Comparation of selected stiffness theories of *FRP composites
Robert Piekarski Politechnika Warszawska, Instytut Mechaniki i Konstrukcji, ul. Narbutta 85, 02-524 Warszawa
Quarterly No. 1, 2006 pages 26-31
DOI:
keywords: *FRP composites, stiffness theories, homogenization, elastics constants, comparative analysis
abstract The article concerns *FRP composites, i.e. unidirectional long fibre - reinforced plastics. The following assumptions are made. A composite is a matrix - fibre two-phase material. Manufacturing technologies protect full contact between fibres and a matrix. Fibres, a matrix and a composite are treated as linearly elastic materials. A matrix is made of a duroplast and modeled as a uniform and isotropic material. A fibre is considered as a uniform and monotropic material. Fibres are rectilinear and packed uniformly in a hexagonal scheme. After homogenization, a composite is modelled as a uniform and monotropic material, with a monotropy axis coinciding the direction of fibres’ alignment. The state-of-the art of two basic groups of stiffness theories of *FRP composites is described. The TM* theories are based on technical mechanics. The MCM* theories are based on mechanics of continuous media (theory of elasticity). Sets of final formulae related to the TM1 and TM2 theories are collected from references (Eqs (1, 2)). The TM3 stiffness theory is developed (Figs. 1-4, Eqs (3-6)). The MCM3 quasi-exact theory has been developed, via incorporating the real fibre volume ratio and deriving the optimal form of the compatibility condition in the 3rd Lamé task. Three composites, PFRP, GFRP and CFRP, have been analysed. Prediction of values of the elastic constants of these composites from the MCM3 theory has been confirmed positively by the experimental data available (Table 1, Fig. 5). The predicted values of the elastic constants according to the TM1, TM2 and TM3 theories have been compared to the results obtained from the MCM3 theory (Table 2, Fig. 5). It has been pointed out that the E11, ν 21 elastic constants can be predicted from the TM1 theory whereas the E22, ν 32, G12 constants should be predicted from the MCM3 theory.