A model for kinking in fiber composites—I. Fiber breakage via micro-buckling

Abstract

Kink band formation in uniaxially compressed fiber composites is studied theoretically. A model is proposed which involves the bowing of a bundle of slightly misaligned fibers (via microbuckling) until fiber fracture, followed by a finite deformation which brings the fibers into the kinked configuration. These two critical steps in the process are treated separately in this two-part paper. In Part I, the critical strain at which the fibers can break is calculated; in Part II the critical strain at which a fully formed kink band can exist is calculated. It is found that the critical strain to form the fiber breaks is comparable to observed compressive failure strains and is, in general, greater than the strain at which a fully formed kink band can exist. This appears to imply that the formation of the fiber breaks is the limiting step in kinking. The theory is consistent with the seminal features of kinking, including: the fiber breaks at the kink band boundary, the relatively small width of the kinks, and the typical orientation relation between the kinked fibers and the kink band boundary. Computations based on the model reveal the dependence of kinking on pertinent material variables.