results of the tests are shown in Table 11. The maximum relative errors for both the HD and HBW are
7.37% and 2.93%, respectively.
The ANN is able to correctly predict both HD and HDW. It can now be used independently from the
COMSOL software. It is easier to use as one only needs to compute the process parameters (within the training
ranges of the ANN ) to obtain re lia ble results instantly.
8. Conclusion
In this paper, a structured and comprehensive approach developed to design an effective ANN-based model for
quality assessment and prediction in LSTHP using a commercial 3 kW Nd:Yag laser is presented. Several laser
hardening parameters and cond itions were analyzed and their correlation with multiple performance characteris-
tics of hardened surface was investigated using a structured experimental investigations and exhaustive 3D FEM
Table 9. Comparison of the results.
Simulation ANN mo dels Absolute error Relative error
HD (µm) H BW (µm) HD (µm) HBW (µm) HD (µm) HBW (µm) HD (%) HBW ( %)
Min 7 00 2000 698 2058 2 58 0.03 0.05
Max 1200 3200 1175 3147 25 53 4.88 4.52
Mea n 937 2557 931 2570 15 39 1.62 1.55
Min 7 00 2200 730 2164 1 2 0.10 0.09
Max 1050 3000 1084 2964 64 94 8.01 3.62
Mea n 894 2522 902 2521 21 40 2.40 1.63
Table 10. Experimental matrix for validation.
Test Powe r (W) Scanning velocity (mm/s) focus radius (µm)
1 465 14 515
2 575 19 515
3 685 17 515
4 685 14 515
5 575 14 581.5
6 685 17 581.5
7 465 17 638
8 685 17 638
Table 11. Experimental validation-results.
Test Network HD
(µm) Exp er imenta l HD
(µm) Relative error for
HD (%) Network HBW
(µm) Experimen tal HB W
(µm) Relative error for
HBW (% )
1 929 909 2.21 2444 2375 2.88
2 864 894 3.35 2302 2320 0.76
3 968 953 1.59 2470 2402 2.83
4 1084 1010 7.37 2726 2653 2.74
5 997 1018 2.04 2735 2702 1.22
6 952 1022 6.86 2603 2591 0.46
7 777 785 0.98 2392 2324 2.93
8 936 1002 6.55 2715 2643 2.73
G. Billaud et al.
simulations under consistent p ractical pro cess conditions. Fo llowing the identi fication of the harden ing parame-
ters and conditions that provide the best information about the LSTHP operation, tow type of modeling tech-
niques were proposed to assess and predict the hardened bead width and hardened depth (HD) of the laser
transformation hardened AISI 4340 steel plate: multiple regression analysis and ANN approach. The results
demonstrate that the regression approach can be used to achieve a relatively accurate predicting model with cor-
relation larger than 90%. The ANN models present greater results. The maximum relative errors for both HD
and HBW are less than 8% an d 3%, respectively. Globally, the performance of the ANN-based model for qual-
ity estimation and prediction in LSTHP shows significant improvement as compared to conventional methods.
With a glob al maxi mum relative error less than 10% under various LSTHP conditions, the modeling procedure
can be considered efficient and have led to conclusive results, due to the complexity of the analyzed process.
The proposed approach can be effectively and gainfully applied to quality assessment for LSTHP, because it in-
cludes the advantages of ease of application, reduced modeling time and sufficient modeling accuracy.
[1] Kannat ey-Asibu , E. (2009) Principles of Laser Materials Processing. Wiley, Hoboken.
[2] Steen, W.M. (2010) Laser Material Pro cess ing. 4th Edition, Springer, London.
[3] Patwa, R. and Shin, Y.C. (2007) Predictive Modeling of Las er Harden ing of AISI5150H Steels. International Journal
of Machine Tools and Manufacture, 47, 307-320.
[4] Mioković, T., Schulze, V., Vöh ringer, O. and Löhe, D. (2006) P rediction of Phase Trans formations during Laser Sur-
face Harden in g of AISI 4140 including the Effects of Inhomogeneous Austenite Formation. Materials Science and En-
gineer ing: A, 435-436, 547-555.
[5] Ashby, M.F. and Easterling, K.E. (1984) The Transformation Hardening of Steel Surfaces by Laser Beams—I. Hyp o-
Eutect oid Steels . Acta Metallurgica, 32, 1935-1948.
[6] Antony, J. and Jiju Antony, F. (2001) Teaching the Taguchi Method to Industrial Engineers. Work Study, 50, 141-149.
[7] Chen, S.L. and Sh en, D. (1999) Optimisation and Quantitative Evaluation of the Qualities for Nd-YAG Laser Trans-
formation Hardening. International Journal of Advanced Manufacturing Technology, 15, 70-78.
[8] Badkar, D., Pandey, K. and Buvanash ekaran, G. (2011) Parameter Optimization of Laser Transformation Hardening by
Using Taguchi Method and Utility Concept. International Journal of Advanced Manufacturing Technology, 52, 1067-
[9] Benyounis, K.Y., Olabi, A.G. and Hashmi, M.S.J. (2005) Effect of Laser Welding Parameters on the Heat Input and
Weld-Bead Profile. Journal of Materials Processing Technology, 164-165, 978-985.
[10] Sathiya, P., Abdul Jaleel, M.Y. and Katherasan, D. (2010) Optimization of Welding Parameters for Laser Bead-on-
Plate Welding Using Taguchi Method. Production Engineering-Research and Development, 4, 465-476.
[11] Hagan, M.T., Demuth, H.B. and Beale, M.H. (1996) Neural Network Design: Pws Boston.
[12] Ciurana, J., Ar ias , G. and Ozel, T. (2009) Neural Net work Modelin g and Particle S warm Optimi zation (P SO) of Proc-
ess Parameters in P ulsed Laser Micromachinin g of Hardened AI SI H13 Steel . Materials & Manufacturing Processes,
24, 358-368.
[13] Pan, Q.Y., Huang, W.D., Song, R.G., Zhou, Y.H. and Zhang, G.L. (1998) The Improvement of Localized Corrosion
Resistance in Sensitized Stainless Steel by Laser Sur fac e Remelting. Surface and Coatings Technology, 102, 245-255.
[14] Munteanu, A. (2012) Surface Hardness Prediction Using Artificial Neural Networks in Case of Electron Beam Ma-
chining Process. Romanian Association of Nonconventional Technologies.
[15] Doane, D. (1979) Applica ti on of Hardenability Concepts in Heat Treatment of Steel. Journal of Heat Treating, 1, 5-30.
[16] Haykin, S. (2010) Neural N etworks: A Comprehensive Foundation, 1994. Mc Millan, New Jersey.
[17] Principe, J., Euliano, N. and Lefebvre, W. (2000) Neural and Adaptive Systems: Fundamentals through Simulations.
John Wiley and Sons, New York.