Effect of Inclusions on Friction Coefficient of Highly Filled Composite Materials

Highly filled composite material systems exhibit, in triaxial compression, a composite strength that is greater than either the weaker particulate or matrix strength. This is due to an amplification of the local confinement in the matrix activating frictional mechanism. The paper quantitatively addresses this increase of the friction coefficient of a matrix reinforced by rigid inclusions using assorted means of nonlinear micromechanics. The approach is based on a nonlinear elastic representation of a Drucker–Prager type frictional strength behavior of the matrix at failure. The key to success of the homogenization procedure relies on the appropriate definition of effective strains in the matrix, to capture local confinement effects and shear effects in the connected matrix phase. It is shown that an effective strain concept based on linear volume averaging (i.e., classical secant method) leads to overestimate the inclusion effects; while an effective strain concept based on quadratic volume averaging (i.e., modified secant method) provides a more realistic representation of shear strains and local confinement effects that develop in triaxial compression in the matrix. Finally, a combination of these two methods leads to a mixed secant method, which gives a relative friction increase of (volume fraction fI). This estimate accurately predicts the experimentally observed frictional behavior of unleached and leached cement-based mortars, composed of a cement paste matrix and rigid sand inclusions.