3D Transient Model for CO2 Laser Hardening

Tani G. a, Orazi L.b, Fortunato A. a, Campana G. a and Ascari A. a

a DIEM - University of Bologna, Via Risorgimento 2, Bologna, Italy;b DISMI - University of Modena & Reggio Emilia, Via Amendola 2, Reggio Emilia, Italy

ABSTRACT

A 3D numerical model for the surface hardening process simulation carried out by means of a CO2 laser sourceis presented. The model is able to predict the extension of the treated area into the workpiece, the type of theresulting micro-structure and the optimal laser path strategy in order to minimize the micro-structural softeningdue to the tempering effect. The Fourier equation is solved using the Finite Difference Method (FDM) appliedon a generical grid obtained by means of the domain discretization. The resulting time dependent temperaturedistribution into the workpiece is used for the evaluation of the induced heating cycle. By calculating the coolingvelocity, the micro-structure transformation is determined together with the hardness in every point of thedomain. The hardness reduction due to the tempering effect is also predictible. The computational times aresmall and the software is very suitable in industrial environment in the early stage of the process planning whenseveral simulation runs must be performed. The modeling activity was developed by considering the class of thehypo-eutectoid steel. The experimental tests were realized on a C43 steel plate. The good agreement betweenthe theoretical and experimental results is shown.

Keywords: Laser hardening, numerical simulation, quenching, tempering, CO2 laser.

1. INTRODUCTION

Laser heat treatment is becoming a very widely used technology for surface hardening processes. It allows totreat complex shapes, usually very difficult to realize with conventional surface hardening, with less distortionsthan that caused by flame or induction hardening. The widespread use of lasers in industry mainly depends onthe costs of the treated component. For the complete exploitation of the laser resources, in fact, it is fundamentalto consider the technological advantages of the laser together with the high capital costs of the systems: thechallenge is nowadays to increase the flexibility of the laser technology. A way, to do this, is to develop a simulatorsoftware of the laser process able to take into account the laser material interaction and to predict the processresult according to the material and the geometry of the workpiece, the spatial and temporal distribution ofthe laser source and shape of the surface that must be treated. Several works have been proposed in last yearshaving the aim to fully model laser surface hardening.

The early studies were due to Ashby et al.,1 who exploited a monodimensional analytic model for the eval-uation of the treated depth relating to the laser parameters. Rappaz et al.2 proposed a two-dimensional modelfor the carbon flux evaluation, which has been applied by Shin et al.3, 4 for the carbon homogenization occuringin the austenization phase of the hypo-eutectoidical steel during the heat cycle. Tani et al.5 proposed a moregeneric model where, starting from the assumption proposed in Shin et al., the optimal path strategy can alsobe predicted by considering and minimizing the effects of the tempering on the hardened micro-structures. Theprevious models allow to predict a very accurate extension of the treated area together with the resulting micro-structures and the associated hardness, but the calculation time is too long, the prediction is two-dimensionaland it is limited to a very narrow workpiece area. In order to develop a useful tool for industry for the processoptmization able to determine the laser parameters and the laser trajectory, the software package should givefast respons regarding a volume as wide as possible. The real problem for the model in3, 5 is the calculus of thecarbon homogenization. The latter implies a very small grid for the accuracy of the solution of the second Fick’s

Further author information: (Send correspondence to L. Orazi)L. Orazi : E-mail: leonardo.orazi@unimore.it, Telephone: +39 0522 98 522 607A. Fortunato : E-mail:alessandro.fortunato@mail.ing.unibo.it, Telephone:+39 051 209 3437

Fundamentals of Laser Assisted Micro- and Nanotechnologies, edited by Vadim P. Veiko, Proc. of SPIE Vol. 6985, 69850A, (2008) · 0277-786X/08/$18 · doi: 10.1117/12.786970

Proc. of SPIE Vol. 6985 69850A-12008 SPIE Digital Library -- Subscriber Archive Copy

law, such as in,2 with an increasing of the calculation time. For laser heat treatment the carbon homogenizationcan be neglected and for the resulting micro-structure the model due to Reti et al.6 or Denis et al.7 can beused. The latter allows to predict also the presence of bainite and pearlite. In this way, it is not necessary tocreate a double grid: one for the Foureir’s and the other for the Fick’s equation and thus computational timeis sensibly reduced. Moreover, the simulation of the resulting micro-structural phases can be 3-dimensional andoptimal laser path trajectory is evaluated by minimizing the tempering effect on the hardened micro-structures.The accuracy of the model and the capabilities in the prediction of 3-D results with small calculation time isshown in this paper. The experimental tests were carried out on a C438 steel workpiece.

2. MODELING

2.1. The thermal model

The first problem to face, in heat treatment modelling, is the evaluation of the time-dependent temperaturedistribution through the workpiece T (t, x, y, z). As pointed out in5 this problem is solved by means of theFourier’s equation which governs the heat-flux into the material, see Eqn. 1:

cpρ∂T

∂t=

∂

∂x

(k

∂T

∂x

)+

∂

∂y

(k

∂T

∂y

)+

∂

∂z

(k

∂T

∂z

)+ q (1)

Where cp is the specific heat in J/kgK, ρ is the material density in kg/m3, k is the target thermal conductivityin W/mK and q is the laser heat flux into the material in W/m3, which depends on the laser beam that, in oursimulator, can be set to assume every spatial and temporal distribution and thus the shape and dimensions ofthe spot. The part to be hardened is modeled as a 3D grid, a moving laser spot hit it and the elements of the gridcan model the laser/material interaction with the physical properties varying with temperature. The softwareimplements a routine which automatically discretize the workpiece so that the grids are smaller at the surface,where the laser beam heat the material, and bigger at the bottom. The simulator evaluates the temperaturedistribution by solving the heat conduction with the FDM.

2.2. Model for the austenite decomposition

When a steel is subjected to a heat cycle, T (t, x, y, z), structural changes occur if the eutectoid temperature isreached. As said in1 a super-heating must be taken into account for the austenite temperature evaluation, whichdepends on the heating velocity. In3, 5 , when this temperature is reached the pearlite is transformed in austeniteand then the calculus of the carbon homogenization starts and it lasts until the temperature remains above theeutectoidic value. For typical laser hardening applications the laser-material interaction time is very small, thedensity power is low and the contact is limited in a very small surface region. In these conditions, the eutectoidtemperature is exceeded for a very short time and considering that the carbon diffusion needs high time rangethe homogenization can be neglected. Under this assumption a differnt model for the austenite transformationcan be used.

As proposed in6, 7 the decomposition of the austenite can be modelled using the Avrami kinetic model ofEqn. 2

yi(t) = Yi(T )[1 − e−bit

mi

](2)

where yi is the fraction of the ith decomposing phase at time t ( i=0 for ferrite, i=1 for perlite, i=2 forbainite, ecc... ), Yi(T ) is the maximum transformed fraction at temperature T as obtained experimentally fromisothermal transformation. The parameters bi and mi are obtained from TT curves using Eqns. 3 and 4:

lnYi

Yi − 0.01Yi= bit

mi

s (3)

lnYi

Yi − 0.99Yi= bit

mi

f (4)

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It can be outlined that the time start ts and the time finish tf of the phases decomposition occur conventionallywhen the fractions of the decomposing phase are respectivelly 0.01 and 0.99. The transformations that occurwith a continuous transformation can be calculated by using Eqns. 5 and 6.

t∗k+1 =ln

(1 −

yik

Yi(k+1)

)1/mi(k+1)

bi(k+1)(5)

yi(k+1) = Yi(k+1)

[1 − e−bi(k+1)(t

∗

k+1+∆tk+1)m

k+1]

(6)

where the variable at the previous integration time are indicated with k, the current time is indicated withk + 1 and the time step is ∆tk+1. When the temperature is under TMs, the temperature at which the residualaustenite starts to transfrom in martensite, the fractions of martensite and residual austenite indicated as ym

and ya are obtained at each time step tk with Eqns. 7

⎧⎨⎩

ymk = (1 −

∑ni yik)

[1 − e−0.011(TMs−Tk)

]

yak = 1 −

∑ni yik − ymk

(7)

The laser hardening process is a very ”quick” thermal process. The simulation conducted by means of thedecomposition model and by means of the microstructural model with carbon diffusion generated very similarresults. On the other hand the calculation time required to simulate an industrial mechanical components withthe micro-structural model can be 10 to 100 times the time requested by the decomposition model.

This result can be easly explained by considering that the intial micro-structure of the workpiece is reproducedby a digitized photomicrograph with a grid of 2 µm dimension. This grid is used for the solution of the secondFick’s law, reported in Eqn.8 for the two-dimension case, which governs the carbon flux.

∂Cν

∂t=

∂

∂x

(Dν

∂Cν

∂x

)+

∂

∂y

(Dν

∂Cν

∂y

)(8)

Cν is the solute concentration in the phase ν and Dν is solute diffusivity in the phase ν. When the stabilitycriterion is applied for the solution of the previous equation, the calculation time step become very small andall the simulation become slow. At the same time, if the grid dimension is increased the accuracy drasticallydecrease. The following Eqn. 9 allows to calculate the time ∆t required to the carbon for crossing a length of∆x in a mono-dimensional case:

∆t =∆x2

D(9)

where D is carbon diffusivity and ∆x is the grid dimension. In our case ∆x = 2 µm. In,9 the carbon diffusivity,as temperature dependent but carbon concentration independent, is of the order of 10−13,10−14 m2/sec. Withthis value, higher as respect to the diffusivity value obtained when the influence of the carbon concentrationin consideration, Eqn. 9 gives a timescale of the carbon diffusion in the grid of the range of 101, 102 secondswhich is a timescale about 2 or 3 order higher than the permanence time of the grid at a temperature abovethe eutectoidic temperature. These considerations prove that the carbon diffusion in the austenite for laserhardening can be neglected while this calculus is appropriate for heat treatment in oven.

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2.3. Tempering

When surfaces larger than the laser beam spot diameter must be hardened the machining is carried out by meansof multiple passes. The necessity to obtain a constant hardness imposes to generate scanning trajectories as closeas possible so that no lack of hardening occurs on the surface, but, in the same time, the softening due to thetempering must be minimized by choosing appropriate laser path. When overlapping trajectories occurs sensiblyreduction of the hardness happens. In our simulator the prediction of the resulting micro-structures is obtainedby means of the model previously described, while the hardness reduction of the martensite as a function of thetempering temperature and time is calculated by means of the following Eqn. 10:

HV = −74 − 434C − 368Si− 25Mn + 37Ni − 335Mo− 2235V +

+103

Pc(260 + 616C + 321Si − 21Mn− 35Ni− 11Cr + 352Mo + 2354V )

(10)

Where Pc is a coefficient depending from the time and the temperature of the tempering according to thelaw10 shown in Eqn. 11:

Pc =

[1

T−

nR

Halog

t

t0

]−1

(11)

T is tempering temperature, Ha the activation entalpy, t the time and t0 = 1h the time unit.

The softening of ferrite-pearlite and bainite is almost negligible.

3. EXPERIMENTAL

The experimental trials were carried out on a C43 mild steel shaft. The nominal chemical composition is:

Table 1. Chemical composition of the C43 UNI 10027-2.

% C % Mn %Si % S % P % Ni % Mo % Cr

0.43 0.65 0.28 <0.0065 <0.0065 0.0 0.0 0.0

The external surface of the shafts were hardened by means of a linear path with a velocity of 0.4m/min, thepower was 1200W and spot diameter of 8mm for each test. The laser source is a CO2 and at this intensity level(I ≈ 31̇07W/m2) the surface reflectivity are critical and for this reason a thin layer of grafite must be depositedon the surface.

4. RESULT AND DISCUSSION

In this paragraph the accuracy of the model will be shown. For the validation of the results we refer to thehardening operation presented in the previous paragraph, so that the process parameters in simulator are: laserpower of 1200 W , scanning velocity of 0.4 m/min and a laser spot of 8mm.

The displacement is a linear trajectory with an amplitude of 150 mm realized by moving the controlled axisX . In the software package the simulation is performed imposing the displacement to the laser beam by usingthe ISO standard command.

The numerical solution of Eqn. 1 is realized by means of a 250µm grid size in the orthogonal direction respectto surface target and by a 500 µm grid size in the x, y directions ortogonal to laser beam.

The simulation was realized by considering the whole laser displacement and the real dimensions of thespecimen in order to better take into account the boundary effects in thermal field evaluation. The absorptivityof the graphite layer is modelled to rise from 0.8 at ambient temperature to 0.95 at the steel melting temperature.

Proc. of SPIE Vol. 6985 69850A-4

Figure 1. Single pass. The trasversal section show that the treated zone is of the same width of the laser spot. The opticalobservation indicates that the hardened depth is about 1 mm, value confirmed by the microhardness measurements.

Figure 2. Not overlapping paths. The distance between the two parallel paths 8 mm as the spot diameter. There is notoverlapping between the hardened sections nor for the heat affected zones.

The software allows to assign different types of materials to each finite elements allowing to simulate nonhomogeneous parts such as coated parts, useful to simulate CO2 laser hardening where graphite coating, or metalmatrix composites are applied. Moreover all the physical parameters of the target material such as conduction,reflectivity, heat capacity, are evaluated as temperature-dependent.

5. CONCLUSIONS

An original software package for Laser Heat Treatment (LHS) has been developed. LHS is able to design suitableprocess condition in surface hardening of hypoeutectoidic steel. The model allows to predict the extension of thetreated area, the micro-structures and the hardeness resulting from the process. The model has been validatedby comparison with experimental data. The data showed the tempering effect in the case of the overlappingpaths by means of a reduction of the micro hardness in the overlapped zone of the material. The model predictedin the same way the softening of the tempered area. The results are fully 3-D and the computational time is lowso that LHS is an useful tool for industry in process planning.

Proc. of SPIE Vol. 6985 69850A-5

800i I

• EXPERIMENT- -•- - SIMULATION

600

12.5 13 13.5 14Position [mm]

14.5 15 15.5 16

000>IU,U,a)£CdI

400

200.— S ———•

Figure 3. Overlapped paths. The distance between the paths is 4 mm that is 50 % of overlapping. There is a stronginfluence between the hardened zones.

Figure 4. Overlapped paths. Vickers micro hardness measured into the depth of the second overlapping pass. Transversesection as in previous Fig. 3

Proc. of SPIE Vol. 6985 69850A-6

600i I

S EXPERIMENT500 - - SIMULATION

12.5 13 13.5 14Position [mm]

14.5 15 15.5 16

000>IU,U,a)£-oCdI

400

300

200

100

.— S

4

1000r I

S EXPERIMENT

800 - - SIMULATION

2.5 5 7.5 10 12.5 15 17.5 20Position [mm]

000>Icncn11)CDI

600

400

200.-. .-.e

Figure 5. Overlapped paths. Vickers micro hardness measured into the depth of the first pass. It is worth to observethe reduction of the material hardness due to the tempering effect. Transverse section as in previous Fig. 3

Figure 6. Overlapped paths.Vickers micro hardness measured -0.2 mm under the upper skin of the steel plate throughthe whole laser hardened zone. Transverse section as in previous Fig. 3

Proc. of SPIE Vol. 6985 69850A-7

REFERENCES

1. M. F. Ashby and K. E. Easterling, “The transformation hardening of steel surfaces by laser beam - ihypo-eutectoid steel,” Acta metall. 32, pp. 1935–1948, 1984.

2. A. Jacot and M. Rappaz, “A two-dimensional diffusion model for the prediction of phase transformation:application to austenization and homogenization of hypoeutectoid fe-c steels,” Acta mater. 45(2), pp. 575–585, 1997.

3. S. Skvarenina and Y. C. Shin, “Predictive modeling and experimental results for laser hardening of aisi 1536steel with complex geometric features by a high power diode laser,” Surface & Coatings Technology 46,pp. 3949–3962, 2006.

4. R. Patwa and Y. C. Shin, “Predictive modeling of laser hardening of aisi5150h steels,” International Journal

of Machine Tools & Manufacture 46, pp. 3949–3962, 2006.

5. G. Tani, L. Orazi, A. Fortunato, G. Campana, and G. Cuccolini, “laser hardening process simulation formechanical parts,” in Proceedings of LASE 2007, San Jose - CA, USA, 2007.

6. S. Denis, D. Farias, and A. Simon, “Mathematical model coupling phase transformations and temperature,”ISIJ International 32(3), pp. 316–325, 1992.

7. T. Reti, Z. Fried, and I. Felde, “Computer simulation of steel quenching process using a multi-phase trans-formation model,” Computational Materials Science 22, pp. 261–278(18), Dec 2001.

8. UNI, ed., UNI EN 10277-2, Italian National Standards catalogue, 2003.

9. H. K. D. H. Bhadesia, “Diffusion of carbon in austenite,” Metal Science 15, pp. 477–479, Oct 1981.

10. A. I. H. Committee, ASM Handbook, Vol. 04: Heat Treating, vol. 4, American Society of Metals, New York,1991.

Proc. of SPIE Vol. 6985 69850A-8