Finite element analysis and verification of laser marking on eggshell

j o u r n a l o f m a t e r i a l s p r o c e s s i n g t e c h n o l o g y 2 0 9 ( 2 0 0 9 ) 470–476

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

Finite element analysis and verification of laser marking on eggshell Ming-Fei Chen ∗ , Yan-Hsin Wang, Wen-Tse Hsiao Department of Mechatronics Engineering, National Changhua University of Education, Changhua 50058, Taiwan, ROC

a r t i c l e

i n f o

a b s t r a c t

Article history:

The first aim of the study was to establish the temperature model of the eggshell by the

Received 15 August 2007

finite element analysis software ANSYS and realize the eggshell temperature field based

Received in revised form

on the laser marking processing. The eggshell surface which created the meshing model,

18 January 2008

set the parameters with the ANSYS Parameter Design Language and simulated that the

Accepted 11 February 2008

Gaussian distributed laser beam acted on the surface were established. In addition, marking characters made use of the CO2 laser processing system on the brittle eggshell to analyze whether laser beams caused damage to the inner of the eggshell. According to the results of

Keywords:

the comparison between the simulation by ANSYS and the experiment of laser marking, it

Temperature field

is revealed that the heat-affected area by laser marking is similar to that of the simulation. © 2008 Published by Elsevier B.V.

ANSYS Eggshell Laser marking

1.

Introduction

In recent years, the laser marking technology was extensively used in mechanical engineering, electronic engineering, photoelectricity, biology, medicine, etc. Even the laser scalpel used in the surgery and the 3C (i.e. computer, communication, and consumer electronics) marking products were produced by the laser processing technology (Steen, 1994). The laser processing is one of the novel processing technologies of the non-contact methods, because it would not damage the surface of the processing objects and provides an elegant solution when a clean, fast, non-contact marking process is required to produce an indelible high-quality mark (McKee, 1996). In general, heat effects produced in the laser processing are influenced by illuminant energy of the laser and material properties. The selection of proper laser wavelength, energy or the number of pulses can be the referential elements to the heat source on the surface of objects. The heat effect was affected by the chosen laser wavelength and heat absorption coefficient of the

∗

material. Different materials get different absorbing results with different wavelength. Chen et al. (2006) marked the eggshell surface with the repeated pulses whose maximum time is fifth pulse, but it did not run through the eggshell. In the food processing, Choi and Li (2006) studied the wavelength and energy dependence of a UV laser used for the drilling and cutting of cheese with a pulsed Nd:YAG laser at wavelengths of 355 nm and 266 nm. While damages and burns occurred around and inside the cutting cross-section with the laser beam of 355 nm, the laser beam of 266 nm produced high quality cutting and drilling and much deeper cutting depth. In the laser machining of brittle materials, Allcock et al. (Allcock et al., 1995) minimized the thermal-induced cracking issue with selected laser sources. Experimental observations and analysis of CO2 laser-induced micro-cracks in glass substrates with both transversely excited atmospheric (TEA) pressure CO2 and modulated continuous-wave (CW) CO2 lasers have been reported in a laser marking processing. The laser-

Corresponding author. Tel.: +886 4 7232105x7283; fax: +886 4 7211149. E-mail address: [email protected] (M.-F. Chen). 0924-0136/$ – see front matter © 2008 Published by Elsevier B.V. doi:10.1016/j.jmatprotec.2008.02.065

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produced marks were formed by a combination of surface cracking and material removal. Lumley’s laser cutting method (Lumley, 1969) of controlled fracture has great potential to be applied in machining brittle material. Only a single laser is used in his invention. The applied laser energy produces a mechanical stress that causes the material to separate along the path of the laser beam. The material separation is similar to a crack extension and the fracture growth is controllable. They successfully applied this technique in the dicing of brittle materials such as alumina ceramic substrate and glass, by using the CO2 laser. The laser power required is less than that for conventional laser evaporative cutting and laser scribing, and the cutting speed is much higher. Grove et al. (1970) proposed a related method of controlled fracture for cutting glass, in which the cutting speed is higher. Li et al. (1997) studied the basic mechanisms and the characteristics of the beam absorption in case of laser marking building materials such as marble, bricks, granite, ceramic tiles, etc. Their work considered the effects of glazing mechanisms, material texture, color, laser process parameters and atmospheric conditions on the marking process. In this study, the heat effect of single pulse on eggshell by the commercially available finite element analysis (FEA) application ANSYS was explored. Besides, the temperature distribution of the eggshell and whether the high temperature damaged internal components of the egg (albumen or the yolk) were studied so that carrying out the marking of valid dates or fulfill other commercial purposes work of marking could be done. The digital image processing was made by carving characters on the brittle eggshell surface with the single pulse of the CO2 laser of infrared wavelength 10.6 ␮m, as shown in Fig. 1. The experimental results showed that the laser marking was successful on the brittle eggshell. Fig. 2 reveals the schematic diagram of characters that were stamped on the eggshell in ink. Compared with ink characters, laser effect was clearly recognized. In the ANSYS simulation, the initial temperature was set at 27 to explore the influence of the heat conduction. The result of the ANSYS simulation will be compared with the experimental outcome as well.

Fig. 2 – Traditional ink jet printing stamped on the eggshell surface.

2.

Theory and simulation

An egg is a complex structure. The egg content contains an air-chamber and a viscous liquid. Shells have diverse thickness, which consist of several layers with different material properties (Burley and Vadehra, 1989). Eggshell membranes are attached to the shell. In the simulation studies a more simplified model is used. The eggshell is set to have only one layer of shell structure and the thickness of the shell is assumed uniform over the whole eggshell surface. The egg content and shell membranes are not included in the model. The analysis was carried out using the ANSYS finite element software. The element type is SOLID70 that has a 3D thermal conduction capability. The element has eight nodes with a single degree of freedom, temperature, at each node. The element is applicable to a 3D, steady state or transient thermal analysis. Besides, the numerical analysis was assumed that a onedimensional heat flow, the thermal parameters are invariant with temperature, no phase change occurs during the laser pulse, and the eggshell has the greatest laser absorption of laser. The ANSYS heat analysis realized the heat state and the surface temperature of the eggshell. The damage and the influence were showed on internal eggshell during the laser pulse in reality.

2.1.

Fig. 1 – CO2 laser irradiated on the eggshell marked.

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Calculation of temperature distribution

The basic principle of FEM is to disassemble the complicated structure to a simple unit element. Sometimes only a simple equation is needed to describe the phenomenon of heat transmission. There are three types of heat transfers involved in eggshell marking with a laser: conduction, convection and radiation heat transfer. The absorbed beam energy is transformed into thermal energy through lattice vibrations in the material at the beam–material interaction zone. An increase in lattice vibration results in a rise in the temperature at that location. When the local temperature reaches the melting temperature, phase changes may occur. Some of the absorbed energy may be transferred to atoms in the eggshell interior through lattice vibration; this effect is called conduction heat transfer. Thermal energy may also be dissipated from the

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beam–material interaction zone to the environment under the influence of fluid flow; this interaction is called convection heat transfer. When the laser beam impinges on the surface of an eggshell, part of this radiant energy may be reflected back to the environment, transmitted into the eggshell interior, or absorbed by the surface. This interaction represents radiation heat transfer (Riley et al., 1997). The time of a pulse is very short (lus); hence, we neglect the effect of the convection and the irradiation. In the thermal analysis by ANSYS software of the laser marking on the eggshell substrate, the following assumptions are made:

tions. The solution is given as (Incropera and DeWitt, 1981): 2(1 − R)I T(z, t) = r2





Kd t k



z ierfc √ − ierfc 2 kt

z2 + r2 √ 2 kt

 (5)

where ierfc is the complementary error function (Riley et al., 1997): 1 2 ierfc(x) = √ e−x − x 

 1−

 2  √



x

 2

e−y dy

(6)

0

For the case of a single laser pulse, the temperature at the surface of the irradiated target solution is (1) The thermal properties are isotropic. (2) Laser beam intensity distribution is a TEM00 Gaussian mode. (3) The heating phenomena due to phase changes are neglected. (4) In the specimen, the heat conduction and thermal radiation in this research are neglected.

The mathematical representation of heat conduction in a solid assumes that a heat flux, ˚, develops across a plane and is proportional to the local temperature gradient (Incropera and De Witt, 1985): ˚(z) = −k

 dT 

(1)

dz

where k is the thermal conductivity of the material and z is the thickness. Using Eq. (1), the heat flow equation can then be written in its standard form (Incropera and De Witt, 1985): ∂ ∂z

 ∂T  k

∂z

=

Cp ∂T V ∂t

(2)

where Cp is the specific heat. The output of the laser can be described by Gaussian distribution (Von Allmen and Blastter, 1995):

q(x, y) =

2(1 − R)I exp r2



−2(x2 + y2 ) r2

 (3)

In this equation, q is the energy density reaches the film/sapphire interface, I is the peak energy of the incident laser light, R is the reflectance, and r is the radius of the beam spot. The incident beam irradiates the target surface at z = 0 then the heat-flow equation can be written as (Von Allmen and Blastter, 1995): ∂T q(x, y) K ∇2T + ∂t d Cp

(4)

where the thermal diffusivity Kd = k/pCp . The heat equation can then be solved analytically assuming the thermal and optical parameters are invariant with temperature. A wellknown approach to solve the heat conduction Eq. (4), given its boundary and initial condition, is by the use of Green’s func-

2(1 − R)P T(0, t) = k



Kd t 

(At the center of the spot)

(7)

The above synthesis can serve as the basis of the temperature distribution and surface temperature after laser irradiation on the object. If the beam goes through about 10−2 ␮m deep, most of the laser energy could be desorbed and switched to heat. Supposed the percentage of the eggshell absorption to the wavelength of the CO2 laser (10.6 ␮m) is 100% (Ion, 2005), the heat influence under the greatest absorptivity can be analyzed.

2.2.

The steps of ANSYS

As to the finite element analysis, the relations among boundary condition, loading model and temperature are discussed. There are three analyzing steps in ANSYS: (1) preprocessors, (2) solution processors and (3) postprocessors. Preprocessors include two main steps: (1) modeling and (2) meshing. The analytical modeling approach assumes temperature independent properties. The thermal properties of the eggshell are the variables p, k, and Cp which represent the density, thermal conductivity and specific heat. They are set to be 930 kg/m3 , 2100 J/(kg ◦ C) and 2.25 W/(m ◦ C), respectively (Denys et al., 2003, 2004). The influences of the phase transform could be ignored. Eggshell thickness is assumed to be uniform over the shell surface. A default value of 400 ␮m is applied. In the simulation of laser irradiation, the grid size of the element unit is 0.1 mm which is one-third of the spot radius, which makes the laser region and the heat-affected zone maintain sufficient density of grids. On the other hand, in the region far away from laser, a larger size of grids was used to reduce calculating time. Fig. 3(a) and (b) shows the established 3D model and denser mesh of eggshell by ANSYS. In solution processors, the boundary conditions and the load of the material are as follows. The initial temperature is 27 ◦ C, the frequency of laser pulse is 1 kHz, the operating time is 1 ms, and a function-editor was employed to define the Gaussian heat source. The heat flux was indicated the laser source to act on the surface. The temperature variation at the eggshell is simulated by a transient form and the full Newton–Raphson method was used to accelerate the convergence rate. The thermal conductivity of eggshell is 2.25 K(W/m k). The ANSYS program calculated the temperature distribution with every 0 s up to an ending time of 1 ms,

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Fig. 3 – The established 3D model of eggshell by ANSYS. (a) The half of eggshell model has been meshed and (b) the portion of the model with denser mesh.

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Fig. 5 – CO2 laser marking system.

and the results are helpful in the understanding of temperature distribution and heat effect of the laser light on the eggshell surface. Postprocessors mainly collect and analyze many data in the process and each datum represents a time point of reacted outputs. The post-processing module is used to deal with data in the spatial distribution of the certain time point. The basic commands include the reading of data, the numerical solution, the graphical output and the creation of action graphs.

3.

Experimental

Laser marking is the work of the processing which transforms radiant energy to thermal energy by irradiating and vaporizing on the eggshell surface. To engrave patterns and characters, laser source must get higher energy. Ways of operating laser marking are labeled primarily. CO2 pulse laser, made by the Coherente Company, applied the highly stable power of 100 W. The beam diameter is 6 mm; illuminant mode is TEM00 ; the diameter of the beam spot is 0.6 mm; repeated frequency is 1 kHz, and the wavelength is 10.6 ␮m. The processing system

Fig. 6 – Heat affected area of laser irradiation on the surface of the eggshell by SEM. There were some cracks around the hole after laser radiation. The diameter of the maximum affected area is approximate ∼300 ␮m.

is composed of a PC control, the laser source and the X–Y scanner. Fig. 4 shows the schematic illustration of the system. A mark imported to the computer program transforms the shape to working coordinates. The laser source and the X–Y scanner will correspond to the working coordinates to scan a mark on the eggshell surface. The high-speed laser processing system is applied. The degree of precision and the cost are between arrays and mask marking. CO2 laser marking system is shown in Fig. 5. After the experiment, the surface morphology of the brittle eggshell was observed by the scanning electron microscope (SEM), shown in Fig. 6.

4.

Fig. 4 – Configuration of the pulsed CO2 laser marking system.

Results and discussion

There were no breaks at the eggshell but some cracks around the hole close to the circle after laser radiation. The formed hole could be divided into two parts. The central part was made by laser pulse. The damage and cracks, around the center, were caused by Gaussian distributed energy which was not strong enough to melt the material to form a hole. Other regions were kept smooth without laser irradiation. The energy of the laser irradiation needs high stability to achieve

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Fig. 7 – The eggshell surface formed the circular temperature distribution due to Gaussian radiation.

Fig. 8 – Cross-section of the temperature distribution with the single pulse simulated temperature profiles for thermal processes of the eggshell.

the demanded output of energy in the working mode. If the energy density is high enough, only the surface of the material will be vaporized; if too low, the energy is going to spread, which makes the melting depth shallow (Tan et al., 2003; Peligrad et al., 2001). So, the surface is used to simulate the surface of the eggshell with the thermal characteristics equation of the superficial heat source. The luminous intensity has decreased to 13% of its axial value and the relative radius is Gaussian beam radius. It forms the Gaussian distribution while the Gaussian laser acts on the surface. After laser beam illuminated, a portion of this irradiated energy may be reflected back to the environment, absorbed by the surface, or transmitted into the eggshell inner. The inner increases the temperature rapidly because its reflectance reduced and absorption increased. The central temperature of the spot reached the decomposition temperature of eggshell and thus caused superficial carving traces with cracks surrounding the spot, shown in Fig. 6. In the top view photography shows the heat-affected zone of laser irradiation on the surface of the eggshell. It can be seen the Gaussian dis-

Fig. 9 – The relationship between the temperature and different depths of the eggshell.

tribution of the laser irradiation area. When it comes to high intensity irradiation (∼108 W/cm2 ), a large density of carriers will build up before the lattice is appreciably heated. After the pulse ends, these high intensities may cause plasma formation and melting status around the irradiated surface. In the simulation, the eggshell surface formed the circular temperature distribution due to Gaussian radiation as shown in Fig. 7. It revealed that the highest temperature is in the central region of the spot and heat-conduction cause that the heated area goes beyond the spot diameter. The result is similar to experimental outcome. Fig. 8 displays cross-section of the temperature distribution with the single pulse. It showed that the center temperature of the spot reached 1779 ◦ C. It revealed the temperature distribution of the profile and the temperature approached a room temperature over 110 ␮m of the depth, which means the heating influence could not cause

Fig. 10 – Temperature distributions of the inner eggshell irradiated at time is from 0 s to 0.5 s. The light blue line, the purple line, the red line, the blue line, and the pink line indicated surface, 50 ␮m-depth, l00 ␮m-depth, 200 ␮m-depth, and 300 ␮m-depth of temperature distributions, respectively. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of the article.).

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account for one-tenth of the total thickness and the width is around 150 ␮m.

5.

Fig. 11 – After laser irradiated, cross-section of the eggshell by SEM.

damage to the inner or even makes it spoil with high temperature. The function of temperature and depth is shown in Fig. 9. It is easy to observe the variation of the temperature in different depths. After 0.15 s later, the temperature of the heating region lowered to room temperature at the eggshell surface which was heated by laser as shown in Fig. 10. It revealed that all lines of temperature distributions declined to almost room temperature over 0.3 s. That means the laser-generated heat is only slightly affected for the eggshell. The cross-section of the eggshell is observed to measure the depth after laser light. It is compared with ANSYS simulation so that they may be found out whether the result of the experiment matches the theory. Fig. 11 shows the thickness of the eggshell is approximately 400 ␮m and the depth of the hole is approximately 47.1 ␮m. Carving depth is around 10–15% of the profile due to the single pulse of laser. The eggshell is composed of 96–97% of calcium carbonate (Burley and Vadehra, 1989) whose decomposition temperature is 894 ◦ C (Anon., 2008). The elements are removed when the temperature is over 894 ◦ C in the temperature distribution, as shown in Fig. 12. Besides, there is no harm in the inner of the eggshell, which matches the result of the ANSYS simulation. The depth of the hole made after laser light was simulated to

Fig. 12 – The ANSYS simulated the cross-section after the laser irradiated.

Conclusions

In this study, marking characters made use of the CO2 laser processing system on the brittle eggshell and simulated the heat effect on the surface by ANSYS program to confirm the reliability of the processing system. The simulation results present the temperature distribution field. The width and the depth of hole are similar to those measured from SEM. The area affected by heat accounts for one-fourth of the total thickness of the eggshell, which does not lead to the deterioration of the inner. Also, it can be observed that there is harmless done to the inner from SEM. Furthermore, the way which stamped the characters in ink may result in permeation of the ink, but there is no similar doubt to adopt the laser. Marking the date by laser on the egg takes only half second; which is less than overlaying ink, but the quality of the products and human health are far more guaranteed. Hence, by utilize laser marked on eggshell cannot damage the inner surface of eggshell. In addition, by using laser irradiation and inking method can be shown in Figs. 1 and 2. Because of inking method make use of organic compounds that can cause pollution of the environment.

Acknowledgement This research was financially supported by the National Science Council of the ROC under grant NSC94-2212-E-018-002.

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