FINITE ELEMENT SIMULATIONS OF LASER BENDING OF SMALL SIZED SHEETS

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1 5 th International & 26 th All India Manufacturing Technology, Design and Research Conference (AIMTDR 2014) December 12 th 14 th, 2014, IIT Guwahati, Assam, India FINITE ELEMENT SIMULATIONS OF LASER BENDING OF SMALL SIZED SHEETS Besufekad. N. Fetene 1*, Uday. S. Dixit 2 1* Department of Mechanical Engineering, Indian Institute of Technology Guwahati b.negash@iitg.ernet.in 2 Department of Mechanical Engineering, Indian Institute of Technology Guwahati uday@iitg.ernet.in Abstract Recently, laser bending has received attention for a wide variety of applications in industries due to its excellent bend quality with high productivity and flexibility. In this work, finite element simulations of bending of small sized sheets are carried out using ABAQUS package. The temperature and strain-rate dependent material properties of D36 shipbuilding steel sheet are considered. Simulation results throw light on the bending behavior of small sized sheet components. Keywords: Laser bending, stationary heat source, moving heat source, FEM 1 Introduction Laser bending is a process of bending the work piece by using controlled laser heat source, which induces thermal stress through a specified path to shape the work piece without any mechanical forces.giger and Vollertsen (1993) identified three most relevant mechanisms to explain the thermomechanical behavior in laser forming depending on specific combinations of component geometries and laser process parameters. These are temperature gradient mechanism (TGM), buckling mechanism (BM) and upsetting mechanism (UM).TGM is the most common mechanism of sheet metal bending and is activated when the beam diameter is much smaller than the work piece thickness. In the case of the BM, the laser beam diameter is much larger than the sheet thickness and laser scan speed is slower than that in TGM. Here, the part can be made to bend in either away from laser beam or towards laser beam depending on a number of factors. UM is activated when the beam diameter is much smaller than the sheet thickness of the work piece. Additionally, a high thermal conductivity of the sample material facilitates the activation of UM [Pretorius (2009)] The laser bending process has been investigated for many materials, such as mild steel [Thomson and Pridham, (2001)], stainless steels [Liu et al., (2009); Vásquez-Ojeda and Ramos-Grez, (2009)], aluminum and its alloys [Merklei et al., (2001)], titanium and its alloys [Walczyk et al., (2000)], and silicon [Xu et al., (2011)]. These studies considered large sized sheets. The geometry parameters like sheet thickness, length and width influence the bend angle. For example, the bending angle is approximately inversely proportional to the square of the sheet thickness [Giger and Vollertsen (1993)]. The length of the work piece has little influence on the bend angle [Shichun and Jinsong(2001)]. However, in the bending of small components, all geometric dimensions will have profound influence on the bend angle. The direction of bend is also influenced by a number of parameters. Li and Yao (2001) suggested that direction of bending can be assessed by evaluating the Fourier number given by α d F D 0 =, (1) 2 s v where α d is the thermal diffusivity, D is the diameter of beam at the surface of the sheet, s is the sheet thickness and v is the scan speed. The objective of this work is to evaluate the effect of laser power, work piece geometry and laser diameter on bending angle for stationery and moving heat sources. Simulations of the 3D laser bending were performed by using ABAQUS package in order to investigate the influence of laser forming with variation of laser parameters on small size work piece. 2 Finite element modeling using ABAQUS Figure 1shows the schematic diagram of laser bending. Numerical simulations are carried out using ABAQUS package in order to analyze the variations in the bend angle and temperature by applying stationery and moving heat sources with different laser parameters. In this work, a coupled thermomechanical analysis is carried out using ABAQUAS/Explicit. In ABAQUAS/Explicit, the heat transfer equations are integrated using an explicit forward-difference time integration rule and the mechanical solution response is obtained using an explicit center-difference integration rule. The strategies for time control are fixed time incrementation. Nonlinear system is solved using full Newton solution technique

2 FINITE ELEMENT SIMULATIONS OF LASER BENDING OF SMALL SIZED SHEETS 5 mm Stationary heat source 10 mm 5 mm 10 mm 5 mm Effective length Clamp 15 mm Total length Figure1Schematic of Laser Bending A laser beam scans the top surface parallel to the fixed side with a constant laser power and a constant scanning speed as shown in Figure 1.D36 steel specimens of size 25 mm 20 mm 2 mm and 15 mm 10 mm 2 mm were consideredd for both lower laser power and speed. Figures 2 and 2 show the top views of work-pieces indicating the locations of moving and stationary heat sources. For each work- piece, 5 mm length is used for clamping at one side of the work piece parallel to scanning direction. Scan line of moving heatt source 5 mm 10 mm 5 mmm Effective length Clamp 15 mm Total length Figure 2 The work-pieces for movable and stationary heat source 25 mm 20 mm 2 mm sheet 15 mm 10 mm 2 mm sheet 10 mm Heat convection is modeled by Newton s law given by q = h( T T ), s (2) 10 mm Scan line of moving heat source where q is the heat flux, h is the heat transfer coefficient, T is the sheet metal temperature and T s is the ambient temperature, taken as 20 ºC. Radiation was neglected. As shown in Figure3, clamped surfaces are considered insulated and h = 10W.m -2.K -1 is used for the exposed surfaces. 20 mm 5 mm Effective length Clamp 25 mm Total length 20 mm The non-linear transient thermo-mechanical analysis is carried out. The temperature dependent thermal and mechanical properties of the D36 shipbuilding steel were used in the analysis, as given in [Dixit el al. (2013)]. During the simulation, the thermal load is given in the form of heat flux that obeys a normal Gaussian distribution as follows: 624-2

3 5 th International & 26 th All India Manufacturing Technology, Design and Research Conference (AIMTDR 2014) December 12 th 14 th, 2014, IIT Guwahati, Assam, India laser process parameters, geometry and material parameters. The bending angle is calculated at one edge after the steady state has reached. The steady state is arrived after a cooling for 15 seconds. Figure 3 Assignment of heat transfer coefficient 3.1 Effect of laser power The effects of laser power on the bending of 25 mm 20 mm 2 mmwork piece size is observed for stationery and moving heat sources. The scanning speed is 20 mm/sec and heating time is 1 s. For one case, the laser diameter is 8 mm and for the other case it is 4 mm. The simulation result reveals that the bend angle is critically dependent on the laser power. As seen in Figure 4 for 8 mm beam diameter, the bending direction is negative (away from laser source) for 100 W 200 W powers, but for more than 200 W power, the bending direction is positive. The non-linear transient thermo-mechanical analysis is carried out. The temperature dependent thermal and mechanical properties of the D36 shipbuilding steel were used in the analysis, as given in [Dixit et al. (2012)]. During the simulation, the thermal load is given in the form of heat flux that obeys a normal Gaussian distribution as follows: 2 2 ( x y ) cη P q ( x, y) = exp c, 2 2 π r r (3) where q is the thermal heat flux density of laser beam, η is the absorptivity of the sheet materialη = 0.8, P is the power of the laser ( W), r is the radius of the laser beam r and c is constant value between 1 and 3. For this work c has been taken equal to 2. Moving heat source along a straight line is modeled as a moving heat flux with small steps, the heating time for every single load step is 0.05 seconds for both the work pieces. The jumping of consecutive heat flux node is kept to a minimum of 1 mm for both 4 mm and 8 mm laser diameters. The total heating time depends on the scanning speed and the width of the work piece. The same scanning speed 20 mm/s is used for both work pieces. The stationery heat source is modeled as a stationery heat flux at the center of the effective length. 3D thermally coupled brick elements (C3D8R) with 8 nodes were used. After mesh sensitivity study, the element of size 0.5 mm 0.5 mm 0.5 mm was chosen throughout. 3 Effect of parameters on bending angle The behavior of material components under this process is influenced by a specific combination of Figure 4 Computational results for the effects of laser power on the bending angle by applying stationary and moving heat source on 25 mm 20 mm 2 mm work piece 8 mm beam diameter 4 mm beam diameter As shown in Figure 4, at stationary heat source of 4 mm beam diameter, the bend direction is negative 624-3

4 FINITE ELEMENT SIMULATIONS OF LASER BENDING OF SMALL SIZED SHEETS at 100 W after which it tends to positive direction increasing up 250 W laser powers. But in the case of scanning laser, the bending angle is negative up to 200 W, but starts increasing beyond 200 W towards positive direction. The similar study is carried out for 15 mm 10 mm 2 mmwork piece. Here, for 8 mm laser beam diameter, the bend angle is very small and the bending is away from the heat source as shown in Figure 5. The trend is different for 4 mmm laser beam diameterfigure 5. In all the cases, the bend angle is greater in the case of stationary heat source. However, in the case of stationary heat source, the bend angle is not uniform across the width as shown in Figure 6. Figure 6 The effects of stationary heat source on bending angle along width direction by using 4 mm laser diameter on 25 mm 20 mm 2 mm work piece For the case of 25 mm 20 mm 2 mm, the effect of change in the power on the bend angle variation along the width direction is studied. For 250 W laser power, the bend angle is the maximum in the middle (Figure7). This is not the case for 100 W power, although the bend angles are very small (Figure7). Figure 5 Computational results for the effects of laser power on the bending angle by applying stationary and moving heat source on 15 mm 10 mm 2 mm work piece 8 mm laser diameter 4 mm laser diameter Figure 7 Effect of laser power on bend angle variation for 4 mm beam diameter and 25 mm 20 mm 2 mm work piece 250 W power 100 W power 624-4

5 5 th International & 26 th All India Manufacturing Technology, Design and Research Conference (AIMTDR 2014) December 12 th 14 th, 2014, IIT Guwahati, Assam, India Figure 8shows the top and bottom surface temperatures versus laser power. Rate of increase of power is more for top surface than for bottom surface. Figure 9 shows that laser beam diameter has profound effect on temperature. Figure 8 Variation of top and bottom temperature with laser power on 25 mm 20 mmm 2 mm work piece Figure 10 Temperature distributions and variation of bend angle with time at the top and bottom surface of the work piece (25 mm 20 mm 2 mm) Stationary Moving heat source Figure 9 Variation of top and bottom surface temperature with beam diameter on 25 mm 20 mm 2 mm work piecee Figure10 and show the temperature and bend angle variation with time. It is observed that the bend angle is negative in the beginning and becomes the highest in the magnitude when the top surface temperature is the highest. During cooling phase sheet starts bending towards the laser beam source. The steady state for bend angle is reached when the temperatures of the top and bottom surface equal. In all the cases of moving heat source, the Fourier number is less than one. No definite conclusions with respect to Fourier number can be drawn at this stage. 4 Conclusions Following conclusions can be drawn: 1. The bending angle is highly dependent on laser power, as the power increasesthe bend angle also increases for both stationary and moving heat sources. 2. The bending angle is highly dependent on type of heat sources, the stationary heat source provides more bend

6 FINITE ELEMENT SIMULATIONS OF LASER BENDING OF SMALL SIZED SHEETS 3. Changing laser beam diameter from 4 mm to 8 mm changed the bend angle and it was greater for small diameter. 4. The pattern of bend angle variation along width direction is different laser power for 100 W and 250 W. 5. During stationary heat source, the bend angle is non-uniform across the width. References Dixit,U.S., Joshi, S.N. and Kumar,V.H.,(2013),Microbending with Lasers, Micromanufacturing Processes, edited by Jain, V.K. CRC Press, Boca Raton, Florida. Geiger, M. and Vollertsen, F., (1993), The mechanisms of laser forming, CIRP Annals Manufacturing Technology, vol. 42, pp Li, W. and Yao, Y. L.,(2001), Numerical and experimental investigation of convex laser forming process, Journal of Manufacturing Processes, vol. 3, pp Liu, J., Sun, S. and Guan, Y., (2009), Numerical investigation on the laser bending of stainless steel foil with pre-stresses, Journal of Materials Processing Technology, vol. 209, pp Merklei,M., Hennige,T. and Geiger,M., (2001)Laser forming of aluminum and aluminum alloysmicrostructural investigation,journal of Materials Processing Technology, vol.115 pp Pretorius,T.,(2009), Laser Forming, The Theory of Laser Materials Processing, edited by Dowden, J., Volume 119, 2009, pp Springer, UK. Thomson,G. and Pridham,M., (2001), Material property changes associated with laser forming of mild steel components,journal of Materials Processing Technology, vol. 118, pp Vásquez-Ojeda,C., and Ramos-Grez,J., (2009), Bending of stainless steel thin sheets by a raster scanned low power CO 2 laser, Journal of Materials Processing Technology, vol. 209, pp Walczyk,D.F., Vittal,S.,and York,N., (2000), Bending of Titanium Sheet Using Laser Forming,Journal of Manufacturing Processes, vol. 2, pp Shichun, W. andjinsong, Z., (2001), An experimental study of laser bending for sheet metals, Journal of Materials Processing Technology, vol. 110, pp Wang, X., Xu, W.X., Xu, W.J., Hu, Y.F., Liang, Y.D. and Wang, L.J., (2011), Simulation and prediction in laser bending of silicon sheet, Transactions of Nonferrous Metals Society of China, vol. 21, pp. s188 s