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A method is proposed for predicting the strength of composites randomly reinforced with short fibres. The fundamental requirements for composites and production technology for thermoplasts with assigned properties and randomly reinforced with short fibres are formulated.Predicting the strength of unidirectional composites reinforced with long high-strength fibres is based on the concept concerning fragmentation of reinforcing fibres when tensile loads act on the composite [1][2][3][4]. The pronounced scale dependence of the strength of fibres on their length is a factor that complicates the calculation. The sites and sequence of fibre breaks are determined by the different degree of hazardousness of the defects stress concentrators. In a unidirectional composite, the reinforcing fibres restore their load-carrying capacity at distance l l.ef from the site of a break (Fig. 1). With an increase in stresses, the ineffective length (l l.ef ) increases. Fragmentation of the fibres into pieces will continue until the length of the fragments is reduced to the critical length δ = 2l l.ef.max and shear stresses τ* on the fibrematrix interface exceed the shear strength τ m . The fibre fragments that attain the critical length will slide in the matrix on further deformation. The critical length δ is calculated with the KellyTyson equation [5]:where σ δ is the maximum stress in fibre fragments attaining the critical length; d f is the fibre diameter; τ m is the shear strength on the fibrematrix interface.Since random reinforcement of thermoplasts with short fibres (l f ≤ δ) was traditionally used to give composites special properties (friction, antifriction, thermal conductivity, electrical conductivity, etc.), the strength problems of randomly reinforced composites were not a priority. However, thermoplasts randomly reinforced with carbon fibres (CF) have recently been competing with nonferrous metals in parts and structures in machine building which are subject to tensile, compressive, and flexural loads. In comparison to unidirectional composites, randomly reinforced thermoplasts have the decided advantage of processability, which allows processing them with highly productive methods and the possibility of recycling.In the present article, we propose an approach to prediction of the strength of composites randomly reinforced with fibres whose length l f is one order of magnitude greater than the diameter d f but does not exceed critical length δ.When such a composite is stretched, the fibres oriented in the direction of or at some angle α to the acting force are taut. At α = 90°, the fibres do not absorb the tension and are usually regarded as a disperse filler which does not strengthen the matrix [3]. Such a composite can be represented as a two-phase system consisting of strengthening oriented fibres and a matrix with an inert filler. The strength of fibres with a length of l f ≤ δ is no lower than the strength of fibres of critical length δ

The adhesion of Realization of the strength of the reinforcing filler is ensured by adhesion interaction with the matrix. Knowledge of the adhesion, in ackiition to indicators of the elastoplastic properties of the fibrous filler and matrix, is required to predict composite strength in developing new materiaJs with assigned properties. There are muny methods of assessing the degree of adhesion interaction on the interphese bo,n~ry in a composite [I-3]. The testing of single-fiber composites (SFC) is the most informative and technically simple method of assessing adhesion.Successive crushing of an elementary fiber in a polymer block into numerous fragments occurs when SFC are tensioned. The extent of the crushing is determined primarily by the adhesion of the fiber to the matrix. The lengths of the fragments formed are found to be limiting for a given fiber-polymer system. According to the Kelly-Tyson model [4], the interphase-shear stress calculated from the formula c~edf = '~, (I) where l c is the critical length as determined from SFC tests, oc is the fiber strength for the critical length, and df is the diameter of the fiber being tested.The stm~ of the kinetics of fiber-ropmre accumulation in a polymer block, which was undertaken in [5][6][7][8][9], has made it poss~le to obtain all information required for adhesion assessment (relative to critical length, scale dependence of fiber strength on length, and, consequently, strength at the criti"""""' length) from tests of two-three SFC specimens.Tamuzh et al.[6] present fiber fragmentation during SFC deformation in the form of a graphical log ~f--log fsp relationship between the average length of the fragments formed and the strain of the specimen. The average fragment length I f is related directly to the number of ruptures EN i by the expressiontf= Y.N, + where/0 is ~e fiber length in the effective section of the specimen prior to testing. log /f-log fsp curves for various systems that are characterized by a break at a certain average fragment length/k are presented in Fig. 1. As is demonstrated in [6], the slope of the inclined segment is determined by the scale dependence of "Uvikom," Moscow Oblast, Russia.

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