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Measurement of Elastic Properties of Epoxy Molding Compound by Single Cylindrical Configuration with Embedded Fiber Bragg Grating Sensor

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Abstract

We propose a novel experimental method, based on a fiber Bragg grating (FBG) sensor, to measure the elastic properties of epoxy molding compound (EMC) from a single specimen configuration. The FBG sensor is embedded in the center of a cylindrical EMC specimen, and deforms together with the EMC. The Bragg wavelength (BW) shifts are documented during compressive and hydrostatic loadings. Young’s modulus and bulk modulus are determined from the BW shifts using the relationships between the elastic constants and the BW shift. Two major developments to accommodate the unique requirements of EMC testing include: (1) a large mechanical pressure to be applied during curing; and (2) a very high gas pressure required for hydrostatic testing. The shear modulus and Poisson’s ratio are calculated from the two measured constants to provide a complete set of elastic properties of EMC.

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Authors and Affiliations

  1. Department of Mechanical Engineering, University of Maryland, College Park, MD, 20742, USA

    Y. Sun, H.-S. Lee & B. Han

Authors
  1. Y. Sun
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  2. H.-S. Lee
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  3. B. Han
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Corresponding author

Correspondence to B. Han.

Appendix

Appendix

Substituting Eq. (2) into Eq. (6) yields:

$$ \begin{array}{l}\varDelta \lambda =\frac{1}{E_f}\left\{\left[1-\frac{n^2}{2}\left({P}_{12}-\left({P}_{12}+{P}_{11}\right){\nu}_f\right)\right]\left[\frac{2{E}_f{\nu}_f{C}_{1f}}{\left(1+{\nu}_f\right)\left(1-2{\nu}_f\right)}+\frac{2{E}_f{\nu_f}^2c}{\left(1+{\nu}_f\right)\left(1-2{\nu}_f\right)}+{E}_fc\right]\;\right.\\ {}\left.-\left[2{\nu}_f+\frac{n^2}{2}\left(\left(1-{\nu}_f\right){P}_{11}+\left(1-3{\nu}_f\right){P}_{12}\right)\right]\left[\frac{E_f}{1+{\nu}_f}\left[\frac{C_{1f}}{1-2{\nu}_f}-\frac{C_{2f}}{r^2}\right]\kern0.5em +\frac{E_f{\nu}_fc}{\left(1+{\nu}_f\right)\left(1-2{\nu}_f\right)}\right]\right\}{\lambda}_i\end{array} $$
(A.1)

Next, substituting Eq. (4) into Eq. (A.1) yields:

$$ \begin{array}{l}\varDelta \lambda =\frac{1}{E_f}\left\{\left[1-\frac{n^2}{2}\left({P}_{12}-\left({P}_{12}+{P}_{11}\right){\nu}_f\right)\right]\left[\frac{2{E}_f{\nu}_f}{\left(1+{\nu}_f\right)\left(1-2{\nu}_f\right)}\left(\frac{CE-BF}{AE-BD}+\left(\frac{1}{\left(1-2{\nu}_p\right)\left(1+{\nu}_p\right)}\frac{CE-BF}{AE-BD}\right.\right.\right.\right.\\ {}\left.\left.\left.+\frac{\nu_p}{\left(1-2{\nu}_p\right)\left(1+{\nu}_p\right)}\frac{CD-AF}{BD-AE}-\frac{P_1}{E_p}\right)\left(1+{\nu}_p\right)\right)+\frac{2{E}_f{\nu_f}^2}{\left(1+{\nu}_f\right)\left(1-2{\nu}_f\right)}\frac{CD-AF}{BD-AE}+{E}_f\frac{CD-AF}{BD-AE}\right]\\ {}-\left[2{\nu}_f+\frac{n^2}{2}\left(\left(1-{\nu}_f\right){P}_{11}+\left(1-3{\nu}_f\right){P}_{12}\right)\right]\left[\frac{E_f}{1+{\nu}_f}\left(\frac{1}{1-2{\nu}_f}\left(\frac{CE-BF}{AE-BD}+\left(\frac{1}{\left(1-2{\nu}_p\right)\left(1+{\nu}_p\right)}\frac{CE-BF}{AE-BD}\right.\right.\right.\right.\\ {}\left.\left.\left.\left.\left.+\frac{\nu_p}{\left(1-2{\nu}_p\right)\left(1+{\nu}_p\right)}\frac{CD-AF}{BD-AE}-\frac{P_1}{E_p}\right)\left(1+{\nu}_p\right)\right)\right)+\frac{E_f{\nu}_f}{\left(1+{\nu}_f\right)\left(1-2{\nu}_f\right)}\frac{CD-AF}{BD-AE}\right]\right\}{\lambda}_i\end{array} $$
(A.2)

Finally, the governing equation can be obtained by substituting Eq. (5) into Eq. (A.2).

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Sun, Y., Lee, HS. & Han, B. Measurement of Elastic Properties of Epoxy Molding Compound by Single Cylindrical Configuration with Embedded Fiber Bragg Grating Sensor. Exp Mech 57, 313–324 (2017). https://doi.org/10.1007/s11340-016-0215-5

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  • DOI: https://doi.org/10.1007/s11340-016-0215-5

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