Surface & Coatings Technology 206 (2012) 3179–3185

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Surface & Coatings Technology

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Numerical evaluation of the reflectivity coefficient in laser surfacehardening simulation

Alessandro Fortunato a, Alessandro Ascari a,⁎, Leonardo Orazi b, Giampaolo Campana a, Gabriele Cuccolini b

a DIEM — Department of Mechanical Constructions Engineering, University of Bologna, 40136, Bologna, Italyb DISMI — Department of Sciences and Methods for Engineering, University of Modena and Reggio Emilia, 42100, Reggio Emilia, Italy

⁎ Corresponding author. Tel.: +39 051 2090494; fax:E-mail address: a.ascari@unibo.it (A. Ascari).

0257-8972/$ – see front matter © 2012 Elsevier B.V. Alldoi:10.1016/j.surfcoat.2011.12.043

a b s t r a c t

a r t i c l e i n f o

Article history:Received 9 November 2011Accepted in revised form 29 December 2011Available online 4 January 2012

Keywords:Laser surface hardeningProcess simulationOptical propertiesReflectivity

This paper reports the results concerning the simulation of a laser surface hardening process of a cylindricalsurface. In particular it focuses on the problems related to the definition of the physical parameter values nec-essary in order to achieve an accurate and reliable simulation. The strict dependency of laser process simula-tion results on the physical parameters describing the target material is, in fact, a well known matter,especially considering that the values of these parameters change during the process dependently on tem-perature and time. Moreover in laser surface hardening this problem is even more important because meltingof the target material should be avoided, surface roughness plays an important role and, sometimes, the sur-face is coated with absorbent layers. These factors increase the complexity of the simulations and make theevaluation of the physical parameters more difficult and critical. The results presented in this paper areobtained on AISI420B steel, coated with graphite and treated with a direct diode laser. Considering theabove mentioned conditions, a plausible temperature dependent reflectivity coefficient was evaluated andits robustness was investigated. This reflectivity coefficient can be used with a good approximation for thesimulation of laser hardening treatments of many carbon steels.

© 2012 Elsevier B.V. All rights reserved.

1. Introduction

Manufacturing process simulations are nowadays widely used notonly in research activities but also in industrial applications thanks totheir capacity to predict process results, allowing to save time andmoney during process setup and optimization. On the other handone of the most relevant matters concerning the accuracy of the sim-ulated results relates to the assessment of the correct values of thephysical parameters used to describe the work piece material. Withparticular reference to laser-based manufacturing processes, the de-termination of these physical quantities is always very difficult as, inturn, they depend on other parameters which are difficult to be eval-uated themselves (e.g. surface finishing and cleaning) and they alsomay vary during the process as a function of time and work piecetemperature. In particular, in laser process simulation, the resultsgreatly depend on physical and optical surface properties. In particu-lar the reflectivity coefficient determines the amount of laser energyabsorbed from the work piece which is directly correlated to the tem-perature distribution and thus to the micro structural evolution andphase changes occurring in the base material. According to theabove mentioned considerations the reflectivity coefficient is one ofthe most important parameter to be evaluated in order to accurately

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simulate a laser-based manufacturing process. In particular, consider-ing laser surface hardening, where material melting must be avoidedand the heat cycle is used just to allow the allotropic transformationsof the iron, the reflectivity coefficient becomes the real key factor inorder to be able to setup a reliable simulation. This particular treat-ment is usually performed on medium carbon steels with the aim toobtain a layer of martensite on the work piece surface. In this casethe most used laser sources are usually solid state ones because of

Fig. 1. Experimental setup and specimen.

Table 1Constant parameters.

Laser power 1250 WRotational speed of the specimen 1150 rpmTranslational speed of laser and pyrometer 1 mm/s

Table 2AISI420B physical parameters.

Temperature [K] λ [W/mK] cp [J/kgK] ρ [kg/m3]

273 30, 2 460 7700673 25 582 7700>1073 19.7 704 7699

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the characteristic fiber-portability of the beam, which enhances pro-cess flexibility, and of the low wavelength (if compared to CO2 laserone), which improves energy absorption in the base material. More-over, work piece surfaces can be coated with few microns of graphitein order to further increase radiation absorptivity.

Typical applications of this treatment concern confined surfaces,which are usually smaller than the spot diameter ([1,2]). When deal-ing with large areas multiple track patterns have to be exploited andthe problem of material softening due back tempering occurs asreported in [3–5], where solid state laser sources were involved insurface treatment of medium carbon steels exploiting an averagepower between 1 and 2 kW, a beam spot between 5 and 10 mm anda scanning speed of about 1 m/min. When the proper process param-eters are chosen the thermal cycle is very fast especially in the coolingphase, due to heat conduction toward the untreated bulk material andthus no quenching media are used. Thanks to these peculiarities inlaser surface treatments a finer, more homogeneous and harder mi-crostructure can be achieved if compared to traditional induction pro-cesses. Several very interesting experimental and theoretical workshave been presented during the last decades [6–9] focused in laserhardening and phase changing but no one of them dealt with theapparent spot technique studied in this work. In fact, when hardnessreduction due to back tempering is not allowed and axisymmetricsurfaces have to be treated, a different technique named apparentspot [10] is used. It consists of creating a high temperature ring, typi-cally above the eutectoid temperature, all around the cylindricalsurface and of propagating it by combining high rotating speed ofthe work-piece, relatively high laser power density and low longitudi-nal laser speed. At this stage, it is clearly a transient problem as aproper temperature, which is the process temperature, should bereached in a few seconds. By means of this technique large surfacescan be laser hardened in a way similar to the one obtained exploitingan inductor. The large amount of heat transferred to the material bythe apparent spot could determine a small cooling rate especiallyif the thickness of the component is low. In this case a quenching me-dium could be necessary. Laser hardening by apparent spot can bevery difficult to be optimized in terms of process parameters. Laserpower, spot dimension, circumferential and longitudinal velocity

Fig. 2. Experimental measurem

and scanning trajectory are hardly determinable by means of a purelyexperimental approach, especially considering that they mainly de-pend on the absorbed energy which, in turn, depends on the workpiece material, surface temperature, surface roughness and surfacecleanliness. The eventual presence of a graphite coating used inorder to enhance absorptivity must also be taken into account in theprocess parameter evaluation. It is evident that such a complex pro-cess can take great advantages from simulation but, in order to devel-op a useful software tool, actual work piece physical and opticalparameters have to be used during the simulation and in particulara suitable reflectivity coefficient has to be determined. By means ofa proper simulation, laser surface hardening can be used in an openloop process setup instead in a closed loop setup with the tempera-ture feedback obtained by means of an on line pyrometer simplifyingindustrial applications. According to the previous considerations thispaper presents the activities carried out in order to develop a temper-ature dependent formula for the reflectivity coefficient evaluationduring laser hardening by means of the apparent spot technique ofAISI420B cylindrical specimens, using a 2 kW diode laser and graphitecoating layer. The robustness of the formula with respect to inputsvariation is also evaluated.

2. Experiments

Experimental activities were carried out on a 135 mm longAISI420B bar with a diameter equal to 20 mm (see Fig. 1), coatedwith graphite and mounted on a rotating mandrel. AISI420B is a mar-tensitic stainless steel and it is very suitable to be laser treated withapparent spot technique because it does not require high cooling ve-locities in order to form martensite thanks to its self-quenching char-acteristics. The laser source involved was a 2.5 kW Rofin diode(wavelength=980 nm) mounted, together with a pyrometer, on ananthropomorphic robot. The laser spot had 1.8×5.9 mm rectangularshape with a flat power distribution and it was set concentric to thepyrometer measuring area. The pyrometer exploited is a laboratory-made device designed, built and calibrated with the purpose of

ent of surface temperature.

Fig. 3. Thermal diffusivity coefficient used in simulations.

Fig. 4. The temperature evaluation obtained with LHS in laser hardening with the ap-parent spot.

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monitoring thermal fields occurring in laser hardening of steels [11]and its characteristic measuring area is 1×1 mm.

In order to avoid boundary effects in heat propagation the laserbeam path was stopped 69 mm before the end of the specimen andthe treated area extension was 20 mm as reported in Fig. 1.

The apparent spot treatment consisted of two separate steps:

1. “Ignition”of the hot ring: the laser beam stood still on the rotatingspecimen at a constant power until the hot ring was formed and asurface temperature equal to 1100 °C was reached.

2. “Propagation”of the hot ring: the laser beam translated linearlyalong the treatment path while the specimen was still rotating.

According to the authors' experience the test was conducted con-sidering the parameters reported in Table 1.

Table 3Reflectivity coefficient variation with temperature used in 5 different simulations.

273 K 323 K 373 K 523 K 573 K 923 K 973 K 1808 K

Test 056 0.14 0.02 – 0.01 – 0.005 – 0.001Test 057 0.24 0.12 – 0.11 – 0.105 – 0.101Test 058 0.14 0.02 – 0.01 – 0.005 – 0.001Test 059 0.14 – 0.02 – 0.01 – 0.005 0.001Test 060 0.145 – 0.025 – 0.015 – 0.005 0.001

Fig. 2 shows the actual instantaneous surface temperature mea-sured by the pyrometer (blue line) and the mean temperature (blackline). It is evident that after about 7 s the 1100 °C hot ring was createdand after that the laser started moving along the 20 mm linear path.When the beam started translating the surface temperature droppedfrom 1100 °C to about 950 °C and then it started rising again until itreached the value of about 1500 °C. This demonstrates that duringthe whole treatment the workpiece temperature remained confinedin the austenitic field without causing any melting of the basematerial.

3. Reflectivity evaluation

Thermal conductivity λ, density ρ and heat capacity cp of AISI420Bwere selected according to [12] and they are reported in Table 2. Bymeans of these values the coefficient of thermal diffusivity can be cal-culated as reported in Fig. 3.

Those physical coefficients were used as input parameters in asimulation software named LHS developed by the authors for predict-ing the hardness in laser surface hardening [13]. In the present case,this software was used only to solve the thermal problem and tocalculate the temperature in the work piece. The optimal reflectivitycoefficient was determined when the calculated temperature fieldwas comparable with the one measured by the pyrometer (seeFig. 2), as pointed out in the next paragraph. In LHS the laser param-eters such as spot shape, dimension, power, velocity, incident angle ofthe beam and trajectories of the beam can be set in order to have themaximum flexibility in terms of process simulation. Fig. 4 shows atypical graphical output of the LHS software. The domain discretiza-tion was obtained by means of the meshing software CUBIT 12.0,while the Fourier equation solution was obtained importing the dis-cretized geometry in LHS. The blue lines shown in Fig. 4 representthe probes whose intersections with the domain define the pointswhere the temperatures are stored in the code. In the present simula-tion they are located 50m below the irradiated surface. The yellowcolor indicates the intensity of the thermal field.

In order to determine an empirical equation for the reflectivityevaluation several numerical tests were carried out. Preliminary con-siderations lead to the assumption that when the melting tempera-ture was reached on the surface, the reflectivity was zero and all thelaser radiation was absorbed, while at room temperature the reflec-tivity was considered to be equal to 0.25 as the workpiece surfacewas covered with spray graphite.

Fig. 5. The reflectivity coefficient versus temperature curves adopted in the simulations.

Fig. 6. The temperature evaluation obtained with LHS in laser hardening with the apparent spot. The continuous line is the measured temperature.

Table 4Differences between the predicted and measured temperatures for the five simulationsafter 7 and 27 s.

7 s 27 s

Test 056 −0.32% −0.54%Test 057 −9.5% −11.0%Test 058 +8.8% −13.0%Test 059 +8.7% +13.0%Test 060 +8.6% +12.9%

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Table 3 summarizes the values of the reflectivity coefficientsused in five different tests, the same values are reported inFig. 5. These values were selected according to the followingconsiderations:

• Simulation 057 is obtained from 056 increasing all the values of0.1.

• Simulation 059 is obtained from 058 increasing the temperature of50 K.

• Simulation 060 is obtained from 059 increasing the first 3 values of0.005 in order to evaluate the influence of the slope.

• Simulation 058 is obtained from 056 reducing the thermal conduc-tivity of 10%.

The results obtained, in terms of the calculated surface temper-ature, are summarized in Fig. 6. The red line reports the measuredtemperature while the dotted lines refer to the simulations. All thesimulations are interrupted after 7 s in order to take into consider-ation only the hot ring ignition phase.

4. Results

The analysis of the results presented in the previous paragraphleads to the following considerations:

• Simulations 057 and 058 lead to two temperature curves which arealmost equidistant from the actual temperature. According to this itcan be stated that the inputs used for these tests can be consideredas the lower and upper limits for an accurate simulation.

Fig. 7. Simulation results after 27 s for 056 simulation set. The continuous line is the measured temperature.

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• Simulations 058, 059 and 060 show very low variations in terms ofthe predicted temperature: the input variations in these cases haveno influences in terms of the results.

• Simulations 058 and 056 show a good variation in terms of resultsand in this case the thermal conductivity has a great influence onthe calculated temperatures.

Table 4 summarizes the errors of the simulations after 7 s and atthe end of the process (after 27 s). Considering the results shown inTable 4 and Fig. 6 it can be concluded that the optimal simulationresults are obtained for simulation number 056.

Fig. 7 shows the complete simulation carried out with the 056configuration setup and Fig. 8 reports the relative error. It is shownthat in this specific test there is a good accordance between simula-tion results and actual measures, as the average error during thewhole process simulation is about −0.53%. It is possible to see thatthe error becomes very high after 27 s, when the laser is turned off.This result can be explained because LHS does not consider the con-vective heat flux which is predominant during cooling when thelaser does not irradiate the surface and the work piece is still rotatingat 1150 rpm.

Fig. 8. Error in the temperature evaluation for the 0

Finally, in order to provide a useful information in laser processsimulation, a regression model of the reflectivity is calculated for056 simulation starting from the values reported in Table 3. The ex-plicit formula for the reflective coefficient evaluation, RL, is reportedin Eq. (1). Fig. 9 shows a comparison between the regression curve(red continuous one) and the actual one (blue dotted). The calculatedregression coefficient is R2=0.89. Those results are in good accor-dance with those in [14] and [15]. Considering the results mentionedabove it can be concluded that the reflectivity coefficient calculated inthis case can be applied to many of the most common steels, whichare characterized by a thermal conductivity similar to the one con-cerning AISI420B and roughness typical of finished surface (about1.5 μm). Besides the influence of the coating can be neglected whensimulating an apparent spot laser treatment because the incrementof reflective coefficient does not influence the calculated temperature.Anyway, more examples will be presented in the future for the samesteel with other surface geometrical or chemical characteristics orcoating layer (i.e. black paint, etc.) and for different steels.

RL ¼ 14178:4 � T−2:2 ð1Þ

56 simulation set. Laser is turned off after 27 s.

Fig. 10. Comparison between predicted and measured hardness for two different reflectivity variations.

Fig. 9. Regression curve for the reflective coefficient evaluation.

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The last step of the results is presented in Fig. 10, in this figurethe comparison between the measured and predicted hardness hasbeen presented. Measurements have been carried out in longitudi-nal direction 500μm below the surface according to Vickers proce-dure by using 1000 g load. Hardness is measured every 100μm andevery measurement has been repeated three times. In Fig. 10 themean value of the 3 repetitions is compared to the predicted hard-ness calculated by means of LHS for the 056 and 057 configura-tions. The algorithm used in LHS is presented in [10]. By means ofthis comparison is evident that configuration 057 underestimatesthe treated zone because it gives a lower temperature at the start-ing point of the treatment as reported in Fig. 5. On the other hand,056 gives a good accuracy in the prediction of treated area exten-sion. Both models predict an extended treated area after the laserturns off mainly due to the boundary condition in LHS for theheat flux convection calculation with the environment.

5. Conclusion

A regression model for the reflectivity coefficient evaluation inlaser surface hardening is presented. The model is numerically

calculated by comparing the actual surface temperature, measuredby a pyrometer, to the theoretical predictions obtained by means ofprocess simulation. The calculated reflectivity allows to achieve anaverage error less than 1% between the simulation results and theactual temperature field. A sensitivity analysis was carried out byvarying the input data and calculating the output temperature varia-tion and a comparison between predicted andmeasured hardness hasbeen presented to different reflectivity evaluation.

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