Experimental Mechanics

, Volume 51, Issue 7, pp 1155–1169 | Cite as

Simultaneous Measurement of Effective Chemical Shrinkage and Modulus Evolutions During Polymerization

  • Y. Wang
  • L. Woodworth
  • B. Han


A novel method is proposed to simultaneously measure the effective chemical shrinkage and modulus evolutions of advanced polymers during polymerization. The method utilizes glass fiber Bragg grating (FBG) sensors. They are embedded in two uncured cylindrical polymer specimens with different configurations and the Bragg wavelength (BW) shifts are continuously documented during the polymerization process. A theoretical relationship is derived between the BW shifts and the evolution properties, and an inverse numerical procedure to determine the properties from the BW shifts is established. Extensive numerical analyses are conducted to provide general guidelines for selecting an optimum combination of the two specimen configurations. The method is implemented for a high-temperature curing thermosetting polymer. Validity of the proposed method is corroborated by two independent verification experiments: a self-consistency test to verify the measurement accuracy of raw data and a warpage measurement test of a bi-material strip to verify the accuracy of evolution properties.


Effective chemical shrinkage Elastic modulus Evolution Fiber Bragg grating Gelation point 


  1. 1.
    Kelly G, Lyden C, Lawton W et al (1996) Importance of molding compound chemical shrinkage in the stress and warpage analysis of PQFP’s. IEEE Trans Compon Packag Manuf Technol Part B, Adv Packag 19(2):296–300CrossRefGoogle Scholar
  2. 2.
    Yang DG, Ernst LJ, van’t Hof C et al () Vertical die crack stresses of Flip Chip induced in major package assembly processes. 1533-1538Google Scholar
  3. 3.
    Oota K, Saka M (2001) Cure shrinkage analysis of epoxy molding compound. Polym Eng Sci 41(2):1373–1379CrossRefGoogle Scholar
  4. 4.
    Lu D, Wong CP (2009) Materials for advanced packaging. Springer-Verlag New YorkGoogle Scholar
  5. 5.
    Cook WD, Forrest M, Goodwin AA (1999) A simple method for the measurement of polymerization shrinkage in dental composites. Dent Mater 15(6):447–449CrossRefGoogle Scholar
  6. 6.
    Hudson AJ, Martin SC, Hubert M et al (2002) Optical measurement of shrinkage in UV-cured adhesives. J Electron Packag 124(4):352–354CrossRefGoogle Scholar
  7. 7.
    Li C, Potter K, Wisnom MR et al (2004) In-situ measurement of chemical shrinkage of MY750 epoxy resin by a novel gravimetric method. Compos Sci Technol 64(1):55–64CrossRefGoogle Scholar
  8. 8.
    Russell JD (1993) Cure shrinkage of thermoset composites. Sample Quarterly 24(2):28–33Google Scholar
  9. 9.
    Snow AW, Armistead JP (1994) A simple dilatometer for thermoset cure shrinkage and thermal expansion measurements. J Appl Polym Sci 52(3):401–411CrossRefGoogle Scholar
  10. 10.
    Thomas CL, Bur AJ (1999) In-situ monitoring of product shrinkage during injection molding using an optical sensor. Polym Eng Sci 39(9):1619–1627CrossRefGoogle Scholar
  11. 11.
    Yu H, Mhaisalkar SG, Wong EH (2005) Cure shrinkage measurement of nonconductive adhesives by means of a thermomechanical analyzer. J Electron Mater 34(8):1177–1182CrossRefGoogle Scholar
  12. 12.
    Spoelstra AB, Peters GWM, Meijer HEH (1996) Chemorheology of a highly filled epoxy compound. Polym Eng Sci 36(16):2153–2162CrossRefGoogle Scholar
  13. 13.
    Zhang ZQ, Beatty E, Wong CP (2003) Study on the curing process and the gelation of epoxy/anhydride system for no-flow underfill for flip-chip applications. J Electron Mater 288(4):365–371Google Scholar
  14. 14.
    Zhang ZQ, Yamashita T, Wong CP (2005) Study on the gelation of a no-flow underfill through Monte Carlo simulation. Macromol Mater Eng 206(8):869–877Google Scholar
  15. 15.
    Wang Y, Han B, Kim DW, Bar-Cohen A, Joseph P (2008) Integrated measurement technique for curing process-dependent mechanical properties of polymeric materials using fiber bragg grating. Exp Mech 48(1):107–117CrossRefGoogle Scholar
  16. 16.
    Adolf D, Martin JE (1990) Time-cure superposition during cross-linking. Macromolecules 23(15):3700–3704CrossRefGoogle Scholar
  17. 17.
    Eom Y, Boogh L, Michaud V et al (2000) Time-cure-temperature superposition for the prediction of instantaneous viscoelastic properties during cure. Polym Eng Sci 40(6):1281–1292CrossRefGoogle Scholar
  18. 18.
    Lange J, Toll S, Manson JAE et al (1995) Residual stress build-up in thermoset films cured above their ultimate glass transition temperature. Polymer 36(16):3135–3141CrossRefGoogle Scholar
  19. 19.
    Markovic S, Dunjic B, Zlatanic A et al (2001) Dynamic mechanical analysis study of the curing of phenol-formaldehyde novolac resins. J Appl Polym Sci 81(8):1902–1913CrossRefGoogle Scholar
  20. 20.
    Sham ML, Kim JK (2005) Experiment and numerical analysis of the residual stresses in underfill resins for flip chip package applications. J Electron Packag 127(1):47–51CrossRefGoogle Scholar
  21. 21.
    Stolov AA, Xie T, Penelle J et al (2000) Simultaneous measurement of polymerization kinetics and stress development in radiation-cured coatings: A new experimental approach and relationship between the degree of conversion and stress. Macromolecules 33(19):6970–6976CrossRefGoogle Scholar
  22. 22.
    Gonzalez L, Ramis X, Salla JM et al (2007) Kinetic analysis by DSC of the cationic curing of mixtures of DGEBA and 6, 6-dimethyl (4, 8-dioxaspiro[2.5]octane-5, 7-dione). Thermochim Acta 464(1–2):35–41CrossRefGoogle Scholar
  23. 23.
    Li WW, Liu F, Wei LH et al (2008) Curing behavior study of polydimethylsiloxane-modified allylated novolac/4, 4′-bismaleimidodiphenylmethane resin. J Appl Polym Sci 107(1):554–561CrossRefGoogle Scholar
  24. 24.
    Luo ZH, Wei LH, Li WW et al (2008) Isothermal differential scanning calorimetry study of the cure kinetics of a novel aromatic maleimide with an acetylene terminal. J Appl Polym Sci 109(1):525–529CrossRefGoogle Scholar
  25. 25.
    Maji PK, Bhowmick AK (2009) Influence of number of functional groups of hyperbranched polyol on cure kinetics and physical properties of polyurethanes. J Polym Sci, A, Polym Chem 47(3):731–745CrossRefGoogle Scholar
  26. 26.
    McGee SH (1982) Curing characteristics of particulate-filled thermosets. Polym Eng Sci 22(8):484–491CrossRefGoogle Scholar
  27. 27.
    Zhang ZQ, Wong CP (2004) Modeling of the curing kinetics of no-flow underfill in flip-chip applications. IEEE Trans Compon Packag Technol 27(2):383–390CrossRefGoogle Scholar
  28. 28.
    Bogetti TA, Gillespie JW (1992) Process-induced stress and deformation in thick-section thermoset composite laminates. J Compos Mater 26(5):626–660CrossRefGoogle Scholar
  29. 29.
    Huang YJ, Liang CM (1996) Volume shrinkage characteristics in the cure of low-shrink unsaturated polyester resins. Polymer 37(3):401–412CrossRefGoogle Scholar
  30. 30.
    Adolf DB, Martin JE, Chambers RS et al (1998) Stresses during thermoset cure. J Mater Res 13(3):530–550CrossRefGoogle Scholar
  31. 31.
    Kluppel M, Schuster RH (1997) Structure and properties of reinforcing fractal filler networks in elastomers. Rubber Chem Technol 70:243–255CrossRefGoogle Scholar
  32. 32.
    Alonso MV, Oliet M, Garcia J et al (2006) Gelation and isoconversional kinetic analysis of lignin-phenol-formaldehyde resol resins cure. Chem Eng J 122(3):159–166CrossRefGoogle Scholar
  33. 33.
    O’Brien DJ, White SR (2003) Cure kinetics, gelation, and glass transition of a bisphenol F epoxide. Polym Eng Sci 43(4):863–874CrossRefGoogle Scholar
  34. 34.
    Yu H, Mhaisalkar SG, Wong EH (2005) Observations of gelation and vitrification of a thermosetting resin during the evolution of polymerization shrinkage. Macromol Rapid Commun 26(18):1483–1487CrossRefGoogle Scholar
  35. 35.
    Yu H, Mhaisalkar SG, Wong EH et al (2006) Time-temperature transformation (TTT) cure diagram of a fast cure non-conductive adhesive. Thin Solid Films 504:331–335CrossRefGoogle Scholar
  36. 36.
    Chen KM, Jiang DS, Kao NH et al (2006) Effects of underfill materials on the reliability of low-K flip-chip packaging. Microelectron Reliab 46(1):155–163CrossRefGoogle Scholar
  37. 37.
    Lange J, Toll S, Manson JAE et al (1997) Residual stress build-up in thermoset films cured below their ultimate glass transition temperature. Polymer 38(4):809–815CrossRefGoogle Scholar
  38. 38.
    Meuwissen MHH, de Boer HA, Steijvers H et al (2006) Prediction of mechanical stresses induced by flip-chip underfill encapsulants during cure. Int J adhes Adhes 26(4):212–225CrossRefGoogle Scholar
  39. 39.
    Yang DG, Jansen KMB, Ernst LJ et al. (2004) Prediction of process-induced warpage of IC packages encapsulated with thermosetting polymers. Electronic Components and Technology Conference, pp. 98–105Google Scholar
  40. 40.
    Yu H, Mhaisalkar SG, Wong EH et al (2004) Evolution of Mechanical Properties and Cure Stresses in Non-Conductive Adhesives Used for Flip Chip Interconnects. Electronic Packaging Technology Conference, pp. 468–472Google Scholar
  41. 41.
    Aggelopoulos A, Karalekas D (2001) Determination of cure shrinkage in SL layer built plates using lamination theory. Adv Compos Lett 10(1):7–12Google Scholar
  42. 42.
    Attin T, Buchalla W, Kielbassa AM et al (1995) Curing shrinkage and volumetric changes of resin-modified glass ionomer restorative materials. Dent Mater 11(5–6):359–362CrossRefGoogle Scholar
  43. 43.
    Braga RR, Ferracane JL (2002) Contraction stress related to degree of conversion and reaction kinetics. J Dent Res 81(2):114–118CrossRefGoogle Scholar
  44. 44.
    Fano V, Ortalli I, Pizzi S et al (1997) Polymerization shrinkage of microfilled composites determined by laser beam scanning. Biomaterials 18:467–470CrossRefGoogle Scholar
  45. 45.
    Ishida H, Low HY (1997) A study on the volumetric expansion of benzoxazine-based phenolic resin. Macromolecules 30(4):1099–1106CrossRefGoogle Scholar
  46. 46.
    Park SH, Krejci I, Lutz F (1999) Consistency in the amount of linear polymerization shrinkage in syringe-type composites. Dent Mater 15(6):442–446CrossRefGoogle Scholar
  47. 47.
    Watts DC, Cash AJ (1991) Determination of polymerization shrinkage kinetics in visible-light-cured materials—methods development. Dent Mater 7(4):281–287CrossRefGoogle Scholar
  48. 48.
    Hocker GB (1979) Fiberoptic sensing of pressure and temperature. Appl Opt 18(9):1445–1448CrossRefGoogle Scholar
  49. 49.
    Gafsi R, El-Sherif MA (2000) Analysis of induced-birefringence effects on fiber Bragg gratings, Opt Fiber Technol 6(3):299–323CrossRefGoogle Scholar
  50. 50.
    Zhang Y, Feng DJ, Liu ZG et al (2001) High-sensitivity pressure sensor using a shielded polymer-coated fiber Bragg grating. IEEE Photonics Technol Lett 13(6):618–619CrossRefGoogle Scholar
  51. 51.
    Rabil CD, Harrington JA (1999) Mechanical properties of hollow glass waveguides. Opt Eng 38(9):1490–1499CrossRefGoogle Scholar
  52. 52.
    Tao XM, Tang LQ, Du WC et al (2000) Internal strain measurement by fiber Bragg grating sensors in textile composites. Compos Sci Technol 60(5):657–669CrossRefGoogle Scholar
  53. 53.
    Lopez-Higuera JM (2002) Handbook of optical fibre sensing technology. Wiley, EnglandGoogle Scholar
  54. 54.
    Cai HY, Li P, Sui G et al (2008) Curing kinetics study of epoxy resin/flexible amine toughness systems by dynamic and isothermal DSC. Thermochim Acta 473(1–2):101–105CrossRefGoogle Scholar
  55. 55.
    Costa ML, Botelho EC, Rezende MC (2006) Monitoring of cure kinetic prepreg and cure cycle modeling. J Mater Sci 41(13):4349–4356CrossRefGoogle Scholar
  56. 56.
    Fernandez-Francos X, Salla JM, Mantecon A et al (2008) Crosslinking of mixtures of DGEBA with 1, 6-dioxaspiro[4, 4]nonan-2, 7-dione initiated by tertiary amines. I. Study of the reaction and kinetic analysis. J Appl Polym Sci 109(4):2304–2315CrossRefGoogle Scholar
  57. 57.
    Han SJ, Wang KK (1997) Analysis of the flow of encapsulant during underfill encapsulation of flip-chips. IEEE Trans Compon Packag Manuf Technol Part B, Adv Packag 20(4):424–433MathSciNetCrossRefGoogle Scholar
  58. 58.
    He Y (2005) Chemical and diffusion-controlled curing kinetics of an underfill material. Microelectron Reliab 45(3–4):689–695CrossRefGoogle Scholar
  59. 59.
    Omrani A, Simon LC, Rostami AA et al (2008) Cure kinetics, dynamic mechanical and morphological properties of epoxy resin-IM6NiBr2 system. Eur Polym J 44(3):769–779Google Scholar
  60. 60.
    Kim KJ, Bar-Cohen A, Han B (2007) Thermo-optical modeling of polymer fiber Bragg grating illuminated by light emitting diode. Int J Heat Mass Transfer 50(25–26):5241–5248MATHCrossRefGoogle Scholar
  61. 61.
    Post D, Han B, Ifju P (1994) High sensitivity Moire. Springer-Verlag New YorkGoogle Scholar
  62. 62.
    Goertzen WK, Kessler MR (2006) Creep behavior of carbon fiber/epoxy matrix composites. Mater Sci Eng, A 421:217–225CrossRefGoogle Scholar
  63. 63.
    Yang J, Zhang Z, Schlarb AK, Friedrich K (2006) On the characterization of tensile creep resistance of polyamide 66 nanocomposites. Part I. Experimental results and general discussions. Polymer 47:2791–2801CrossRefGoogle Scholar

Copyright information

© Society for Experimental Mechanics 2010

Authors and Affiliations

  1. 1.Department of Mechanical EngineeringUniversity of MarylandCollege ParkUSA

Personalised recommendations