Modelling of cooling rates by comparison of experimental determined and numerical simulated temperature-time-functions at laser beam welding

Transcription

1 Modelling of cooling rates by comparison of experimental determined and numerical simulated temperature-time-functions at laser beam welding of steels G. Bruggemann, Th. Benziger, A. Mahrle & J. Schmidt gunnar. uni-magdeburg.de Abstract The quality of laser beam welds is strongly influenced by the technological parameters. These parameters have an effect on the temperature field of the melt. Simulations of the temperature distribution accompanied by verifying experiments can help to obtain optimal process parameters. 1 Introduction The result of laser beam welding is decisively influenced by the technological parameters. Amongst others the instabilities of the melt pool as well as cooling rates reduce the quality of the weld. This leads to weld defects like cracks and to a deterioration of the mechanical properties especially in the heat-affected zone. For the assessment of the joint depending on the adjustment of the process parameters it is necessary to have informations about the temperature field of the workpiece. Besides the measurement of the temperature field its numerical simulation gains importance. The description of the absorption process can be done using a source distribution which is adapted to the experimental conditions. It is possible to carry out two-dimensional as well as three-dimensional calculations of the temperature field. After a dimensional analysis the results can be calculated depending - amongst others - on the peclet number and on a heat flux number. In simulation calculations the influence of technological parameters on the temperature distribution can be estimated if the parameters of the model are adapted to the experiment. Therefore an on-line process control based on the temperature

2 298 Surface Treatment, Computer Methods and Experimental Measurements field can be realised. To prove the simulation, experiments were done using a thermographical system and a special CCD-camera. The interaction zone laser beam - material was observed in the visible and near infrared range. The analysis of the on-line captured images allows the detection of irregularities which cannot be calculated by the simulation. The analysis of the microstructures allows to establish facts about the correctness of two-dimensional calculations as well as the adaption of the distribution function of the absorption for the three-dimensional calculation. The experiments were done using a low-alloyed steel St 52-3 N as well as an austenitic-ferritic steel X2CrNiMoN Experimental determination of the temperature fields 2.1 Temperature measurement with a Silicon CCD array The radiation of the laser plasma extends from the ultraviolet to the near infrared spectral range. The steel materials heated above 500 C emit at the end of the visible and at the beginning of the infrared wavelength range. Thus the laser plasma has depending on the process gas in the interval [500 < l(nm) < 1000] local minimums [1]. Therefore the most favourable conditions for temperature measurements are reached by narrowband filtration in the near infrared range. The spectral sensitivity of silicon detectors reaches to approx. 2 pm. Thus commercial CCD arrays are sufficient for the proof of the temperature distribution at this welds in the interval [1500 < 9( C) < 500]. This area is bigger than the grey scale area ascertainable by the camera. Therefore an inter-focal plane produced in which complex variable domains get by a polarizing filter self-contained becomes in the camera optics. Therefore in the thermogram two areas appear with various sensitivities. Fig. 1 shows the virtually stationary temperature field at the laser welding of the two test materials. The temperature grey scale function is represented with and without polarizing filters. After the welding tests the CCD camera with the special optics was calibrated for the materials. The grey scale distribution registered by the CCD camera was recorded and parallelly to this the pyrometric temperature measurement was carried out. Since the emissivity wasn't known the temperature at selected reference points under stationary conditions was measured using a thermocouple and the emissivity adjusted so that both temperatures agreed. In fig. 2 the curve interpolation of the calibration for the duplex steel is approximated by the following polynomial. - o = a + (/) + c a = 6,79-10-" 6 = 5,21 10" c = -1,3 10^ = 9,7 10^ g = G... grey value GO... grey value at closed objective, T... temperature, X... wave length

3 Surface Treatment, Computer Methods and Experimental Measurements 299 fig. 1: temperature field at laser beam welding of (left) and (right) MO 1000 MM T[ C] fig. 2: temperature-grey value correspondence and calibration curve G (x) = f (T) fig. 3: thermogram (e=const.) at P^=5,6 kw, v^=l,5 m/min, St37, th.: 5 mm fig. 4: linescans LI02 (left) and LI05 (right) corresponding to fig.

4 300 Surface Treatment, Computer Methods and Experimental Measurements 2.2 Measurements with a thermographical system For the comparison of the acquired temperature fields additional measurements with a high-resolution thermographical system (0.2 mm/pixel, 8-12 im, CO,- laser filters) were done. The acquisition of the infrared image was carried out immediately after switching the laser off to eliminate the influence of the laser plasma. In fig. 3 a thermogram is shown. The melting dimensions are very well recognizable due to the rapid change of the emissivity and can be used for the comparison with the simulation. Fig. 4 shows the corresponding temperature profiles cross and axial to the weld seam. The infrared thermogram doesn't represent the stationary condition. 3 Numerical calculation of the temperature distribution 3.1 Source equations In comparison with the measuring of the temperature distribution the simulation of the welding process is carried out. At choice of a coordinate system bound to the laser beam the Fourier-Kirchhoff ' differential equation has to be applied. This can be written down for constant substance qualities and for the virtually stationary case after the transformation into the dimensionless form as follows: X, Y, and Z resp. are the coordinates related to the computational keyhole radius r, and 0 = (B - 8J/(8^ -8J is the temperature which is normalized with respect to the environmental temperature 8^ and the evaporation temperature 8^. Then the temperature distribution depends on the Peclet number as well as the heat source distribution f if considering the boundary conditions. The Peclet number is defined as the ratio of convective to conductive transport: (2) a with the feed velocity v, and the computational keyhole radius r, as characteristic length 1^. The essential influence of the thermal conductivity shows fig. 5 for various materials in the area of the technologically relevant welding speeds. The heat source distribution can be written down as follows: In this equation X is the heat conductivity and q the volumetric source power. An useful statement however is only possible after the evaluation of extensive experiments. Alternatively the capillary geometry can be provided, assuming the evaporation temperature. This procedure offers himself in the range of thin

5 Surface Treatment, Computer Methods and Experimental Measurements 301 sheets which is indicated by almost parallel seam flanks. The calculation can be carried out in this case two-dimensionally in which polar coordinates are chosen for the description: I V ( 3 0 U %%- + -%- = l^t-r n ^~^r>2 8R R 6cp J" 9R' R 9R R' U and V are the components of the speed vector related to the feed velocity v, in the coordinate directions R and 9. The simulation of the temperature distribution basing on eq. 4 allows the examination of the influence of the dimensionless characteristic quantities independent of the experiment. At first the potential flow around a cylinder was chosen as an approximate solution for the speed distribution. This describes particularly the boundary conditions in the steam capillary which is characterized as gliding condition very well. More exact calculations require the solution of the Navier-Stokes-equations with a free edge, which results from the coupling with the temperature field. The corresponding calculations are very extensive and they only were used for special investigations [2, 3, 4]. For further examinations an adapted algorithm was developed for the solution of the fluiddynamic equations on the base of an explicit difference method which allows extensive simulation calculations within acceptable computing times. 3.2 numeric solutions The numeric solution of the descriptive differential equations is carried out using a difference method. The solution of the resulting system of equations is carried out iteratively under the use of the GauB Seidel method with overtaxation. This requires a very fine mesh in immediate proximity of the capillary particularly due to the extremely high temperature gradients. On the other hand the solution area must be sufficiently more suitably big for the setup of the boundary conditions. Therefore a graded grid of the solution area is created fig results of simulation The calculated temperature distributions for different values of the Peclet Number shows fig. 7. The influence of the convective energy is represented especially in the temperature course across the seam (fig. 8). For the adaptation to the experiment the power transported across the capillary bound is determined. From the Fourier's law of the heat conduction one gets the local heat current numbers to where q is the local heat flux density. (5)

6 302 Surface Treatment, Computer Methods and Experimental Measurements %. 6: mesh of the computational do- main using polar coordinates u<, x U in 10* m'/min fig. 5: dependence of the Peclet-number to the materials properties temperature Oisti temperature distribution for Pe = 1.0 fig. 7: computated temperature distributions depending on different Pe-numbers fig. 8: temperature profile cross (left) and axial (right) to the weld seam for different Pe-numbers

7 Surface Treatment, Computer Methods and Experimental Measurements 303 Under use of the heat flux numbers the input power arises corresponding to the sheet thickness h according to the following equation: (6) 0 0 The calculated local heat flux numbers and the calculated power input at a sheet thickness of h = 3mm for the used steels are presented in fig comparison of simulation and experiment The welding experiments were done with sheet thicknesses of 3 mm. The sheets were made of steel and The beam power was varied in the range between 900 and 1800 watts. In a similar way the workpiece feed was varied between 0,5 and 1 m/min. The analysis of the experimental data will be described exemplary for one setup of parameters. The analysis of the thermograms obtained with the CCD camera revealed a cooling time tg/5 = 4,5 s for a beam power Pj = 1500 W and the steel The workpiece feed was Vf = 0,5 m/min. The simulation for these settings results in a Pe^ = 1,0 (fig. 9). The calculated characteristic length is 1^ = 0,96 mm. This leads to a cooling time tg^ = 6,9 s. The difference is due to the fact that the beam power is coupled into the material only to a certain extent. Basing on the experimental determined time t^ the analysis provided for 1^ = 0,62 mm a value for the Peclet number Pe^, = 0,64. The affiliated beam power is P^llOO W. The effectiveness is %=73%. The calculated temperature distribution leads to a melt pool width of 2,6 mm. This value corresponds to the seam width of 3 mm determined in the microstructure. If the experimental data are sufficient exact it is possible to determine the effectiveness of the welding process from the simulation. All other interesting values can determined too. For the comparison of the applied welding methods additionally welds were done with beam power P^=5600 W for the steel with a thickness of 5 mm and a workpiece feed of Vf= 1,5 m/min. Especially good are the dimensions of the melt to be determined from the thermogram due to the rapid change of emissivity. The correspondence between experiment and simulation is good especially for an effectiveness of 1^=80%: IR camera CCD camera simulation melt pool length 7,9mm 8,1 mm 8,0mm melt pool 3,4 mm 4,1 mm 3,1 mm width For the assumed parameter values the correspondence between experiment and simulation was sufficient. For special technological applications the measurement data as well as the material data have to be edited systematically.

8 304 Surface Treatment, Computer Methods and Experimental Measurements P» P* Pe Pft f.o fig. 9: local heat flux numbers and calculated power input depending on different Pe-numbers cooling time from K50*C to 500 C fig. 10: SZTU-diagram and composition of microstructure of the steel St 52-3N fig. 11: comparison of measured (left) and calculated (right) hardness values across the weld seam

9 Surface Treatment, Computer Methods and Experimental Measurements correlation between temperature field and seam properties For the construction steels the comparison of the materials characteristics calculated from the temperature field with the experimental determined mechanical properties shall give information about the feasibility of a process monitoring. The forecast of the material qualities of a weld requires the knowledge of the structure transformations going off in the material. For this special weld time temperature transformation-diagrams (SZTU) are used (fig. 10). From here it is possible to determine the developing micro structure and e. g. the hardness as a characteristic quality in dependence of the cooling rate. The cooling time from 850 C to 500 C must therefore being taken into account as essential variable in the mathematical model besides the chemical composition. After assignment of the variables the hardness can be calculated as follows: = ( C + 620C^ M%) M The needed carbon equivalent is calculated as follows: ATF+20 = (1,06-2,8C + 1,3C' -0,08M? + 0,054 lnfg/jm + (1,3-1,6C - 0,08M?)Zw, + (1,47-1,8C + 0,8C" (8) - 0,076 Mn - 0,045 In t^ ) FP According to [5] one can start from this, that values in this cool down interval [0,5 < tg/;(s) < 200 ] can be investigated. The percentage structure of the base material can be taken from the SZTU diagrams (m Martensit, Zw-interstage structures, FP ferrite Perlit, ). For the determination of the time t^ for an arbitrary distance to the middle of the seam a grey value line is applied to the thermogram taken at the test. The analysis of the of grey value line allows to determine the cooling cycle considering the temperature calibrations at the respective welded seam positions. The agreement of results determined arithmetically and experimentally can be estimated as satisfying. The raise of the workpiece feed [0,5 < v^m/min) < 1] leads for the steel to a reduction of the hardness measured crossways to the weld seam. Fig. 1 1 reports the hardness values determined at cross-sections of the weld seam and the forecast values obtained by in lines evaluation of the temperature field during welding. At the example of the duplex steel was examined, to what extent the cooling time from 1200 C on 800 C influences the formation of the microstructure of 50 % ferrite and 50 % austenite. The material solidificates primary ferritic due to the welding process. At about 1300 C the structure is purely ferritic. The further transformation into austenite is heavily influenced by the cooling time t^/g. If this time is too short, the material has no time for a complete transformation in austenite.

10 306 Surface Treatment, Computer Methods and Experimental Measurements The cooling time t^/g is determined in analogous way to the tg ^-time. For conventional welding methods a cooling time of i^/s = 10 s is recommended to reach a balance of ferrite and austenite. The t^/g times are in the case of the laser welding 2-3 times shorter. The major characteristic of the duplex steel is the resistance against corrosion. This behaviour was tested after the weldings. The critical pitting corrosion temperature was examined at weldings they were carried out in dependence from the cooling time interval [1,5 < t^/g (s) < 5]. The critical pitting corrosion temperature is 42,5 C for untreated duplex sheets. After the welding the corrosion resistance reduces as expected. The highest pitting corrosion temperatures are got in pickled condition of 37,5 C at cooling times t^/g < 3,5 s for laser welded specimen. All other examined conditions showed critical temperatures of 30 C-35 C. One can assume that an optimum value for t^/g = 10 s for conventional welding methods moves himself for the laser beam welding of duplex steel towards shorter times. 6 Summary The application of experimental thermography in comparision to the numerical simulation of the temperature field during the welding of various steels is demonstrated on some selected results. For selected process parameters a good correspondence between experiment and simulation could be obtained. For special technological applications the measurement data as well as the material data have to be edited systematically. The self developped measuring technique allows the usability for online condition monitoring. By inclusion of calculation models a process control becomes possible. Reference 1. Ignatiev, M.; Ermolaev, A & I. Titiov: The high speed pyrometer system for lasers welding for temperature process control, in: Laser treatment (ed Mordike, B.), pp , froc<wm&? J^^CI^T, Gottingen, Beck, M.: Modellierung des LasertiefschweiBens. Teubner Verlag, Stuttgart, Berger, P.: Physical models on deep penetration welding with emphasis on fluid dynamic, in: SPIE Vol. 1810, 1992, pp , Proceedings of the Conf. "Gas Flow and chemical lasers " 4. Becker, D. & Schulz, W.: Evaporation in deep penetration welding with laser radiation, in: Laser in Engineering (ed Waidelich, W.), pp , Proceedings of the ll*h Conf. LASER, Munchen, Germany, 1993, Springer Verlag, Berlin, Seyffarth, P. : Aspects of the weldability of mild steels, in: ECLAT ' 94 (ed Sepold, G.), pp , frocfwmgj of f&e J^ ECL47, Bremen, Germany, 1994, DVS-Verlag, Diisseldorf 1994