Finite Element Analysis on Pulsed Laser Forming of Sheet Metal

5 th International & 26 th All India Manufaturing Tehnology, Design and Researh Conferene (AIMTDR 214) Deember 12 th 14 th, 214, IIT Guwahati, Assam, India Finite Element Analysis on Pulsed Laser Forming of Sheet Metal Kuntal Maji 1, D. K. Pratihar 2*, A. K. Nath 3 1,2,3 Department of Mehanial Engineering Indian Institute of Tehnology, Kharagpur Kharagpur-721 32, India E-mail: 1 kuntalmajiiitkgp@gmail.om, 2 dkpra@meh.iitkgp.ernet.in, 3 aknath@meh.iitkgp.ernet.in Abstrat Pulsed laser forming is a non-ontat thermal forming proess, where sheet metal gets plastially deformed by thermal residual stresses indued by ontrolled disontinuous laser irradiations. The aim of this paper is to determine the temperature and deformation fields using finite element analysis under different proessing onditions. Two types of pulsed laser forming proesses, i.e., overlapped and disrete spot forming have been identified depending on the ombinations of proess parameters. Bending angle is found to inrease with the degree of overlap and derease with the inrease of gap in ase of the two types of spot forming proesses. A omparative study between pulsed and ontinuous laser forming hasalso been performed using both finite element simulation and experiments.bending angle in ase of disrete spot pulsed laser forming is found to be more ompared to the ontinuous laser forming. The results of finite element simulations have been found to be in good agreement with the experimental results. Keywords: pulsed laser forming, Finite element analysis, Experimental Study 1 Introdution Laser forming is a flexible thermal forming proess,in whih sheet metal get deformed by thermal stresses indued by a ontrolled laser beam either in ontinuous or pulsed modeof irradiations. It has potential appliations in maro and miro sale manufaturing for rapid prototyping and preision adjustment in ship building, aerospae, automobile, miroeletronis industries (Steen and Mazumder, 21).Extensive studies had been arried out by various researhers (Shen and Vollertsen, 29) to investigate the ontinuous laser bending proess.sheet metal forming using pulsed mode of laser irradiation was also investigated by some researhers to study the effets of different proess parameters on the deformation and properties of the laser formed samples. Numerial and experimental investigations were arried out by various researhers (Chen et al., 1999; Lee and Lin, 22; Zhang et al., 22; Hseih and Lin, 24) to determine the temperature and deformation fields, and others in pulsed laser forming onsidering different proess parameters, i.e., laser parameters, laser beam shapes, single and multiple pulses et. Good orrelations were found between the numerial and experimental results of deformation in their studies.transient nonlinear 3D finite element (FE) simulation of pulsed laser forming proess is omputationally expensive beause of finer mesh sizes at the laser irradiated zone and the small time steps required for the onvergene and good auray. Zhang et al. (22) proposed aneffiient method to redue the omputational time in determining bending angle using FE method in pulsed laser bending of thin stainlesssteel sheet.experimental investigations and empirial modeling were arried out by Gollo et al. (28) in laser bending of sheet metal with a Nd:YAG pulsed laser. Taguhi experimental design was used and regression analysis was performed onsidering thevarious proess parameters likelaser power, beam diameter, san speed andpulse duration to express the bending angle in terms of proess parameters. Yang et al. (21) investigated the metallurgial hanges of surfae properties of stainless steel due to pulsed laser forming. The effets of different proess parameters on the surfae properties of heat 436-1

Finite Element Analysis on Pulsed Laser Forming of Sheet Metal affeted zone (HAZ) like mirostruture, mirohardness et. was studiedwith the metallographi mirosope, sanning eletron mirosope (SEM) and miro-hardness tester, respetively.golloetal. (211)investigatedfurther the effets of different proess parameters, suh as laser power, beam diameter, san speed, sheet thikness, number of passes and pulse duration on bending angle using FE simulations and experiments. Signifiant proess parameters were identified through Taguhi experimental design method and regression analysis was also performed to predit the bending angle in pulsed laser forming proess. However, a few studies had been done on the different types of proessing onditions and their effets on deformation in pulsed laser forming proess. Moreover, muh less attention had been given on omparative study of ontinuous and pulsed laser forming proesses for energy effiieny. Reently, Maji et al. (212, 13) have performed empirial modeling of pulsed laser bending proess using statistial and soft omputing-based methods to predit bending angle and study the effets of different proess parameters. However, transient temperature and deformation fields determined through FE analysis gives better insight of the proess. The objetive of this study is to investigate the effets of different types of pulsed laser forming, i.e., effets of gap and overlapping on deformation in disrete spots and overlapped spots pulsed laser forming, respetively. The effiieny of ontinuous and pulsed laser forming proesses isalsoinvestigated in terms of energy requirement and produed deformation. 2 Theory of pulsed laser forming In pulsed laser forming proess, the laser spot beomes elliptial in the san diretion (Tzeng, 2; Yang, 21). Depending on the ombinations of proess parameters, like san speed ( v), spot diameter ( d), frequeny ( f ) and duty yle ( Cd ), two types of spots, i.e., disontinuous or disrete and overlapping may be formed as shownin Fig. 1. The major diameter of the elliptial spot an be determined as d m = d + v τ ; and the distane moved by the spot during a yle time ( T ) an be alulated as d = v T. For forming overlapping spots, d m has to be greater than d ( d d ). The degree or m perent of overlapping an be alulated as d m d 1. d m Fig. 1: Different types of spots (disrete and overlapped) formed in pulsed laser forming proess. Similarly, in ase of disrete spots forming, the perent of gap an also be alulated as d d m 1. The frequeny ( f =5 Hz), d m duty yle ( C =5%), pulse duration ( τ =1 ms), d laser power and beam diameter (d=1. mm)have been kept onstant. Both finite element simulations and experiments have been performed to study the effets of gap between spots and their overlapping on bending angle. 3 Finite element formulation Numerial simulation of pulsed laser forming proess has been arried out to determine temperature distribution and deformations. Laser bending or forming is a weakly-oupled thermomehanial proess. A nonlinear transient indiret oupled field analysis has been performed using the ANSYS APDL (ANSYS theory manual, 211). The simulation proess ours in a few steps. First step involves model generation and seletion of input proess parameters. The next step deals with the thermal and strutural analyses. The thermal equilibrium equation for heat transfer analysis of an isotropi material an be written as given in equation (1). 2 2 2 T T T k + q& = ρt, & + + 2 2 2 x y z (1), where ρ, and k are the density, speifi heat and thermal ondutivity of the material, respetively, and q& is the rate of heat generation per unit volume of the material. The heat flux density of moving laser beam (Fiber laser) is assumed to obey the normal distribution along radial diretion as given in equation (2). I 2 2 AP 2 r exp 2 2 π rb r = b ( 2 ), 436-2

5 th International & 26 th All India Manufaturing Tehnology, Design and Researh Conferene (AIMTDR 214) Deember 12 th 14 th, 214, IIT Guwahati, Assam, India where I is the heat flux density at a radial distane r from the enter of the laser beam. The symbols A, P and r b stand for the absorptivity of the sheet metal surfae, laser power and laser beam radius, respetively. The basi FEM equation for the indiretly-oupled thermo-mehanial alulation an be written as given in equation (3). [ ] [ ] { u& } [ ] [ C] T& { } + [ K] [ ] { u} [ ] [ K ] { T} T where [ C ] [ N ][ N ] { F} { Fth } { Q} + = (3), T = V ρ dv is the heat apaity matrix; T ep [ K ] = [ B ] [ D ][ B ]dv is the tangential V stiffness matrix; T [ K ] = V k [ B ][ B ] dv the heat ondution matrix; { u } and { } T represents T are the nodal displaement and temperature vetor, respetively; [ N ] and [ B ] denote the shape funtion matrix and the general geometri matrix, ep respetively; [ D ] is the elasto-plasti stressstrain matrix; F and F th are the applied nodal fore and the fore aused by the thermal strain, respetively; { Q } is the heat flux vetor. Solid 7 and solid 185 elements (ANSYS theory manual, 211) have been used for the thermal and strutural analysis, respetively.the following assumptions have been onsidered for the FE analysis of pulsed laser bending proess. (i) The workpiee material has been assumed to beisotropi, and onsidered flat and free of residual stresses. (ii) The laser beam energy follows a Gaussian distribution.(iii) Melting of the workpiee surfae has been negleted and no external fore has been applied to the sheet metal. (iv) Cooling of the laser irradiated material ourred through free onvetion to air and radiation has been negleted. (v) Temperature dependent properties (i.e., thermal ondutivity, speifi heat, density, Young s Modulus, Poisson s ratio et.) have been onsidered and their variations have been determined by means of linear interpolation of the data given in Cheng and Lin (2). (vi) Von Mises Criteria has been used for plasti yielding in the simulation proess. (vii) The hardening effet of material behaviour has been onsidered as bilinear isotropi hardening model. (viii) The dissipation of energy due to plasti deformation has been negleted ompared to energy input from the laser beam. For the appliation of the proposed FE model, the required different parameters are the plate dimensions (length, width and thikness), laser power, laser beam diameter, san speed, material absorption oeffiient et. The alulated outputs aremainly the transient temperature and deformation fields, and the final bending angle. The FE model results have been validated through experiments as disussed in the following setions. Numerial simulations have been arried out for studying the effets of gap and overlap on bending angle in the two types of pulsed laser forming proesses. Simulation has been onduted by taking the model size to be equal to the size of workpiee exluding the lamped length, and laser irradiation has been done at the middle of the workpiee and parallel to the free edge of the sample as shown in Fig. 2. Fine mesh size has been used in the laser irradiated zone and gradually oarse meshing has been used away from the irradiated zone to redue the omputational time as shown in Fig. 2. Fig. 2: Model of the sample with meshing. The laser beam has been moved for a small distane at eah time-step for simulating the moving pulsed laser beam. A small time-step has been taken during laser heating for onvergene and gradually inreasing time-steps have been taken during ooling to redue the total omputational time. For studying the effets of gap and overlap, other proess parameters, i.e., laser power and spot diameter have been kept onstant. AISI34 steel samples of the size of 1 3.5 mm 3 have been used for the study. One end of the sample has been lamped, therefore,this end has been kept fixed or the displaement of that end has been made zero as boundary ondition. 4 Experimental validations Laser bending experiments have been onduted on a fiber laser (wavelength = 1.7 µm, Model YLR- 2) having a maximum laser power of 2. kw (refer to Fig. 3). A 1 mm diameter ollimated laser beam is delivered through an optial fiber 436-3

Finite Element Analysis on Pulsed Laser Forming of Sheet Metal onto a fousing optial system onsisting of a lens of 2 mm foal length. This minimum spot diameter available is 25 µm at the foal plane, andnitrogen gas at.5 bar pressure has been used for shielding to protet the optial system. Epsilon, Model: Opto-NCDT 142). Measurements have been taken at 3-4 loations along the sanning diretion and their average value has been alulated. Bending angle has been alulated by the triangulation method. Results have been ompared with that obtained from the finite element simulations of the laser bending proess. 5 Results and disussion Experiments and FE simulations have been performed to study the effets of gap between spots and their overlapping on bending angle in pulsed laser bending (PLB). The degrees of overlap and gap have been ontrolled by varying the san speed keeping the other parameters onstant. Fig. 3: 2 kw Fiber laser system. The work-piees are AISI 34 stainless steel sheets of 12 mm 3 mm.5 mm dimensions. The samples have been leaned using aetone to remove any unwanted dirt and grease. A 1 W- LpOphir power meter has been used to measure the laser power. By measuring the inident and refleted laser power, the average absorption oeffiient of the work-piee surfae was estimated to be in the range of.35 to.45. During laser bending experiment, one end of the retangular workpiee is held in a lamp and laser sans have been performed parallel to the free edge of the samples, as shown in Fig. 4. Fig. 5: Temperature profile during heating Fig. 5 shows the temperature profile obtained during heating with a laser power of 6 W and 5% gap. The orresponding deformation field is shown in Fig. 6. 1NODAL SOLUTION STEP=114 SUB =2 TIME=2.617 USUM (AVG) RSYS= DMX =.131 SMX =.131 MX Z Y X MN.146E-3.291E-3.437E-3.582E-3.728E-3.873E-3.119.1164.131 Fig. 6: Deformation field due to pulsed laser forming with 5% gap and 6 W laser power. Fig. 4: Experimental setup. The defletion of the sample has been measured using a laser displaement sensor (Make: Miro- Fig. 7 shows the variations of bending angle, both experimentally obtained and FE alulated, with the degree of gap between spots, obtained at onstant laser power (6 W) and laser spot 436-4

5 th International & 26 th All India Manufaturing Tehnology, Design and Researh Conferene (AIMTDR 214) Deember 12 th 14 th, 214, IIT Guwahati, Assam, India diameter (1. mm). At onstant laser power, as the gap is inreased by inreasing the san veloity, the disrete line energy input redues, and the power density also dereases, as the spot size inreases at the higher san speed. As a result, the bending angle dereases. is found to inrease with the inrease of overlap and derease with the inrease of gap. FE simulation and experiments have been onduted to study the deformation and proess effiieny in thermal forming of sheet metal under ontinuous and disrete laser heat inputs. The variation of bending angle with the line energy is plotted in Fig. 9 for both the ases. The line energy for ontinuous laser bending is given by LE = p v, and that for pulsed laser bending is alulated as follows: p τ p τ LE p = = = LE C v T v T d, Fig. 7: Effet of gap on bending angle. The bending angle inreases with the inrease of perentage of overlap at onstant laser power, as shown in Fig. 8. Laser power and beam diameter have been kept onstant at 3 W and 1. mm, respetively, to study the effets of overlapped pulsed laser irradiation. With the inrease of overlap, the line energy inreases, whih inreases the thermal energy input and thermal stress, and resulting in a higher bending angle. where the symbols arry usual meaning as stated above. The bending angle obtained in ase of pulsed laser forming is found to be more ompared to that in ontinuous laser forming for the same line energy as shown in Fig. 9. The larger bending angle in ase of disrete spots pulsed laser bending (gap between two spots has been kept 25%) an be attributed to the fat that the disontinuous thermal energy input produes more thermal stress due to the higher resistane imposed by the old material, whih is not getting laser irradiation during laser pulse-off time. The rise in surfae temperature at the irradiated spot is also expeted to be high in ase of pulsed laser forming ompared to that of ontinuous laser forming at onstant line energy (MBride et al., 25). This ould also be another reason for produing more bending in ase of pulsed laser bending proess. Fig. 8: Effet of overlap on bending angle FE simulation results also math well with the experimental trend of the bending angle with the gap and overlap (refer to Figs. 7 and 8). At higher degree of overlap, the workpiee surfae melts and this effet has not been taken into aount in the FE simulation to alulate the bending angle. Finite element analyses of pulsed laser irradiations have been arried out, and transient temperature and deformations have been alulated for different proessing onditions. Bending angle Fig. 9: Comparison of pulsed and ontinuous laser forming. Therefore, pulsed laser forming is found to be more energy effiient ompared to that of ontinuous mode of laser forming. In future, the omparative study will be mode for more number of proessing onditions and for 3D forming also. 436-5

Finite Element Analysis on Pulsed Laser Forming of Sheet Metal 6 Conlusions Finite element analyses of laser bending proess with both ontinuous wave and pulsed laser irradiations have been arried out. Transient temperature and deformations have been alulated for different proessing onditions. The effets of different proessing onditions on deformation have also been studied. Deformation in pulsed laser forming has been found to derease and inrease with the inrease of gap and that of overlap between spots, respetively.a omparative study of CW and pulsed laser bending proesses has been done through FE simulations and experiment. Disrete spot pulsed laser forming has been found to be more energy effiient ompared to the ontinuous laser forming. Results of finite element simulations have been validated through experimental results and these are found to be satisfatory. Referenes ANSYS In., (211), ANSYS Theory Manual, Release 12, USA. Chen, G.,Xu, X., Poon, C.C. andtam, A.C. (1999), Experimental and Numerial Studies on Mirosale Bending of Stainless Steel With Pulsed Laser, Journal of Applied Mehanis,Vol. 66,pp. 772-779. Gollo, H.M., Mahdavian, S.M. and Naeini, H.M. (211), Statistial analysis of parameter effets on bending angle in laser forming proess by pulsed Nd:YAG laser, Optis & Laser Tehnology, Vol. 43, pp. 475 482. Gollo,M.H.,Naeini,H.M.,Liaghat,G.H., Torkamany, M.J., Jelvani, S. and Panahizade, V. (28), An experimental study of sheet metal bending by pulsed Nd:YAG laser with DOE method, International Journal of Material Forming, Vol. 1, pp. 137 14. Hsieh, H.S. and Lin, J. (24), Thermal mehanial analysis on the transient deformation during pulsed laser forming,international Journalof Mahine Tools and Manufature,Vol. 44, pp. 191-199. Lee, K.C. and Lin, J. (22), Transient deformation of thin metal sheets during pulsed laser forming,optis and Laser Tehnology, Vol. 34, pp. 639-648. Maji, K., Pratihar, D.K. and Nath, A.K. (212), Modeling of pulsed laser bending of sheet metal using neuro-fuzzy system, In:4 th International and 25 th All India Manufaturing Tehnology, Design and Researh (AIMTDR) Conferene, Jadavpur University, Kolkata, India, Vol. 1, pp. 46-51. Maji, K., Pratihar, D.K. and Nath, A.K. (213), Experimental investigations and statistial analysis on pulsed laser bending of AISI34 stainless steel sheet, Optis and Laser Tehnology, Vol. 49, pp. 18-27. MBride, R., Bardin, F., Gross, M., Hand, D.P., Jones, J.D.C. and Moore, A.J. (25), Modeling and alibration of bending strains for iterative laser forming, Journal of Physis D: Applied Physis, Vol. 38, pp. 427-436. Shen,H. andvollertsen, F. (29), Modeling of laser forming An review, Computational Materials Siene, Vol. 46, pp. 834 84. Steen, W.M. andmazumder, J. (21), Laser material proessing, 4 th ed. Springer-Verlag, London. Tzeng, Y. (2), Parametri analysis of the pulsed Nd:YAG laser seam-welding proess,journal of materials Proessing Tehnology,Vol. 12, pp. 4-47. Yang, L.J, Tang, J., Wang, M.L., Wang, Y. and Chen, Y.B. (21), Surfae harateristis of stainless steel sheet after pulsed laser forming,applied Surfae Siene, Vol. 256, pp. 718-726. Zhang, X.R., Chen, G. and Xu, X. (22), Numerial simulation of pulsed laser bending,journal of Applied Mehanis,Vol. 69, pp. 254-26. 436-6