Skip to main content
SpringerLink
Log in

Constitutive Response of Electronics Materials

  • Conference paper
  • First Online:
Challenges In Mechanics of Time-Dependent Materials and Processes in Conventional and Multifunctional Materials, Volume 2

Abstract

Electronics in mission- or safety-critical systems are expected to survive a wide range of harsh environments including thermal cycling, thermal ageing, vibration, shock, and combinations of the aforementioned stresses. The materials used in these electronic systems are diverse and frequently change as the electronics industry rapidly innovates. These materials are dual use, fulfilling both electrical and mechanical functions. Of particular interest are electronic materials classes such as polymers (e.g., encapsulants/potting and packaging), composites (e.g., hard potting and printed circuit boards), and interconnect materials (e.g., solder). Thus, predicting the operational response of electronics systems in harsh environments requires understanding of the materials constitutive response to the environmental characteristics for all the relevant materials. The paper estimates the rate-, temperature-, and pressure-dependent constitutive response of representative electronic materials. Experimental response of circuit boards, potting materials, and solder interconnects are measured in low and intermediate strain rate dynamic tests. Traditional mechanical sensors (e.g. strain gages and accelerometers) are complemented by non-contact techniques (e.g., laser velocimetery, high speed digital image correlation) to obtain high fidelity experimental data on material response. Estimates of the corresponding constitutive parameters are calculated, and observed features of the dynamic response are discussed.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 219.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Abbreviations

\( \rho \) :

Density

\( \sigma \) :

Stress

\( \varepsilon,\dot{\varepsilon} \) :

Strain strain rate

\( \gamma,\dot{\gamma} \) :

Shear strain shear strain rate

\( \tau,\dot{\tau} \) :

Shear stress shear stress rate

g :

Acceleration (due to gravity)

\( {k_B} \) :

Boltzmann’s constant

\( {C_p} \) :

Heat capacity

E :

Elastic modulus

P :

Pressure

T :

Temperature

References

  1. (2008) Test method standard for environmental engineering considerations and laboratory tests. MIL-STD-810G, Department of Defense

    Google Scholar 

  2. Custer W (2011) Business outlook for the global electronics industry. IPC Outlook (downloaded from www.ipc.org)

  3. JEDEC (2003) JEDEC solid state technology association JESD22-B111. Board level drop test method of components for handheld electronic products

    Google Scholar 

  4. JEDEC (2006) JEDEC solid state technology association JESD22-B103B. Vibration, Variable Frequency

    Google Scholar 

  5. Mishiro K, Ishikawa S, Abe M, Kumai T, Higashiguchi Y, Tsubone K-i (2002) Effect of the drop impact on BGA/CSP package reliability. Microelectron Reliab 42(1):77–82

    Article  Google Scholar 

  6. Jing-En L, Tong Yan T (2004) Analytical and numerical analysis of impact pulse parameters on consistency of drop impact results. In: Proceedings electronics packaging technology conference. EPTC 2004. Proceedings of 6th, pp 664–670

    Google Scholar 

  7. Tan VBC, Tong MX, Kian Meng L, Chwee Teck L (2005) Finite element modeling of electronic packages subjected to drop impact. IEEE Trans Compon Packag Technol 28(3):555–560

    Article  Google Scholar 

  8. Jing-En L, Tong Yan T, Pek E, Chwee Teck L, Zhaowei Z, Jiang Z (2006) Advanced numerical and experimental techniques for analysis of dynamic responses and solder joint reliability during drop impact. IEEE Trans Compon Packag Technol 29(3):449–456

    Article  Google Scholar 

  9. Lall P, Panchagade DR, YueLi L, Johnson RW, Suhling JC (2006) Models for reliability prediction of fine-pitch BGAs and CSPs in shock and drop-impact. IEEE Trans Compon Packag Technol 29(3):464–474

    Article  Google Scholar 

  10. Wang Y, Low KH, Pang HLJ, Hoon KH, Che FX, Yong YS (2006) Modeling and simulation for a drop-impact analysis of multi-layered printed circuit boards. Microelectron Reliab 46(2–4):558–573

    Google Scholar 

  11. Chong DYR, Che FX, Pang JHL, Ng K, Tan JYN, Low PTH (2006) Drop impact reliability testing for lead-free and lead-based soldered IC packages. Microelectron Reliab 46(7):1160–1171

    Article  Google Scholar 

  12. Wong EH, Seah SKW, van Driel WD, Caers JFJM, Owens N, Lai YS (2009) Advances in the drop-impact reliability of solder joints for mobile applications. Microelectron Reliab 49(2):139–149

    Article  Google Scholar 

  13. Yeh C-L, Lai Y-S, Kao C-L (2006) Evaluation of board-level reliability of electronic packages under consecutive drops. Microelectron Reliab 46(7):1172–1182

    Article  Google Scholar 

  14. Lall P, Gupte S, Choudhary P, Suhling J (2007) Solder joint reliability in electronics under shock and vibration using explicit finite-element submodeling. IEEE Trans Electron Packag Manuf 30(1):74–83

    Article  Google Scholar 

  15. Jenq ST, Sheu HS, Yeh C-L, Lai Y-S, Wu J-D (2007) High-G drop impact response and failure analysis of a chip packaged printed circuit board. Int J Impact Eng 34(10):1655–1667

    Article  Google Scholar 

  16. Syed A, Seung Mo K, Wei L, Jin Young K, Eun Sook S, Jae Hyeon S (2007) A Methodology for drop performance modeling and application for design optimization of chip-scale packages. IEEE Trans Electron Packag Manuf 30(1):42–48

    Article  Google Scholar 

  17. Qu X, Chen Z, Qi B, Lee T, Wang J (2007) Board level drop test and simulation of leaded and lead-free BGA-PCB assembly. Microelectron Reliab 47(12):2197–2204

    Article  Google Scholar 

  18. Wong EH, Seah SKW, Shim VPW (2008) A review of board level solder joints for mobile applications. Microelectron Reliab 48(11–12):1747–1758

    Google Scholar 

  19. Wong EH, Selvanayagam CS, Seah SKW, Driel WD, Caers JFJM, Zhao XJ, Owens N, Tan LC, Frear DR, Leoni M, Lai YS, Yeh CL (2008) Stress–strain characteristics of tin-based solder alloys for drop-impact modeling. J Electron Mater 37(6):829–836

    Article  Google Scholar 

  20. Xu ZJ, Yu TX (2008) Board level dynamic response and solder ball joint reliability analysis under drop impact test with various impact orientations. In: Proceeding electronics packaging technology conference, 2008. EPTC 2008. 10th, pp 1080–1085

    Google Scholar 

  21. Zhang B, Ding H, Sheng X (2008) Modal analysis of board-level electronic package. Microelectron Eng 85(3):610–620

    Article  Google Scholar 

  22. Lee Y-C, Wang B-T, Lai Y-S, Yeh C-L, Chen R-S (2008) Finite element model verification for packaged printed circuit board by experimental modal analysis. Microelectron Reliab 48(11–12):1837–1846

    Google Scholar 

  23. Long W, Xingming F, Jianwei Z, Qian W, Jaisung L (2008) Dynamic properties testing of solders and modeling of electronic packages subjected to drop impact. In: Proceeding electronic packaging technology & high density packaging, 2008. ICEPT-HDP 2008. International Conference on, pp 1–7

    Google Scholar 

  24. Chou C-Y, Hung T-Y, Yang S-Y, Yew M-C, Yang W-K, Chiang K-N (2008) Solder joint and trace line failure simulation and experimental validation of fan-out type wafer level packaging subjected to drop impact. Microelectron Reliab 48(8–9):1149–1154

    Google Scholar 

  25. Lall P, Lowe R, Suhling J, Goebel K (2009) Leading-indicators based on impedance spectroscopy for prognostication of electronics under shock and vibration loads. In: Proceedings 2009 ASME interPack conference, IPACK2009, American Society of Mechanical Engineers, 19–23 Jul 2009, pp 903–914

    Google Scholar 

  26. Lall P, Lowe R, Suhling J, Goebel K (2009) Prognostication based on resistance-spectroscopy for high reliability electronics under shock-impact. In: Proceeding 2009 ASME international mechanical engineering congress and exposition, IMECE2009, American Society of Mechanical Engineers, 13–19 Nov 2009, pp 383–394

    Google Scholar 

  27. Weiping L, Ning-Cheng L, Porras A, Min D, Gallagher A, Huang A, Chen S, Lee JCB (2009) Shock resistant and thermally reliable low Ag SAC solders doped with Mn Or Ce. In: Proceedings electronics packaging technology conference, 2009. EPTC '09. 11th, pp 49–63

    Google Scholar 

  28. Yu AM, Jun-Ki K, Jong-Hyun L, Mok-Soon K (2009) Tensile properties and drop/shock reliability of Sn-Ag-Cu-In based solder alloys. In: Proceeding electronics packaging technology conference, 2009. EPTC '09. 11th, pp 679–682

    Google Scholar 

  29. Wong EH, Mai Y-W (2009) The damped dynamics of printed circuit board and analysis of distorted and deformed half-sine excitation. Microelectron Reliab 49(8):916–923

    Article  Google Scholar 

  30. Yu AM, Kim J-K, Lee J-H, Kim M-S (2010) Pd-doped Sn–Ag–Cu–In solder material for high drop/shock reliability. Mater Res Bull 45(3):359–361

    Article  Google Scholar 

  31. Amy RA, Aglietti GS, Richardson G (2010) Board-level vibration failure criteria for printed circuit assemblies: an experimental approach. IEEE Trans Electron Packag Manuf 33(4):303–311

    Article  Google Scholar 

  32. Amy RA, Aglietti GS, Richardson G (2010) Accuracy of simplified printed circuit board finite element models. Microelectron Reliab 50(1):86–97

    Article  Google Scholar 

  33. Nguyen TT, Park S (2011) Characterization of elasto-plastic behavior of actual SAC solder joints for drop test modeling. Microelectron Reliab 51(8):1385–1392

    Article  Google Scholar 

  34. Le Coq C, Tougui A, Stempin M-P, Barreau L (2011) Optimization for simulation of WL-CSP subjected to drop-test with plasticity behavior. Microelectron Reliab 51(6):1060–1068

    Article  Google Scholar 

  35. An T, Qin F (2011) Cracking of the intermetallic compound layer in solder joints under drop impact loading. J Electron Packag 133(3):031004–031004

    Article  Google Scholar 

  36. An T, Qin F, Li J (2011) Mechanical behavior of solder joints under dynamic four-point impact bending. Microelectron Reliab 51(5):1011–1019

    Article  Google Scholar 

  37. Anuar MA, Isa AAM, Ummi ZAR (2012) Modal characteristics study of CEM-1 single-layer printed circuit board using experimental modal analysis. Procedia Eng 41:1360–1366

    Article  Google Scholar 

  38. Amy RA, Aglietti GS, Richardson G (2009) Reliability analysis of electronic equipment subjected to shock and vibration – a review. Shock Vib 16(1):45–59

    Google Scholar 

  39. Norris KC, Landzberg AH (1969) Reliability of controlled collapse interconnections. IBM J Res Dev 13(3):266–271

    Article  Google Scholar 

  40. Goldmann LS (1969) Geometric optimization of controlled collapse interconnections. IBM J Res Dev 13(3):251–265

    Article  Google Scholar 

  41. Dally JW, Lall P, Suhling JC (2008) Mechanical design of electronic systems. College House Enterprises, Knoxville

    Google Scholar 

  42. Lall P, Pecht M, Hakim E (1997) Estimating the influence of temperature on microelectronic reliability. CRC Press, Boca Raton

    Google Scholar 

  43. (2003) Restriction of the use of certain hazardous substances in electrical and electronic equipment directive (2002/95/EC). European Union

    Google Scholar 

  44. Qin F, An T, Chen N (2010) Strain rate effects and rate-dependent constitutive models of lead-based and lead-free solders. J Appl Mech 77:011008

    Article  Google Scholar 

  45. Motalab M, Cai Z, Suhling JC, Lall P (2012) Determination of Anand constants for SAC solders using stress–strain or creep data. In: Proceeding thermal and thermomechanical phenomena in electronic systems (ITherm), 2012. 13th IEEE Intersociety Conference on, pp 910–922

    Google Scholar 

  46. Lall P, Shantaram S, Suhling J, Locker D (2012) Mechanical deformation behavior of SAC305 at high strain rates. In: Proceeding thermal and thermomechanical phenomena in electronic systems (ITherm), 2012. 13th IEEE Intersociety Conference on, pp 1037–1051

    Google Scholar 

  47. Wang GZ, Cheng ZN, Becker K, Wilde J (2001) Applying Anand model to represent the viscoplastic deformation behavior of solder alloys. J Electron Packag 123(3):247–253

    Article  Google Scholar 

  48. Siviour CR, Walley SM, Proud WG, Field JE (2005) Mechanical properties of SnPb and lead-free solders at high rates of strain. J Phys D: Appl Phys 38(22):4131

    Article  Google Scholar 

  49. Johnson GR, Cook WH A constitutive model and data for metals subjected to large strains, high strain rates and high temperatures. In: Proceeding of the seventh international symposium on Ballistics, pp 541–547

    Google Scholar 

  50. Anand L (1982) Constitutive equations for the rate-dependent deformation of metals at elevated temperatures. J Eng Mater Technol 104(1):12–17

    Article  MathSciNet  Google Scholar 

  51. Zener C, Hollomon JH (1944) Effect of strain rate upon plastic flow of steel. J Appl Phys 15(1):22–32

    Article  Google Scholar 

  52. Frear DR (1999) Materials issues in area-array microelectronic packaging. J Mater 51(3):22–27

    Google Scholar 

  53. Zerilli FJ, Armstrong RW (1987) Dislocation-mechanics-based constitutive relations for material dynamics calculations. J Appl Phys 61(5):1816–1825

    Article  Google Scholar 

  54. Zerilli FJ, Armstrong RW (1999) Application of eyring’s thermal activation theory to constitutive equations for polymers. In: Furnish MD, Chhabildas LC, Hixson RS (eds) Proceedings shock compression of condensed matter – 1999, American Institute of Physics, pp 531–534

    Google Scholar 

  55. Zerilli FJ, Armstrong RW (2000) Thermal activation based constitutive equations for polymers. Journal de Physique IV France 10(9):3–8

    Google Scholar 

  56. Zerilli FJ, Armstrong RW (2001) Thermal activation constitutive model for polymers applied to polytetrafluoroethylene. In: Furnish MD, Thadhani NN, Horie Y (eds) Proceeding shock compression of condensed matter-2001, American Institute of Physics, pp 657–660

    Google Scholar 

  57. Zerilli FJ, Armstrong RW (2007) A constitutive equation for the dynamic deformation behavior of polymers. J Mater Sci 42:4562–4574

    Article  Google Scholar 

  58. Jordan J, Foley J, Siviour C (2008) Mechanical properties of Epon 826/DEA epoxy. Mech Time-Depend Mater 12(3):249–272

    Article  Google Scholar 

  59. (2009) Abaqus/CAE User’s Manual (version 6.7), DSS Simulia

    Google Scholar 

  60. Avalone EA, Baumeister T, Sadegh AM (2007) Marks’ standard handbook for mechanical engineers. McGraw-Hill, New York

    Google Scholar 

  61. Timoshenko S, Woinowsky-Krieger S (1959) Theory of plates and shells. McGraw-Hill, New York

    Google Scholar 

  62. IPC (1997) IPC-4101: specification for base materials for rigid and multilayer printed boards. IPC (Institute for Interconnecting and Packaging Electronic Circuits), Northbrook

    Google Scholar 

  63. Harris CM (1996) Shock and vibration handbook. McGraw-Hill, New York

    Google Scholar 

  64. Auersperg J, Schubert A, Vogel D, Michel B, Reichl H Fracture and damage evaluation in chip scale packages and flip chip assemblies by FEA and Microdac. In: Proceedings symposium application fracture mechanics electronic packaging, ASME, pp 133–139

    Google Scholar 

  65. Bell W, Davie N (1987) Reverse Hopkinson bar testing. Sandia National Labs, Albuquerque

    Google Scholar 

  66. Dodson JC, Lowe RD, Foley JR (2013) Dispersive wave propagation analysis and correction in Hopkinson bar experiments. In preparation for the Journal of Shock and Vibration

    Google Scholar 

  67. (2010) OFV-552 Laser Vibrometer, Polytec

    Google Scholar 

  68. (2010) DMA Q800 Specifications, TA Instruments

    Google Scholar 

  69. (2011) TA Instruments Dynamic Mechanical Analyzer (TA284), TA Instruments

    Google Scholar 

  70. Foley JR, Jordan JL, Siviour CR (2012) Probabilistic estimation of the constitutive parameters of polymers. EPJ Web Conf 26:04041

    Article  Google Scholar 

Download references

Acknowledgements

The authors would like to thank the Air Force Office of Scientific Research and the Department of Defense for supporting this research. Opinions, interpretations, conclusions and recommendations are those of the authors and are not necessarily endorsed by the United States Air Force.

Author information

Authors and Affiliations

  1. U.S. Air Force Research Laboratory AFRL/RWMF, 306 W. Eglin Blvd., Bldg. 432, Eglin AFB, FL, 32542-5430, USA

    Ryan D. Lowe, Jacob C. Dodson & Jason R. Foley

  2. U.S. Army Armament Research, Development, and Engineering Command, New Jersey, USA

    Christopher S. Mougeotte, David W. Geissler & Jennifer A. Cordes

Authors
  1. Ryan D. Lowe
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jacob C. Dodson
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Jason R. Foley
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Christopher S. Mougeotte
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. David W. Geissler
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Jennifer A. Cordes
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ryan D. Lowe .

Editor information

Editors and Affiliations

  1. Sandia National Laboratories, Livermore, California, USA

    Bonnie Antoun

  2. University of Colorado, Boulder, USA

    H. Jerry Qi

  3. Air Force Research Laboratory, Wright-Patterson AFB, Ohio, USA

    Richard Hall

  4. University of Dayton Research Institute, Dayton, Ohio, USA

    G P Tandon

  5. University of Texas-Dallas, Dallas, USA

    Hongbing Lu

  6. University of Kentucky, Paducah, USA

    Charles Lu

  7. Los Alamos National Laboratory, Los Alamos, New Mexico, USA

    Jevan Furmanski

  8. University California San Diego, La Jolla, California, USA

    Alireza Amirkhizi

Rights and permissions

Reprints and permissions

Copyright information

© 2014 The Society for Experimental Mechanics, Inc.

About this paper

Cite this paper

Lowe, R.D., Dodson, J.C., Foley, J.R., Mougeotte, C.S., Geissler, D.W., Cordes, J.A. (2014). Constitutive Response of Electronics Materials. In: Antoun, B., et al. Challenges In Mechanics of Time-Dependent Materials and Processes in Conventional and Multifunctional Materials, Volume 2. Conference Proceedings of the Society for Experimental Mechanics Series. Springer, Cham. https://doi.org/10.1007/978-3-319-00852-3_8

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-00852-3_8

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-00851-6

  • Online ISBN: 978-3-319-00852-3

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation