Limitations of the Predictive Capacity of Newtonian Fluid Theories on the Shear Moduli Ratio (Gc/Gm) of Particulate Composites: An Analytical Approach

The objective of this chapter is to undertake a theoretical review of three equations of Newtonian fluids that are used to predict the mechanical properties of particulate filler composites, test their utility and further attempt to identify their limitations and weaknesses. Expressions are presented here from existing literature that relate the viscosity of 2-phase Newtonian fluids to the shear modulus ratio of 2-phase Hookean particulate composites. This approach is based on the rationale that for similar geometries the two types of materials, Newtonian fluids and Hookean solids, obey similar rules. Since Newtonians fluids are practically incompressible, the Hookean solids are also taken to be incompressible to facilitate comparison of the two, with a Poisson’s ratio therefore of 0.5. Application of these expressions to filler reinforced composites with their known properties give rise to values of the (Gc/Gm) ratio that are independent of the shear moduli of fillers that are correct at a 0% filler volume fraction but wrong at a 100% filler volume fraction. This highlights the limitation of these Newtonian fluid theories in predicting the properties of particulate composites. A case is made, therefore, for modifying these expressions to improve their predictive capacity by tying them to the known values of this ratio of shear moduli for different particulate reinforced composites and replacing the constants in them with variables to be determined.