Fracture of fibers by a crack propagating in a composite

Abstract

Failure of a composite is a complicated process accompanied by irreversible changes in the microstructure of the material~ Micromechanisms are known of the accumulation of damage and failure of the type of localized and multiple ruptures of the fibers, delamination along interphase boundaries [1-3], and also micromechanisms associated with fracture of fibers [2]. In this work, we proposed a mathematical model of the micromechanism of failure of a composite material randomly reinforced with a system of short fibers. The model is constructed for describing the phenomenon of fracture of the fibers taking place during crack propagation in composites reinforced with whiskers or in fiber-reinforced polycrystalline materials. It is assumed that the angular distribution of the fibers is isotropic and the elastic characteristics of the fibers are considerably higher than the elastic constants of the matrix. The following assumptions are used as the main hypotheses used as a basis for constructing the model. The matrix contains a nucleation crack. When the load is increased the crack grows and its boundary comes into contact with the reinforcing fibers. A further increase of the stress causes bending of the fiber. When the fiber curvature reaches a specific critical value, the fiber ruptures. If the stress at infinity is given, the fibers no longer delay the development of failure during crack propagation. The degree of distortion of the fiber in the vicinity of the boundary of the crack is determined by the moment model of the material. The need to take into account the moment stresses in the failure theory of the reinforced material was stressed in [4]~ We should also mention the studies [5-10] concerned with examination of the effect of the moment stresses in fracture mechanics. i. Comparison of Mechanisms of Fracture and Rupture of Fibers It is evident that the fracture mechanism of the fibers is one of the many possible mechanisms of failure of the material [2, II]. The rupture of fibers under the effect of axial loading is a competing process. We determine the stress at which the ruptures of fibers starts to take place in the vicinity of the boundary of a circular crack in a randomly reinforced material~ We also carry out elementary calculations of the stress at which the fibers start to fracture. Since all considerations are of qualitative nature, to simplify these considerations, we shall examine a material in which all the fibers are oriented along the same direction given, for example, by the Z axis of the cylindrical coordinate system R, ~, Z. We assume that the body contains a circular crack with radius R 0 (Fig. I). It is also assumed that the crack has already ruptured several fibers during its propagation. The