Some problems about internal stability loss and stress distribution in an elastic and viscoelastic unidirected fibrous composites

ABSTRACT It is well known that the curving of the fibers in the structure of the unidirectional fibrous composite materials may be the result of specific structural characteristics of composite materials caused by design factors as well as a consequence of technological processes under the action of various factors. Therefore, the curving of fibers in the structure of composites can be taken as structural features as well as damage of the structure of these materials. Moreover, the curving of the fibers is taken as a model for the investigations of various failure and stability loss problems of composites in compression. In this study, within the framework of the piece-wise homogeneous body model with the use of the three-dimensional geometrically non linear exact equations of the theory of elasticity, the method for the determination of the stress-strain state before stability loss and stability loss in the undirected fibrous composites with periodically curved fibers is developed. All concrete investigations are made for the infinite elastic and viscoelastic body containing one and two periodically curved fibers. For the infinite elastic and viscoelastic body containing two periodically curved fibers case, it is assumed that these fibers are located along two parallel lines. The stress distribution and stability loss problems are studied when the body is loaded at infinity by uniformly distributed normal forces, which act in the direction along which lie the fibers. For the considered stability loss problems, at the first it is assumed that the filler concentration in the composite is very small and interacting between the fibers is ignored. Consequently, the material is modelled as an infinite viscoelastic body containing a single fiber. Then, this approach is developed for the case where the interactions between the fibers are taken into account, and the corresponding analysis are made on the infinite viscoelestic media containing two neighbouring fibers. It is assumed that these fibers are located along two parallel lines which are on the same and on the different parallel planes and each of them has the same initial insignificant small curving. These curvings are periodic and sin-phase. The case where the imperfection starts to increase and becomes indefinitely is taken as a stability loss criterion. In this way, using the mentioned modelling it is estimated the influence of the interaction between the fibers to the corresponding values of the critical time. It is used Rabotnov operator to determine viscoelastic material and investigate the influence of reological parameters and interaction between the fibers to the critical time. The numerous numerical results related to this influence are given. For the considered stress-strain state before stability loss problems, at the first the investigations of the influence of the geometricel non linearity to the stress distribution in the unidirectional fibrous composites with curved fibers are carried out for small concentration of fibers and in this case composite material is modelled as an infinite elastic body containing a single periodical curved fiber. Then, the method is developed for the stress analyses in the infinite elastic body containing two neighbouring periodically curved fibers, which are located along two parallel lines. Two location cases are considered, namely, the co-phase and anti-phase curving cases of the fibers with respect to each other. In this case, it is assumed that the middle lines of the fibers are in the same plane. The influence of the interaction between the fibers on the stress distribution caused by the curving of the fibers is studied and the numerical results, related to the self-balanced normal and shear stresses, which act on the interface, are given. The influence of the geometrical non linearity to the considered stress distribution, is also investigated. Keywords: Fibrous composite, stress distribution, geometrical non lineerity, internal stability loss, critical time xi