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Characterization of the laser cleaving on glass sheets with a line-shape laser beam
ARTICLE IN PRESS
Optics & Laser Technology 39 (2007) 892–899 www.elsevier.com/locate/optlastec
Characterization of the laser cleaving on glass sheets with a line-shape laser beam Yu-Zan Wang, Jehnming Lin Department of Mechanical Engineering, National Cheng Kung University, Tainan, Taiwan, ROC Received 18 November 2005; received in revised form 4 July 2006; accepted 10 July 2006 Available online 6 September 2006
Abstract A CO2 laser with a line-shape beam was used to cleave a soda-lime glass substrate at various beam-rotation angles to the cutting direction. The stress distribution on the glass substrate cleaved by the laser beam has been analyzed in this study. An uncoupled thermalelastic analysis was achieved by the ABAQUS software based on the finite element method. The numerical results show that the stress field of the fracture is caused by a complex stress state and the cleavages are significantly affected by the heat diffusion and beam rotation angle. At the rotation angle of zero degree to the cleaving direction, the phenomena of the chip formation have been found due to a large temperature gradient at the cleaving depth of the glass substrate. r 2006 Elsevier Ltd. All rights reserved. Keywords: CO2 laser cleaving; Thermo-elastic analysis
1. Introduction Laser machining is one of the most popular applications of the laser material processing [1]. New processes such as laser marking and laser ablation have been evolved ever since laser machining became popular in the manufacturing industries over the past decades. One of the new technologies that have been developed rapidly is the laser cleaving, which was used for manufacturing brittle materials such as glass, ceramics and many others [2]. The main concern in the industry is, as might be expected, of the machining quality (surface appearance) and efficiency, both of which are influenced by the heat generation around the cutting zone of laser machining and in this case of laser cleaving. The laser cleaving process can be applied to separate the materials with the thermal shock effects without the removal of the substrate materials. Similar to the machining processes such as the diamond tipped scribing, laser cleaving has many advantages such as narrow cleaving width and high cutting speed. According Corresponding author. Tel.: +886 6 2757575X62100; fax: +886 6 2352973. E-mail address: [email protected] (J. Lin).
0030-3992/$ - see front matter r 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.optlastec.2006.07.005
to the extraordinary cutting performance of the brittle materials by the focused laser beam, many studies have been carried out in literature [3–10]. For example, Chui [6] has applied CO2 laser to the glass cutting at various elevated temperatures. Saifi et al. [7] used continuous and pulsed CO2 lasers on the glass cutting by the laser ablation mechanisms. Ikeda et al. [8] adopted the CO2 laser and a diamond cutter to cleave the LCD glass panels. Unger et al. [9] developed a new technique to control the cleaving direction by a laser beam followed with a cooling water jet. Paterson et al. [10] found that a tremendous tensile stress state was generated to cleave the glass sheets by a lineshape beam due to a high-temperature gradient on the glass substrate. Since the thermal cleaving process is mainly based on the fracture mechanism of the brittle substrates caused by the large temperature gradient. Using a focused heat source such as laser beam to generate a noticeable temperature rise near the heating zone, the thermal shock could be generated and the propagation direction of the crack may coincide with the laser beam path in a controllable situation. However, the laser beam could melt and vaporize the substrate and induce a stress filed in all directions. The stress field and the cracking area were significant affected
ARTICLE IN PRESS Y.-Z. Wang, J. Lin / Optics & Laser Technology 39 (2007) 892–899
by the temperature gradient near the beam spot. Therefore, the shape of the beam spot is one of the factors to dominate the heat diffusion, temperature and stress distributions on the cutting area, very few studies have been made in detail to investigate the effects of the intensity profile of the laser beam in the cleaving process [2]. In literature the line-shape laser beam has been proposed in the laser cutting on glass substrate to extend the heat affected zone along the cutting direction [10], but the stress distributions have not been fully studied with the experimental evidences to analyze the effects of the beam rotation angle and process parameters on the glass substrate by laser cleaving. The stress fields of the glass sheets in the line-shape laser cleaving have been analyzed by the ABAQUS software. The fracture modes of the glass cracking have been evaluated by experiments at various rotation angles of the line-shape beam mode. The phenomenon of the chip formation caused by the thermal stress in the cleaving process was also studied.
893
A soda-lime glass specimen is selected as 76 mm in length, 26 mm in width and 1 mm in thickness as illustrated in Fig. 1(a). A CW CO2 laser beam is then delivered through a cylindrical lens forming a beam spot onto the upper surface of the specimen as illustrated. The 3-D quadratic brick elements (DC3D8) [11] with 8 nodes is adopted in the mechanical model and the computational domain with the meshes are shown in Fig. 1(b) and (c), where a fine meshing around the laser beam was applied to analyze the steep temperature gradients around the heating zone. The specimen consists of 16,000 elements. The domain meshes used for the thermal model and mechanical model are the same, but the element type is C3D8R to calculate the stress and displacement by ABAQUS [11]. The temperature-dependent nonlinear properties such as the thermal conductivity, specific heat, Poisson’s ratio and Young’s modulus of soda-lime glass are all considered in the simulation and the relationships at various temperatures are shown in the figures of Appendix A [12].
2. Numerical simulation Laser cleaving, 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 property 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 cleaving process is negligible. Therefore, to simplify the analysis, the laser-cleaving 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.
2.1. Thermal analysis In the thermal analysis by ABAQUS of the laser cleaving on a thin glass substrate, the following assumptions are made: (1) The thermal properties are isotropic. (2) The laser intensity distribution is 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.
Fig. 1. (a) The setup for the laser cleaving process and the coordinate system; (b) the grid structure of the substrate in the analysis; (c) cross-section view of the meshed domain of the glass substrate.
ARTICLE IN PRESS Y.-Z. Wang, J. Lin / Optics & Laser Technology 39 (2007) 892–899
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A circular laser beam with a Gaussian mode passing through a cylindrical lens will condense into a line-shape beam mode, and the intensity is expressed in Eq. (1) based on the coordinate system as illustrated in Fig. 2. " # ð1 RÞP x0 2 y0 2 I l ðx; yÞ ¼ exp 2 þ 2 , (1) pwl w l where, Il(x, y) is the laser intensity absorbed by the substrate, R is the reflectivity of the material under laser radiation, P is the laser power, w is the length of the minor axis of the ellipse, l is the length of the major axis of the ellipse. The moving line beam is modeled in FEM by the following coordinate system transformation. A new coordinate system (x0 , y0 ) of the laser beam at a cutting speed v and a rotation angle y to the cleaving direction can be transformed from the original coordinate system (x, y) as expressed by the following equations: " 0# " # x x cos y sin y ¼ , (2) 0 y sin y cos y y where x0 ¼ x cos y þ yðv; tÞ sin y, y0 ¼ x sin y þ yðv; tÞ cos y, and t is the time of the traveling beam. Numerous factors affect the reflectivity and they include the irradiation angle, roughness of the specimen surface, thickness of the oxidized layer, surface temperature and so on. For simplification, R is taken as an average value of 0.2 for the soda-lime glass [13]. The initial temperature of the specimen is assumed to be the ambient temperature TN ¼ 25 1C. The thermal radiation has therefore the heat of radiation is been considered, q ¼ s T 4 T 41 , where the surface emissivity is e ¼ 0.8 [14] 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 kðqT=qnÞ ¼ hðT T 1 Þ, where the coefficient of the heat convection is quoted as h ¼ 21 W/m2 1C [15] at the upper and lower surfaces of the substrate as shown on Fig. 1(a), y y' θ
x'
x
Fig. 2. Definition of the rotation angle of the line-shape beam in laser cleaving process.
and the other surfaces are assumed to be adiabatic, kðqT=qnÞ ¼ 0. 2.2. Stress analysis The following assumptions are made in the stress simulation of the laser cleaving process: (1) The material is isotropic. (2) The specimen is assumed to be annealed; therefore, its initial condition is free of stress. (3) The stress–strain relationship of the substrate material is perfectly elastic. (4) The gravity effects are neglected. The stress and strain responses were assumed to be the quasi-static state at each time interval and the thermoelastic model was used. As the specimen was clamped at one side and the other surfaces are free of stress, the boundary conditions are expressed as follows: ux ðx; y; z; tÞ ¼ 0
x ¼ 0.
(3)
uy ðx; y; z; tÞ ¼ 0
y ¼ 0.
(4)
uz ðx; y; z; tÞ ¼ 0
z ¼ 0.
(5)
The threshold value of stress required to initiate cracks in the soda-lime glass is given as the fracture strength of approximately 70 MPa for the most practical applications [16]. 3. Numerical results In order to verify the numerical results of the ABAQUS software for a moving heat source problem on the meshed domain and boundary conditions discussed above, the Rosenthal’s solution of the point heat source on a thick plate [17] was applied and the results are shown in Fig. 3, it can be seen that the temperature contours of the analytical and numerical solutions are approximately identical in the present study. In the laser cleaving on the glass substrate, the brittle fracture phenomenon will dominate the cleaving process due to the thermal shock effects on the glass. As the line-shape beam moving into the center of the substrate at the cutting time of 0.147 s and the rotation angle of 01, the stress field of sxx along the Y-axis is shown in Fig. 4. It can be seen that the maximum compressive stress sxx is located at the distance about 11.44 mm to the staring point of the cleaving path. Since the thermal expansion of the glass substrate causes a compressive stress state in the heat affected zone of the laser interaction, and the stress field changes to the tensile stress state during the cooling stage. In the case of the rotation angle of 01, the heat of the laser beam has been accumulated at the interaction zone. Thus the compressive stress occurs at the front of the cutting edge and the crack due to the thermal shock propagating along the cleaving direction. As the
ARTICLE IN PRESS Y.-Z. Wang, J. Lin / Optics & Laser Technology 39 (2007) 892–899
1000
600
-100 Stress (MPa)
Temperature (°C)
0
X:0.3mm,Y=8.3mm Analytical Solution Z=1mm Numerical Solution Z=1mm Analytical Solution Z=0.75mm Numerical Solution Z=0.75mm Analytical Solution Z=0.5mm Analytical Solution Z=0.5mm Analytical Solution Z=0.25mm Numerical Solution Z=0.25mm Analytical Solution Z=0mm Numerical Solution Z=0mm
800
895
400
-200 Power=42W Cutting Speed=5000mm / sec Spot major axis=15mm Spot minor axis=0.7mm Rotating angle=0 degree Rotating angle=45 degree Rotating angle=90 degree
200
-300
0 0
0.2
0.4
0.6
0.8
1
0
Fig. 3. Numerical results and analytical solutions of the thermal cycles at various locations for a moving point laser beam spot on the glass substrate. 60 Power=42W Cutting Speed=5000mm / min Spot major axis=15mm Spot minor axis=0.7mm Rotating angle=0 degree Rotating angle=45 degree Rotating angle=90 degree
Stress (MPa)
20
0
-20
-40
-60 0
10
20
30
Y axis (mm)
Time (sec)
40
10
20
30
Fig. 5. Profiles of the stress syy along the Y-axis at the center of the substrate with various rotation angles.
the side cracking could be prevented by large compressive stress state at a small rotation angle. Furthermore a large compressive stress syy in Fig. 5 and a small tensile stress sxx in Fig. 4 generated around the line beam show the condition for a stable crack formation. Based on the similar results from the other study for laser cleaving [18], a stable crack will be formed under a condition of surrounding compressive stress during heating stage and transferring to a tensile stress state in cooling stage in laser cleaving. Figs. 6–8 show the numerical examples at the same cutting speed but various rotation angles from 01 to 901, it can be found that the state of szz at the center of the Y-axis is a maximum tensile stress at various depths and rotation angles. The magnitude of szz decreases with the increase of the rotation angles. Due to a large temperature gradient, there is a peak tensile stress state of szz at the location of z ¼ 0.75 mm and the rotation angle of 01 on the substrate center. It may cause the elongation inside the glass substrate and the upper surface radiated by laser may bend upwards in the laser-cleaving process.
Y axis (mm)
Fig. 4. Profiles of the stress sxx along the Y-axis at the center of the substrate with various rotation angles.
rotation angle increasing from 01 to 901, the magnitude of the compressive stress sxx in Y-direction decreases. Therefore the stress state becomes tensile at the front of the cutting edge and it significantly affects the propagation of the crack on the both sides of the cleaving path at large rotation angles. The stress fields of syy at the center of the Y-axis with various rotation angles are shown in Fig. 5. A compressive stress of syy occurs at the interaction zone of the laser beam and its magnitude decreases with the rotating angle. It means that
4. Experiments The experimental arrangement of the laser cleaving was illustrated in Fig. 1(a), a CO2 (the wavelength of 10.6 mm) laser was used as the heat source and the beam spot was transformed through a cylindrical lens to form an elliptic beam spot with a length of the major axis of 15 mm and a length of the minor axis of 0.7 mm, respectively. In the cutting conditions of the laser energy of 42 W and a cutting speed of 5000 mm/min, a soda-lime glass sheet was used as the substrate material in the experiment. The appearances of the cleaving surface were examined by an optical microscope.
ARTICLE IN PRESS Y.-Z. Wang, J. Lin / Optics & Laser Technology 39 (2007) 892–899
896 15
3 Power=42W Cutting Speed=5000mm / min Spot major axis=15mm Spot minor axis=0.7mm
1 Stress (MPa)
Stress (MPa)
2
Z=1mm Z=0.75mm Z=0.5mm Z=0.25mm Z=0mm
10
Power=42W Cutting Speed=5000mm /min Spot major axis=15mm Spot minor axis=0.7mm Z=1mm Z=0.75mm Z=0.5mm Z=0.25mm Z=0mm
5
0
0
-1
-5
-2
-3
-10 0
10
20
30
0
Fig. 6. Profiles of the stress szz at the center of the substrate with a rotation angle of 01 and various depths of substrate.
Power=42W CuttingSpeed=5000mm /min Spot major axis=15mm Spot minor axis=0.7mm Z=1mm Z=0.75mm Z=0.5mm Z=0.25mm Z=0mm
Stress (MPa)
2
0
-2
-4 0
10
20
30
Y axis (mm)
Y axis (mm)
4
10
20
30
Y axis (mm)
Fig. 8. Profiles of the stress szz at the center of the substrate with a rotation angle of 901 and various depths of substrate.
the front of the laser beam and the cleaving process was seized. The width of the heat-affected region is about 1.55 mm. In the case of the rotation angle of 901, the crossing cracks have been found in the path of the laser cleaving and the crossing angle is about 501. This type of the fracture mode was mainly generated by the shearing stresses during the laser heating. As shown in Fig. 10, continuous chips were formed at the rotation angle of 01. Since the temperature gradient at the cutting depth may cause a significant variance of the szz at the depth of substrate, a bending moment may cause the substrate to be deformed upwards with the residual stress larger than the fracture strength at a specific depth of the substrate. With a round laser spot on the glass substrate, the glass temperature easily reached the melting point and the chip formation may not occur. Based on the process parameters of the present experiment, the maximum stress szz located at a depth of 0.25 mm (i.e. z ¼ 0.75 mm), which is close the chip thickness of 0.16 mm measured in the experiment. Therefore, the stress state of szz dominates the chip formation in the laser-cleaving process.
Fig. 7. Profiles of the stress szz at the center of the substrate with a rotation angle of 451 and various depths of substrate.
5. Discussions
As shown in Fig. 9, the typical patterns of the crack propagation in laser cleaving are different at various beam rotation angles. A straight and clean cleavage without surface melting was generated at the rotation angle of 01. The width of the cut is about 0.77 mm, which is larger than the length of the minor axis of 0.7 mm of the laser beam. As the rotation angle being 451, the surface was fractured at
According to the numerical results of the stress fields as shown in Figs. 11–13, the appearance of cleavage surfaces has been examined in detail. As shown in Fig. 11(a) for the case at the rotation angle of 01, a symmetric distribution of the maximum principal stress along the cleaving direction has been found. The compressive stress state is in the region of the line-shape beam and the tensile stress state causing the glass cracking is outside the beam region.
ARTICLE IN PRESS Y.-Z. Wang, J. Lin / Optics & Laser Technology 39 (2007) 892–899
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Fig. 9. Surface appearances of the soda-lime glass along a vertical cleaving direction at beam rotation angles of (a) 01; (b) 451; (c) 901.
Fig. 10. Cross-section view of the chip formation on a soda-lime glass in laser cleaving.
The contours of the shear stress txy are shown in Fig. 11(b), which show a concentrated and symmetric distribution of the shear stress along the cleaving path. According to Fig. 12(a) for the case at the rotation angle of 451, an asymmetric distribution of the maximum principal stress is found. Due to a large heat affected zone near the cleaving depth, a tremendous thermal effect and a large area of the compressive stress state occurred before the laser beam approaching. Therefore an unstable fracture mode with the shear-cracking phenomenon appeared in the cleaving path. However, the contours of the shear stress txy are significantly affected by the rotation angle as shown in Fig. 12(b). In the case of the rotation angle of 901, a symmetric contour of the principal stress was shown in Fig. 13(a). Since the heat-affected area is larger than those cases with small rotation angles, it causes a region of the compressive principal stress in the rear of the line-shape beam. According to Fig. 13(b), the locations of the peak shear stress txy are at the edges of the crossing cracks as shown in Fig. 9(c). 6. Conclusions Since the heating by a line-shape laser beam is difficult to be aligned with the cleaving path at a large beam rotation
Fig. 11. Contours of the stress states at a rotation angle of 01; (a) maximum principal stress; (b) shear stress txy.
angle, the thermal cleaving effects are reduced with the increase of the rotation angles in the present study. As the line-shape laser beam rotated far from the cleaving direction, the stress field at the cracking edge became asymmetric. The stress state at the front of the cracking edge changes from compressive to tensile. Thus the propagation of the crack is not aligned with the beam direction, and it may cause an unstable fracture on the surrounding region of the cleaving path. At a large rotation angle, the shear mechanism dominates the crack propagation with a crossing type fracture mode along the beam path. Due to a large tensile stress occurring inside the glass substrate at a small beam rotation angle, it may generate a continuous chip in cleaving process with a line-shape laser beam. According to the numerical analysis,
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Acknowledgements This work is supported by the National Science Council under the Grant no.: NSC 94-2622-E-006-037-CC3.
Appendix A The temperature-dependent nonlinear properties such as the thermal conductivity, specific heat, Poisson’s ratio and Young’s modulus of soda-lime glass are shown in Figs. A1–A4. 2.2
Fig. 12. Contours of the stress states at a rotation angle of 451; (a) maximum principal stress; (b) shear stress txy.
Thermal conductivity (W / °C)
2
1.8
1.6
1.4
1.2 0
200
400
600
Temperature (°C)
Fig. A1. Thermal conductivity of the soda-lime glass at various temperatures.
1300
Specific heat (J / Kg°C)
1200
1100
1000
900
800 Fig. 13. Contours of the stress states at a rotation angle of 451; (a) maximum principal stress; (b) shear stress txy.
700 0
the location of the peak tensile stress of szz is approximately equal to the thickness of the chip measured in experiment.
200
400
600
800
1000
Temperature (°C) Fig. A2. Specific heat of the soda-lime glass at various temperatures.
ARTICLE IN PRESS Y.-Z. Wang, J. Lin / Optics & Laser Technology 39 (2007) 892–899
References
0.2
Possion's ratio
0.19
0.18
0.17
0.16 0
200
400
600
800
1000
Temperature (°C) Fig. A3. Poison ratio of the soda-lime glass at various temperatures.
82
80 Young's modulus (GPa)
899
78
76
74
72 0
200
400
600
800
1000
Temperature (°C) Fig. A4. Young’s modulus of the soda-lime glass at various temperatures.
[1] Steen WM. Laser material processing. Berlin: Springer; 1991. [2] Lumley RM. Controlled separation of brittle materials using a laser. Am Ceram Soc Bull 1969;48(9):850–4. [3] Morita M. Generation and propagation behavior of laser induced thermal cracks. J Ceram Soc Jpn 1993;101(5):510–5. [4] Finucane MA, Back I. CO2 laser cutting of stained glass. Int J Adv Manuf Technol 1996;12(1):47–59. [5] Zhou YC, Zhu ZM. Thermal fracture characteristics induced by laser beam. Int J Solids Struct 2001;38(32-33):5647–60. [6] Chui GK. Laser cutting of hot glass. Am Ceram Soc Bull 1975;54(5):514–8. [7] Saifi MA, Paek U- C. Scribing glass with pulsed and Q-switched CO2 laser. Ceram Bull 1973;52(11):838–41. [8] Ikeda M, Shibata T, Makino E, Takahashi Y, Ono A, Matsumoto F. Study on laser breaking of glass plate (1st report)-generation and growth of vertical cracks by scribing. J Jpn Soc Precis Eng 1996;62(3):413–7. [9] Unger W, Wittenbecher W. The cutting edge of laser technology. Glass Process 1998;75(4):101–2. [10] Paterson N, Tawn T, Williams K, Nurse AD. On the numerical modeling of laser shearing of glass sheets used to optimize production methods. Proc Inst Mech Eng C: J Mech Eng Sci 2004;218:1–11. [11] ABAQUS user’s manual volume II, H.K.S. Inc. Pawtuckett, RI, 1998. [12] Narottam PB, Doremus RH. Handbook of glass properties, Orlando, 1986. [13] Helebrant A, Buerhop C, Weibmann R. Mathematical modeling of temperature distribution during CO2 laser irradiation of glass. Glass Technol 1993;34(4):154–8. [14] Burhop C, Weibmann R. Temperature development of glass during CO2 laser irradiation. Part 1. Measurement and calculation. Glass Technol 1996;37(2):69–74. [15] Incropera FP, de Witt DP. Fundamentals of heat and mass transfer, 4th ed. New York: Wiley; 1996. [16] Narottam PB, Doremus RH. Handbook of glass properties. New York: Academic Press; 1986. [17] Kou S. Welding metallurgy. New York: Wiley; 1987. [18] Tsai CH, Liou CS. Fracture mechanism of laser cutting with controlled fracture, Trans. ASME, J Manuf Sci Eng 2003;125:519–28.
Optics & Laser Technology 39 (2007) 892–899 www.elsevier.com/locate/optlastec
Characterization of the laser cleaving on glass sheets with a line-shape laser beam Yu-Zan Wang, Jehnming Lin Department of Mechanical Engineering, National Cheng Kung University, Tainan, Taiwan, ROC Received 18 November 2005; received in revised form 4 July 2006; accepted 10 July 2006 Available online 6 September 2006
Abstract A CO2 laser with a line-shape beam was used to cleave a soda-lime glass substrate at various beam-rotation angles to the cutting direction. The stress distribution on the glass substrate cleaved by the laser beam has been analyzed in this study. An uncoupled thermalelastic analysis was achieved by the ABAQUS software based on the finite element method. The numerical results show that the stress field of the fracture is caused by a complex stress state and the cleavages are significantly affected by the heat diffusion and beam rotation angle. At the rotation angle of zero degree to the cleaving direction, the phenomena of the chip formation have been found due to a large temperature gradient at the cleaving depth of the glass substrate. r 2006 Elsevier Ltd. All rights reserved. Keywords: CO2 laser cleaving; Thermo-elastic analysis
1. Introduction Laser machining is one of the most popular applications of the laser material processing [1]. New processes such as laser marking and laser ablation have been evolved ever since laser machining became popular in the manufacturing industries over the past decades. One of the new technologies that have been developed rapidly is the laser cleaving, which was used for manufacturing brittle materials such as glass, ceramics and many others [2]. The main concern in the industry is, as might be expected, of the machining quality (surface appearance) and efficiency, both of which are influenced by the heat generation around the cutting zone of laser machining and in this case of laser cleaving. The laser cleaving process can be applied to separate the materials with the thermal shock effects without the removal of the substrate materials. Similar to the machining processes such as the diamond tipped scribing, laser cleaving has many advantages such as narrow cleaving width and high cutting speed. According Corresponding author. Tel.: +886 6 2757575X62100; fax: +886 6 2352973. E-mail address: [email protected] (J. Lin).
0030-3992/$ - see front matter r 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.optlastec.2006.07.005
to the extraordinary cutting performance of the brittle materials by the focused laser beam, many studies have been carried out in literature [3–10]. For example, Chui [6] has applied CO2 laser to the glass cutting at various elevated temperatures. Saifi et al. [7] used continuous and pulsed CO2 lasers on the glass cutting by the laser ablation mechanisms. Ikeda et al. [8] adopted the CO2 laser and a diamond cutter to cleave the LCD glass panels. Unger et al. [9] developed a new technique to control the cleaving direction by a laser beam followed with a cooling water jet. Paterson et al. [10] found that a tremendous tensile stress state was generated to cleave the glass sheets by a lineshape beam due to a high-temperature gradient on the glass substrate. Since the thermal cleaving process is mainly based on the fracture mechanism of the brittle substrates caused by the large temperature gradient. Using a focused heat source such as laser beam to generate a noticeable temperature rise near the heating zone, the thermal shock could be generated and the propagation direction of the crack may coincide with the laser beam path in a controllable situation. However, the laser beam could melt and vaporize the substrate and induce a stress filed in all directions. The stress field and the cracking area were significant affected
ARTICLE IN PRESS Y.-Z. Wang, J. Lin / Optics & Laser Technology 39 (2007) 892–899
by the temperature gradient near the beam spot. Therefore, the shape of the beam spot is one of the factors to dominate the heat diffusion, temperature and stress distributions on the cutting area, very few studies have been made in detail to investigate the effects of the intensity profile of the laser beam in the cleaving process [2]. In literature the line-shape laser beam has been proposed in the laser cutting on glass substrate to extend the heat affected zone along the cutting direction [10], but the stress distributions have not been fully studied with the experimental evidences to analyze the effects of the beam rotation angle and process parameters on the glass substrate by laser cleaving. The stress fields of the glass sheets in the line-shape laser cleaving have been analyzed by the ABAQUS software. The fracture modes of the glass cracking have been evaluated by experiments at various rotation angles of the line-shape beam mode. The phenomenon of the chip formation caused by the thermal stress in the cleaving process was also studied.
893
A soda-lime glass specimen is selected as 76 mm in length, 26 mm in width and 1 mm in thickness as illustrated in Fig. 1(a). A CW CO2 laser beam is then delivered through a cylindrical lens forming a beam spot onto the upper surface of the specimen as illustrated. The 3-D quadratic brick elements (DC3D8) [11] with 8 nodes is adopted in the mechanical model and the computational domain with the meshes are shown in Fig. 1(b) and (c), where a fine meshing around the laser beam was applied to analyze the steep temperature gradients around the heating zone. The specimen consists of 16,000 elements. The domain meshes used for the thermal model and mechanical model are the same, but the element type is C3D8R to calculate the stress and displacement by ABAQUS [11]. The temperature-dependent nonlinear properties such as the thermal conductivity, specific heat, Poisson’s ratio and Young’s modulus of soda-lime glass are all considered in the simulation and the relationships at various temperatures are shown in the figures of Appendix A [12].
2. Numerical simulation Laser cleaving, 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 property 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 cleaving process is negligible. Therefore, to simplify the analysis, the laser-cleaving 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.
2.1. Thermal analysis In the thermal analysis by ABAQUS of the laser cleaving on a thin glass substrate, the following assumptions are made: (1) The thermal properties are isotropic. (2) The laser intensity distribution is 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.
Fig. 1. (a) The setup for the laser cleaving process and the coordinate system; (b) the grid structure of the substrate in the analysis; (c) cross-section view of the meshed domain of the glass substrate.
ARTICLE IN PRESS Y.-Z. Wang, J. Lin / Optics & Laser Technology 39 (2007) 892–899
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A circular laser beam with a Gaussian mode passing through a cylindrical lens will condense into a line-shape beam mode, and the intensity is expressed in Eq. (1) based on the coordinate system as illustrated in Fig. 2. " # ð1 RÞP x0 2 y0 2 I l ðx; yÞ ¼ exp 2 þ 2 , (1) pwl w l where, Il(x, y) is the laser intensity absorbed by the substrate, R is the reflectivity of the material under laser radiation, P is the laser power, w is the length of the minor axis of the ellipse, l is the length of the major axis of the ellipse. The moving line beam is modeled in FEM by the following coordinate system transformation. A new coordinate system (x0 , y0 ) of the laser beam at a cutting speed v and a rotation angle y to the cleaving direction can be transformed from the original coordinate system (x, y) as expressed by the following equations: " 0# " # x x cos y sin y ¼ , (2) 0 y sin y cos y y where x0 ¼ x cos y þ yðv; tÞ sin y, y0 ¼ x sin y þ yðv; tÞ cos y, and t is the time of the traveling beam. Numerous factors affect the reflectivity and they include the irradiation angle, roughness of the specimen surface, thickness of the oxidized layer, surface temperature and so on. For simplification, R is taken as an average value of 0.2 for the soda-lime glass [13]. The initial temperature of the specimen is assumed to be the ambient temperature TN ¼ 25 1C. The thermal radiation has therefore the heat of radiation is been considered, q ¼ s T 4 T 41 , where the surface emissivity is e ¼ 0.8 [14] 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 kðqT=qnÞ ¼ hðT T 1 Þ, where the coefficient of the heat convection is quoted as h ¼ 21 W/m2 1C [15] at the upper and lower surfaces of the substrate as shown on Fig. 1(a), y y' θ
x'
x
Fig. 2. Definition of the rotation angle of the line-shape beam in laser cleaving process.
and the other surfaces are assumed to be adiabatic, kðqT=qnÞ ¼ 0. 2.2. Stress analysis The following assumptions are made in the stress simulation of the laser cleaving process: (1) The material is isotropic. (2) The specimen is assumed to be annealed; therefore, its initial condition is free of stress. (3) The stress–strain relationship of the substrate material is perfectly elastic. (4) The gravity effects are neglected. The stress and strain responses were assumed to be the quasi-static state at each time interval and the thermoelastic model was used. As the specimen was clamped at one side and the other surfaces are free of stress, the boundary conditions are expressed as follows: ux ðx; y; z; tÞ ¼ 0
x ¼ 0.
(3)
uy ðx; y; z; tÞ ¼ 0
y ¼ 0.
(4)
uz ðx; y; z; tÞ ¼ 0
z ¼ 0.
(5)
The threshold value of stress required to initiate cracks in the soda-lime glass is given as the fracture strength of approximately 70 MPa for the most practical applications [16]. 3. Numerical results In order to verify the numerical results of the ABAQUS software for a moving heat source problem on the meshed domain and boundary conditions discussed above, the Rosenthal’s solution of the point heat source on a thick plate [17] was applied and the results are shown in Fig. 3, it can be seen that the temperature contours of the analytical and numerical solutions are approximately identical in the present study. In the laser cleaving on the glass substrate, the brittle fracture phenomenon will dominate the cleaving process due to the thermal shock effects on the glass. As the line-shape beam moving into the center of the substrate at the cutting time of 0.147 s and the rotation angle of 01, the stress field of sxx along the Y-axis is shown in Fig. 4. It can be seen that the maximum compressive stress sxx is located at the distance about 11.44 mm to the staring point of the cleaving path. Since the thermal expansion of the glass substrate causes a compressive stress state in the heat affected zone of the laser interaction, and the stress field changes to the tensile stress state during the cooling stage. In the case of the rotation angle of 01, the heat of the laser beam has been accumulated at the interaction zone. Thus the compressive stress occurs at the front of the cutting edge and the crack due to the thermal shock propagating along the cleaving direction. As the
ARTICLE IN PRESS Y.-Z. Wang, J. Lin / Optics & Laser Technology 39 (2007) 892–899
1000
600
-100 Stress (MPa)
Temperature (°C)
0
X:0.3mm,Y=8.3mm Analytical Solution Z=1mm Numerical Solution Z=1mm Analytical Solution Z=0.75mm Numerical Solution Z=0.75mm Analytical Solution Z=0.5mm Analytical Solution Z=0.5mm Analytical Solution Z=0.25mm Numerical Solution Z=0.25mm Analytical Solution Z=0mm Numerical Solution Z=0mm
800
895
400
-200 Power=42W Cutting Speed=5000mm / sec Spot major axis=15mm Spot minor axis=0.7mm Rotating angle=0 degree Rotating angle=45 degree Rotating angle=90 degree
200
-300
0 0
0.2
0.4
0.6
0.8
1
0
Fig. 3. Numerical results and analytical solutions of the thermal cycles at various locations for a moving point laser beam spot on the glass substrate. 60 Power=42W Cutting Speed=5000mm / min Spot major axis=15mm Spot minor axis=0.7mm Rotating angle=0 degree Rotating angle=45 degree Rotating angle=90 degree
Stress (MPa)
20
0
-20
-40
-60 0
10
20
30
Y axis (mm)
Time (sec)
40
10
20
30
Fig. 5. Profiles of the stress syy along the Y-axis at the center of the substrate with various rotation angles.
the side cracking could be prevented by large compressive stress state at a small rotation angle. Furthermore a large compressive stress syy in Fig. 5 and a small tensile stress sxx in Fig. 4 generated around the line beam show the condition for a stable crack formation. Based on the similar results from the other study for laser cleaving [18], a stable crack will be formed under a condition of surrounding compressive stress during heating stage and transferring to a tensile stress state in cooling stage in laser cleaving. Figs. 6–8 show the numerical examples at the same cutting speed but various rotation angles from 01 to 901, it can be found that the state of szz at the center of the Y-axis is a maximum tensile stress at various depths and rotation angles. The magnitude of szz decreases with the increase of the rotation angles. Due to a large temperature gradient, there is a peak tensile stress state of szz at the location of z ¼ 0.75 mm and the rotation angle of 01 on the substrate center. It may cause the elongation inside the glass substrate and the upper surface radiated by laser may bend upwards in the laser-cleaving process.
Y axis (mm)
Fig. 4. Profiles of the stress sxx along the Y-axis at the center of the substrate with various rotation angles.
rotation angle increasing from 01 to 901, the magnitude of the compressive stress sxx in Y-direction decreases. Therefore the stress state becomes tensile at the front of the cutting edge and it significantly affects the propagation of the crack on the both sides of the cleaving path at large rotation angles. The stress fields of syy at the center of the Y-axis with various rotation angles are shown in Fig. 5. A compressive stress of syy occurs at the interaction zone of the laser beam and its magnitude decreases with the rotating angle. It means that
4. Experiments The experimental arrangement of the laser cleaving was illustrated in Fig. 1(a), a CO2 (the wavelength of 10.6 mm) laser was used as the heat source and the beam spot was transformed through a cylindrical lens to form an elliptic beam spot with a length of the major axis of 15 mm and a length of the minor axis of 0.7 mm, respectively. In the cutting conditions of the laser energy of 42 W and a cutting speed of 5000 mm/min, a soda-lime glass sheet was used as the substrate material in the experiment. The appearances of the cleaving surface were examined by an optical microscope.
ARTICLE IN PRESS Y.-Z. Wang, J. Lin / Optics & Laser Technology 39 (2007) 892–899
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3 Power=42W Cutting Speed=5000mm / min Spot major axis=15mm Spot minor axis=0.7mm
1 Stress (MPa)
Stress (MPa)
2
Z=1mm Z=0.75mm Z=0.5mm Z=0.25mm Z=0mm
10
Power=42W Cutting Speed=5000mm /min Spot major axis=15mm Spot minor axis=0.7mm Z=1mm Z=0.75mm Z=0.5mm Z=0.25mm Z=0mm
5
0
0
-1
-5
-2
-3
-10 0
10
20
30
0
Fig. 6. Profiles of the stress szz at the center of the substrate with a rotation angle of 01 and various depths of substrate.
Power=42W CuttingSpeed=5000mm /min Spot major axis=15mm Spot minor axis=0.7mm Z=1mm Z=0.75mm Z=0.5mm Z=0.25mm Z=0mm
Stress (MPa)
2
0
-2
-4 0
10
20
30
Y axis (mm)
Y axis (mm)
4
10
20
30
Y axis (mm)
Fig. 8. Profiles of the stress szz at the center of the substrate with a rotation angle of 901 and various depths of substrate.
the front of the laser beam and the cleaving process was seized. The width of the heat-affected region is about 1.55 mm. In the case of the rotation angle of 901, the crossing cracks have been found in the path of the laser cleaving and the crossing angle is about 501. This type of the fracture mode was mainly generated by the shearing stresses during the laser heating. As shown in Fig. 10, continuous chips were formed at the rotation angle of 01. Since the temperature gradient at the cutting depth may cause a significant variance of the szz at the depth of substrate, a bending moment may cause the substrate to be deformed upwards with the residual stress larger than the fracture strength at a specific depth of the substrate. With a round laser spot on the glass substrate, the glass temperature easily reached the melting point and the chip formation may not occur. Based on the process parameters of the present experiment, the maximum stress szz located at a depth of 0.25 mm (i.e. z ¼ 0.75 mm), which is close the chip thickness of 0.16 mm measured in the experiment. Therefore, the stress state of szz dominates the chip formation in the laser-cleaving process.
Fig. 7. Profiles of the stress szz at the center of the substrate with a rotation angle of 451 and various depths of substrate.
5. Discussions
As shown in Fig. 9, the typical patterns of the crack propagation in laser cleaving are different at various beam rotation angles. A straight and clean cleavage without surface melting was generated at the rotation angle of 01. The width of the cut is about 0.77 mm, which is larger than the length of the minor axis of 0.7 mm of the laser beam. As the rotation angle being 451, the surface was fractured at
According to the numerical results of the stress fields as shown in Figs. 11–13, the appearance of cleavage surfaces has been examined in detail. As shown in Fig. 11(a) for the case at the rotation angle of 01, a symmetric distribution of the maximum principal stress along the cleaving direction has been found. The compressive stress state is in the region of the line-shape beam and the tensile stress state causing the glass cracking is outside the beam region.
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Fig. 9. Surface appearances of the soda-lime glass along a vertical cleaving direction at beam rotation angles of (a) 01; (b) 451; (c) 901.
Fig. 10. Cross-section view of the chip formation on a soda-lime glass in laser cleaving.
The contours of the shear stress txy are shown in Fig. 11(b), which show a concentrated and symmetric distribution of the shear stress along the cleaving path. According to Fig. 12(a) for the case at the rotation angle of 451, an asymmetric distribution of the maximum principal stress is found. Due to a large heat affected zone near the cleaving depth, a tremendous thermal effect and a large area of the compressive stress state occurred before the laser beam approaching. Therefore an unstable fracture mode with the shear-cracking phenomenon appeared in the cleaving path. However, the contours of the shear stress txy are significantly affected by the rotation angle as shown in Fig. 12(b). In the case of the rotation angle of 901, a symmetric contour of the principal stress was shown in Fig. 13(a). Since the heat-affected area is larger than those cases with small rotation angles, it causes a region of the compressive principal stress in the rear of the line-shape beam. According to Fig. 13(b), the locations of the peak shear stress txy are at the edges of the crossing cracks as shown in Fig. 9(c). 6. Conclusions Since the heating by a line-shape laser beam is difficult to be aligned with the cleaving path at a large beam rotation
Fig. 11. Contours of the stress states at a rotation angle of 01; (a) maximum principal stress; (b) shear stress txy.
angle, the thermal cleaving effects are reduced with the increase of the rotation angles in the present study. As the line-shape laser beam rotated far from the cleaving direction, the stress field at the cracking edge became asymmetric. The stress state at the front of the cracking edge changes from compressive to tensile. Thus the propagation of the crack is not aligned with the beam direction, and it may cause an unstable fracture on the surrounding region of the cleaving path. At a large rotation angle, the shear mechanism dominates the crack propagation with a crossing type fracture mode along the beam path. Due to a large tensile stress occurring inside the glass substrate at a small beam rotation angle, it may generate a continuous chip in cleaving process with a line-shape laser beam. According to the numerical analysis,
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Acknowledgements This work is supported by the National Science Council under the Grant no.: NSC 94-2622-E-006-037-CC3.
Appendix A The temperature-dependent nonlinear properties such as the thermal conductivity, specific heat, Poisson’s ratio and Young’s modulus of soda-lime glass are shown in Figs. A1–A4. 2.2
Fig. 12. Contours of the stress states at a rotation angle of 451; (a) maximum principal stress; (b) shear stress txy.
Thermal conductivity (W / °C)
2
1.8
1.6
1.4
1.2 0
200
400
600
Temperature (°C)
Fig. A1. Thermal conductivity of the soda-lime glass at various temperatures.
1300
Specific heat (J / Kg°C)
1200
1100
1000
900
800 Fig. 13. Contours of the stress states at a rotation angle of 451; (a) maximum principal stress; (b) shear stress txy.
700 0
the location of the peak tensile stress of szz is approximately equal to the thickness of the chip measured in experiment.
200
400
600
800
1000
Temperature (°C) Fig. A2. Specific heat of the soda-lime glass at various temperatures.
ARTICLE IN PRESS Y.-Z. Wang, J. Lin / Optics & Laser Technology 39 (2007) 892–899
References
0.2
Possion's ratio
0.19
0.18
0.17
0.16 0
200
400
600
800
1000
Temperature (°C) Fig. A3. Poison ratio of the soda-lime glass at various temperatures.
82
80 Young's modulus (GPa)
899
78
76
74
72 0
200
400
600
800
1000
Temperature (°C) Fig. A4. Young’s modulus of the soda-lime glass at various temperatures.
[1] Steen WM. Laser material processing. Berlin: Springer; 1991. [2] Lumley RM. Controlled separation of brittle materials using a laser. Am Ceram Soc Bull 1969;48(9):850–4. [3] Morita M. Generation and propagation behavior of laser induced thermal cracks. J Ceram Soc Jpn 1993;101(5):510–5. [4] Finucane MA, Back I. CO2 laser cutting of stained glass. Int J Adv Manuf Technol 1996;12(1):47–59. [5] Zhou YC, Zhu ZM. Thermal fracture characteristics induced by laser beam. Int J Solids Struct 2001;38(32-33):5647–60. [6] Chui GK. Laser cutting of hot glass. Am Ceram Soc Bull 1975;54(5):514–8. [7] Saifi MA, Paek U- C. Scribing glass with pulsed and Q-switched CO2 laser. Ceram Bull 1973;52(11):838–41. [8] Ikeda M, Shibata T, Makino E, Takahashi Y, Ono A, Matsumoto F. Study on laser breaking of glass plate (1st report)-generation and growth of vertical cracks by scribing. J Jpn Soc Precis Eng 1996;62(3):413–7. [9] Unger W, Wittenbecher W. The cutting edge of laser technology. Glass Process 1998;75(4):101–2. [10] Paterson N, Tawn T, Williams K, Nurse AD. On the numerical modeling of laser shearing of glass sheets used to optimize production methods. Proc Inst Mech Eng C: J Mech Eng Sci 2004;218:1–11. [11] ABAQUS user’s manual volume II, H.K.S. Inc. Pawtuckett, RI, 1998. [12] Narottam PB, Doremus RH. Handbook of glass properties, Orlando, 1986. [13] Helebrant A, Buerhop C, Weibmann R. Mathematical modeling of temperature distribution during CO2 laser irradiation of glass. Glass Technol 1993;34(4):154–8. [14] Burhop C, Weibmann R. Temperature development of glass during CO2 laser irradiation. Part 1. Measurement and calculation. Glass Technol 1996;37(2):69–74. [15] Incropera FP, de Witt DP. Fundamentals of heat and mass transfer, 4th ed. New York: Wiley; 1996. [16] Narottam PB, Doremus RH. Handbook of glass properties. New York: Academic Press; 1986. [17] Kou S. Welding metallurgy. New York: Wiley; 1987. [18] Tsai CH, Liou CS. Fracture mechanism of laser cutting with controlled fracture, Trans. ASME, J Manuf Sci Eng 2003;125:519–28.