Characteristics of Compositions of Unidirectional Short Boron Fibers and Metal Matrices

Abstract

Compositions of unidirectional short boron fibers and titanium, magnesium, and aluminum matrices are considered. The Rosen and Kelly parameters (the ineffective and critical lengths) characterizing the interaction of short fibers and the matrix are studied. These parameters as functions of material characteristics of components of the composites are established on rectangular (with a 2D reinforcement) or rectangular parallelepiped samples (with a 3D one) containing an inclusion in the form of a single short fiber. It is shown that the Rosen parameter is determined only by material characteristics of fibers and matrices, but the critical fiber length (Kelly parameter), in addition, also depends on the strain state of composition. In order to assess the interaction of a short reinforcing fiber with the matrix, a new parameter — the effective length — is introduced. This is the part of the short fiber whose stresses make up 100φ % (0.95 < φ < 1) of the stiffness of the same sample with a continuous fiber. A method for constructing the representative volumes of metal matrices statistically uniformly reinforced by unidirectional short boron fibers is proposed. It is shown that the ratio of the characteristic size of the representative volume of composite to the fiber length can reach two or more units. The elastic characteristics of unidirectionally reinforced short-fiber composites in relation to the fiber length are studied. On the basis of a numerical analysis of this dependence, the concept of the equivalent length of a short fiber is formulated. This length provides the stiffness of a short-fiber-reinforced sample equal to 100φ % (0.95 < φ < 1) of that in the case of a continuous reinforcing fiber. Results of the studies are illustrated by graphs and tables.