FUNDAMENTAL AND APPLICATION OF HIGH PRECISION LASER MICRO-BENDING X. Richard Zhang and Xianfan Xu * School of Mechanical Engineering Purdue University West Lafayette, IN 47907-1288 * To whom correspondence should be addressed. xxu@ecn.purdue.edu; phone (765) 494-5639; fax (765) 494-0539 ABSTRACT This paper presents the technique of high precision microscale laser bending and the study of the thermomechanical phenomena involved. The use of pulsed and CW lasers for microscale bending of ceramics, silicon, and stainless steel is demonstrated. Experimental studies are conducted to find out the relation between bending angles and laser operation parameters. Bending results obtained by a pulsed and a CW laser are compared. Changes of surface composition after laser irradiation are analyzed. Numerical calculations based on thermo-elasto-plastic theory are conducted and results are compared with the experimental data. Examples of industrial applications of high precision laser bending are given. INTRODUCTION Laser bending or laser forming is a newly developed, flexible technique to modify the curvature of sheet metals or hard materials. The schematic of a laser bending process is shown in Fig. 1. A target is irradiated by a focused laser beam passing across its surface with a certain speed. Heating and cooling cause plastic deformation in the laser-heated area, thus change the curvature of the target permanently. Bending mechanisms are determined by the specimen thickness, the thermophysical properties of the specimen, and the temperature field, Target Clamped end Focused laser beam Scanning line Bending angle z y x Fig. 1 Schematic of the laser bending process which in turn is determined by laser processing parameters. The common laser bending mechanisms include the temperature gradient mechanism and the buckling mechanism [1]. For the temperature gradient mechanism, only surface layer is heated (thus there is a temperature gradient with the highest temperature at the surface), residual stress and strain will be concentrated in the near surface region. Thus, the specimen will always bend toward the laser beam. This type of heating and bending is preferred when a consistent bending direction is required. If laser heating is uniform across its thickness, the specimen will bend just like a beam under compression (buckling); the bending direction depends on the pre-curvature and the residual stress of the specimen. Applications of laser bending include ship construction [2], removing welding distortion and straightening car body parts [3], forming in space [4,5], and rapid prototyping [6,7]. Recently, Chen et al. [8] studied high precision laser bending for manufacturing computer components. They achieved a bending precision of sub- microradian, far exceeding those obtained using any other method. Finite element methods have been used to model laser bending [9-11]. Influence of laser operating parameters on bending can be estimated from these calculations. While in most laser bending researches a continuous wave (CW) laser is used, bending using a pulsed laser for micro-scale bending and a 2-D finite element study on the relation between bending angles and the pulsed laser parameters were also reported [12]. Although a 3-D model is more appropriate for predicting the actual pulsed laser bending process, the computation of 3-D pulsed laser bending is inhibited by the computer power. This is because thousands of laser pulses are irradiated onto the target in pulsed laser bending, therefore it is extremely time-consuming to compute thermal and thermo-mechanical effects caused by all the pulses. Zhang et al. [13] developed an efficient calculation method for 3-D finite element analysis of pulsed laser bending. In that method, only a fraction of the total laser pulses instead of all the laser pulses need to be calculated, thus reducing the computation time considerably. This paper presents high precision bending of ceramics, silicon, and stainless steel specimens using a pulsed laser and a CW laser. Laser beams are tightly focused onto the target surface to induce localized residual stress and strain, thus to obtain high precision of bending. The relation between bending angles and laser operating parameters, such as laser power, laser scanning velocity, and number of scanning lines are obtained experimentally. The dependence of bending on optical and thermophysical properties of the target material is illustrated. In order to understand the effects of laser irradiation, surface composition before and after laser bending are analyzed using electron probe microanalyser (EPMA). Results obtained by a pulsed laser and a CW laser are compared. 3D numerical simulations of stainless steel bending using a pulsed laser and a CW laser are performed. Results of the simulations are compared with experimental data. 1 EXPERIMENTAL For experiments, a 2 W Nd:VA nanosecond pulsed laser and a 9 W CW fiber laser are used. The operation parameters of these two lasers are summarized in Table 1. Table 1. Parameters of pulsed laser and CW laser Pulsed laser CW laser Laser wavelength 1.06 ?m 1.10 ?m Laser pulse full width 120 ns Laser pulse repetition 22 kHz Laser maximum power 2.0 W 9.0 W Laser beam diameter 50-60 ?m 40-80 ?m The experimental setup for performing laser bending as well as for measuring the bending angle has been discussed in previous work [11,12]. Ceramics, silicon, and stainless steel (AISI 301) sheets are used as test specimens. The parameters of the specimens are listed in Table 2. The Al 2 O 3 /TiC ceramics is used in computer hard disks as the material for the read/write head. Table 2. Specimen parameters Specimen material Ceramics Silicon Stainless steel Length 10.0 mm 8.0 mm 10.0 mm Width 1.25 mm 1.50 mm 1.00 mm Thickness 0.35 mm 0.20 mm 0.10 mm Before laser treatment, all the samples are polished and cleaned with acetone. The elemental distribution maps of ceramic specimens are recorded with EPMA before and after laser treatment. High magnification photos of the surface topography and quantitative composition analyses of the surface area irradiated by the lasers are also obtained with EPMA. 2 EXPERIMENTAL RESULTS AND DISCUSSIONS Bending angles of the ceramic specimens are obtained at various laser processing conditions, as shown in Fig. 2–Fig. 5. The results of 0 10 20 30 40 50 0 1 2 3 4 5 6 7 Pulsed laser CW laser Bending angle ( ? rad) Laser power (W) Fig. 2 Bending angle of ceramics as a function of laser power. (a) pulsed laser, 3.25 mm/s, (b) CW laser, 130 mm/s 5 10 15 20 25 30 35 40 0 5 10 15 20 25 30 35 0 100 200 300 400 Pulsed laser CW laser Pulsed laser scanning velocity (mm/s) CW laser scanning velocity (mm/s) Bending angle ( ? rad) Fig. 3 Bending angle of ceramics as a function of scanning velocity. (a) pulsed laser, 1.1 W, (b) CW laser, 5.0 W pulsed laser and CW laser bending are compared. As expected, the bending angle increases when the input laser power increases, and decreases with an increase of the scanning velocity, as can be seen from Fig. 2 and Fig. 3. It is found that the specimens always bend toward the laser beam for pulsed laser bending, but they bend away from the laser beam for CW laser bending when the scanning velocity is reduced. Figure 4 indicates that for both the pulsed laser and the CW laser, scanning over the specimen surface repetitively would increase total bending angle, but the amount of additional bending angle decreases with the number of scanning lines. For the pulsed laser, the bending angle obtained by the second laser scan drops to about 25% of the angle obtained by the first scan, and no additional bending occurs after four scans. For the CW laser, the bending angle of the second scan is about 70% of the first scan, and no additional bending occurs after six scans. 0 5 10 15 20 25 30 0 1 2 3 4 5 6 7 Pulsed laser CW laser Bending angle ( ? rad) Number of scanning lines Fig. 4 Additional ending angle of ceramics as a function of number of laser scanning lines. (a) pulsed laser, 1.1 W, 3.25 mm/s, (b) CW laser, 5.0 W, 130 mm/s 0 5 10 15 20 25 30 35 40 0 50 100 150 200 250 300 350 Pulsed laser CW laser Bending angle ( ? rad) Distance between scanning lines ( ?m) Fig. 5 Bending angle of ceramics as a function of distance between adjacent scanning lines. (a) pulsed laser, 1.1 W, 3.25 mm/s , (b) CW laser, 5.0 W, 130 mm/s Bending angles induced by the pulsed laser and the CW laser are compared while keeping a same laser generated stress-affected zone. The size of the stress-affected zone is determined in the experiments as the separation distance above which any two adjacent laser scans do not influence each other. The bending angle as a function of the separation distance between two scans is measured. As shown in Fig. 5, the stress affected zone is 100 ?m for the pulsed laser bending when the scanning velocity is 3.25 mm/s and the power is 1.1 W. The same stress affected zone is obtained for the CW laser when the scanning velocity is 130 mm/s and the power is 5 W. However, the resulting bending angles for the two lasers are different, the bending angle obtained with the CW laser is about twice of that obtained from the pulsed laser, which is due to the longer thermal diffusion length in the CW laser heating. (a) (b) Fig. 6 BSE images of ceramic specimen surface after (a) pulsed laser bending, 1.1 W, 13 mm/s, (b) CW laser bending, 5 W, 130 mm/s The backscattered electron (BSE) images of laser irradiated Al 2 O 3 /TiC ceramic specimens obtained by EPMA are shown in Fig. 6. The magnification is 2000X. TiC grains are white irregular “islands” and alumina grains are the background “sea”. The bending angle obtained is 9 ?rad for the pulsed laser and 30 ?rad for the CW laser. After the pulsed laser irradiation, the surface becomes gray. In addition, a few microcracks can be seen in Fig. 6a in the laser- irradiated area. After the CW laser irradiation, an extensive gray color region appears as shown in Fig. 6b. A 30 ?m wide band of new homogeneous material replaces the original ceramic composite material and a curved, 1 ?m wide microcrack is located at the center of the scanning line, connected with several transverse microcracks. Formation of the gray substance is possibly due to diffusion of TiC into Al 2 O 3 , and/or oxidation of TiC to form TiO 2 or TiAl 2 O 5 . Considering the microcracks produced after the laser irradiation, more material damages are produced by the CW laser than the pulsed laser, though a larger bending angle is obtained by the CW laser. 20 25 30 35 40 0 1 2 3 4 5 Al Ti The weight percent (%) Number of scanning lines (a) 10 20 30 40 50 0 1 2 3 4 5 6 Al Ti The weight percent (%) Laser power (W) (b) Fig. 7 Al and Ti weight percent changes versus (a) number of pulsed laser scanning lines, 1.1 W, 13 mm/s, (b) CW laser, 130 mm/s Al and Ti weight percentage changes are also obtained using EPMA. Two sets of experiments are carried out. For the first set of experiments, the pulsed laser is used with a power of 1.1 W and a scanning velocity of 13 mm/s. The element weight percentage change versus the number of scanning lines is given in Fig. 7a. It can be seen that the weight percent of Al decreases slightly with an increase in the number of lines scanning at the same location. For the second set of data shown in Fig. 7b, the CW laser is used at a scanning velocity of 130 mm/s. It can be seen that there is almost no change in the weight percent when the laser power is increased from 1 W to 5 W. The weight percent of Ti increases slightly from 23.8% to 24.8% when the laser power is increased from 1 W to 3 W, and then decreases significantly to 17.0% at 5 W. The behavior of the ceramics under laser irradiation shown in Fig. 6 and Fig. 7 can be qualitatively understood by analyzing the optical and thermal properties of the ceramics. In the ceramics specimen, the alumina grains are transparent to the laser irradiation, while the TiC grains absorb the laser energy. Heating of alumina is through heat conduction from the TiC grains to the alumina grains. On the other hand, alumina has lower melting temperature (2345 K) and vaporization temperature (3803 K) compared to those of TiC (3413 K and 5093 K) [14]. During pulsed laser irradiation, a certain amount of alumina grains are evaporated, and possibly some TiC grains as well. TiO 2 and other oxides such as TiAl 2 O 5 can be produced due to oxidation. TiC and its oxides form a gray pattern on the surface as shown in Fig. 6a. Overall, the evaporation is weak because of the short heating time; relatively less material is ablated, causing a small change in the element weight percentages. For the CW laser irradiation, at low laser powers (<3 W), the temperature reached in the TiC grains could be lower than its vaporization temperature (5093 K) but it could be higher than the vaporization temperature of alumina (3803 K) in the alumina grains. Therefore, more alumina is evaporated and TiC and its oxides are left on the surface. Evaporation is rather weak and the element percentage changes are small. On the other hand, at high laser powers (>3 W), a higher peak temperature is reached on the surface of the TiC grains, causing stronger evaporation and stronger oxidation. However, it is noticed that the slight increase in Al does not offset the large decrease in Ti, indicating other compounds are formed such as oxides. Forming of TiO 2 from TiC would reduce the weight percentage of the Ti element. Thus, it can be concluded that more oxides are formed with a high laser power, resulting in reduced C and Ti concentrations. 0 5 10 15 20 0 1 2 3 4 5 6 7 8 Pulsed laser CW laser Bending angle ( ? rad) Laser power (W) Fig. 8 Bending angle of silicon as a function of laser power at scanning velocity 3.25 mm/s for (a) pulsed laser, (b) CW laser Figure 8 shows the bending angle of silicon specimens as a function of the power of the pulsed laser and the CW laser, respectively. The thermal diffusivity ??of silicon is much larger than that of ceramics. For pulsed laser bending, the larger ? value of silicon does not cause much difference in the bending angle since the pulse duration is very small (120 ns), and the heat diffusion depth is much smaller than the thickness of the specimen. However, for the CW laser, the temperature gradient in the silicon specimen is not as steep as that in the ceramic specimen because of the larger ? value and a relatively long heating time. Another factor that affects the temperature profile in the thickness direction is the optical absorption depth of materials. The optical absorption depth of silicon is about 0.5 mm and that of ceramics is less than 100 nm. The longer optical absorption depth of silicon results in a more uniform heating but a lower peak temperature. Using the CW laser and a scanning velocity of 3.25 mm/s, the ratio of the heat diffusion depth to the silicon specimen thickness is on the order of 10, thus, bending could be caused by the buckling mechanism. It can be seen from Fig. 8 that, for the CW laser, the bending angles of the silicon specimen are less than half of the bending angles of the ceramics specimen at most power levels, even the scanning velocity of the latter is 40 times faster than the former. 0 5 10 15 20 0 0.001 0.002 0.003 0.004 0.005 0 0.5 1 1.5 2 2.5 Pulsed laser CW laser Laser power (W) Pulsed laser bending angle ( ? rad) CW laser bending angle (rad) Fig. 9 Bending angle of stainless steel as a function of laser power (a) pulsed laser, at scanning velocity 195 mm/s, (b) CW laser, at scanning velocity 8 mm/s, laser beam diameter 40 ?m Figure 9 shows the bending angle of the stainless steel as a function of the power of the pulsed laser and the CW laser. The laser beam diameter of the CW laser is 40 ?m. At these laser powers, melting does not occur. Compared with the pulsed laser bending of ceramics and silicon, it is found that comparable bending angles can be obtained for steel when the scanning velocity is about 60 times higher and with only half of the laser power. This is because steel is much more ductile, and the steel specimen used is thinner than other two materials. 3 NUMERICAL SIMULATIONS The CW and pulsed laser bending induced by the temperature gradient mechanism is simulated using 3-D finite element models. Thermal analysis and stress analysis are needed in the simulation. The two analyses are treated as uncoupled since the heat dissipation due to deformation is negligible compared with the heat provided by the lasers. In an uncoupled thermo-mechanical model, a transient temperature field is obtained first in the thermal analysis, and is then used as a thermal loading in the subsequent stress analysis to obtain transient stress, strain, and displacement distributions. For the CW laser bending simulation, the laser beam is considered as a constant heat source moving at a constant velocity. The time step in the calculation must be small enough so that the continuously moving laser flux can be accurately approximated. Hence, the CW laser bending can be simulated using a 3-D model directly. For the pulsed laser bending, direct simulation using a 3-D model is impractical in terms of the computer power, since there are too many pulses along a single laser scanning line. An efficient method for simulating pulsed laser bending has recently developed by Zhang et al. [13]. In most pulsed laser bending processes, constant stress and strain fields along the laser scanning direction are obtained. Although a single laser pulse generates non-uniform stress and strain distributions, in practice, laser pulses with the same pulse energy, separated by a very small distance compared with the laser beam diameter are used. Thus, the laser-induced stress and strain vary little along the scanning direction. Also, the stress and strain fields induced by a laser pulse are contained within a short distance from the laser- irradiated area. With these in mind, it is only necessary to calculate several laser pulses until the stress and strain fields in an x-z cross- section area are not changed by a new laser pulse. Then, the residual strain field in this cross-section can be imposed onto the whole domain to calculation the deformation distribution. In other words, a strain field {? r }, which can be used to calculate displacements of the target after pulsed laser scanning, is generated by calculating only a fraction of the total pulses. Details of calculating displacements from a strain field were provided elsewhere [13]. The non-linear finite element solver, ABAQUS is employed for both CW and pulsed laser bending simulations. Only bending of the stainless steel is simulated since more property data of stainless steel are available compared with the other two materials. The maximum temperatures obtained in all simulations are lower than the melting point of steel (1650 K). Properties of stainless steel 301 [15] used in the calculation are considered as temperature dependent. 3.1 MESH GENERATION For both CW and pulsed laser calculations, a dense mesh is used around the laser path and a coarse mesh is used outside the primary processing region. Transition elements are created to connect the dense mesh and the coarse mesh. The Eight-node linear brick elements are used. The mesh used for the CW laser bending simulation is shown in Fig. 10. The Cartesian coordinate system is attached to the computational domain and the center of laser beam moves along the y- axis at x = 0. The computational domain is the same as the dimensions of the steel sheet used in the experiments, 10 mm x 1 mm x 0.1 mm. The total element number is 20,790. The mesh for the pulsed laser bending simulation is similar except a different element size is used and the total element number is 99,440. Mesh refinement tests are performed by increasing the mesh density until calculations are independent of the mesh density. For each case, the same mesh is used for both thermal and stress analyses. o x y z Fig. 10 Mesh for the 3D simulation of CW laser bending 3.2 THERMAL AND STRESS ANALYSES The thermal analysis is based on solving the 3D heat conduction equation. The initial condition is that the whole specimen is at the room temperature (300 K). The laser flux is handled as a volumetric heat source absorbed by the target. Using the transient temperature data obtained from the thermal analysis as thermal load, the transient stress, strain, and displacement distributions are obtained by solving the quasi-static force equilibrium equations. The material is assumed to be linearly elastic-perfectly plastic. The Von Mises yield criterion is used to model the onset of plasticity. The left edge is completely constrained, and all other boundaries are force free. Material properties including density, yield stress, and Young’s modulus are considered as temperature dependent. The strain rate enhancement effect is neglected since temperature dependent data are unavailable. Due to the same reason, a constant Poisson’s ratio of 0.3 is used. Effects of unknown material properties on the computational results have been discussed by Chen and Xu [12]. Creep is neglected due to very short laser pulse duration. 3.3 NUMERICAL RESULTS AND COMPARISON WITH EXPERIMENTAL DATA Figure 11 and Figure 12 are the off-plane displacement and residual stress ? xx profile along the x direction. Only half of the computational domain is calculated because of the symmetry. For pulsed laser bending as shown in Fig. 11, a “V” shape off-plane displacement is obtained after laser scanning, with the valley located at around 10 ?m from the center of the scanning line. The positive off- plane displacement near the center of the scanning line is produced by thermal expansion along the positive z-direction. The stress ? xx is tensile and its value is around 1.1 GPa in the region within 15 ?m from the pulse center. This agrees with the theoretical prediction that the tensile residual stress will be obtained near the center of the laser- irradiated area due to the thermal shrinkage during cooling. The tensile stress drops quickly to zero at about 25 ?m from the center of the laser beam. For CW laser bending as shown in Fig. 12, the off-plane displacement has a similar profile but a much larger (hundreds times) magnitude. However, the peak tensile residual stress, about 700 MPa, is smaller than that induced by a pulsed laser. For the pulsed laser energy of 4.4 ?J, 5.4 ?J and 6.4 ?J, bending angles obtained by simulations are compared with experimental results, as shown in Fig. 13. It is seen that the experimental results agree with the calculated values within the experimental uncertainty. Both the experiment and simulation results show the bending angle increases almost linearly with the pulse energy. Figure 14 compares the measured and calculated bending angles obtained by a 2W CW laser with a fixed beam diameter of 80 µm, but at different scanning velocities. Increasing the scanning velocity decreases the bending angle because of the decrease of the energy input. The calculated bending angles are about 20% lower than the experimental data. 0 0.5 1 1.5 2 0 200 400 600 800 1000 1200 0 50 100 150 200 Displacement Residual stress Off-plane displacement w (nm) x (? m) Residual stress ? xx (MPa) Fig. 11 Simulation results of pulsed laser (a) off-plane displacement, (b) residual stress ? xx distributions (Laser pulse energy 5.4 ?J, scanning velocity 195 mm/s) 0 0.1 0.2 0.3 0.4 0.5 0 200 400 600 800 0 500 1000 1500 2000 2500 3000 Displacement Residual stress Off-plane displacement w ( ? m) x (? m) Residual stress ? xx (MPa) Fig. 12 Simulation results of CW laser (a) off-plane displacement, (b) residual stress ? xx distributions (Laser power 2 W, scanning velocity 8 mm/s, laser beam diameter 80 ?m) 0 2 4 6 8 10 12 0.09 0.1 0.11 0.11 0.12 0.13 0.14 0.14 0.15 0.2 0.25 0.3 0.35 Experimental Simulation Bending angle ( ? rad) Laser fluence (J/cm 2 ) Laser power (W) Fig. 13 Comparison of experimental and numerical results of bending angles versus laser power (Pulsed laser, scanning velocity 195 mm/s) 200 400 600 800 1000 5 10 15 20 25 30 Experimental Simulation Bending angle ( ? rad) Scanning velocity (mm/s) Fig. 14 Comparison of experimental and numerical results of bending angles versus scanning velocity (CW laser, laser power 2 W, laser beam diameter 80 ?m) 4 CONCLUSIONS This work demonstrated using pulsed and CW lasers for microscale bending of ceramic, silicon, and stainless steel samples. Experimental studies were conducted to find out relations between bending angles and laser operation parameters. Bending results obtained by a pulsed and a CW lasers were compared. It was found that when the laser generated stress-affected zone was kept the same, the CW laser produced more bending than the pulsed laser did. However, the pulsed laser caused much less surface composition change and thermomechanical damage to the specimens. Numerical calculations using the thermo-elasto-plastic theory were conducted and the results of the calculations agreed with the experimental data. ACKNOWLEDGMENTS Support of this work by the National Science Foundation is acknowledged. The authors are most grateful to Dr. Andrew C. Tam of IBM Almaden Research Center for his contribution to this work. The authors also thank SDL, Inc. for providing the CW fiber laser system, and Mr. Carl Hager (EAS Department, Purdue University) for his help on the EMPA measurements. REFERENCES 1. 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Zhang, X., Chen, G., and Xu, X., 2001, “Numerical Simulation of Pulsed Laser Bending,” J. Applied Mechanics, submitted. 14. Swain, M.V., 1994, Structure and properties of Ceramics in Materials Science and Technology: A Comprehensive Treatment, 11, VCH, New York. 15. Maykuth, D.J., 1980, Structural Alloys Handbook, 2, Metals and ceramics information center, Battelee Columbus Laboratories, Columbus, Ohio, pp. 1-61. . technique of high precision microscale laser bending and the study of the thermomechanical phenomena involved. The use of pulsed and CW lasers for microscale bending of ceramics, silicon, and stainless. stress and strain, thus to obtain high precision of bending. The relation between bending angles and laser operating parameters, such as laser power, laser scanning velocity, and number of scanning. 2.5 Pulsed laser CW laser Laser power (W) Pulsed laser bending angle ( ? rad) CW laser bending angle (rad) Fig. 9 Bending angle of stainless steel as a function of laser power (a) pulsed laser,