Measurement of the mechanical properties of brightness enhancement films (BEFs) for LCDs by optical interferometry

Displays 30 (2009) 140–146

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Measurement of the mechanical properties of brightness enhancement films (BEFs) for LCDs by optical interferometry Lu-Ping Chao a, Jiong-shiun Hsu b,*, Wen-Chin Tsai c, Ming-Chi Chen a a

Department of Mechanical and Computer Aided Engineering, Feng Chia University, Taichung 40724, Taiwan Department of Power Mechanical Engineering, National Formosa University, Yunlin 63208, Taiwan c Institute of Mechanical and Aeronautical Engineering, Feng Chia University, Taichung 40724, Taiwan b

a r t i c l e

i n f o

Article history: Received 27 October 2007 Received in revised form 20 February 2009 Accepted 11 March 2009 Available online 20 March 2009 Keywords: Brightness enhancement film (BEF) Liquid crystal displays (LCDs) Mechanical properties Micro tensile test Optical interferometry

a b s t r a c t The brightness enhancement film (BEF) is one of the important components in the liquid crystal displays (LCDs). Since the thicknesses of BEFs are very less, it increases the difficulty to measure their mechanical properties. In this paper, we successfully propose a methodology by combining the micro tensile test and optical interferometry to characterize Young’s moduli and Poisson’s ratios of BEFs. In addition, the thermal and hygrothermal effects on the mechanical properties of BEFs were also investigated. The finite element analysis (FEA) was utilized to verify the precision of our proposed methodology. The results show that Young’s moduli of BEFs are influenced by temperature and humidity whereas Poisson’s ratios of BEFs are less influenced by temperature and humidity. Ó 2009 Elsevier B.V. All rights reserved.

1. Introduction The BEF is one of important components in LCDs and it is made from the polymer. It is well known that the common disadvantage of polymer is that its mechanical properties are quite unstable. The environments in which LCDs may be operated are elevated temperature and/or high humidity especially for the island countries during summer. The mechanical properties of constituent components in LCDs are unavoidably distinct and the elements in LCDs are in narrow contact. From the viewpoint of mechanics, large deformation of the elements in LCDs may have arisen due to the significant mismatch of mechanical properties between the constituent components in LCDs. Therefore, the considerable deformation of BEFs could possibly lead to poor display quality of LCDs but attention has not been paid on this issue no matter in industrial or academic research. Moreover, Young’s modulus and Poisson’s ratio are the most fundamental properties in mechanics investigation. However, from the viewpoint of experimental mechanics, it has to be emphasized that Young’s modulus and Poisson’s ratio of BEFs are difficult to be measured because they are less thick and are not stiff. For this reason, the aim of this paper is to propose a methodology to characterize Young’s modulus and Poisson’s ratio of BEFs in LCDs such that further investigation on the display quality of

* Corresponding author. Tel.: +886 5 6315409; fax: +886 5 6312110. E-mail address: [email protected] (J.-s. Hsu). 0141-9382/$ - see front matter Ó 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.displa.2009.03.004

LCDs resulting from the mismatch of mechanical properties between the components in LCDs is possible. In the published literature, the investigation on the mechanical properties of the BEFs is very limited. Kim [1] investigated the effect of relative humidity and stiffness on the warpage of a poly methyl methacrylate (PMMA) diffusing plate modified with glass fibers in a direct-lit BLU of an LCD. Kim et al. [2] investigated the effect of water absorption and thermo-physical properties on the warpage of a diffusing plate fabricated with poly ethyleneterephthalate polycarbonate/polybutyleneterephthalate copolymer in a direct-lit BLU of an LCD. Because the BEFs are less thick and are not stiff, it increases the difficulty to experimentally measure their mechanical properties. In this paper, we first proposed a methodology combining the micro tensile test and optical interferometry to characterize Young’s modulus and Poisson’s ratio of the BEFs (BEF II 95/50, 3 M). The micro tensile test was first employed to directly measure Young’s modulus. Traditionally, Poisson’s ratio of a material is usually measured using the tensile test with the aid of the strain gauge. However, as the BEFs are less thick the strain gauge is not appropriately used to measure their Poisson’s ratio. For this reason, we combine the micro tensile test and optical interferometry to individually measure Young’s modulus and Poisson’s ratio of the BEFs. For optical interferometry, the traditional electronic speckle pattern interferometry (ESPI) and amplitude fluctuation ESPI (AF-ESPI) were successively adopted to experimentally measure the resonant frequencies and the corresponding mode shapes of the circular BEFs with clamped boundary. Poisson’s

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ratio of the BEFs can be obtained from the experimental result of optical interferometry along with the vibration theory of a circular film with clamped boundary. To verify the accuracy of the proposed methodology, the measurement results were, respectively, substituted into a numerical model based on the finite element analysis (FEA) and the above-mentioned vibration theory to compare their difference of resonant frequencies and mode shapes with those of the experimental results. Finally, the thermal and hygrothermal effects on the mechanical properties of the BEFs were also investigated. ESPI was proposed by Butter and Leendertz [3] in 1971. Owing to its non-contact, full-field, and highly sensitive characteristics, ESPI has been widely used in many categories [4–7]. Although the EPSI can be utilized to measure both the static and vibration behaviors of the objects, the contrast of traditional ESPI fringe pattern needs to be improved for the vibration measurement. To overcome this drawback of the traditional EPSI, based on the concept of amplitude fluctuation of a vibration object, Wang et al. [8] proposed the AF-EPSI to not only enhance the contrast but also increase the sensitivity of the traditional EPSI fringe pattern. Due to the aforementioned advantages of AF-ESPI, it has been used to study the different vibration problems [9–13]. It should be emphasized that the exciting sources of the vibration in Refs. [9–13] were generated by a shaker which was attached to the surface of the specimen. The vibration excited by a shaker may be appropriate to investigate the specimen with high stiffness and mass such as those studied in Refs. [9–13]. However, as it is known that both stiffness and mass of the BEFs are quite small, it means that the vibration of the BEFs excited by a shaker is inappropriately adopted to measure their vibration characteristics. To increase the measurement precision, we apply an acoustic speaker to provide the vibration source of the BEFs instead of the contact exciting method. Because the vibration of the BEFs was excited by an acoustic speaker through air transmission, the vibration characteristics and the measurement results of the BEFs are not influenced by the exciting source. 2. Theoretical background 2.1. Theory of micro tensile test A methodology is proposed herein to measure the mechanical properties of the BEFs. The micro tensile test was first employed to directly measure Young’s modulus of the BEFs. The principle of micro tensile test is to apply a tensile force on the BEFs with the geometry depicted in Fig. 1 by a micro tensile testing machine. The elongation (d) and applied load (F) are recorded by the micro tensile testing machine. From the definition of strain (e) and stress (r), we have

d L F r¼ A

e¼

where L is the gauge length and A is the cross-sectional area of the tested specimen. Suppose the behavior of the tested material is linear elastic when the load is applied, then Eqs. (1) and (2) satisfy Hooke’s law, i.e.

E¼

r e

ð3Þ

where E is Young’s modulus of the tested material. Thus, Young’s modulus of the tested material can be calculated from the slope of the fitting curve for the relation between stress and strain obtained in the experiment. 2.2. Theory of ESPI 2.2.1. Theory of traditional ESPI The out-of-plane ESPI was used to characterize the transverse vibration characteristics of BEFs. The schematic of the experimental arrangement of ESPI is illustrated in Fig. 2. A 35 mW He–Ne laser (Coherent Inc.) with 633 nm wavelength was used as the light source. The laser beam was expanded and the noise filtered out by the spatial filter. Then the laser beam was divided into two beams through a beam splitter, object beam and reference beam. The object beam was reflected by the BEF, and the reference beam was reflected by the reference plate. Then the two beams are interfered on the chip of the CCD camera, and the ESPI fringe pattern can be observed on the monitor. For the traditional ESPI, the fringe pattern is obtained by subtracting the speckle images before and after deformation. When the BEF is static, the light intensity captured by the CCD camera (IA) is

pffiffiffiffiffiffiffiffi IA ¼ I1 þ I2 þ 2 I1 I2 cosð/Þ

pffiffiffiffiffiffiffiffi IB ¼ I1 þ I2 þ 2 I1 I2 J 0 ðXAÞ cos /

pffiffiffiffiffiffiffiffi IT ¼ 2 I1 I2 ½J0 ðXAÞ  1 cos /

Unit: mm

Gripped region

10

Gripped region

Fig. 1. The specimen geometry of the micro tensile test.

ð5Þ

where J0 is the first kind Bessel function with zero order, X ¼ 2kp ðcos h1 þ cos h2 ÞðA cos xtÞ, where k is the wavelength of the laser beam, h1 is the reflected angle of the object beam, h2 is the reflected angle of the reference beam, and A is the vibration amplitude of the BEF. It can be seen in Fig. 2 that h1 and h2 are both to zero degree. After subtracting the light intensity before and after deformation of BEF, the light intensity of the fringe pattern for the traditional ESPI (IT) is

ð2Þ

50

ð4Þ

where I1 is the light intensity of the object beam, I2 is the light intensity of the reference beam, and / is the initial phase difference between the object and reference beams. When the BEF is harmonically vibrated by the acoustics speaker through air transmission, the light intensity (IB) is

ð1Þ

10

141

Fig. 2. The schematic of experimental arrangement of ESPI.

ð6Þ

142

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2.2.2. Theory of AF-ESPI Since the fringe pattern of traditional ESPI used for vibration measurement is not clear, Wang et al. [8] proposed the AF-ESPI to not only improve the contrast of the fringe pattern but also to increase its sensitivity. The optical arrangement of AF-ESPI is identical to that of traditional ESPI (Fig. 2). However, two speckle images are successively captured while the BEFs are under vibration. When the BEFs are harmonically vibrated, the light intensity of the first image for AF-ESPI is identical to Eq. (5). Although the second image of AF-ESPI is also captured under the same condition as the first image, the intensities of two images are distinct due to the amplitude fluctuation phenomenon [8]. The light intensity of the second image for AF-ESPI (IAF2) is

pffiffiffiffiffiffiffiffi IAF2 ¼ I1 þ I2 þ 2 I1 I2 J 0 ðXðA þ DAÞÞ cos /

IAF ¼

x

n

0 1 2 3

0

1

2

3

3.196 6.306 9.440 12.577

4.611 7.799 10.958 14.108

5.906 9.197 12.402 15.579

7.143 10.537 13.795 17.005

where k is an arbitrary constant, Jn(kr) and In(kr) are, respectively, first and second kind Bessel functions both with nth order. Details about the deduced processes can be found in Ref. [14]. 3. Experiment 3.1. Experiment of micro tensile test

½J 21 ð

1=2

XAÞ cos u

ð8Þ

where x is the circular frequency of BEF, and J1 is the first kind Bessel function with first order. 2.3. Vibration theory of a circular film In the EPSI experiment, a circular BEF film with clamped boundary was excited by the acoustic speaker through air transmission. The vibration theory for this film configuration is available [14]. Geometrical configuration of the circular film with clamped boundary is illustrated in Fig. 3. The equation of motion for free vibration of the film is

Dr4 w þ qh

m

ð7Þ

where DA is the amplitude fluctuation. Therefore, the light intensity of the fringe pattern for AF-SPI (IAF) is

pffiffiffiffi 2 Io Ir

Table 1 The values of kmn used in the vibration theory of a circular film.

@2w ¼0 @t2 2

Regarding the experiment of micro tensile test, the BEFs were first prepared in the dimensions following the suggestion in the ASTM D-822-02 [15], and its geometrical configuration is shown in Fig. 1. After the preparation of the BEF according to the prescribed geometry, it was gripped by the jigs of the micro tensile testing machine (Tytron 250, MTS Inc.). Then the tensile force was applied, and the displacement and the applied load were simultaneously recorded by the micro tensile testing machine.

ð9Þ 2

3

1 @ðÞ 1 @ ðÞ Eh where r2 ðÞ ¼ @@rðÞ ; D ¼ 12ð1 2 þ r @r þ r 2 m2 Þ, E is Young’s modulus, @h2 m is Poisson’s ratio, h is thickness, w is the transverse displacement, q is density, and t is time. The derivation of the vibration theory aims to express the resonant frequencies and their corresponding mode shapes. After some derivation, the resonant frequency (fmn) can be expressed as

fmn

ðkaÞmn ¼ 2pa2

sffiffiffiffiffiffi D qh

ð10Þ Fig. 4. Photography of the bonded configuration of BEF.

where a is the radius of the BEF film, and the values of (kmn) are listed in Table 1. In addition, the mode shape (w(r, h)) can be deduced as

  J ðkaÞ wðr; hÞ ¼ k J n ðkrÞ  n In ðkrÞ cos nðh  /Þ In ðkaÞ

3.0

ð11Þ

2.5

Experimental data Fitted curve

Stress (MPa)

2.0

y

1.5

1.0

P r

0.5

x a BEF film Fixed region

Fig. 3. Geometrical configuration of the circular film with clamped boundary.

0.0 0.0000 0.0002 0.0004 0.0006 0.0008 0.0010 0.0012 0.0014 0.0016 0.0018

Strain (mm/mm) Fig. 5. The experimental result of stress–strain relation of the virgin BEF obtained from micro tensile test.

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For the experimental setting, the acquisition frequency of experimental data is 10 times/s, and the maximum load and displacement are smaller than 4 N and 0.1 mm, respectively. The relation between the stress and strain had been addressed in the theoretical description of the micro tensile test. Finally, Young’s modulus of BEFs can be calculated from the slope of the fitting curve for stress versus strain relation. Young’s moduli of five pieces of BEFs were

Table 2 The measurement results of mechanical properties of the BEFs. Type of BEF

Virgin Thermo Hygrothermo

Properties Density (kg/m3)

Young’s modulus (MPa)

Poisson’s ratio

234.9 229.4 235.0

1549.20 ± 4.29 1427.28 ± 4.32 1407.90 ± 4.64

0.408 ± 0.005 0.405 ± 0.005 0.406 ± 0.007

143

measured, and their results are averaged to represent Young’s modulus of BEF. 3.2. Experiment of optical interferometry So far, Young’s moduli of BEFs have been directly measured through the micro tensile test. The optical interferometry was used herein to characterize Poisson’s ratio of BEFs. Since Poisson’s ratio of BEFs will be measured by characterizing the vibration characteristics of BEFs, the density of BEFs has to be measured before carrying out the optical experiment. For the density measurement of BEFs, a piece of BEF with dimensions of 1 cm  cm was first prepared, and its mass was measured by a precise electronic balance (Sartorius Co.). When the weight of the prepared BEF was obtained, it was placed into the chamber of the pycnometer (AccuPyc 1330, Micromeritics Instrument Co.) to measure its density. The helium gas was then supplied to pressurize the chamber until the

Fig. 6. The mode shapes of the virgin BEF obtained from AF-ESPI: (a) 1st mode, (b) 2nd mode, (c) 3rd mode, (d) 4th mode, (e) 5th mode, and (f) 6th mode.

144

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equilibrium pressure was achieved. The volume of the BEF can be measured based by the ideal gas equation. Finally, the density of BEFs can be calculated from the obtained volume and mass. Regarding the experiment of optical interferometry, an aluminum alloy frame with a central hole of 40 mm diameter was first manufactured. A circular BEF with 63 mm diameter was prepared, and it was bonded to the surface of the aluminum alloy frame using adhesive (Anylok N-545X AB, EuroSun Inc.). Photography of the bonded configuration is shown in Fig. 4. After one day, the adhesive was completely cured, and optical interferometry was employed to measure Poisson’s ratio of BEF. The experimental arrangement is illustrated in Fig. 2. The traditional ESPI was first carried out to measure the resonant frequencies of BEFs. Prior to vibration, a reference speckle image was grabbed and stored by the digital image board (Meteor II Standard, Matrox Inc.). The BEF was excited by the acoustics speaker through air transmission. The exciting frequency of the acoustics speaker was controlled by the function generator (33220A, Agilent Technologies Co.), and the exciting amplitude was adjusted by the amplifier (Baiontz Co.). The image was continuously grabbed by the digital image board, and the image was continuously subtracted from the reference image. The ESPI fringe pattern can be observed real-time on the monitor. Next, the exciting frequency of the acoustics speaker was gradually increased, and therefore the ESPI fringe pattern varies with the exciting frequency. It is known that the vibration amplitude of an object significantly increases when the exciting frequency is equal to the resonant frequency. For this reason, the resonant frequencies of BEFs were determined when the fringe pattern displayed on the monitor suddenly increases. After the resonant frequencies of BEFs were measured by the traditional ESPI, the AF-ESPI was employed to obtain the corresponding mode shapes. The BEFs were continuously vibrated by the acoustics speaker under the same resonant frequency. Two speckle images were successively grabbed and subtracted from each other, and the mode shape of the BEFs was then obtained by AF-ESPI. In this paper, the resonant frequencies of BEFs and their corresponding mode shapes for the first six modes are measured. After completing the optical interferometry experiment, the resonant frequencies of BEFs for the first six modes were obtained. The only one unknown in Eq. (10) is Poisson’s ratio. Poisson’s ratio of BEFs can be obtained by substituting the resonant frequencies into Eq. (10). Because the resonant frequencies of BEFs for the first six modes were, respectively, measured, the six values of Poisson’s ratio were thus obtained for one BEF. These six values were then averaged to represent Poisson’s ratio of BEFs measured by the proposed methodology.

according to the dimensions depicted in Figs. 1 and 4 for the micro tensile test and optical experiment. Finally, the measurement results were compared to investigate the influence of heat and humidity on the mechanical properties of BEFs. 4. Result and discussion The experimental result of stress–strain relation of the virgin BEF obtained from micro tensile test is shown in Fig. 5 in which the curve between the stress and strain is quite linear. Young’s modulus of BEFs can be calculated from the slope of the fitting line indicated in the figure. In fact, the experimental results of BEFs after both the thermal and hygrothermal treatments are close to linear and it can be shown that the magnitude of the applied load in the micro tensile test does not exceed the yield stress of BEFs. The measurement results of Young’s modulus of BEFs are listed in Table 2 and the micro tensile test is valid for the measurement of Young’s modulus of BEFs due to the small uncertainty in the table. It can also be seen in Table 2 that Young’s modulus of the BEFs decreases when subjected to thermal environment. Furthermore, Young’s modulus of the BEFs significantly decreases when the BEFs are subjected to both the elevated temperature and high humidity environments. For the measurement results of ESPI for the BEFs,

Table 3 The comparison of resonant frequencies from different approaches. Type of BEF

Mode

ESPI (Hz) (A)

FEA (Hz) (B)

Theory (Hz) (C)

(A  B)/A (%)

(A  C)/A (%)

Virgin

1st 2nd 3rd 4th 5th 6th

555 1150 1158 1889 1898 2177

554 1152 1152 1885 1885 2151

555 1155 1155 1895 1895 2161

0.211 0.174 0.518 0.233 0.706 1.181

0.0006 0.4476 0.2444 0.3240 0.1507 0.7556

Thermo

1st 2nd 3rd 4th 5th 6th

539 1118 1124 1835 1841 2083

538 1119 1119 1831 1831 2090

539 1122 1122 1841 1841 2099

0.197 0.080 0.454 0.248 0.570 0.311

0.0059 0.3565 0.1779 0.3107 0.0521 0.7386

Hygrothermo

1st 2nd 3rd 4th 5th 6th

529 1101 1107 1801 1809 2042

528 1098 1098 1796 1796.2 2050.4

529 1101 1101 1807 1807 2060

0.214 0.272 0.813 0.267 0.708 0.410

0.0104 0.0209 0.5212 0.3127 0.1299 0.8574

3.3. Experiment of thermal and hygrothermal investigation A methodology combining the micro tensile test and ESPI is proposed to individually measure Young’s modulus and Poisson’s ratio of BEFs. The experimental procedures were described in the aforementioned sections. On the other hand, people often place their notebook, cell phone, etc. inside the vehicle, and the temperature behind the window of the vehicle may rise to 90 °C during summer. Moreover, the humidity is significant in some regions especially in island countries, even up to 90% RH. To understand the effect of heat and humidity on the mechanical properties of BEFs, the proposed methodology was also performed to investigate this issue. The experimental procedures of the proposed methodology were previously addressed for the virgin BEF. Furthermore, for the thermal investigation, the BEFs were first placed into an oven with 90 °C for 24 h. For the hygrothermal investigation, the BEF was first placed into an oven with 90 °C and 90% RH for 24 h. After the thermal and hygrothermal treatments, the BEFs were cut

Fig. 7. The FEA meshed diagram.

L.-P. Chao et al. / Displays 30 (2009) 140–146

the resonant frequencies and the corresponding mode shapes of the virgin BEF are shown in Fig. 6. The white dotted lines indicated in the figure denote the region where zero displacement occurs. Since the boundary condition of circular BEFs is fixed, the circular white dotted line always appears on the boundary of BEFs among the different mode shapes shown in Fig. 6. To more clearly visualize the mode shape, the signs ‘‘+” and ‘‘” are marked in the ESPI fringe patterns such that the vibration phase of BEFs can be distinguished. It can be observed in Fig. 6a that the vibration of the first mode is in-phase in the interior region of BEF and the contour is in concentric fashion. Regarding the second mode, the vibration of BEF can be divided into two parts by the nodal line across the circular BEF indicated in Fig. 6b and the vibration in these two regions is out-of-phase. The shape of the third mode is similar to that of the second mode but the orientation is approximately rotated by about 90° (Fig. 6c). On the other hand, as can be seen in Fig. 6d, the vibration of the fourth mode can be divided into four regions by two

145

approximately orthogonal nodal lines and the vibration in the neighboring regions is out-of-phase. The shape of the fifth mode is similar to that of the fourth mode but the orientation is rotated by a small angle (Fig. 6e). For the sixth mode, a circular nodal line appears in the interior region of the BEF (Fig. 6f) and the vibrations are out-of-phase in the regions inside and outside the circular nodal line. Moreover, because the mode shapes of BEFs for the thermal and hygrothermal investigations are very similar to those of the virgin BEF, their mode shapes are not shown here. The resonant frequencies of BEFs obtained by ESPI are listed in Table 3. It can be seen that the elevated temperature would decrease the resonant frequencies. Furthermore, the resonant frequencies decrease further after the BEF is placed in both elevated temperature and high humidity conditions. To calculate Poisson’s ratio, the resonant frequencies of the first six modes of BEFs obtained by ESPI experiment are successively substituted into Eq. (10). The calculated results of Poisson’s ratio are also listed in Table

Fig. 8. The mode shapes of the virgin BEF obtained from FEA (a) 1st mode, (b) 2nd mode, (c) 3rd mode, (d) 4th mode, (e) 5th mode, and (f) 6th mode.

146

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2. It was found that Poisson’s ratio of BEFs is less influenced by temperature and/or humidity. So far, the proposed methodology was demonstrated to measure Young’s modulus and Poisson’s ratio of BEFs used in LCDs and the influence of thermal and hygrothermal effects on the mechanical properties of BEFs was investigated. To verify the accuracy of the proposed methodology, the numerical approach based on FEA was employed to construct the simulation model. The commercially available software, ANSYS, was utilized and the Shell 63 [16] element was used to mesh the numerical model. The meshed diagram is shown in Fig. 7, and the number of the elements is 704. The mechanical properties listed in Table 2 were substituted into the numerical model. The resonant frequencies and their corresponding mode shapes obtained from the FEA are compared with those of the ESPI results to ensure the precision of the proposed methodology. Moreover, the mechanical properties listed in Table 2 were also substituted into the vibration theory addressed previously to re-examine the appropriateness of the adopted theory. Fig. 6 shows the mode shapes of the virgin BEF obtained from FEA. Comparing Fig. 6 with Fig. 8, the mode shapes obtained from FEA are similar to those of the ESPI fringe patterns. Both the resonant frequencies of BEFs obtained from FEA and the vibration theory are listed in Table 3. It can be seen that the resonant frequencies obtained from FEA and vibration theory are close to those obtained from the ESPI experiment. In addition, it should be noticed that the resonant frequencies of second and third modes are the same for both FEA and vibration theoretical results. This is because this vibration problem is an eigenvalue and eigenvector problem. The resonant frequencies are eigenvalues and their corresponding mode shapes are eigenvectors. The second and third eigenvalues of this vibration problem are the repeated roots and thus the resonant frequencies of second and third modes are the same. Although the second and third eigenvalues of this vibration problem are the repeated roots, their corresponding mode shapes are different. This is the reason that the resonant frequencies of second and third modes are identical in Table 3 but their mode shapes are distinct in Fig. 6. As can be seen in Table 3 and Fig. 6, the same phenomenon also occurs for the fourth and fifth modes. Finally, in Table 3, the maximum difference between the ESPI and FEA is less than 1.2%, and the maximum difference between the ESPI and the vibration theory is less than 1%. The correctness of the proposed methodology is therefore verified. 5. Conclusions In this paper, we successfully proposed a methodology combining the micro tensile test and optical interferometry to characterize the mechanical properties, Young’s modulus and Poisson’s ratio, of BEFs used in LCDs. The FEA was employed to demonstrate that our proposed methodology can be precisely used to measure the mechanical properties of BEFs used in LCDs. The proposed technique was also performed to investigate the thermal and hygro-

thermal effects on the mechanical properties of BEFs. The results reveal that Young’s moduli of BEFs decrease with increasing environmental temperature. It should be emphasized that Young’s moduli of BEFs significantly decrease while they are simultaneously subjected to elevated temperature and high humidity environments. On the other hand, Poisson’s ratios of BEFs are less influenced by temperature or humidity. Because the components in LCD are in narrow contact, the display quality of LCD may be degraded due to the mismatch of mechanical properties between the components within the LCD. The proposed methodology is applicable to measure the mechanical properties of BEFs and to understand the effect of the environment on the mechanical properties. The obtained properties of BEFs can be further investigated to understand the degree of mismatch between the BEF and other components within the LCD such that the display quality of the LCD could probably be improved or controlled through mechanics. References [1] G.H. Kim, A PMMA composite as an optical diffuser in a liquid crystal display backlighting unit (BLU), European Polymer Journal 41 (2005) 1729–1737. [2] G.H. Kim, W.J. Kim, S.M. Kim, J.G. Son, Analysis of thermo-physical and optical properties of a diffuser using PET/PC/PBT copolymer in lcd backlight units, Displays 26 (2005) 37–43. [3] J.N. Butter, J.A. Leendertz, Holographic and video techniques applied to engineering measurement, Journal of Measurement and Control 4 (1971) 349–354. [4] S.J. Huang, H.L. Lin, H.W. Liu, Electronic speckle pattern interferometry applied to the displacement measurement of sandwich plates with two fully potted inserts, Composite Structures 79 (2007) 157–162. [5] L. Yang, P. Zhang, S. Liu, Measurement of strain distributions in mouse femora with 3D-digital speckle pattern interferometry, Optics and Lasers in Engineering 45 (2007) 843–851. [6] F. Labbe, Strain-rate measurements by electronic speckle pattern interferometry (ESPI), Optics and Lasers in Engineering 45 (2007) 827–833. [7] P. Sun, The separation of out-of-plane displacement from in-plane components by Fringe carrier method based on large image-shearing ESPI, Optics Communications 275 (2007) 305–310. [8] W.C. Wang, C.H. Hwang, S.Y. Lin, Vibration measurement by the time-averaged electronic speckle pattern interferometry method, Applied Optics 35 (1996) 4502–4509. [9] W.C. Wang, C.H. Hwang, Experimental analysis of vibration characteristics of an edge-cracked composite plate by ESPI, International Journal of Fracture 91 (4) (1998) 311–321. [10] W.C. Wang, Y.H. Tsai, Experimental vibration of the shadow mask, Optics and Lasers in Engineering 30 (6) (1998) 539–550. [11] W.C. Wang, J.S. Hsu, Investigation of the size effect of composite patching repaired on edge-cracked plates, Composite Structures 49 (2000) 415–423. [12] C.H. Huang, C.C. Ma, Y.C. Lin, Theoretical, numerical and experimental investigation on resonant vibrations of piezoceramic annular disks, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control 52 (8) (2005) 1204–1216. [13] C.H. Huang, Inverse evaluation of material constants for piezoceramic rectangular plates by out-of-plane vibration, AIAA Journal 44 (7) (2006) 1411–1418. [14] S. Werner, Vibration of Shells and Plates, Marcel Dekker, New York, 1936. [15] Annual Book of ASTM Standards, American Society for Testing and Materials, 2005. [16] ANSYS 7.1 User’s Manual, ANSYS Inc., Southpointe, Canonsburg, PA, USA, 2004.