Analysis of the Maximum Tensile Strength of a Composite with Spherical Particulates

Abstract

Good theoretical composite models have been developed to address the modulus as a function of filler volume fraction and tensile strength as a function of time. However, very little has been done to understand the observation that the tensile yield strength appears to go through a maximum as a function of the volume fraction of filler for a particulate composite. While several factors undoubtedly influence the location of this maximum, it is apparent that the necessary generation of voids in the formulation has been largely overlooked as a primary source for this maximum. A simple parallel strain composite tensile strength model is developed from the different tensile strength components in the composite. For this simple model the tensile strength of the composite is set to go to zero at the ‘zero limit’ packing fraction. The most important result from this simple model is that a maximum in composite tensile strength is clearly indicated when the tensile strength of the filler is greater than that of the matrix and the transfer efficiency from the filler to the matrix is not near zero. A more detailed generalized tensile strength model is also developed from the existing modulus models. This derivation is initiated from the definition of modulus which includes both stress and strain. The ratio of the tensile yield strength of the composite to that of the matrix is equated to corresponding ratios for yield strain and secant yield modulus. It is assumed that the strain ratio could be described by the reciprocal of a modified Kerner equation and the modulus ratio could be described by the generalized modulus equation developed earlier by this author. This new tensile strength model nicely describes a maximum tensile strength as well as a minimum tensile strength at the zero limit packing fraction. It is clearly shown that the new generalized tensile strength model developed in this study gives a much better fit of four sets of tensile strength data than the Turcsanyi model, the Dibenedetto model and a second-order polynomial model. This result applies equally for data that shows a clear maximum as well as data where the tensile strength decreases steadily from the tensile strength of the matrix itself.