Stability of Fibrous Composites

Abstract

In this review article the three-dimensional linearized theory is presented of the internal and the surface instability of fibrous composite materials. The possible mechanisms of the stability loss in the structure of these materials are investigated. In this investigation the strict model is used of the nonlinearly elastic compressible and incompressible piecewise-homogeneous medium with the arbitrary form of the elastic potential for the theory of finite deformation and for two variants of the theory of small precritical deformations. Problems for a single fiber (fibrous materials with low concentration of the filler, when at stability loss the interaction between fibers is not accounted for), for two fibers (fibrous materials with low concentration of the filler, when as a result of the structure irregularity at the stability loss two neighbouring fibers may interact) for the infinite row and for a doubly periodic system of fibers (fiber materials with nonsmall filler concentration, taking into account fiber interaction), in the infinite and semiinfinite matrix, are considered. Results are obtained for these cases, predominantly when conditions are satisfied of the complete contact on the fiber and matrix polymer or metal interfaces. In the case of the metal matrix at plastic deformations the conception of continuing loading is used, and the change of the unloading zones in the process of stability loss is not accounted for. The influence of the inhomogeneity of the precritical stressed state, resulting from the difference of coefficients of the transverse expansion, of the mechanical properties, and of the volume concentrations of the fibers and the matrix, on the critical parameters is investigated. Application is presented of the obtained results in the fracture mechanics of fibrous composite materials under compression along the reinforcing elements.

On internal stability loss of a row unidirected periodically located fibers in the visco-elastic matrix

“…and according to [12], do not have only considerable effect on numerical results. Thus, taking the above stated into account consider the determination of each approximation separately.…”

“…As we can see some of them in [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19], there are a lot of experimental and theoretical investigations focus on composites including fibers and nanofibers. It is very important to know the mechanisms of the fracture of the composites under uniaxial compression along the reinforcing elements.…”

“…So, the theoretical investigations of the fracture on the unidirectional composites under uniaxial compression along the reinforcing elements are mean to investigate the stability loss in the material structure, and the value of the external critical forces is taken as the failure forces value in compression (see: [14,15,[19][20][21][22]). The review of investigations carried out in this field is given in [4,6,12,13,17,23].…”

The stability loss of a locally curved double-walled carbon nanotube in visco-elastic matrix

“…Moreover, it is assumed that υ0(1)=υ(2)=υ(3)=0.3, normalE(2)=normalE (3) and ϵ=p/normalE0(1). When inspecting the loss of stability problems in viscoelastic materials, it is known that the external compressive force p must provide the inequalities below 39 where ϵcr,0 is the critical load at t′=0 and ϵcr,∞ is the critical load at t′=∞.…”