Analytical modeling of particle size and cluster effects on particulate-filled composite

A three-layer built-in model, extended from Christensen and Lo’s three-phase sphere model for particulate-filled composites (PFC) containing no clusters [R.M. Christensen and K.H. Lo, J. Mech. Phys. Solids, 27 (1979) 315.], is proposed to evaluate the particle size and cluster effect on the mechanical properties of PFC. Different from the self-consistent model used by Corbin and Wilkinson [S.F. Corbin and D.S. Wilkinson, Acta Metall. Mater., 42 (1994) 1311], which gives only average stress–strain distribution, this model can be used to estimate the point-by-point stress–strain distribution induced by either external force or temperature variation. Particles that are harder and softer than matrix are studied. It is found from the calculated results that reducing cluster and particle size, using less scattered particles, reinforcing the bonding strength at the interface of particles and matrix, enhancing the deformability of matrix, and employing particles with a coefficient of thermal expansion smaller than that of matrix are efficient methods to resist damages of PFC. In addition, reducing cluster concentrations and increasing particle contents are preferred for PFC containing hard particles and have negative effect for PFC involving soft particles. The selection of particle rigidities should be based on a balanced comparison between strength and rigidity requirements of PFC.