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Microelectronics Reliability 53 (2013) 1996–2004

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Optimization of flexible printed circuit board electronics in the flow environment using response surface methodology W.C. Leong ⇑, M.Z. Abdullah, C.Y. Khor School of Mechanical Engineering, Universiti Sains Malaysia, Engineering Campus, 14300 Nibong Tebal, Penang, Malaysia

a r t i c l e

i n f o

Article history: Received 27 March 2013 Received in revised form 12 June 2013 Accepted 14 June 2013 Available online 4 July 2013

a b s t r a c t A flexible printed circuit board (FPCB) is flexible, thin and lightweight; however, FPCBs experience more deflection and stress in the flow environment because of fluid–structure interaction (FSI), which affects their performance. Therefore, the present study focuses to optimize a typical FPCB electronic in order to minimize the deflection and stress induced in the system. In this study, numeric parameters (i.e., flow velocity, component size, component thickness, misalignment angle, as well as the length and width of the FPCB) were optimized using response surface methodology (RSM) with the central composite design technique. The separate effects of the independent variables and their interactions were investigated. The optimized condition was also examined to substantiate the empirical models generated using RSM. At a flow velocity of 5 m/s, the optimum values of the component size, component thickness, misalignment angle, as well as the length and width of the FPCB were determined at 11.69 mm, 12.37 mm, 0.73°, as well as 180 mm and 180 mm, respectively. This optimized condition resulted in a maximum deflection of 0.402 mm and a maximum stress of 0.582 MPa. The findings conveyed can contribute to the development of FPCB industries. Ó 2013 Elsevier Ltd. All rights reserved.

1. Introduction The flexible printed circuit board (FPCB) can be an alternative to the rigid printed circuit board (PCB) in certain applications because of its lightweight, reduced thickness, and ability to adapt to various shapes. However, recognized for its soft and flexible features, FPCB inevitably experience more significant deflection and stress in the flow environment. These issues are key factors that can affect the durability and reliability of the FPCB, thus influencing its lifespan. Efforts toward minimizing deflection and stress are valuable for FPCB industries. A review of previous studies is presented to establish the background of the current study. Azar and Russell [1] investigated the effects of component layout and geometry on the flow distribution in a circuit pack. Lee and Mahalingam [2] used a computational fluid dynamics (CFD) tool to determine the velocity and temperature fields of airflow in a computer system enclosure. Focused on component-PCB heat transfer, Rodgers et al. [3–5] and Lohan et al. [6] performed both numerical and experimental research to evaluate the predictive accuracy of CFD tools for the thermal analysis of electronic systems. Cole et al. [7] analyzed the aerodynamic and thermal interactions of ball grid array packages for the component-PCB system. Grimes et al. [8–11] conducted detailed experiments and constructed models to examine axial flow fan-cooled electronic systems. The flow in ⇑ Corresponding author. Tel.: +60 124913898. E-mail address: [email protected] (W.C. Leong). 0026-2714/$ - see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.microrel.2013.06.008

the suction mode was found steady, uniform, and easily predictable using laminar model; whereas the flow in the blowing mode was unsteady, swirling, and too complex to predict with reasonable accuracy using turbulent model. Leicht and Skipor [12,13] developed a test method to clarify the mechanical bending fatigue issues in packages attached to rigid PCB, whereas Lau et al. [14] studied plastic ball grid array (PBGA) package assemblies under a three-point bending condition. Using digital image correlation, Yu et al. [15] analyzed the full-field dynamic responses of PCBs at the product level. On the contrary, Arruda et al. [16,17], Sun et al. [18], and Das et al. [19] focused on the study of rigid–flex printed circuit boards. For FPCB, Li and Jiao [20] investigated the effects of temperature and aging on Young’s moduli of polymeric-based flexible substrates. Barlow et al. [21] successfully demonstrated the feasibility and viability of FPCBs on integrated power modules for miniaturization purposes. Furthermore, van Driel et al. [22], Han et al. [23], and Huang et al. [24,25] focused on the reliability of FPCB products. Siegel et al. [26] fabricated several low-cost flexible electronic circuits on paper substrates. Recently, the authors [27–30] also focused on the fluid–structure interaction (FSI) of FPCB applications. Response surface methodology (RSM) has been widely used and proven effective for parametric optimization in various industries [31–34]. With the soft nature of FPCB considered, the importance of the FSI phenomenon for FPCB electronics was constantly emphasized in the previous studies by the authors [27–30]. Different with other

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W.C. Leong et al. / Microelectronics Reliability 53 (2013) 1996–2004

area of study, FSI focuses on the deflection and stress caused by interaction between the fluid and solid domain. The electrical signal consideration and thermal stress were beyond the scope in the present study. For FPCB, extensive research is still required to gain an in-depth understanding of the FPCB behavior in the flow environment. Therefore, as extension of the recent research by the authors [29], the present study aimed at investigating the optimized condition for FPCB electronics under the flow condition using RSM. The present study focused on deflection and stress output, which strongly affect device performance. The examined numeric parameters were selected according to their influences on the deflection and stress induced in the FPCB. In this study, the flow velocity [27–30], component size, thickness [29], misalignment angle [29], as well as the length and width of the FPCB were considered. The findings conveyed in the present study can contribute to the development of FPCB industries. These FSI problems were addressed using the FLUENT fluid-flow solver and the ABAQUS structural solver, coupled online by the mesh-based parallel code coupling interface (MpCCI). First, the paper will present the numerical method employed, and then followed by the discussion on the RSM technique used. In the results and discussions, the results and ANOVA will first be analyzed, and subsequently investigate on the effects and interactions of the variables. Lastly, the paper will be ended with the optimization study. 2. Methodology 2.1. Numerical study 2.1.1. Modeling strategy The present FSI study was performed using two main platforms: the FLUENT 6.3.26 fluid flow solver and the ABAQUS/CAE 6.9 structural solver. The general-purpose finite volume based FLUENT was used to study the fluid domain air flow, whereas the ABAQUS was used to investigate the FPCB behavior in the structural domain. To complete the FSI environment, MpCCI 3.1.0 was employed for the exchange of data between the two solvers through the coupling regions. During analysis, the forces induced on the FPCB and the components were transferred from FLUENT to ABAQUS for a simultaneous structural study. The deflection and stress levels induced in the FPCB were analyzed in the present FSI study. In fact, this technique was same as the one employed in Ref. [29]; however, the present study additionally included the RSM tool to achieve for the optimization purpose. Throughout this paper, the deflections are defined as directions perpendicular to the FPCB plane, in which deflection toward component side is denoted as positive. For the present study, these numerical predictions were validated in good agreement with the experimental measurements [29]. The capability of this numerical technique in handling FSI problems had also been proven in the authors’ previous studies [28], encapsulation of the molded packaging [35], and PBGA with wire bonding [36]. Hence, these numerical predictions are expected to provide reliable outcomes for the present study. 2.1.2. Structural modeling The structural domain model was generated in ABAQUS, as shown in Fig. 1. The FPCB consists of 16 squared components attached on one side such that the components were equally spaced. Such general physical layout was applied in the present study in order to maintain the generality for the findings, as quoted in Ref. [29]. In fact, this idea was inspired and drawn from Lohan et al. [6], Cole et al.[7] and Grimes et al. [8–11]. The components were appropriate to be idealized as simple blocks rigidly attached to the FPCB [27–30,37,38]. The fully constrained boundary conditions (Ux = Uy = Uz = URx = URy = URz = 0) were assigned to the FPCB

Fig. 1. Modeling of structural domain.

fixed regions, where U and UR are the linear and rotational displacements, respectively. In this model, the FPCB was assumed in vertical orientation; hence, gravity was defined in the negative y direction. The current optimization study did not focus on other orientations (gravity acting in the direction perpendicular to the FPCB plane) because such configurations worsen deflection and stress conditions [29]. The FPCB material was tested according to ASTM D638 [39], and the material properties were defined according to Table 1 [29]. The structural models were meshed with 21,509–42,540 hexagonal elements. 2.1.3. Fluid flow modeling The fluid domain model was built in FLUENT, as shown in Fig. 2. Applying the same conditions as in the previous study [29], the FPCB was considered in the test enclosure space of 600 mm 300 mm 297 mm. This computational model was assumed as three-dimensional, laminar, and incompressible. The laminar model is appropriate and sufficient for the current purpose of the study [1,8–11,27–30]. The fluid models were meshed with 414,591–479,614 tetrahedral elements. At the boundary conditions, the intended velocity was set at the inlet velocity boundary and the ambient condition was applied at the pressure outlet boundary. The boundary conditions were as follows: u ¼ 0. (a) On FPCB and enclosure wall: ~ (b) At the inlet: ~ u¼~ udesired . (c) At the outlet: P = 0. 2.2. Design, analysis and optimization using response surface methodology (RSM) RSM is a collection of mathematical and statistical techniques, which is widely used for fitting a second-order response surface. An alternative to the one-factor-at-a-time design, RSM rapidly and efficiently investigates the effect of simultaneous variation in independent variables. In RSM, the separate effects of individual variables and the interactions between the variables are identified using a minimum number of runs.

Table 1 Material properties. Regions

Effective modulus (Pa)

Density (kg/m3)

FPCB Component

5.24 109 2.70 109

3636 1170

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Fig. 2. Modeling of fluid domain. Fig. 4. Various misalignment angles. Table 2 Levels of the independent variables. Independent variables

Coded value 1 (Low)

0 (Middle)

+1 (High)

3 18 8.5 0 200 200

5 31 16 20 220 220

Actual value A. Flow velocity (m/s) B. Component size (mm) C. Component thickness (mm) D. Misalignment angle (deg) E. Length of FPCB (mm) F. Width of FPCB (mm)

1 5 1 20 180 180

Design Expert 6.0.6 was employed to aid in the design, mathematical modeling, and optimization in the present study. As shown in Table 2, the six independent variables, namely, flow velocity, component size and thickness, misalignment angle, as well as the length and width of the FPCB were coded as A, B, C, D, E, and F, respectively. These independent variables were varied over three coded levels between 1 (low level), 0 (middle level), and +1 (high level). Fig. 3 illustrates the case associated with the examined independent variables, whereas Fig. 4 clearly describes the definition of

misalignment angle in further. The two important responses of maximum deflection (Y1) and maximum stress (Y2) were selected for evaluation and optimization to improve the conditions in FPCB electronics. In the study, the applied central composite design (CCD) consists of half-fractional factorial design (1/2 2k), axial or star points (2k), and center points, where k denotes the number of independent variables. With six independent variables, a total of 52 runs were required in this study according to the equation CCD = 1/2 2k + 2k + 8, in which the runs were improved with eight replications at the design center. The regression analysis was then conducted to fit each response into mathematical representation according to the following quadratic model:

Y ¼ bo þ

k X i¼1

bi X i þ

k k X k X X bii X 2i þ bij X i X j þ þ e i¼1

i61

ð1Þ

j

where Y is the response; Xi and Xj are the variables; b0 is a constant coefficient; bi, bii, and bij denote the interaction coefficients of linear, quadratic, and second-order terms, respectively; and e represents the random error. The significance and adequacy of the equations were also assessed in the RSM analysis. 3. Results and discussion 3.1. Results of the central composite design

Fig. 3. Independent variables in the present RSM analysis.

The main objective of the optimization study was to minimize the maximum deflection (Y1) and maximum stress (Y2) induced in the flow environment to ensure a more efficient system performance. Stress reduction provides electronic systems with enhanced reliability and thus, is desirable. Significant deflection is usually avoided because it can impose physical contact among the components and with other nearby objects especially under miniaturized conditions, adversely affecting the system performance [27–30]. The results of 52 CCD batch runs conducted in this study could be found in Appendix A. Unlike the traditional rigid PCB, the FPCB behavior was more sensitive to changes in independent variables because of the soft and flexible characteristics of the FPCB. The optimization in the study is important to improve understanding and help advance FPCB industries. The highest deflection (2.870 mm) was observed in run 18, whereas the highest stress (10.189 MPa) occurred in run 50. Hence, these conditions of independent variables were not recommended for FPCB application. The effect of the independent variables and their interactions are explained in the subsequent sections of this study.


3.2. Regression model and analysis of variance (ANOVA) According to Sequential Model Sum of Squares and Model Summary Statistics, the models were selected based on the highest order of polynomials, in which significance of the additional terms was secured in the absence of the aliased model. Moreover, the models with high coefficient of determination (R-squared) and low standard deviation were also prioritized in the selection. In the study, the most appropriate fitting models for the responses of maximum deflection (Y1) and maximum stress (Y2) were quadratic, which was also suggested in Design Expert. To improve the model accuracy, model reduction was performed by identifying and removing insignificant terms. Eqs. (2) and (3) show the final empirical models in terms of coded factors, and their

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corresponding ANOVA analyses were presented in Appendix B. The response for maximum stress (Y2) was transformed into a square-root form to improve the model accuracy, as suggested by Design Expert.

Y 1 ¼ 0:4 þ 0:015A þ 0:02B 0:001538C þ 1:42D þ 0:018E þ 0:009668F þ 0:15C 2 0:52D2 þ 0:75AD 0:14BD þ 0:16DE þ 0:17DF

ð2Þ

pffiffiffiffiffiffi Y 2 ¼ 0:76 þ 0:62A þ 0:093B þ 0:10C þ 0:029D þ 0:17E þ 0:17F þ 0:97D2 0:11AB 0:083AC þ 0:15AE þ 0:11AF þ 0:086BC

Fig. 5. Perturbation plots for (a) maximum deflection, and (b) maximum stress.

Fig. 6. Interaction plots of maximum deflection for (a) AD, (b) BD, (c) DE, and (d) DF.

ð3Þ

2000


Fig. 7. Interaction plots of maximum deflection for (a) AB, (b) AC, (c) AE, (d) AF and (e) BC.

Fig. 8. 3D response surface plots for (a) maximum deflection, and (b) maximum stress.

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Fig. 9. Maximum deflection and maximum stress for various misalignment angles at flow velocity of 5 m/s.

Table 3 Optimized conditions at A = 5 m/s, B = 11.69 mm, C = 12.37 mm, D = 0.73°, E = 180 mm and F = 180 mm. Empirical models

Maximum deflection (mm) Maximum stress (MPa)

FSI simulation

Prediction

95% CI low

95% CI high

0.3443 0.613

0.1910 0.318

0.4975 1.003

0.4021 0.582

Fig. 10. FSI simulation results for (a) deflection and (b) stress, at A = 5 m/s, B = 11.69 mm, C = 12.37 mm, D = 0.73°, E = 180 mm and F = 180 mm.

ANOVA results showed that both quadratic models were significant and adequate. The quality of the equations was also assessed based on the R-squared value. The R-squared value for the two models Y1 and Y2 were favorably high at 0.99 and 0.94, respectively, which indicates a reliable prediction from the empirical models. The standard deviations associated with each model were 0.19 and 0.22, respectively. As such, a total variability of 99% and 94% were accredited to each of the empirical models Y1 and Y2, respectively. 3.3. Effect of the independent variables The perturbation plots presented in Fig. 5 were analyzed to evaluate the effects of each independent variable on the responses of maximum deflection (Fig. 5a) and maximum stress (Fig. 5b). These results were generated by varying a particular independent variable while all other independent variables remained constant at the reference value. The plots indicate that maximum deflection (Y1) was mostly influenced by the misalignment angle (Fig. 5a), whereas maximum stress (Y2) was substantially affected by both misalignment angle and flow velocity (Fig. 5b). Different indepen-

dent variables exhibited different effects on various responses. Hence, the use of perturbation plots allowed the direct and efficient identification of the effects of each independent variable. The flow velocity (A) apparently influenced the maximum stress and slightly affected the maximum deflection, compared with other independent variables. Both the maximum deflection and the maximum stress increased as flow velocity increased, with a significant increment in maximum stress. This behavior is due to the greater flow impact induced by higher velocity on the FPCB and its components. Despite these findings, it has to be put on notice that the effect of flow velocity varied depending on the values of the other independent variables because of the significant interaction between them. The interaction identification is one of the advantages of using RSM and is discussed in the subsequent section. The investigation also discovered that the component factors (B and C) as well as the FPCB factors (E and F) slightly affected the responses. However, the misalignment angle (D) had a dominant effect on maximum deflection and maximum stress. The positive misalignment produced a positive maximum deflection, and negative misalignment produced a negative maximum deflection, which

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Table A1 Results of the central composite design. Run

Independent variables A (m/s)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52

3 1 5 3 5 1 5 1 3 5 3 1 1 5 3 1 3 5 5 3 5 1 1 5 3 1 1 5 5 3 3 3 3 5 1 1 1 5 1 3 3 3 1 5 5 3 1 1 3 5 3 5

B (mm)

18 31 31 18 31 5 5 31 18 31 18 5 31 5 18 31 18 5 31 18 5 5 31 31 5 5 18 5 5 31 18 18 18 5 5 31 5 31 5 18 18 18 5 5 31 18 31 31 18 31 18 18

Responses C (mm)

8.5 1 1 8.5 16 1 16 1 8.5 1 8.5 16 16 16 8.5 16 8.5 1 1 8.5 1 1 1 1 8.5 16 8.5 1 16 8.5 8.5 8.5 8.5 1 16 16 16 16 1 8.5 8.5 8.5 1 16 16 16 16 1 1 16 8.5 8.5

D (deg)

0 20 20 0 20 20 20 20 0 20 0 20 20 20 0 20 0 20 20 20 20 20 20 20 0 20 0 20 20 0 20 0 0 20 20 20 20 20 20 0 0 0 20 20 20 0 20 20 0 20 0 0

E (mm)

220 180 180 200 220 180 220 220 200 180 200 180 220 180 200 220 200 220 220 200 220 180 180 220 200 180 200 180 180 200 200 200 200 180 220 180 220 180 220 200 180 200 220 220 180 200 180 220 200 220 200 200

F (mm)

200 180 220 200 180 180 180 220 200 180 200 180 220 180 200 180 180 220 220 200 180 220 220 180 200 220 200 180 220 200 200 200 220 220 220 220 180 180 220 200 200 200 180 220 220 200 180 180 200 220 200 200

Simulation

Model predicted

Y1 (mm)

Y2 (MPa)

Y1 (mm)

Y2 (MPa)

0.432 0.472 2.108 0.397 1.767 0.629 2.283 0.891 0.397 1.675 0.397 0.625 0.534 1.859 0.397 0.570 0.336 2.870 2.626 1.620 2.283 0.755 0.669 2.060 0.110 0.744 0.153 1.888 2.328 0.393 1.539 0.397 0.430 2.350 0.948 0.434 0.739 1.404 0.935 0.397 0.348 0.397 0.746 2.829 1.793 0.383 0.282 0.656 1.052 2.540 0.397 0.628

0.541 0.690 6.429 0.581 5.903 0.646 6.336 1.192 0.581 1.983 0.581 0.643 2.727 3.465 0.581 1.991 1.026 7.820 8.637 3.841 6.346 0.699 0.916 5.807 0.088 0.688 0.425 3.885 5.840 0.997 3.364 0.581 0.591 5.869 1.093 3.323 0.773 2.074 0.944 0.581 0.533 0.581 0.784 7.841 5.471 1.430 2.145 0.779 0.083 10.189 0.581 0.908

0.418 0.209 2.098 0.400 1.948 0.511 2.332 0.924 0.400 1.661 0.400 0.446 0.799 1.984 0.400 0.562 0.390 2.694 2.266 1.300 2.265 0.808 0.512 2.095 0.380 0.835 0.385 1.979 2.335 0.420 1.540 0.400 0.410 2.302 1.161 0.565 0.798 1.736 1.116 0.400 0.382 0.400 0.805 2.589 1.985 0.549 0.194 0.475 0.552 2.451 0.400 0.415

0.865 0.986 4.924 0.578 5.988 0.491 5.603 1.329 0.578 2.563 0.578 0.908 2.667 2.786 0.578 2.468 0.348 9.394 7.846 3.094 5.988 0.773 1.113 5.285 0.445 1.030 0.020 3.478 5.230 0.728 2.893 0.578 0.865 5.603 1.239 2.726 0.874 3.478 0.741 0.578 0.348 0.578 0.638 8.231 5.603 0.740 2.170 0.951 0.436 9.394 0.578 1.904

A, B, C, D, E and F = flow velocity, component size, component thickness, misalignment angle, length of FPCB and width of FPCB. Y1 and Y2 = maximum deflection and maximum stress.

was caused by the FPCB reaction toward the airflow. The magnitudes of the maximum deflection and maximum stress were amplified when the misalignment angle moved further from zero degree. The reason for this behavior was that the misalignment caused a larger FPCB projection toward the airflow and thus, created more impingement on the FPCB. The results agreed with those in previous studies [29]. In the plots, the highest deflection and highest stress of 1.299 mm and 3.108 MPa, respectively, were obtained. 3.4. Interaction of independent variables In RSM, it is quite beneficial to identify and determine the interactions between the independent variables that directly influence the responses. Interaction occurs when the effect of one indepen-

dent variable varies at different values of the other independent variables. This behavior is usually analyzed from the interaction plot. In a particular interaction plot, if no interaction occurs between the independent variables, parallel line plots appear. The ANOVA identified few significant interactions in the present study. Fig. 6 shows the interactions of AD, BD, DE, and DF toward the response of maximum deflection (Y1). The other independent variables that were not considered in each plot remained at reference value. The line plots in these interaction plots were non-parallel. Therefore, the independent variables were interacting with one another, in conjunction with the signal given by ANOVA. For AD (Fig. 6a), the maximum deflection increased with the flow velocity at 20° misalignment but decreased with the flow velocity at 20° misalignment. The maximum deflection for BD (Fig. 6b) decreased

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W.C. Leong et al. / Microelectronics Reliability 53 (2013) 1996–2004 Table B1 ANOVA of the quadratic models. Source

Sum of squares

Degree of freedom

Mean square

F value

Prob > F

Model (Y1) A B C D E F C2 D2 AD BD DE DF Residual Lack of fit Pure error Std. dev. Mean C.V. Press p Model ( Y2) A B C D E F D2 AB AC AE AF BC Residual Lack of fit Pure error Std. dev. Mean C.V. Press

91.41279 0.008014 0.013801 8.04E05 69.03869 0.010948 0.003178 0.087045 1.000716 18.04773 0.586878 0.864612 0.916658 1.355812 1.355812 0 0.186452 0.155327 120.0385 2.782357

12 1 1 1 1 1 1 1 1 1 1 1 1 39 32 7

7.617733 0.008014 0.013801 8.04E05 69.03869 0.010948 0.003178 0.087045 1.000716 18.04773 0.586878 0.864612 0.916658 0.034764 0.042369 0 R-squared Adj R-squared Pred R-squared Adeq precision

219.1244 0.23053 0.396979 0.002314 1985.901 0.314911 0.091408 2.503853 28.78564 519.1439 16.88157 24.87062 26.36771