assumed spherical and both the matrix and the filler are isotropic elastic. The
material properties involved are as follows:
ATH: E 1 ¼ 70 GPa, v 1 ¼ 0.24.
PMMA: E 0 ¼ 3.5 GPa, v 0 ¼ 0.31
Particle volume fraction: φ ¼ 0.48
Experimental mean value of Young’s modulus for this composite is about
10.2 GPa at room temperature. Figure 6.1 shows the comparisons among the
analytical solution (including pairwise interacting solution and noninteracting solution) and experimental results. It is observed that agreement between the pairwise
interacting prediction and experimental data is very good for the effective Young’s
modulus. Based on the foregoing preliminary analytical and experimental comparisons, it appears that Ju and Chen’s analytical micromechanical approach offers a
simple, approximate, yet sufficiently accurate framework for the prediction of
effective elastic moduli of two-phase composites.
Particle-filled composites consist of bulk matrix, filler particles, and interfacial
transition zone around particles, which often have very different properties such as
coefficient of thermal expansion (CTE) and stiffness. Within the particulate composite microstructure, there are micro-stresses due to the coefficient of the thermal
expansion (CTE) mismatch between the matrix and the filler particles. For the
composite prepared using lightly cross-linked poly-methyl methacrylate (PMMA)
filled with alumina trihydrate (ATH), these micro-stresses can be imaged using the
fact that PMMA is optically birefringent. The micro-stresses imaged using this
technique are indeed due to CTE mismatch as they dissipate at temperatures close
Fig. 6.1 Effective Young’s modulus as a function of particle volume fraction (Nie 2005)
6.1 Introduction
279
material properties involved are as follows:
ATH: E 1 ¼ 70 GPa, v 1 ¼ 0.24.
PMMA: E 0 ¼ 3.5 GPa, v 0 ¼ 0.31
Particle volume fraction: φ ¼ 0.48
Experimental mean value of Young’s modulus for this composite is about
10.2 GPa at room temperature. Figure 6.1 shows the comparisons among the
analytical solution (including pairwise interacting solution and noninteracting solution) and experimental results. It is observed that agreement between the pairwise
interacting prediction and experimental data is very good for the effective Young’s
modulus. Based on the foregoing preliminary analytical and experimental comparisons, it appears that Ju and Chen’s analytical micromechanical approach offers a
simple, approximate, yet sufficiently accurate framework for the prediction of
effective elastic moduli of two-phase composites.
Particle-filled composites consist of bulk matrix, filler particles, and interfacial
transition zone around particles, which often have very different properties such as
coefficient of thermal expansion (CTE) and stiffness. Within the particulate composite microstructure, there are micro-stresses due to the coefficient of the thermal
expansion (CTE) mismatch between the matrix and the filler particles. For the
composite prepared using lightly cross-linked poly-methyl methacrylate (PMMA)
filled with alumina trihydrate (ATH), these micro-stresses can be imaged using the
fact that PMMA is optically birefringent. The micro-stresses imaged using this
technique are indeed due to CTE mismatch as they dissipate at temperatures close
Fig. 6.1 Effective Young’s modulus as a function of particle volume fraction (Nie 2005)
6.1 Introduction
279