Spatial Buckling Modes of a Fiber (Fiber Bundle) of Composites with a [±45]_2s Stacking Sequence Under the Tension and Compression of Test Specimens

A refined formulation is presented for linearized problems on internal multiscale spatial buckling modes of a fiber or fiber bundle — the structural elements of fibrous composites — that is in a subcritical (unperturbed) state under the action of shear and tensile (compressive) stresses in the transverse direction. Such an initial stress state is formed in fibers and fiber bundles in tension and compression tests of plane test specimens of angle-ply composites reinforced with straight fibers. To formulate the problem, equations are constructed by reducting a consistent variant of geometrically nonlinear equations of elasticity theory to one-dimensional equations of the theory of straight rods taking into account their interaction with the surrounding matrix. These equations are based on using the refined Timoshenko shear model in the perturbed state of composite with account of tension-compression strains in the transverse direction for a rigid fiber (fiber bundle) represented in the form of a rod with a rectangular cross section and the model of a transversely soft layer with a fixed outer boundary of the periodicity cell of composite for four binder elements introduced into consideration. It is shown that, in loading test specimens with a [±45]_2s structure, a continuous rearrangement of the composite structure is possible in both compression and tension. This occurs owing to the realization and continuous changes of internal buckling modes with continuous variations of the parameter of wave formation. This fact, in particular, can explain the phenomenon of decreasing of the averaged shear modulus of a fibrous composite with growing shear strains and the formation of a reversible nonlinearly elastic component of its total strain.