Buckling of elastic composite rings under internal impulsive loading

Abstract

The experimentally detected phenomenon of compression fracture of a composite ring made of unidirectional fiberglass plastic under initial internal impulsive (explosive) loading is analyzed,Fracture results from bending in the compression phase because of loss of stability of the radial axisymmetric mode of motion.introduction. The loss of stability of the radial axisymmetric vibration mode of cylindrical shells or rings and transition to nonaxisymmetric flexural modes of motion accompanied by an exponential increase in the amplitudes of normal deflections has been the subject of extensive theoretical and experimental investigations [1][2][3][4][5][6]. This deformation and fracture pattern is observed for a thin-walled shell or a ring under sudden loading by an external radial pressure [1, 3, 5, 6]. However, for shells or rings made of composites, this fracture mechanism is also possible under internal impulsive loading [7][8][9][10]. This phenomenon is explained by the fact that composites, in particular unidirectional composites, in contrast to metals, have much larger limiting elastic strains for stretching in the direction of reinforcement (0.04-0.05 and 0.002-0.005, respectively) with almost complete absence of plastic strains until fracture [11]. During impulsive stretching of a composite shell or a ring in the radial direction, this makes it possible to accumulate a sufficient amount of elastic energy to ensure bending fracture of the material in the compression phase due to loss of stability of radial axisymmetric vibrations and transition to nonaxisymmetric flexural vibrations. One additional factor (along with initial irregularities and nonuniformity in the application of initial loads and distribution of initial velocities) that is responsible for loss of stability and fracture of this type for an elastic shell or a ring is the low (as compared to metals) shearing rigidity of the packet of reinforcing fibers in the plane of the ring.In the present paper, we consider an elastic uniform (but not isotropic) cylindrical ring that models a ring made of a unidirectional composite reinforced with a fiber in the circumferential direction with zero angle of reinforcement. In this case, the composite material is considered transversely isotropic and is described by five independent elastic constants [12]. Since the ring deforms in its plane, only two of the elastic constants are used: the modulus of longitudinal elasticity E in the circumferential direction of reinforcement and the modulus of transverse shear G in the ring plane.1. Derivation of the Equations of Motion of an Elastic Ring Taking into Account Transverse Shear Deformations. We convert the system of differential equations of equilibrium for a cylindrical shell [13] to a system of differential equations of equilibrium for a ring of radius R. For this, we eliminate the longitudinal coordinate a and the corresponding longitudinal displacement u, the axial and transverse forces N1 and Q1, the moments M12 and M21, and the surface forces X. In addition, w...