E1 Constituents: Matrix and Reinforcement

Topic

This composite consists of two constituents—the matrix and the reinforcement—with the volume fractions and intrinsic properties of each serving as the model's fundamental inputs. Because the matrix and reinforcement are combined, their volume fractions are governed by a joint balance: the sum of the matrix volume fraction and the reinforcement volume fraction equals the total volume of the composite; thus, knowing one fraction allows the other to be determined by subtraction.

Furthermore, the volume fraction of each constituent can be converted into its corresponding mass fraction, and vice versa. Since the mass of each constituent is the product of its volume and density, knowing the densities of the matrix and the reinforcement enables conversion between volume fraction and mass fraction in either direction.

This same volume fraction, combined with the phase densities of the matrix and reinforcement, determines the density of the composite as a whole according to the rule of mixtures: the composite density is the average of the matrix and reinforcement densities, each weighted by its respective volume fraction. A higher reinforcement volume fraction—where the reinforcement is denser than the matrix—results in a higher overall composite density; conversely, a lower reinforcement volume fraction causes the composite density to approach that of the matrix alone.

In addition to its volume fraction and density, the reinforcement possesses a specific geometry characterized by its aspect ratio—the ratio of its length to its thickness or diameter. A high aspect ratio results in the reinforcement taking the form of a long, continuous fiber; The low aspect ratio means that the reinforcement takes the form of a short particle or a chopped fiber.

Consequently, this model—along with the matrix and reinforcement specifications established at the outset—serves as an input for two other models in the set: the one describing the composite's effective elastic properties and the one describing its effective thermal properties. Establishing the volume fractions, composite density, and reinforcement aspect ratio here allows those other two models to utilize these parameters directly, without the need to redefine them.

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