超薄玻璃應用於R2R製程（Roll-to-Roll processing）時，玻璃會因為其邊緣之微裂紋而導致在傳輸時產生破裂。因此，雷射劈裂技術就被應用來劈開這些微裂紋。本研究藉由COMSOL Multiphysics 模擬不同玻璃於雷射劈裂過程之熱傳現象，並考慮穿透熱源與高溫時玻璃熔融所發生之物理性質的改變，模擬出玻璃之溫度場分布並預測不同玻璃劈裂時之溫度範圍。結果顯示當玻璃之吸收係數大於100（1/mm）時，其穿透的效應可忽略，並且可假設成由表面完全吸收。另一方面，不同玻璃因其熱容與熱傳導係數之不同，會使表面及深度內之溫度變化產生極大的影響。研究最後提出特定深度下之最高溫度與玻璃之平均熱力性質（Cp、k）之經驗關係式，此式提供使用者預測不同玻璃其劈裂機制之溫度參考。
整體而言，研究結果增加了不同玻璃進行雷射劈裂時之溫度分布與熱傳現象的了解，並有助於劈裂機制的探討。

Thermal Simulation on Laser Peeling for Different Ultrathin Glasses

Author：Yi Wen Huang
Advisor：Chang Da Wen
National Cheng Kung University Department of Mechanical Engineering
SUMMERY

When the ultrathin glass is used in R2R (Roll-to-Roll) process, the glass will be broken apart due to the presence of micro-cracks on the edge. Therefore, the technique of laser peeling is used to peel off cracks prior to rolling process. This research simulates the heat transfer phenomena of different ultrathin glasses during the laser peeling process by COMSOL Multiphysics, and considers the effect of laser penetration and the change of physical properties of glass in high temperature in order to get the actual temperature distributions during the laser peeling process. The results show that while the absorption coefficient of the glass is greater than 100 (1/mm), the effect of penetration can be neglected. On the other hand, heat capacity and thermal conductivity would also affect the temperature distribution. Finally, this study proposes an empirical equation which indicates the relation among maximum temperature, average heat capacity and thermal conductivity, and peeling depth. With this empirical equation, the maximum temperature of peeling depth for different glasses can be predicted.

Key words: ultrathin glass, R2R processing, micro-cracks, laser peeling.

INTRODUCTION

Nowadays, the ultrathin glass with thickness less than 0.1mm has been developed successfully. The glass substrate has considerable degree of flexing and relatively thin thickness; however, it still has drawbacks: the glass itself is hard and brittle. Therefore, the ultrathin glass in R2R processing is sometimes broken because of the edge of glass micro-cracks. How to get rid of the micro-cracks on the edge of glass becomes an important issue for R2R processing.

It has been a big challenge to maintain smooth surface with no micro-cracks on the edge of glass using laser process. This is because thermal stress induced by laser creates micro-cracks on the edge of glass. Studies to remove or reduce the thermal-induced cracking issue have been performed by researchers. The laser peeling process might be caused by the expansion and contraction cycles generated in glass during the laser irradiation, and creates a smooth surface by peeling off the glass edge. It is mentioned in another study that the laser beam energy and the laser scanning speed are important factors which result in removal, melting and crack formation at glass surface during laser peeling process. Namely, there is an optimal range in laser power and scanning speed for peeling off the glass continuously. Another study shows that laser cannot peel off glass with smooth edge. This means the micro-cracks on the edge of the glass is an important factor in laser peeling process. Without micro-cracks, there is not enough driving force to peel off glass by only thermal expansion or contraction. On the other hand, it is believed that maximum temperature of peeling depth is lower than the temperature at strain point. When the temperature approaches the strain point, the glass becomes soft and thus increases the viscosity of the glass so that the laser cannot peel it off.

In this study, the main goal is to achieve further understanding of temperature distribution and heat transfer phenomena for different ultrathin glasses in laser peeling. This study used COMSOL Multiphysics to build the three-dimensional heat transfer model and considered the effect of laser penetration and the change of physical properties of glass in high temperature. The simulation results showed the three-dimensional transient temperature field of different glass during the laser peeling process. In the last, this study provides a method to predict the maximum temperature of the peeling depth with different average thermal properties.

NUMERICAL MODEL

The model’s dimensions and coordinates are shown in the Fig. 1. According to the ultrathin flexible glass substrate used in R2R processing, this is a three-dimensional solid with 25 mm length, 1 mm width, and 0.1 mm thickness.

In this research, the mathematical model is established based on these assumptions as follows: (1) convection between the surface and the environment is assumed to be air natural convection. (2) The distribution of laser power is Gaussian profile. (3) The density and emissivity of glass is independent of temperature.

This study considers the effect of laser penetration by beer-lambert law. In order to set up the change of thermal properties in the high temperature, the change of thermal conductivity is predicted by using the empirical equation of thermal conductivity and the heat capacity is predicted by using method of curve fitting from experimental data. Both of the empirical equation and experimental data are from other studies. The laser scanning path is shown in Fig. 2. Because when laser spent 20pulses, it will hit 5 pulses on the glass. The power of these 5 pulses is equal 2 pulses on the glass totally, as shown in the Fig. 3.

Figure 1 A schematic diagram and dimension of the model

Figure 2 The moving path of laser

Figure 3 Five pulses laser on the top surface of glass
RESULTS AND DISCUSSION

Fig. 4 shows under the different absorption coefficient, the temperature distribution in depth-direction at x = 7.5 mm, y=0.05 mm, t=0.3s. When the absorption coefficient is close or larger than 100 (1/mm), the temperature distribution with the effect of laser penetration is close to the temperature distribution without considering the penetration. This means the laser power is absorbed by the surface of glass totally. Most of the glasses are found to have the absorption coefficient more than 100 (1/mm) at wavelength of CO2 laser beam (10.6 μm). The temperature distribution in depth-direction of different glasses at x = 7.5 mm, y = 0.05 mm, t = 0.3s is shown in the Fig. 5. Also, Fig. 6 and Fig. 7 show the variation of heat capacity and of thermal conductivity with temperature. Comparing to these three figures, the changes of heat capacity and thermal conductivity cause a strong impact on the distribution of temperature in depth-direction. Fig. 8 shows that the relationship between the maximum temperature and average thermal properties (heat capacity and thermal conductivity) at peeling depth 171μm and liquid zone depth 50μm with glass density 2420 (kg/m3). This figure apparently shows that the thermal properties affect the maximum temperature under specific depth. Due to the peeling condition in the experimental case (T171μm < 872.15 K, T50μm > 1500 K), the range of equivalent average heat capacity is found between 1520 and 2100 (J/kg-K), and the range of thermal conductivity is found between 1.4 and 1.6 (W/m-K). According to the relationship between heat capacity, thermal conductivity and maximum temperature of specific depth in Fig. 8, an empirical equation can be derived and expressed as follows:

Where
: The maximum temperature in the specific depth,
,



: The depth in the glass.
From this correlation, if the average thermal properties of the glass are known, the maximum temperature of specific depths obtained from the peeling process can be predicted. It provides a reference to users to predict the temperature of peeling depth of different glasses.

Figure 4 Comparisons of different absorption coefficients in temperature distribution in the depth-direction

Figure 5 Comparisons of different glasses in the temperature distribution in the depth-direction

Figure 6 Comparisons of different glasses in t heat capacity with temperature

Figure 7 Comparisons of different glasses in thermal conductivity with temperature

Figure 8 The relationship between average thermal properties and maximum temperature in the specific depth.

CONCLUSION

A thermal model is developed to investigate the process of laser peeling of different ultrathin glasses. The main conclusions are listed below：
1. The effect of laser penetration in the glassed can be neglected when the absorption coefficient of glass is higher than 100 (1/mm) at the wavelength 10.6 μm.
2. Heat capacities and thermal conductivities would cause an extremely impact on the distribution of temperature.
3. This study proposes an empirical equation which indicates the relation among maximum temperature, average heat capacity and thermal conductivity, and peeling depth. With this empirical equation, the maximum temperature of peeling depth for different glasses can be predicted.

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