Research Papers

Regional Stiffness Reduction Using Lamina Emergent Torsional Joints for Flexible Printed Circuit Board Design

[+] Author and Article Information
Bryce P. DeFigueiredo

Department of Mechanical Engineering,
Brigham Young University,
Provo, UT 84602
e-mail: bdefig@gmail.com

Trent K. Zimmerman

Department of Mechanical Engineering,
Brigham Young University,
Provo, UT 84602
e-mail: trentzim@gmail.com

Brian D. Russell

Department of Mechanical Engineering,
Brigham Young University,
Provo, UT 84602
e-mail: brian.russ247@gmail.com

Larry L. Howell

Department of Mechanical Engineering,
Brigham Young University,
Provo, UT 84602
e-mail: lhowell@byu.edu

Contributed by the Electronic and Photonic Packaging Division of ASME for publication in the JOURNAL OF ELECTRONIC PACKAGING. Manuscript received November 15, 2017; final manuscript received May 25, 2018; published online July 3, 2018. Assoc. Editor: Satish Chaparala.

J. Electron. Packag 140(4), 041001 (Jul 03, 2018) (9 pages) Paper No: EP-17-1120; doi: 10.1115/1.4040552 History: Received November 15, 2017; Revised May 25, 2018

Flexible printed circuit boards (PCBs) make it possible for engineers to design devices that use space efficiently and can undergo changes in shape and configuration. However, they also suffer from tradeoffs due to nonideal material properties. Here, a method is presented that allows engineers to introduce regions of flexibility in otherwise rigid PCB substrates. This method employs geometric features to reduce local stiffness in the PCB, rather than reducing the global stiffness by material selection. Analytical and finite element models are presented to calculate the maximum stresses caused by deflection. An example device is produced and tested to verify the models.

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Harris, K. , Elias, A. , and Chung, H.-J. , 2016, “ Flexible Electronics Under Strain: A Review of Mechanical Characterization and Durability Enhancement Strategies,” J. Mater. Sci., 51(6), pp. 2771–2805. [CrossRef]
Sa'd Hamasha , and Borgesen, P. , 2016, “ Effects of Strain Rate and Amplitude Variations on Solder Joint Fatigue Life in Isothermal Cycling,” ASME J. Electron. Packag., 138(2), p. 021002. [CrossRef]
Howell, L. L. , 2001, Compliant Mechanisms, Wiley, New York.
Weight, B. L. , Mattson, C. A. , Magleby, S. P. , and Howell, L. L. , 2007, “ Configuration Selection, Modeling, and Preliminary Testing in Support of Constant Force Electrical Connectors,” ASME J. Electron. Packag., 129(3), pp. 236–246. [CrossRef]
Chen, W. , Bhat, A. , and Sitaraman, S. K. , 2015, “ Impact Isolation Through the Use of Compliant Interconnects for Microelectronic Packages,” ASME J. Electron. Packag., 137(4), p. 041005. [CrossRef]
Park, S. , Vosguerichian, M. , and Bao, Z. , 2013, “ A Review of Fabrication and Applications of Carbon Nanotube Film-Based Flexible Electronics,” Nanoscale, 5(5), pp. 1727–1752. [CrossRef] [PubMed]
Zhu, S. , So, J.-H. , Mays, R. , Desai, S. , Barnes, W. R. , Pourdeyhimi, B. , and Dickey, M. D. , 2013, “ Ultrastretchable Fibers With Metallic Conductivity Using a Liquid Metal Alloy Core,” Adv. Funct. Mater., 23(18), pp. 2308–2314. [CrossRef]
Yao, S. , and Zhu, Y. , 2015, “ Nanomaterial-Enabled Stretchable Conductors: Strategies, Materials and Devices,” Adv. Mater., 27(9), pp. 1480–1511. [CrossRef] [PubMed]
Benight, S. J. , Wang, C. , Tok, J. B. , and Bao, Z. , 2013, “ Stretchable and Self-Healing Polymers and Devices for Electronic Skin,” Prog. Polym. Sci., 38(12), pp. 1961–1977. [CrossRef]
Sun, D.-M. , Liu, C. , Ren, W.-C. , and Cheng, H.-M. , 2013, “ A Review of Carbon Nanotube-and Graphene-Based Flexible Thin-Film Transistors,” Small, 9(8), pp. 1188–1205. [CrossRef] [PubMed]
Lipomi, D. J. , and Bao, Z. , 2011, “ Stretchable, Elastic Materials and Devices for Solar Energy Conversion,” Energy Environ. Sci., 4(9), pp. 3314–3328. [CrossRef]
Zardetto, V. , Brown, T. M. , Reale, A. , and Di Carlo, A. , 2011, “ Substrates for Flexible Electronics: A Practical Investigation on the Electrical, Film Flexibility, Optical, Temperature, and Solvent Resistance Properties,” J. Polym. Sci. Part B, 49(9), pp. 638–648. [CrossRef]
Zeng, W. , Shu, L. , Li, Q. , Chen, S. , Wang, F. , and Tao, X.-M. , 2014, “ Fiber-Based Wearable Electronics: A Review of Materials, Fabrication, Devices, and Applications,” Adv. Mater., 26(31), pp. 5310–5336. [CrossRef] [PubMed]
Leterrier, Y. , Medico, L. , Demarco, F. , Månson, J.-A. , Betz, U. , Escola, M. , Olsson, M. K. , and Atamny, F. , 2004, “ Mechanical Integrity of Transparent Conductive Oxide Films for Flexible Polymer-Based Displays,” Thin Solid Films, 460(1–2), pp. 156–166. [CrossRef]
Vella, D. , Bico, J. , Boudaoud, A. , Roman, B. , and Reis, P. M. , 2009, “ The Macroscopic Delamination of Thin Films From Elastic Substrates,” Proc. Natl. Acad. Sci., 106(27), pp. 10901–10906. [CrossRef]
Kim, S.-R. , and Nairn, J. A. , 2000, “ Fracture Mechanics Analysis of Coating/Substrate Systems—Part I: Analysis of Tensile and Bending Experiments,” Eng. Fract. Mech., 65(5), pp. 573–593. [CrossRef]
Wang, J. , Sugimura, Y. , Evans, A. , and Tredway, W. , 1998, “ The Mechanical Performance of Dlc Films on Steel Substrates,” Thin Solid Films, 325(1–2), pp. 163–174. [CrossRef]
Lewis, J. , 2006, “ Material Challenge for Flexible Organic Devices,” Mater. Today, 9(4), pp. 38–45. [CrossRef]
Martynenko, E. , Zhou, W. , Chudnovsky, A. , Li, R. , and Poglitsch, L. , 2002, “ High Cycle Fatigue Resistance and Reliability Assessment of Flexible Printed Circuitry,” ASME J. Electron. Packag., 124(3), pp. 254–259. [CrossRef]
Karjalainen, P. H. , and Heino, P. , 2007, “ On-Wafer Capacitors Under Mechanical Stress,” ASME J. Electron. Packag., 129(3), pp. 287–290. [CrossRef]
Jacobsen, J. O. , Winder, B. G. , Howell, L. L. , and Magleby, S. P. , 2010, “ Lamina Emergent Mechanisms and Their Basic Elements,” ASME J. Mech. Rob., 2(1), p. 011003.
Delimont, I. L. , Magleby, S. P. , and Howell, L. L. , 2015, “ A Family of Dual-Segment Compliant Joints Suitable for Use as Surrogate Folds,” ASME J. Mech. Des., 137(9), p. 092302. [CrossRef]
Delimont, I. L. , Magleby, S. P. , and Howell, L. L. , 2015, “ Evaluating Compliant Hinge Geometries for Origami-Inspired Mechanisms,” ASME J. Mech. Rob., 7(1), p. 011009. [CrossRef]
Jacobsen, J. O. , Chen, G. , Howell, L. L. , and Magleby, S. P. , 2009, “ Lamina Emergent Torsional (LET) Joint,” Mech. Mach. Theory, 44(11), pp. 2098–2109. [CrossRef]
Xie, Z. , Qiu, L. , and Yang, D. , 2017, “ Design and Analysis of Outside-Deployed Lamina Emergent Joint (Od-Lej),” Mech. Mach. Theory, 114, pp. 111–124. [CrossRef]
Xie, Z. , Qiu, L. , and Yang, D. , 2018, “ Design and Analysis of a Variable Stiffness Inside-Deployed Lamina Emergent Joint,” Mech. Mach. Theory, 120, pp. 166–177. [CrossRef]
Boehm, K.-J. , Gibson, C. R. , Hollaway, J. R. , and Espinosa-Loza, F. , 2016, “ A Flexure-Based Mechanism for Precision Adjustment of National Ignition Facility Target Shrouds in Three Rotational Degrees of Freedom,” Fusion Sci. Technol., 70(2), pp. 265–273. [CrossRef]
Chen, G.-M. , and Howell, L. L. , 2018, “ Symmetric Equations for Evaluating Maximum Torsion Stress of Rectangular Beams in Compliant Mechanisms,” Chin. J. Mech. Eng., 31(1), p. 14. [CrossRef]
Pilkey, W. D. , and Pilkey, D. F. , 2008, Peterson's Stress Concentration Factors, Wiley, Hoboken, NJ.
Chen, G. M. , Magleby, S. P. , and Howell, L. L. , 2018, “ Membrane-Enhanced Lamina Emergent Torsional Joints for Surrogate Folds,” ASME J. Mech. Des., 140(6), p. 062303.
Wilding, S. E. , Howell, L. L. , and Magleby, S. P. , 2012, “ Introduction of Planar Compliant Joints Designed for Combined Bending and Axial Loading Conditions in Lamina Emergent Mechanisms,” Mech. Mach. Theory, 56, pp. 1–15. [CrossRef]
Wu, C. , Liu, J. , and Yeung, N. , 2001, “ The Effects of Bump Height on the Reliability of Acf in Flip-Chip,” Soldering Surf. Mount Technol., 13(1), pp. 25–30. [CrossRef]
Miura, K. , 1980, “ Method of Packaging and Deployment of Large Membranes in Space,” 31st Congress of the International Astronautical Federation, Tokyo, Japan, Sept. 21–28, pp. 1–10.
Waitukaitis, S. , and van Hecke, M. , 2016, “ Origami Building Blocks: Generic and Special Four-Vertices,” Phys. Rev. E, 93(2), p. 023003. [CrossRef] [PubMed]
Hedengren, J. D. , Shishavan, R. A. , Powell, K. M. , and Edgar, T. F. , 2014, “ Nonlinear Modeling, Estimation and Predictive Control in APMonitor,” Comput. Chem. Eng., 70, pp. 133–148. [CrossRef]
Wächter, A. , and Biegler, L. T. , 2006, “ On the Implementation of an Interior-Point Filter Line-Search Algorithm for Large-Scale Nonlinear Programming,” Math. Program., 106(1), pp. 25–57. [CrossRef]


Grahic Jump Location
Fig. 1

Current techniques for producing flexible electronics allow for uncontrolled deflection of the entire substrate. When the circuit is (a) undeflected, components and solder joints experience low stresses. When the circuit is (b) deflected, components and solder joints experience high stresses.

Grahic Jump Location
Fig. 2

(a) A single LET joint and (b) an array of LET joints. LET joint geometry lowers stiffness by transferring an applied bending load over the joint to torsional loads in the legs.

Grahic Jump Location
Fig. 3

(a) A single LET joint with its corresponding spring system and (b) geometric parameters for Eqs. (1)(14)

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Fig. 4

Deflected LET joint with parameters from Eq. (1) labeled

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Fig. 5

Detail view of LET joint array

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Fig. 6

The stress distribution for a 1 × 1 joint using the dimensions and material properties listed in Table 1. The shear stress resulting from a 30 deg angular displacement load is shown.

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Fig. 7

Comparison of analytical and FEA model results for various 1 × n joints. Shear stress at the center of the torsion members is plotted versus the number of joints in series (n), due to a 30 deg angular displacement load.

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Fig. 8

(a) Prototype solar array with LET joint hinge in folded and (b) unfolded configurations, along with (c) a detail view of the LET joint array surrogate hinge

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Fig. 9

(a) Diagram and (b) photograph of fatigue testing setup

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Fig. 10

Map-fold origami pattern: (a) Origami fold pattern. Solid lines represent mountain folds, and dashed lines represent valley folds. Labels A, B, and C designate the three folding steps in order of folding sequence. (b) The fold area to be made flexible with surrogate hinges is shown shaded. (c) Surrogate hinge areas are shaded. Arrows show the direction of the fold axis. Labels a, b, and c designate regions of optimized surrogate fold geometry. Shaded regions without arrows show areas where material is removed.

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Fig. 11

Origami-like folding structure designed with optimized surrogate hinge LET joint arrays and fabricated from a single sheet of copper-clad FR-4

Grahic Jump Location
Fig. 12

Possible form factors for various applications of this regional stiffness reduction technique. Circuit boards could be folded to stow in small spaces or to conform to an arbitrary shape.




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