Failure of composite tubes in the Chinese lantern mode under a weight-type load

Abstract

In [1], an equation is derived for calculating the critical stress of failure of unidirectional composite tubes in the form of a Chinese lantern (splitting of a tube into strips with subsequent loss of stability):where ~ is the specific work of failure upon splitting along the fibers, E is the elastic modulus in the direction of the axis of a thin-walled tube, R is the radius, and L is the length of the tube. Equation (1) is widely used both for scientific-methodical purposes and for calculating certain composite structures. Thus, for example, in [2] this equation was used to choose the optimum sizes of elements of a multisectional tubular structure subjected to bending and to calculate the stem of bamboo.However, when applying Eq.(1), we should bear in mind that it is valid only in some special conditions of loading, which is very seldom realized in actual structures. To derive this equation, the energy approach is used [3] based on the comparison of compression energy of a composite bar in the precritical state with the total energy in the elements of a split bar in the postcritical state. It is assumed that failure is possible if the energy of precritical compression is not smaller than the sum of the postcritical energy and the work of failure, which is necessary for splitting a bar into strips. In [1], the energy balance is given bywhere U 0 is the energy of precritical compression, U 1 is the energy of compression in the new state, U z is the energy of bending of strips, and F is the work of failure. The equality in the last expression leads to formula (1). Expression (2) is valid only when, upon failure of the bar, there is no additional displacement of its edges, i.e., at loading of the so-called "press" type. Such loading can be realized, for example, in a testing machine. However, for machine-building constructions, the action of a load of "weight" type is more characteristic when the acting force retains its magnitude after splitting of a tube. For such loads, Eq. (2) must be modi-