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Study of the buckling mechanism in laser tube forming
ARTICLE IN PRESS
Optics & Laser Technology 37 (2005) 402–409 www.elsevier.com/locate/optlastec
Study of the buckling mechanism in laser tube forming Hom-Shen Hsieh, Jehnming Lin Department of Mechanical Engineering, National Cheng Kung University, Tainan 701, Taiwan Received 3 June 2003; accepted 2 June 2004 Available online 12 August 2004
Abstract The buckling mechanism of a thin metal tube during laser forming was investigated numerically and experimentally in this study. Metal tubes made of 304 stainless steel were heated by a CO2 Gaussian laser beam, which induced the buckling phenomenon on the tube surface due to elastic–plastic deformation. This uncoupled thermal–mechanical problem was solved using a three-dimensional finite element method and was subsequently satisfactorily verified with displacement measurements. The transient bending angle and residual stress of the thin metal tube under specific operation conditions were also studied. r 2004 Elsevier Ltd. All rights reserved. Keywords: Buckling mechanism; Laser tube forming
1. Introduction The laser forming technique has recently been developed and applied in the metal industries. It is a novel way of bending a metal sheet without the use of a mold or additional loading. From the distribution of the thermal stress generated by the laser heating, a precise and complex shape of the workpiece could be formed by a controllable laser beam without pre-processing. Laser forming has been thoroughly studied by various investigators in this decade [1–8]. In 1986, Namba first attempted to apply the laser heat source to form the metal sheet without using a mold [1]. Based on energy conservation, Vollertsen proposed three basic modes in the laser forming of sheet metals [9]. They were defined quantitatively as temperature gradient, buckling and shortening mechanisms. By specifically selecting process parameters, the sheet metals could be formed in concave, convex or shortening shapes. The forming mechanism of complex sheet geometry has been precisely analyzed by computational software based on the finite element method (FEM) [10–17]. The basic Corresponding author. Tel.: +886-6-2757575x62100; fax: +886-6235-2973. E-mail address: [email protected] (J. Lin).
0030-3992/$ - see front matter r 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.optlastec.2004.06.004
focus was on the influence of material properties, the beam mode and the heating paths of the laser. Ji and Wu [12] solved the temperature distribution problem in laser forming with a moving laser beam using the FEM code. Kyrsanidi et al. [13], on the other hand, simulated the bending angle of metal sheets under laser forming using ANSYS. Hennige [14] used the FEM code, SYSWELD, to simulate the laser forming of a flat metal sheet into a bowl-shape deformation with straight and curve laser beam paths. Recently, Li and Yao [15] attempted in solving the bending problem of a metal tube with the FEM software ABAQUS. The mechanism of the wall bulge due to the geometrical constraints of a thin metal tube was mentioned. The characteristics of the process parameters such as laser power, beam size, scanning velocity were also considered. As far as the authors are concerned, the forming mechanism of the bulging of a thin metal tube has not yet been discussed in detail in most applications. This is of particular importance as tube buckling in laser forming is an instability phenomenon, with the direction of bending almost random. The occurrence of the bending mechanism in laser forming has been determined by the laser operating parameters, the geometrical and thermal properties of the specimen. It has been known to occur if the thermal gradient in the thickness is low and the heated area is large compared to
ARTICLE IN PRESS H.-S. Hsieh, J. Lin / Optics & Laser Technology 37 (2005) 402–409
the thickness of the specimen [5]. However, open literatures on the contouring mechanisms of the laser tube forming are scarce, especially for the transient phase of the deformation process during laser radiation. The only certainty is that the unpredictable deformation and dynamic characteristics of thin metal tube in many similar applications such as laser welding for miniature devices are increasingly important in modern manufacturing technologies, due to the expanding use of laser energy. In this paper, the transient state of a thin metal tube under buckling due to a continuous wave CO2 laser beam has been simulated and compared with the measurements, such as the elongation of the tube, taken in the experiments. The problem was assumed to be 3-D uncoupled thermo-elastoplastic and was solved using ABAQUS in order to investigate the influence of temperature, the stress state, the residual stress distribution and bending angle of the specimen on the buckling deformation mechanism during laser forming.
403
Clamp
X Laser beam V
Specimen 0.5mm 50
Y
Z
mm 8m
m
(a)
r
θ
2. Numerical simulation Laser forming, as with other laser material processing applications such as laser heat treatment, involves many non-linear physical phenomena that include temperature distribution, stress field and microstructure variation, all of which are significantly inter-related. When compared with the input laser beam energy, the heat generated due to the strain energy in the bending process is negligible. Therefore, to simplify the analysis, the laser forming problem herein will be decoupled by two distinct analytical models: the thermal model and the mechanical model. This essentially means that the temperature and the stress fields can be solved separately in the numerical analysis. The 304 stainless steel tube specimen is 50 mm long, 8 mm in diameter and 0.5 mm thick as illustrated in Fig. 1(a). A CW CO2 laser beam is then delivered through a concave lens forming a beam spot onto the outer surface of the specimen. The 3-D quadratic brick elements (DC3D8) [18] with 8 nodes is adopted in the mechanical model and the computational domain with the meshes are shown in Fig. 1(b), where a fine meshing around the laser beam is applied to analyze the steep temperature gradients around the heating zone. The specimen consists of 5400 elements. As the computation domain is asymmetry, the analysis of the entire domain is considered. The domain meshes used for the thermal model and mechanical model are the same, but the element type is C3D8R for the purpose of calculating the stress and displacement by ABAQUS [18]. The temperature-dependent non-linear properties such as the thermal expansion coefficient, heat conduction coefficient, specific heat, density, yielding strength,
z (b) Fig. 1. Configurations of the laser tube forming: (a) geometrical domain (b) grid structure.
and Young’s modulus of 304 stainless steels are all considered in the simulation [19,20]. The substrate material is further treated as isotropic with a constant Poisson’s ratio, n, of 0.3 for stainless steel. 2.1. Thermal analysis 2.1.1. Assumptions In the thermal analysis by ABAQUS of the laser forming of a thin metal tube, the following assumptions are made: (1) The thermal properties are isotropic. (2) The laser intensity distribution is in Gaussian mode. (3) Heat conduction in the specimen, free convection and thermal radiation in the surrounding air are considered. (4) The heating phenomena due to phase changes are neglected. (5) The heat due to the strain energy is neglected.
2.1.2. Initial and boundary conditions A circular laser beam with a Gaussian mode that passes through a concave lens will condense into a beam
ARTICLE IN PRESS 404
H.-S. Hsieh, J. Lin / Optics & Laser Technology 37 (2005) 402–409
spot, and its intensity is expressed in Eq. (1) based on the coordinate system as illustrated in Fig. 1(a): ! Zp r2m Q¼ exp 2 ; ð1Þ Rb pR2b where Q is the laser intensity, Z the absorptivity of the material under laser radiation, p the laser power, rm the radius from the laser beam center and Rb the radius of the laser beam spot. Numerous factors affect the reflection coefficient and they include the irradiation angle, roughness of the specimen surface, the thickness of the oxidized layer, the surface temperature and so on. For simplification, Z is taken as an average of 0.3 for 304 stainless-steel tubes [13]. The initial temperature of the specimen is assumed to be the ambient temperature, Tðr; y; z; 0Þ ¼ 25 C. Thermal radiation is considered, therefore, q ¼ sðT 4 T 41 Þ, where the surface emissivity ¼ 0:7 [21] and the Stefan–Boltzmann constant is s ¼ 5:670 108 W=m2 K4 . The heat convection from the surface of the specimen to the surrounding air is expressed as kqT=qn ¼ hðT T 1 Þ, where the coefficient of the heat convection is quoted as h ¼ 20:5 W=m2 C [21] and kqT=qn ¼ 0 at z ¼ 25 mm. At the clamping end, kqT=qn ¼ hðT T 1 Þ, where the heat convection coefficient of the contact surface is approximated at 1894 W=m2 C [22]. Based on the initial thermal boundary conditions and the material properties, the transient temperature distribution is solved with the heat flux over every node of the elements in ABAQUS. The solution is then substituted into the mechanical model for the stress analysis.
condition there is fully constrained. In summary, ur ðr; y; z; tÞ ¼ 0;
z ¼ 25 mm;
uz ðr; y; z; tÞ ¼ 0;
z ¼ 25 mm:
2.3. Numerical results A typical testing case is selected in the numerical simulation with a TEM00 CW CO2 laser beam of 150 W at a scanning speed of 30 =s and a total scan angle of 360 on a 304 stainless-steel tube. The tube is 50 mm long, 0.8 mm thick and 5.0 mm wide at the outer diameter. The interaction time of the laser beam on the specimen is 12 s with a duration of 120 s allowed for air cooling in the simulation. The temperature history at the center of the laser interaction zone is shown in Fig. 2. As expected, the temperature increases with the heating time. The distribution of the residual stress and strain after laser heating at the location of the 180 is shown in Fig. 3. The plastic deformation is clearly enhanced by the input energy of the laser beam as seen by the numerous high stress and strain regions in the heat affected zone. However, the residual stress and strain in the cooling stage shows a similar trend under various laser powers. As shown in Fig. 2, the scanned region of the tube is heated almost homogeneously in the thickness direction. It undergoes compressive plastic deformation with wall thickening due to the restriction on thermal expansion by the surrounding material. As the flow stress in the region of the buckle is low due to the temperature increase, bending will be nearly pure plastic. However, 1000
2.2. Stress analysis 2.2.1. Assumptions The following assumptions are made in the stress simulation of the laser forming process.
The transient stress and strain responses are assumed to be quasi-static at each time interval and the thermo–elastoplastic model is associated with the plastic flow rule and von Mises yielding criterion is used [18]. 2.2.2. Initial and boundary conditions The specimen is assumed to be annealed, therefore its initial condition is stress-free. The boundary conditions in the stress analysis are further illustrated in Fig. 1. As the specimen is clamped at one end, the boundary
800
Temperature(°C)
(1) The material is isotropic. (2) The Bauschinger’s effect is neglected. (3) The material is incompressible when plastically deformed. (4) The material is elastic-perfectly plastic.
Laser power = 150W Spot size = 5mm Heating time = 12sec Rotating velocity = 30 deg/s Thickness = 0.5mm Outer surface Inner surface
600
400
200
0 0
30
60
90
120
Time(sec)
Fig. 2. Temperature histories of the scanned surfaces in laser tube forming.
ARTICLE IN PRESS H.-S. Hsieh, J. Lin / Optics & Laser Technology 37 (2005) 402–409
405
300 Spot size = 5mm Heating time = 12sec Thickness = 0.5mm 150W σrr 150W σ θθ 150W σzz 200W σrr 200W σθθ 200W σzz
Stress(MPa)
200
100
0
Fig. 4. Stress states of the buckling mechanism in laser tube forming [15].
-100
160
-200 0 (a) 40
0.1 0.2 0.3 0.4 Radial distance from the outer surface(mm)
120 Axial displacement(µm)
150W σ rr 150W σ θθ 150W σ zz
20 Plastic strain(x10-3)
Laser power = 150W Spot size = 5mm Heating time = 12sec Rotating velocity = 30 deg/s Thickness = 0.5mm
0.5
80
40
0
0
-40 0
-20
40
80
120
Time (sec)
200W σrr 200W σ θθ 200W σzz
-40 0 (b)
0.1 0.2 0.3 0.4 Radial distance from the outer surface(mm)
Fig. 5. Transient response of the axial displacement at the free end.
0.5
Fig. 3. Distributions of: (a) residual stress and (b) residual strain at y ¼ 180 at the cooling stage.
the temperature of the region not subjected to laser scanning is at room temperature, approximately, therefore bending is purely elastic in this region. The reduction in the heat affected zone along the axial direction of the tube causes the tube to bend towards the laser beam. As shown in Fig. 4, the compressive thermal stresses are induced on the heat-affected region in both the axial and circumferential directions. The axial stress is significant and is responsible for the bending of the tube, while the vertical component of the circumferential stress forces the surface outwards. Therefore, the deformation in the region is a combination of the
shortening along the axial direction and the displacement outward in the radial direction of the tube. The transient response of the average axial displacement at the tube end is shown in Fig. 5. It demonstrates that the axial displacement approaches the peak value at the end of the heating time, which then declines to a negative value due to the tube shrinkage in the cooling stage. Fig. 6 shows the buckling deformations on the outer and inner surfaces during the cooling stage at the scanned location of 0 . Figs. 7 and 8 represent the contours of the axial and radial strains, respectively, along the circumference of the tube. Due to the asymmetry of the heating path of the laser scan, the contours of the various thicknesses at the cooling stage are shown in Figs. 9 and 10. In order to investigate the bending angle caused by buckling, two angles on the tube are defined. They are a and b, corresponding to the X and Y axes, respectively,
ARTICLE IN PRESS H.-S. Hsieh, J. Lin / Optics & Laser Technology 37 (2005) 402–409
406
10
6
Radial displacement(µm)
4
2
8 Radial plastic strain(x10-3)
Laser power = 150W Spot size = 5mm Heating time = 12sec Thickness = 0.5mm Outer surface Inner surface
6 Laser power = 150W Spot size = 5mm Heating time = 12sec Thickness = 0.5mm Outer surface Inner surface
4
2
0 0
-2
-2 -5
0
0
5
60
120 180 240 Rotating angle(degree)
300
360
Axial distance(mm) Fig. 6. Numerical results of the contours of the heat affected zone ðy ¼ 0Þ at the longitudinal direction.
Fig. 8. Radial contours of the heat affected zone at the cooling stage.
3 Laser power = 150W Spot size = 5mm Heating time = 12sec Thickness = 0.5mm
2
2.5
-2
-4
Laser power = 150W Spot size = 5mm Heating time = 12sec Thickness = 0.5mm Outer surface Inner surface
-6
Thickness variation(µm)
Axial plastic strain(x10-3)
0
2
1.5
1
-8
0.5 -10
0 0
60
120 180 240 Rotating angle(degree)
300
360
Fig. 7. Radial contours of the heat affected zone at the heating time of 12 s.
as illustrated in Fig. 11. The laser beam rotates around the tube at a constant speed of 30 =s. Fig. 12 shows the history of the bending angles at y ¼ 180 during the heating and cooling periods with laser interaction. A clear cycle of the bending–unbending of the tube with laser interaction can be observed, with the bending angle approaching a constant negligible value due to the asymmetric heating path on the tube surface. Surface buckling will generate a longitudinal elongation in the heat affected zone during laser heating, which causes the tube to bend towards the direction of the moving laser.
60
120
180
240
300
360
Rotating angle(degree) Fig. 9. Thickness variation of the heat affected zone at the cooling stage.
Fig. 13 shows that the magnitudes of a and b at the cooling stage increases with increasing laser powers.
3. Experiment The experimental arrangement for the laser tube forming is illustrated in Fig. 14. A laser displacement sensor (Wenglor) with an accuracy of 10 mm was used to measure the axial displacement at the end of the tube. The voltage signal of the displacement sensor was
ARTICLE IN PRESS H.-S. Hsieh, J. Lin / Optics & Laser Technology 37 (2005) 402–409
407
12 Laser power = 150W Spot size = 5mm Heating time = 12sec Rotating velocity = 30 deg/s Thickness = 0.5mm α forming angle β forming angle
Forming angle(mrad)
8
4
0
-4
-8
-12 0 Fig. 10. Cross-sectional view of the wall contour at the heat-affected zone.
10
20 30 Time(sec)
40
50
Fig. 12. Transient response of the bending angles during laser tube forming.
0
X Laser beam V
Neutral axial α
Y
β
Z
Forming angle(mrad)
Specimen
-1
-2
Fig. 11. Definition of the bending angles of the tube in analysis.
sampled by a computer with an A/D card. The workpiece was made of AISI 304 with the dimension and process parameters as listed in Table 1. To free any residual stress, the 304 stainless-steel specimens were first annealed above 500 C. A CW CO2 laser with TEM00 mode and set at 150 W was used in the experiment. The experimental result and the numerical evaluation are shown in Fig. 15. The agreement between the two approaches is satisfactory. In the experiment, the axial elongation approaches to the maximum value at the end of laser heating and then declines to a negative value during the cooling stage. The disparity in the displacement values in the two approaches is mainly caused by the bending–unbending motion of the tube during laser heating, as was discussed previously. Further, the tube contour of the laser irradiated area was measured off-line with a scanned probe, used mainly for measuring surface roughness, and the results are shown in Fig. 16. A similar trend between the experimental and numerical results is observed. It must be noted that in the experiment, the
Spot size = 5mm Heating time = 12sec Thickness = 0.5mm α forming angle β forming angle
-3 100
120
140
160
180
200
Laser power(W)
Fig. 13. Bending angles of the free end at y ¼ 0 in the cooling stage at various laser power radiation.
Laser beam Laser displacement sensor Specimem
A/D card
Clamp Computer
Fig. 14. Experimental arrangement in laser tube forming.
tilting angle of the profile cannot be detected by the scanned probe method. By varying the laser power from 100 to 200 W, the peak heights of the surface profiles after laser irradiation at y ¼ 0 and at room temperature are
ARTICLE IN PRESS H.-S. Hsieh, J. Lin / Optics & Laser Technology 37 (2005) 402–409
408
Table 1 Specimen dimensions and process parameters in experiments 50 mm 8 mm 0.5 mm 100–200 W 5 mm 5 rpm 360
160 Laser power = 150W Spot size = 5mm Heating time = 12sec Thickness = 0.5mm Experiment Simulation
Axial displacement(µm)
120
12
8
4
0 100
80
120
140
160
180
200
Laser power(W)
Fig. 17. Experimental and numerical results of the peak height of the bulged profiles at y ¼ 0 with various laser powers during cooling stage.
40
0
4. Conclusions
-40 0
20
40
60
Time(sec)
Fig. 15. Experimental and numerical results of the axial displacement at the free end.
8
Radial displacement(µm)
Spot size = 5mm Heating time = 12sec Thickness = 0.5mm Experiment Simulation
16 Radial displacement(µm)
Specimen length Specimen outer diameter Specimen thickness Laser power Spot size Rotating speed Rotating angle
20
Laser power = 150W Spot size = 5mm Heating time = 12sec Exp. outer surface Exp. inner surface Sim. outer surface Sim. inner surface
6
4
2
0
20
25
30
Distance(mm)
This study investigated numerically, using a 3D meshed domain, and experimentally the tube buckling mechanism of thin stainless steel tube under laser plastic forming. Due to the non-linear coupling effects amongst the stress, strain and temperature of the material properties of the stainless steel tube during laser forming, a number of phenomena, namely, heat conduction, plasticity and the microstructure variations of the specimen can occur. Good agreement has been obtained in terms of the angular as well as the longitudinal displacements numerically and in the experiments. From the simulation and the experimental results, it was observed that the bending angle oscillated significantly with laser interaction on a thin tube. The peak height of the bulged surface during the buckling increased with increasing laser power, as the peak temperature was maintained under the melting point of the workpiece. It was shown that the buckling mechanism of thin metal tubes under laser forming was initiated by a uniform temperature gradient combined with plastic deformation. The latter was dependent upon various operation parameters, the main ones of which were the laser power, the heating time, the clamping arrangement, the thickness, the thermal properties and even the original stress states of the specimen.
Fig. 16. Experimental and numerical results of the surface profiles at y ¼ 0.
obtained and are shown in Fig. 17. It can be seen that the height of the bulged surface increases with the laser power for the same scanned speed.
References [1] Namba Y. Laser forming in space. In: Proceedings of the international conference on Lasers’85.; 1986. p. 403–7.
ARTICLE IN PRESS H.-S. Hsieh, J. Lin / Optics & Laser Technology 37 (2005) 402–409 [2] Namba Y. Laser forming of metal and alloys. In: Proceedings of LAMP. Osaka,; 1987. p. 601–6. [3] Geiger M, Vollertsen F, Deinzer G. Flexible straightening of car body shells by laser forming. Sheet metal and stamping symping symposium SAE special publication, n944, 1993. p. 37–44. [4] Geiger M, Arnet H, Vollertsen F. Laser forming. Manuf Systems 1995;1(24):43–7. [5] Vollersten F, Komel I, Kals R. The laser bending of steel foils microparts by the buckling mechanism—a model. Model Simul Mater Sci Eng 1995;3:107–19. [6] Widlaszewski J. Precise laser bending. In: Proceedings of the LAME’97.; 1997. p. 393–8. [7] Lawrence J, Schmidt MJJ, Li L. The forming of mild steel plates with a 2.5 kW high power diode laser. Int J Mach Tools Manuf 2001;41:967–77. [8] Vollertsen F. An analytical model for laser bending. Lasers Eng 1994;2:261–76. [9] Arnet H, Vollertsen F. Extending laser bending for the generation of convex shapes. J Eng Manuf 1995;209:433–42. [10] Pridham MS, Thomson GA. An investigation of laser forming using empirical methods and finite element analysis. J Des Manuf 1995;5:203–11. [11] Kraus J. Basic processes in laser bending extrusions using the upsetting mechanism. In: Proceedings of the LANE’97, Erlangen, Germany; 1997. p. 431–8. [12] Ji Z, Wu S. FEM simulation of the temperature field during the laser forming of sheet metal. J Mater Process Technol 1998;74:89–95.
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[13] Kyrsanidi AnK, Kermanidis ThB, Pantelakis SpG. Numerical and experimental investigation of the laser forming process. J Mater Process Technol 1999;87:281–90. [14] Hennige T. Development of irradiation strategies for 3D-laser forming. J Mater Process Technol 2000;103:102–8. [15] Li W, Yao YL. Numerical and experimental investigation of laser induced tube bending, Section D-ICALEO, 2000. p. 53–62. [16] Yu G, Masubuchi K, Maekawa T, Patrikalakis NM. FEM simulation of laser forming of metal plates. J Manuf Sci Eng 2001;123:405–10. [17] Wu S, Ji Z. FEM simulation of the deformation field during the laser forming of sheet metal. J Mater Proc Technol 2002;121: 269–72. [18] ABAQUS/Standard user’s manual. Pawtuckett, RI: H.K.S. Inc.; 1998. [19] Ueda Y, Iida K, Saito M, Okamoto A. Finite element model and residual stress calculation for multi-pass welded joint between a sheet metal and the penetrating pipe. In: Proceedings of the fifth international conference on modeling of casting, welding and advanced solidification processes. Switzerland,; 1991. p. 219–27. [20] Peckner D, Bernstein IM. Handbook of stainless steels. New York: McGraw-Hill; 1977. p. 19–31. [21] Incropera FP, DeWitt DP. Fundamental of heat mass transfer. New York: Wiley; 1996. p. 624–8. [22] Holman JP. Heat transfer. New York: McGraw-Hill; 1981. p. 48–51.
Optics & Laser Technology 37 (2005) 402–409 www.elsevier.com/locate/optlastec
Study of the buckling mechanism in laser tube forming Hom-Shen Hsieh, Jehnming Lin Department of Mechanical Engineering, National Cheng Kung University, Tainan 701, Taiwan Received 3 June 2003; accepted 2 June 2004 Available online 12 August 2004
Abstract The buckling mechanism of a thin metal tube during laser forming was investigated numerically and experimentally in this study. Metal tubes made of 304 stainless steel were heated by a CO2 Gaussian laser beam, which induced the buckling phenomenon on the tube surface due to elastic–plastic deformation. This uncoupled thermal–mechanical problem was solved using a three-dimensional finite element method and was subsequently satisfactorily verified with displacement measurements. The transient bending angle and residual stress of the thin metal tube under specific operation conditions were also studied. r 2004 Elsevier Ltd. All rights reserved. Keywords: Buckling mechanism; Laser tube forming
1. Introduction The laser forming technique has recently been developed and applied in the metal industries. It is a novel way of bending a metal sheet without the use of a mold or additional loading. From the distribution of the thermal stress generated by the laser heating, a precise and complex shape of the workpiece could be formed by a controllable laser beam without pre-processing. Laser forming has been thoroughly studied by various investigators in this decade [1–8]. In 1986, Namba first attempted to apply the laser heat source to form the metal sheet without using a mold [1]. Based on energy conservation, Vollertsen proposed three basic modes in the laser forming of sheet metals [9]. They were defined quantitatively as temperature gradient, buckling and shortening mechanisms. By specifically selecting process parameters, the sheet metals could be formed in concave, convex or shortening shapes. The forming mechanism of complex sheet geometry has been precisely analyzed by computational software based on the finite element method (FEM) [10–17]. The basic Corresponding author. Tel.: +886-6-2757575x62100; fax: +886-6235-2973. E-mail address: [email protected] (J. Lin).
0030-3992/$ - see front matter r 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.optlastec.2004.06.004
focus was on the influence of material properties, the beam mode and the heating paths of the laser. Ji and Wu [12] solved the temperature distribution problem in laser forming with a moving laser beam using the FEM code. Kyrsanidi et al. [13], on the other hand, simulated the bending angle of metal sheets under laser forming using ANSYS. Hennige [14] used the FEM code, SYSWELD, to simulate the laser forming of a flat metal sheet into a bowl-shape deformation with straight and curve laser beam paths. Recently, Li and Yao [15] attempted in solving the bending problem of a metal tube with the FEM software ABAQUS. The mechanism of the wall bulge due to the geometrical constraints of a thin metal tube was mentioned. The characteristics of the process parameters such as laser power, beam size, scanning velocity were also considered. As far as the authors are concerned, the forming mechanism of the bulging of a thin metal tube has not yet been discussed in detail in most applications. This is of particular importance as tube buckling in laser forming is an instability phenomenon, with the direction of bending almost random. The occurrence of the bending mechanism in laser forming has been determined by the laser operating parameters, the geometrical and thermal properties of the specimen. It has been known to occur if the thermal gradient in the thickness is low and the heated area is large compared to
ARTICLE IN PRESS H.-S. Hsieh, J. Lin / Optics & Laser Technology 37 (2005) 402–409
the thickness of the specimen [5]. However, open literatures on the contouring mechanisms of the laser tube forming are scarce, especially for the transient phase of the deformation process during laser radiation. The only certainty is that the unpredictable deformation and dynamic characteristics of thin metal tube in many similar applications such as laser welding for miniature devices are increasingly important in modern manufacturing technologies, due to the expanding use of laser energy. In this paper, the transient state of a thin metal tube under buckling due to a continuous wave CO2 laser beam has been simulated and compared with the measurements, such as the elongation of the tube, taken in the experiments. The problem was assumed to be 3-D uncoupled thermo-elastoplastic and was solved using ABAQUS in order to investigate the influence of temperature, the stress state, the residual stress distribution and bending angle of the specimen on the buckling deformation mechanism during laser forming.
403
Clamp
X Laser beam V
Specimen 0.5mm 50
Y
Z
mm 8m
m
(a)
r
θ
2. Numerical simulation Laser forming, as with other laser material processing applications such as laser heat treatment, involves many non-linear physical phenomena that include temperature distribution, stress field and microstructure variation, all of which are significantly inter-related. When compared with the input laser beam energy, the heat generated due to the strain energy in the bending process is negligible. Therefore, to simplify the analysis, the laser forming problem herein will be decoupled by two distinct analytical models: the thermal model and the mechanical model. This essentially means that the temperature and the stress fields can be solved separately in the numerical analysis. The 304 stainless steel tube specimen is 50 mm long, 8 mm in diameter and 0.5 mm thick as illustrated in Fig. 1(a). A CW CO2 laser beam is then delivered through a concave lens forming a beam spot onto the outer surface of the specimen. The 3-D quadratic brick elements (DC3D8) [18] with 8 nodes is adopted in the mechanical model and the computational domain with the meshes are shown in Fig. 1(b), where a fine meshing around the laser beam is applied to analyze the steep temperature gradients around the heating zone. The specimen consists of 5400 elements. As the computation domain is asymmetry, the analysis of the entire domain is considered. The domain meshes used for the thermal model and mechanical model are the same, but the element type is C3D8R for the purpose of calculating the stress and displacement by ABAQUS [18]. The temperature-dependent non-linear properties such as the thermal expansion coefficient, heat conduction coefficient, specific heat, density, yielding strength,
z (b) Fig. 1. Configurations of the laser tube forming: (a) geometrical domain (b) grid structure.
and Young’s modulus of 304 stainless steels are all considered in the simulation [19,20]. The substrate material is further treated as isotropic with a constant Poisson’s ratio, n, of 0.3 for stainless steel. 2.1. Thermal analysis 2.1.1. Assumptions In the thermal analysis by ABAQUS of the laser forming of a thin metal tube, the following assumptions are made: (1) The thermal properties are isotropic. (2) The laser intensity distribution is in Gaussian mode. (3) Heat conduction in the specimen, free convection and thermal radiation in the surrounding air are considered. (4) The heating phenomena due to phase changes are neglected. (5) The heat due to the strain energy is neglected.
2.1.2. Initial and boundary conditions A circular laser beam with a Gaussian mode that passes through a concave lens will condense into a beam
ARTICLE IN PRESS 404
H.-S. Hsieh, J. Lin / Optics & Laser Technology 37 (2005) 402–409
spot, and its intensity is expressed in Eq. (1) based on the coordinate system as illustrated in Fig. 1(a): ! Zp r2m Q¼ exp 2 ; ð1Þ Rb pR2b where Q is the laser intensity, Z the absorptivity of the material under laser radiation, p the laser power, rm the radius from the laser beam center and Rb the radius of the laser beam spot. Numerous factors affect the reflection coefficient and they include the irradiation angle, roughness of the specimen surface, the thickness of the oxidized layer, the surface temperature and so on. For simplification, Z is taken as an average of 0.3 for 304 stainless-steel tubes [13]. The initial temperature of the specimen is assumed to be the ambient temperature, Tðr; y; z; 0Þ ¼ 25 C. Thermal radiation is considered, therefore, q ¼ sðT 4 T 41 Þ, where the surface emissivity ¼ 0:7 [21] and the Stefan–Boltzmann constant is s ¼ 5:670 108 W=m2 K4 . The heat convection from the surface of the specimen to the surrounding air is expressed as kqT=qn ¼ hðT T 1 Þ, where the coefficient of the heat convection is quoted as h ¼ 20:5 W=m2 C [21] and kqT=qn ¼ 0 at z ¼ 25 mm. At the clamping end, kqT=qn ¼ hðT T 1 Þ, where the heat convection coefficient of the contact surface is approximated at 1894 W=m2 C [22]. Based on the initial thermal boundary conditions and the material properties, the transient temperature distribution is solved with the heat flux over every node of the elements in ABAQUS. The solution is then substituted into the mechanical model for the stress analysis.
condition there is fully constrained. In summary, ur ðr; y; z; tÞ ¼ 0;
z ¼ 25 mm;
uz ðr; y; z; tÞ ¼ 0;
z ¼ 25 mm:
2.3. Numerical results A typical testing case is selected in the numerical simulation with a TEM00 CW CO2 laser beam of 150 W at a scanning speed of 30 =s and a total scan angle of 360 on a 304 stainless-steel tube. The tube is 50 mm long, 0.8 mm thick and 5.0 mm wide at the outer diameter. The interaction time of the laser beam on the specimen is 12 s with a duration of 120 s allowed for air cooling in the simulation. The temperature history at the center of the laser interaction zone is shown in Fig. 2. As expected, the temperature increases with the heating time. The distribution of the residual stress and strain after laser heating at the location of the 180 is shown in Fig. 3. The plastic deformation is clearly enhanced by the input energy of the laser beam as seen by the numerous high stress and strain regions in the heat affected zone. However, the residual stress and strain in the cooling stage shows a similar trend under various laser powers. As shown in Fig. 2, the scanned region of the tube is heated almost homogeneously in the thickness direction. It undergoes compressive plastic deformation with wall thickening due to the restriction on thermal expansion by the surrounding material. As the flow stress in the region of the buckle is low due to the temperature increase, bending will be nearly pure plastic. However, 1000
2.2. Stress analysis 2.2.1. Assumptions The following assumptions are made in the stress simulation of the laser forming process.
The transient stress and strain responses are assumed to be quasi-static at each time interval and the thermo–elastoplastic model is associated with the plastic flow rule and von Mises yielding criterion is used [18]. 2.2.2. Initial and boundary conditions The specimen is assumed to be annealed, therefore its initial condition is stress-free. The boundary conditions in the stress analysis are further illustrated in Fig. 1. As the specimen is clamped at one end, the boundary
800
Temperature(°C)
(1) The material is isotropic. (2) The Bauschinger’s effect is neglected. (3) The material is incompressible when plastically deformed. (4) The material is elastic-perfectly plastic.
Laser power = 150W Spot size = 5mm Heating time = 12sec Rotating velocity = 30 deg/s Thickness = 0.5mm Outer surface Inner surface
600
400
200
0 0
30
60
90
120
Time(sec)
Fig. 2. Temperature histories of the scanned surfaces in laser tube forming.
ARTICLE IN PRESS H.-S. Hsieh, J. Lin / Optics & Laser Technology 37 (2005) 402–409
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300 Spot size = 5mm Heating time = 12sec Thickness = 0.5mm 150W σrr 150W σ θθ 150W σzz 200W σrr 200W σθθ 200W σzz
Stress(MPa)
200
100
0
Fig. 4. Stress states of the buckling mechanism in laser tube forming [15].
-100
160
-200 0 (a) 40
0.1 0.2 0.3 0.4 Radial distance from the outer surface(mm)
120 Axial displacement(µm)
150W σ rr 150W σ θθ 150W σ zz
20 Plastic strain(x10-3)
Laser power = 150W Spot size = 5mm Heating time = 12sec Rotating velocity = 30 deg/s Thickness = 0.5mm
0.5
80
40
0
0
-40 0
-20
40
80
120
Time (sec)
200W σrr 200W σ θθ 200W σzz
-40 0 (b)
0.1 0.2 0.3 0.4 Radial distance from the outer surface(mm)
Fig. 5. Transient response of the axial displacement at the free end.
0.5
Fig. 3. Distributions of: (a) residual stress and (b) residual strain at y ¼ 180 at the cooling stage.
the temperature of the region not subjected to laser scanning is at room temperature, approximately, therefore bending is purely elastic in this region. The reduction in the heat affected zone along the axial direction of the tube causes the tube to bend towards the laser beam. As shown in Fig. 4, the compressive thermal stresses are induced on the heat-affected region in both the axial and circumferential directions. The axial stress is significant and is responsible for the bending of the tube, while the vertical component of the circumferential stress forces the surface outwards. Therefore, the deformation in the region is a combination of the
shortening along the axial direction and the displacement outward in the radial direction of the tube. The transient response of the average axial displacement at the tube end is shown in Fig. 5. It demonstrates that the axial displacement approaches the peak value at the end of the heating time, which then declines to a negative value due to the tube shrinkage in the cooling stage. Fig. 6 shows the buckling deformations on the outer and inner surfaces during the cooling stage at the scanned location of 0 . Figs. 7 and 8 represent the contours of the axial and radial strains, respectively, along the circumference of the tube. Due to the asymmetry of the heating path of the laser scan, the contours of the various thicknesses at the cooling stage are shown in Figs. 9 and 10. In order to investigate the bending angle caused by buckling, two angles on the tube are defined. They are a and b, corresponding to the X and Y axes, respectively,
ARTICLE IN PRESS H.-S. Hsieh, J. Lin / Optics & Laser Technology 37 (2005) 402–409
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10
6
Radial displacement(µm)
4
2
8 Radial plastic strain(x10-3)
Laser power = 150W Spot size = 5mm Heating time = 12sec Thickness = 0.5mm Outer surface Inner surface
6 Laser power = 150W Spot size = 5mm Heating time = 12sec Thickness = 0.5mm Outer surface Inner surface
4
2
0 0
-2
-2 -5
0
0
5
60
120 180 240 Rotating angle(degree)
300
360
Axial distance(mm) Fig. 6. Numerical results of the contours of the heat affected zone ðy ¼ 0Þ at the longitudinal direction.
Fig. 8. Radial contours of the heat affected zone at the cooling stage.
3 Laser power = 150W Spot size = 5mm Heating time = 12sec Thickness = 0.5mm
2
2.5
-2
-4
Laser power = 150W Spot size = 5mm Heating time = 12sec Thickness = 0.5mm Outer surface Inner surface
-6
Thickness variation(µm)
Axial plastic strain(x10-3)
0
2
1.5
1
-8
0.5 -10
0 0
60
120 180 240 Rotating angle(degree)
300
360
Fig. 7. Radial contours of the heat affected zone at the heating time of 12 s.
as illustrated in Fig. 11. The laser beam rotates around the tube at a constant speed of 30 =s. Fig. 12 shows the history of the bending angles at y ¼ 180 during the heating and cooling periods with laser interaction. A clear cycle of the bending–unbending of the tube with laser interaction can be observed, with the bending angle approaching a constant negligible value due to the asymmetric heating path on the tube surface. Surface buckling will generate a longitudinal elongation in the heat affected zone during laser heating, which causes the tube to bend towards the direction of the moving laser.
60
120
180
240
300
360
Rotating angle(degree) Fig. 9. Thickness variation of the heat affected zone at the cooling stage.
Fig. 13 shows that the magnitudes of a and b at the cooling stage increases with increasing laser powers.
3. Experiment The experimental arrangement for the laser tube forming is illustrated in Fig. 14. A laser displacement sensor (Wenglor) with an accuracy of 10 mm was used to measure the axial displacement at the end of the tube. The voltage signal of the displacement sensor was
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12 Laser power = 150W Spot size = 5mm Heating time = 12sec Rotating velocity = 30 deg/s Thickness = 0.5mm α forming angle β forming angle
Forming angle(mrad)
8
4
0
-4
-8
-12 0 Fig. 10. Cross-sectional view of the wall contour at the heat-affected zone.
10
20 30 Time(sec)
40
50
Fig. 12. Transient response of the bending angles during laser tube forming.
0
X Laser beam V
Neutral axial α
Y
β
Z
Forming angle(mrad)
Specimen
-1
-2
Fig. 11. Definition of the bending angles of the tube in analysis.
sampled by a computer with an A/D card. The workpiece was made of AISI 304 with the dimension and process parameters as listed in Table 1. To free any residual stress, the 304 stainless-steel specimens were first annealed above 500 C. A CW CO2 laser with TEM00 mode and set at 150 W was used in the experiment. The experimental result and the numerical evaluation are shown in Fig. 15. The agreement between the two approaches is satisfactory. In the experiment, the axial elongation approaches to the maximum value at the end of laser heating and then declines to a negative value during the cooling stage. The disparity in the displacement values in the two approaches is mainly caused by the bending–unbending motion of the tube during laser heating, as was discussed previously. Further, the tube contour of the laser irradiated area was measured off-line with a scanned probe, used mainly for measuring surface roughness, and the results are shown in Fig. 16. A similar trend between the experimental and numerical results is observed. It must be noted that in the experiment, the
Spot size = 5mm Heating time = 12sec Thickness = 0.5mm α forming angle β forming angle
-3 100
120
140
160
180
200
Laser power(W)
Fig. 13. Bending angles of the free end at y ¼ 0 in the cooling stage at various laser power radiation.
Laser beam Laser displacement sensor Specimem
A/D card
Clamp Computer
Fig. 14. Experimental arrangement in laser tube forming.
tilting angle of the profile cannot be detected by the scanned probe method. By varying the laser power from 100 to 200 W, the peak heights of the surface profiles after laser irradiation at y ¼ 0 and at room temperature are
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Table 1 Specimen dimensions and process parameters in experiments 50 mm 8 mm 0.5 mm 100–200 W 5 mm 5 rpm 360
160 Laser power = 150W Spot size = 5mm Heating time = 12sec Thickness = 0.5mm Experiment Simulation
Axial displacement(µm)
120
12
8
4
0 100
80
120
140
160
180
200
Laser power(W)
Fig. 17. Experimental and numerical results of the peak height of the bulged profiles at y ¼ 0 with various laser powers during cooling stage.
40
0
4. Conclusions
-40 0
20
40
60
Time(sec)
Fig. 15. Experimental and numerical results of the axial displacement at the free end.
8
Radial displacement(µm)
Spot size = 5mm Heating time = 12sec Thickness = 0.5mm Experiment Simulation
16 Radial displacement(µm)
Specimen length Specimen outer diameter Specimen thickness Laser power Spot size Rotating speed Rotating angle
20
Laser power = 150W Spot size = 5mm Heating time = 12sec Exp. outer surface Exp. inner surface Sim. outer surface Sim. inner surface
6
4
2
0
20
25
30
Distance(mm)
This study investigated numerically, using a 3D meshed domain, and experimentally the tube buckling mechanism of thin stainless steel tube under laser plastic forming. Due to the non-linear coupling effects amongst the stress, strain and temperature of the material properties of the stainless steel tube during laser forming, a number of phenomena, namely, heat conduction, plasticity and the microstructure variations of the specimen can occur. Good agreement has been obtained in terms of the angular as well as the longitudinal displacements numerically and in the experiments. From the simulation and the experimental results, it was observed that the bending angle oscillated significantly with laser interaction on a thin tube. The peak height of the bulged surface during the buckling increased with increasing laser power, as the peak temperature was maintained under the melting point of the workpiece. It was shown that the buckling mechanism of thin metal tubes under laser forming was initiated by a uniform temperature gradient combined with plastic deformation. The latter was dependent upon various operation parameters, the main ones of which were the laser power, the heating time, the clamping arrangement, the thickness, the thermal properties and even the original stress states of the specimen.
Fig. 16. Experimental and numerical results of the surface profiles at y ¼ 0.
obtained and are shown in Fig. 17. It can be seen that the height of the bulged surface increases with the laser power for the same scanned speed.
References [1] Namba Y. Laser forming in space. In: Proceedings of the international conference on Lasers’85.; 1986. p. 403–7.
ARTICLE IN PRESS H.-S. Hsieh, J. Lin / Optics & Laser Technology 37 (2005) 402–409 [2] Namba Y. Laser forming of metal and alloys. In: Proceedings of LAMP. Osaka,; 1987. p. 601–6. [3] Geiger M, Vollertsen F, Deinzer G. Flexible straightening of car body shells by laser forming. Sheet metal and stamping symping symposium SAE special publication, n944, 1993. p. 37–44. [4] Geiger M, Arnet H, Vollertsen F. Laser forming. Manuf Systems 1995;1(24):43–7. [5] Vollersten F, Komel I, Kals R. The laser bending of steel foils microparts by the buckling mechanism—a model. Model Simul Mater Sci Eng 1995;3:107–19. [6] Widlaszewski J. Precise laser bending. In: Proceedings of the LAME’97.; 1997. p. 393–8. [7] Lawrence J, Schmidt MJJ, Li L. The forming of mild steel plates with a 2.5 kW high power diode laser. Int J Mach Tools Manuf 2001;41:967–77. [8] Vollertsen F. An analytical model for laser bending. Lasers Eng 1994;2:261–76. [9] Arnet H, Vollertsen F. Extending laser bending for the generation of convex shapes. J Eng Manuf 1995;209:433–42. [10] Pridham MS, Thomson GA. An investigation of laser forming using empirical methods and finite element analysis. J Des Manuf 1995;5:203–11. [11] Kraus J. Basic processes in laser bending extrusions using the upsetting mechanism. In: Proceedings of the LANE’97, Erlangen, Germany; 1997. p. 431–8. [12] Ji Z, Wu S. FEM simulation of the temperature field during the laser forming of sheet metal. J Mater Process Technol 1998;74:89–95.
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[13] Kyrsanidi AnK, Kermanidis ThB, Pantelakis SpG. Numerical and experimental investigation of the laser forming process. J Mater Process Technol 1999;87:281–90. [14] Hennige T. Development of irradiation strategies for 3D-laser forming. J Mater Process Technol 2000;103:102–8. [15] Li W, Yao YL. Numerical and experimental investigation of laser induced tube bending, Section D-ICALEO, 2000. p. 53–62. [16] Yu G, Masubuchi K, Maekawa T, Patrikalakis NM. FEM simulation of laser forming of metal plates. J Manuf Sci Eng 2001;123:405–10. [17] Wu S, Ji Z. FEM simulation of the deformation field during the laser forming of sheet metal. J Mater Proc Technol 2002;121: 269–72. [18] ABAQUS/Standard user’s manual. Pawtuckett, RI: H.K.S. Inc.; 1998. [19] Ueda Y, Iida K, Saito M, Okamoto A. Finite element model and residual stress calculation for multi-pass welded joint between a sheet metal and the penetrating pipe. In: Proceedings of the fifth international conference on modeling of casting, welding and advanced solidification processes. Switzerland,; 1991. p. 219–27. [20] Peckner D, Bernstein IM. Handbook of stainless steels. New York: McGraw-Hill; 1977. p. 19–31. [21] Incropera FP, DeWitt DP. Fundamental of heat mass transfer. New York: Wiley; 1996. p. 624–8. [22] Holman JP. Heat transfer. New York: McGraw-Hill; 1981. p. 48–51.