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Optics & Laser Technology 41 (2009) 318– 327

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Optics & Laser Technology

0030-39

doi:10.1

� Corr

E-m

salman.

journal homepage: www.elsevier.com/locate/optlastec

Effect of thermal stresses on chip-free diode laser cutting of glass

Salman Nisar a,�, M.A. Sheikh a, Lin Li a, Shakeel Safdar b

a Manufacturing and Laser Processing Research Group, School of Mechanical, Aerospace and Civil Engineering, The University of Manchester, Manchester, M60 1QD, UKb College of Aeronautical Engineering, Department of Aerospace Engineering, NUST, Risalpur, Pakistan

a r t i c l e i n f o

Article history:

Received 1 April 2008

Received in revised form

19 May 2008

Accepted 29 May 2008Available online 9 July 2008

Keywords:

Controlled fracture technique (CFT)

Cut deviation

Finite element method

92/$ - see front matter & 2008 Elsevier Ltd. A

016/j.optlastec.2008.05.025

esponding author. Tel.: +44161306 2350; fax

ail addresses: salmannisar@gmail.com,

nisar@postgrad.manchester.ac.uk (S. Nisar).

a b s t r a c t

In laser cleaving of brittle materials using controlled fracture technique, thermal stresses are used to

induce a crack and the material is separated along the cutting path by extending this crack. In this study,

a glass sheet is stressed thermally using a 808–940 nm diode laser radiation. One of the problems in

laser cutting of glass with controlled fracture technique is the cut deviation at the leading and the

trailing edges of the glass sheet. In order to avoid this damage it is necessary to understand the stress

distributions which control crack propagation. A study is conducted here to analyse the cut deviation

problem of glass by examining the stress fields during diode laser cutting of soda-lime glass sheets.

Optical microscope photographs of the breaking surface are obtained to examine the surface quality and

cut path deviation while the latter is explained from the results of the stress fields which are obtained

from a finite element simulation.

& 2008 Elsevier Ltd. All rights reserved.

1. Introduction

With the advancements in glass industry, glass has become anincreasingly important engineering material in architecture,medical, automotive, flat panel display and electronics industries.Desired shape and size of the glass can only be achieved throughaccurate and precise cutting technique.

The conventional method of glass cutting with the help of ametal or diamond point tool has been used for decades. Irregularcut path, poor surface finish and chip formation are usuallyobserved when these methods are used for glass cutting [1–3]. Ithas also been reported that with mechanical cutting the strengthof glass reduces to 60% [4].

Various techniques of laser glass cutting such as scribing andbreaking and controlled fracture technique are being used inindustry and some are still in their developmental stages.Controlled fracture technique has great potential in laser glasscutting because it uses less laser power and enables high cuttingspeeds compared to other laser cutting methods. It was pioneeredby Lumley [5] in 1968. In this technique, cutting is performedbelow glass transition temperature Tg which results in smoothedges and hence requires no further cleaning or grinding.

ll rights reserved.

: +44161306 3803.

In controlled fracture technique, the cracks were initiateddue to absorbed photons heating up the material. The stressesnear the laser spot are compressive due to high temperature.After the passage of the laser beam, these compressive stressesrelax and induce local residual tensile stresses. If these stressesexceed the failure stress sf given by the critical energy release rateGc of the glass, the crack propagates. This condition is givenby [6]

Gc ¼s2

f pc

E(1)

where E is Young’s modulus and c is the crack length.Tsai and Liou [7] divided the cutting process into three stages.

In the first stage, fracture initiates due to tensile stresses. Stablecrack growth is observed in the second stage, and in the thirdstage, crack extends unstably due to complete domination oftensile stresses. Dekker et al. [8] proposed a method similar tocontrolled fracture technique for cutting glass. A small scratch isformed at the start of the cut which helps in initiating the crackand leads to the separation of the glass. Controlled fracturetechnique has been improved by introducing water–air mixturealong the cutting path to generate tensile stresses and to maintainthe temperature below the glass transition temperature[3,4]. However, coolant adds extra cost and complexity to theprocess.

In controlled fracture technique, it is difficult to control crackpropagation inside the glass because of its fracture characteristicsand stress distribution. A major problem for this process is the

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S. Nisar et al. / Optics & Laser Technology 41 (2009) 318–327 319

difficulty to generate precise thermal and stress fields. Anotherproblem is the cut deviation (out of flatness) at the leading andthe trailing edges of the glass [3,9,10]. In this study, this cutdeviation problem is examined by analysing the stress fields in theglass.

2. Experimental method

2.1. Experimental procedure

The laser used in the experiments was a fibre-optic-coupledhigh-power diode laser, emitting at 810–940 nm and operating inthe (continuous wave) CW mode. A soda lime glass fromPilkington plc was used as the workpiece material. The dimensionof the workpiece used in the investigation was 100�100�5 mm3.After taking into account the power loss due to fibre coupling, atotal of 770 W of the laser power was used while the size of thelaser beam (dia) and the cutting speed were kept at 3 mm and31 mm/s respectively. The workpiece was placed below the focalpoint and the distance from the focusing lens was changed toobtain the required beam spot size on the workpiece. The spot sizeis normally kept large at a defocused distance because of lowtransition temperature of the glass in order to minimise melting

Diode LaserGenerator

CNC Table Controller CNC x-y Table

Glass workpieceAluminium sheet

Focal point

z-Axis

Shroudgas

Laser beam

Focusing lens

Thermalcamera

Fig. 1. Schematic of the experimental setup.

Chip-free edge

Fig. 2. Optical microscope photographs of the separation surfaces of the Optifloat gl

and evaporation. This has been reported to give better cuttingquality and higher cutting speed [7]. The laser beam irradiated theglass workpiece placed on an aluminium sheet by traversing thesample along y-axis of the CNC gantry table, as shown in Fig. 1.A thermal imaging camera and a thermocouple were used tomeasure temperatures and to calibrate emissivity.

2.2. Surface quality and cut path deviation

Optical microscope photographs of the cutting surface areshown in Fig. 2. As can be seen in Fig. 2a, the surface qualityobtained from controlled fracture technique is very smooth andhas chip-free edges. The cutting surface of the glass separated bymechanical cutting method has chips visible in the breakingsurface as seen in Fig. 2b.

In the controlled fracture technique, precise thermal stressesare needed to control the crack propagation inside the glass foraccurate splitting. The cut deviation can occur from the desiredlaser cutting path due to inconsistent stress fields at the leadingand trailing edges of the cut. Fig. 3 shows the cut deviation path atthe leading and the trailing edges of the glass while the desiredlaser cutting path is denoted by dashed lines.

3. Volumetric heat source

According to Helebrant et al. [11], a good representation of thelaser heat source is volumetric when optical penetration depth(absorption length) is greater than thermal penetration depth(diffusion length). The depth of the heat affected zone depends onthe absorption length as well as on the diffusion length. Whenthe absorption length is greater than the diffusion length, thedepth of the heat affected zone is governed by optical penetrationdepth, Ad, and vice versa [12]. The thermal diffusion length, Dd, isgiven as [13]

Dd ¼ 2ðbtÞ1=2 (2)

where b is the thermal diffusivity and t is the interaction time.An Ocean Optics SD 2000 fibre optic spectrometer was used to

measure reflectivity and absorbance of the glass between 808 and940 nm wavelengths. The reflectivity value for the thickness ofglass, ranging from 2 to 8 mm, was found to be between 5% and 7%while the absorbance value for 5 mm glass thickness was between9% and 13%. Measured value of absorbance was used to calculatethe absorption coefficient, K, and the absorption value using

Chipping

ass using (a) controlled fracture technique and (b) mechanical cutting method.

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Laser path

Cut deviation atleading edge

Laser path

Cut deviation attrailing edge

Fig. 3. Cut path deviation of the glass at (a) leading edge and (b) trailing edge.

Focusing lens

Increasing laserbeam size

Uniform laserbeam size

Glass

Fig. 4. Schematic of real and assumed laser beam behaviour inside the glass

during volumetric absorption of the diode laser.

S. Nisar et al. / Optics & Laser Technology 41 (2009) 318–327320

Beer–Lambert law [14]:

absorbance ¼ A ¼ �log10T ¼ �log10I1

I0

� �(3)

transmittance ¼ T ¼I1

I0¼ 10�Kz

¼ 10�A (4)

A ¼ Kz (5)

where A is the absorbance, T is the trasmittance, I0 is the intensityof the incident light, I1 is the intensity of light coming out of thesample and z is the material thickness.

The absorption length Ad is reciprocal of absorption coefficientK. The thermal diffusion and absorption lengths were calculated

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Table 1Temperature-dependent physical properties of float glass [16]

Temperature 1C

(T)

Density kg/m3 (r) Young’s modulus

GPa (E)

Poisson’s ration

(g)

Thermal conductivity

W/m K (k)

Specific heat J/kg K (Cp) Thermal expansion

coefficient 1/K (a)

25 2.43E+03 72.9 0.23 1.06 8.28E+02 9.0E-06

200 – 71.1 – 1.23 1.01E+03 9.1E-06

400 – 69.1 – 1.38 1.16E+03 9.3E-06

500 – 68.0 – – – 9.4E-06

Table 2Parameters used for the simulation

Laser power (absorbed) 196.7 W

Workpiece dimensions 100�100�5 mm3

Heat source Volumetric

Laser scanning speed 31 mm/s

Laser beam size 3 mm dia

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using Eqs. (2) and (5), respectively. It was found that theabsorption length was greater than the thermal diffusion lengthfor the glass used and the wavelength of diode laser. Thecalculated values for the absorption and thermal diffusion lengthswere found to be 38.4 and 2.67 mm respectively. The absorptionvalue was obtained as 26.3%. As the measured values of reflectionincluded the effect from both the top and the bottom surfaces ofthe glass, therefore, only a single reflection value was consideredin estimating the absorbed power. The absorbed power of 196.7 Wwas calculated by using the reflection value of 3% (out of a total6%) for a glass of 5 mm thickness while the reflection from thealuminium sheet was neglected in this study.

As glass is a denser medium than air, the size of the laser beamincreases inside the glass when it is placed below the focal pointduring the cutting process. In the finite element simulations,however, the size of the laser beam was assumed to be uniformthroughout the thickness, as shown in Fig. 4.

4. Finite element analysis

In this study, the experimental temperatures are comparedwith FE results obtained by using ABAQUS. A sequentially coupledthermal-stress analysis was used in which the heat generated dueto deformation response i.e. crack propagation in the cleavingprocess, was neglected [15]. The temperature-dependent thermaland physical properties of the material were used in the analysis,given in Table 1 [16]. The parameters used for the three-dimensional thermal analysis with a moving heat source aresummarised in Table 2. The initial temperature, T0, of the glasswas set at 25 1C. 3D brick elements DC3D8 [17] with 8 nodes wereused in the thermal model with a finer mesh around the laserbeam due to steep temperature gradients around the heatingzone. The final model consisted of 148,800 elements. The numberof elements used in thermal and mechanical models was thesame but the element type used for the mechanical model wasC3D8R [17], a 3D brick element with 8 nodes but with reducedintegration.

A volumetric heat source was used in the thermal model, as theabsorption length was greater than the diffusion length for thegiven parameters. The temperature field T(x, y, z, t) was obtainedusing a transient solution procedure governed by the followingheat diffusion equation [7]:

kq2T

qx2þq2T

qy2þq2T

qz2

!þ Q ¼ rCp

qT

qt(6)

where k is the thermal conductivity, r is the density, Cp is thespecific heat and Q is the amount of heat generated per unitvolume due to laser irradiation. The initial condition for thesubstrate was taken as follows:

Tðx; y; z;0Þ ¼ T0 (7)

Following assumptions were made in the thermal analysis:

(1)

The material (glass sheet) was homogenous and isotropic. (2) The laser intensity distribution was uniform. (3) The effect of natural convection was neglected.

Following assumptions were made in the stress analysis ofthe process,

(1)

The material was isotropic. (2) The specimen was annealed and hence free of any residual

stresses.

(3) An elastic stress–strain relationship for the workpiece

material.

The analysis was performed without a crack in the glass sheetwhich was clamped from one side so that ux ¼ uy ¼ uz ¼ 0, asshown in Fig. 5(b).

5. Results

For thermal analysis, after taking into account the reflectionand the absorbance of the glass, the power absorbed in the glasswas estimated as 196.7 W. A global coordinate system for themodel, as shown in Fig. 5(a), has x-axis representing thetransverse direction, y-axis the scanning direction and z-axisthe depth. The temperature field was obtained at a point P definedby the coordinates x ¼ 50, y ¼ 10, z ¼ 5. The point P was selectedto obtain the temperature field once a quasi-steady-state hadbeen reached. Fig. 6 shows a comparison of modelling andexperimental results for temperature at the selected point.It can be seen from Fig. 6 that the experimental results agreewell with the modelling results. The maximum temperatureobtained with the circular beam is 251 1C from the model and252 1C from the experiments. It is followed by slow temperaturedecay after the laser beam has crossed 10 mm from the leadingedge in the middle of the beam path on the top surface, as seenin Fig. 6.

A fracture stress of approximately 70 MPa is required to initiatecracks in soda-lime glass [15]. Many researchers have proposed

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100 mm

100 mm

5 mm

Scan speed ‘v’

zy

x

(ux = uy = uz = 0)

Fig. 5. (a) The coordinate system, (b) FE model with the constraints and (c) cross-section view of the meshed domain.

Fig. 6. Temperature versus time on surface (model and experiment).

Fig. 7. Temperature and stress distribution across the thickness at leading edge of

the glass at 0.2 s along the scanning direction.

S. Nisar et al. / Optics & Laser Technology 41 (2009) 318–327322

stable and unstable fracture conditions for laser cleaving of glassusing the controlled fracture technique. Lin and Wang [15] andTsai and Liou [7] proposed that a large compressive stress (syy)and a small tensile stress (sxx) generated around the laser beamspot along the cutting path is the condition for stable crackpropagation. However, these fracture conditions are for particularprocess parameters and can change with laser type and thematerial being cut.

Figs. 7–9 show the temperature and stress distributions acrossthe depth of cut for the glass at 0.2, 1.7 and 3.2 s in the scanningdirection, respectively. The x-component of the stress (sxx) isshown as this component plays a dominant role in mode-Ifracture (stress normal to the crack faces). As shown in Figs. 7–9,

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Fig. 8. Temperature and stress distribution across the thickness at the centre of

the glass at 1.7 s along the scanning direction.

Fig. 9. Temperature and stress distribution across the thickness at the trailing edge

of the glass at 3.2 s along the scanning direction.

S. Nisar et al. / Optics & Laser Technology 41 (2009) 318–327 323

the tensile stresses exist at the top and the bottom surfaces of theglass sheet whereas compressive stresses occur in the middle. Inthe case of heat generation, with increasing depth, the internaltemperature becomes less sensitive to the cooling process;therefore, a compressive stress occurs inside. On the other hand,due to fast cooling, particularly because of high temperaturedifference, a tensile stress is observed at the top and the bottomsurfaces of the glass.

Fig. 10 shows the stress (sxx) on the top and bottom surfaces ofthe glass at the leading edge, centre and the trailing edge,respectively. A maximum tensile stress (sxx) of 145 MPa isobserved at 0.2 s at the leading edge. Similarly, at 1.7 and 3.2 s(sxx), of 55 and 155 MPa are observed at the centre and the trailingedge of the glass, respectively, as shown in Fig. 10. Fig. 11 showsthe stress (sxx) in the middle of the glass (z ¼ 2.5 mm) at the

leading edge, centre and the trailing edge respectively. Themaximum tensile stress (sxx) of 85 and 107 MPa are observed at0.2 and 3.2 s at the leading edge and the trailing edge of the glass,respectively, as shown in Fig. 11. Similarly, at 1.7 s, stress (sxx) is�52 MPa at the centre of the glass.

Fig. 12 shows the stress (syy) on the top and bottom surface ofthe glass at the leading edge, centre and the trailing edge,respectively. It can be seen from Fig. 12 that the small magnitudeof an average value of 0.5 MPa prevails throughout the cuttingtime at the leading and the trailing edges of the glass. However, inthe centre of the glass maximum compressive stress (syy) of�111 MPa is observed at 1.9 s as shown in Fig. 12. Fig. 13 showsthe stress (syy) in the middle of the glass (z ¼ 2.5 mm) at theleading edge, centre and the trailing edge respectively. Themagnitude of stress (syy) on the leading and the trailing edgesremain at an average value of 0.3 MPa throughout the cutting timeas can be seen in Fig. 13. On the other hand, maximumcompressive stress (syy) of �139 MPa remained constant betweenthe cutting time of 1.75 and 1.95 s in the centre of the glass, asshown in Fig. 13.

Fig. 14 shows the stress (szz) on the top and bottomsurface of the glass at the leading edge, centre and trailingedge, respectively. A maximum compressive stress (szz) of �2.1and �3.5 MPa are observed at 0.05 and 1.7 s at the leading edgeand in the centre of the glass. Similarly, at 3.2 s, maximumtensile stress (szz) of 1.9 MPa is observed at the trailing edge ofthe glass, as shown in Fig. 14. Fig. 15 shows the stress (szz) in themiddle of the glass (z ¼ 2.5 mm) at the leading edge, centreand the trailing edge, respectively. The maximum compressivestress (szz) of �38 and �64 MPa are observed at 0.05 and 1.7 sat the leading edge and in the centre of the glass, as shown inFig. 15. Similarly, at 3.18 s, maximum tensile stress (szz) of 22 MPais observed at the trailing edge of the glass which changesto compressive stress (szz) of �22 MPa at 3.22 s, as shownin Fig. 15.

6. Discussion

The experimental results of this study show a clear differencein the surface quality of the glass between controlled fracturetechnique and mechanical cutting method as can be seen in Fig. 2.It also identifies the problem of cut deviation, at the leading andthe trailing edges of the glass, from the desired laser cutting pathas shown in Fig. 3.

The current study suggests that high magnitudes of thetensile stress (sxx) at the leading edge and at the trailing edgecompared to the centre of the glass on the top and the bottomsurfaces (cf. Fig. 10), and high magnitudes of tensile stress (sxx) atthe leading and the trailing edges compared to the compre-ssive stress (sxx) in the middle (z ¼ 2.5 mm) of the glass(cf. Fig. 11), provides a simple explanation for cut deviation.The stress (sxx) at the leading edge is compressive initially for ashort period of 0.03 s but then remains tensile for the rest of thecutting process, as shown in Figs. 10 and 11. This change in thenature of the stress field equals the cut deviation at the leadingedge. The high magnitude of the tensile stress (sxx) at the edges(Fig. 10) is due to large temperature difference while a smalltemperature difference results in lower magnitude of the tensilestress (sxx) in the centre of the glass. It can be seen in Fig. 11 thatdeeper in the centre of the glass, the stresses (sxx) remain incompression. An explanation for this is that the temperaturevariations inside the glass are lower as compared to thetemperatures on the surfaces. The leading and the trailing edgesare at ambient temperature which cause large temperaturevariations.

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Fig. 10. Profiles of stress sxx on the top and bottom surfaces of the glass at the leading edge, centre and the trailing edge.

Fig. 11. Profiles of stress sxx in the middle of the glass (z ¼ 2.5 mm) at the leading edge, centre and the trailing edge.

S. Nisar et al. / Optics & Laser Technology 41 (2009) 318–327324

It is interesting to note that the stress (syy), shown inFigs. 12 and 13, at the leading and the trailing edges isnegligible as compared to the stresses (sxx) and (szz),shown in Figs. 10, 11, 14 and 15. Similarly, stress (syy) at theleading and the trailing edges is negligible as comparedto the stress (syy) in the centre of the glass, as shown inFigs. 12 and 13. A plane stress condition exists due to negligiblestress (syy) at the leading and the trailing edges as shownin Figs. 12 and 13. From these results, it can be concludedthat a triaxial stress condition which exists in the centre of the

glass is relaxed at the leading and the trailing edges, as shown inFigs. 12 and 13.

7. Conclusions

A laser cutting technique of controlled fracture has been usedfor the cutting of soda-lime glass. The driver for this study is tounderstand and analyse the cut deviation at the leading and thetrailing edges of the glass sheet by examining the stress fields

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Fig. 12. Profiles of stress syy on the top and bottom surface of the glass at the leading edge, centre and the trailing edge.

Fig. 13. Profiles of stress syy in the middle of the glass (z ¼ 2.5 mm) at the leading edge, centre and the trailing edge.

S. Nisar et al. / Optics & Laser Technology 41 (2009) 318–327 325

during diode laser cutting. A commercial FE package ABAQUS isused to predict the stress distribution at the leading edge, centreand trailing edge of the glass. It has been established thatinteraction of CO2 laser with glass results in surface absorptionwhile diode laser, due its low absorption coefficient, producesvolumetric absorption, thereby resulting in different thermal andstress fields in the glass. It is found that the high magnitudes oftensile stresses (sxx) at the leading and the trailing edges

compared to the tensile stress (sxx) in the centre of the glass(cf. Fig. 10) and high magnitudes of tensile stress (sxx) at theleading and the trailing edges compared to the compressive stress(sxx) in the middle (z ¼ 2.5 mm) of the glass (cf. Fig. 11) is thereason for cut deviation. A possible solution to this problem is theuse of a different beam geometry which may generate precise andaccurate stress fields at the leading and the trailing edges of theglass sheet.

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Fig. 14. Profiles of stress szz on the top and bottom surface of the glass at the leading edge, centre and the trailing edge.

Fig. 15. Profiles of stress szz in the middle of the glass (z ¼ 2.5 mm) at the leading edge, centre and the trailing edge.

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Acknowledgement

Financial support for this work by the National University ofSciences and Technology of Pakistan is gratefully acknowledged.

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