Continuum-mechanical modelling of kink-band formation in fibre-reinforced composites

Abstract

A kink is a singular surface across which the displacement is continuous but the deformation gradient and the fibre direction suffer a discontinuity. A kink band is a highly deformed or even damaged region bounded by two kinks. The objective of modelling kink-band formation, within the framework of finite elasticity theory, is to find a suitable strainenergy function, guided by results from a finite number of simple experiments, that can be used to predict what have been observed and what might be possible under other loading conditions. In this paper, we explain a theoretical basis for choosing such strain-energy functions. More precisely, for a given strain-energy function that allows formation of kinks and a given deformation field, we characterize all possible deformation fields that can join the given deformation field through a kink and explain a procedure that can be used to assess the stability properties of any kink solution that is mathematically possible. In contrast with most previous studies in the engineering community where, for instance, the kink orientation angle is undetermined, the present theory completely determines the kink propagation stress, the kink orientation angle and the fibre direction within the kink band.

On the evolution of the scientific information environment

“…The results reported on in the paper [4] published in the journal (21) in 2006 are similar to and less general than those obtained and published by the author of the present paper more than 35 years ago. In 1982 through 2005, these results were further developed and generalized, which was reported on in English-language publications, and thus can be considered readily available.…”

“…In their paper, Fu and Zhang (2006) outline the continuum theory of fracture of compressed composites based on the non-ellipticity criterion for the system of differential equations of the three-dimensional linearized theory of elasticity. This theory predicts the ultimate compressive strength of composites.…”

“…In addition to predicting the ultimate compressive strength, Guz's approach (1969Guz's approach ( , 1971) also yields surfaces over which fracture propagates, i.e., is more general than that due to Fu and Zhang (2006). The numerous results obtained based on Guz's approach (1969Guz's approach ( , 1971 were later published in periodicals and generalized in the monograph Guz (1990) on pp.…”

“…In this connection, it is unclear why no references to these publications were provided in the paper Fu and Zhang (2006) published in so authoritative journal.…”

A macroscopic model for kink banding instabilities in fiber composites

“…Their results, which are carried out for purely elastic materials, bear some resemblance to the results reported in the literature for fiber reinforced materials with a polymer matrix [Vogler and Kyriakides 1997;Lee and Waas 1999;Oguni et al 2000]. This work has recently been further extended by Fu and Zhang [2006], who have considered the rotation of the kink band with continued loading.…”