Stress-Strain Relationships in Yarns Subjected to Rapid Impact Loading

Abstract

The behavior of an infinitely long flexible filament after transverse impact is treated theoretically. The filament is assumed to have a tension-strain curve which is always concave downwards and to have no short time creep or stress relaxation effects. Under most conditions the impact initiates a variable strain that propagates down the filament between an "elastic wave" front and a "plastic wave" front. A transverse wave, shaped like an inverted "V," then travels in the constant strain region behind the plastic wave front. Under special conditions the transverse wave front may propagate faster than the plastic wave front, but the shape of the transverse wave remains the same. The theory for both cases is worked out in detail and some illustrative examples given.

Transverse Impact Response of a Linear Elastic Ballistic Fiber Yarn

“…They tried to obtain the stress-strain relationship in a fiber yarn through transverse impact testing because of immature dynamic experimental techniques for obtaining the stress-strain response six decades ago. Both experiments and theoretical analyses were conducted [11][12][13]. Similar analyses have also been conducted by Vinson and Zukas [14] and Roylance et al [15,16].…”

“…The transverse impact response of a single fiber yarn has been investigated, both analytically and experimentally, since the 1950s [9][10][11][12][13][14][15][16][17]. Cole et al [10] developed a nonlinear theory for constant-strain waves in elastic strings subjected to transverse impact.…”

“…However, no experimental result was presented to support their analysis. Since the late 1950s, Smith and his colleagues [11][12][13] conducted a series of comprehensive research on the transverse response of a fiber yarn subjected to impact loading. They tried to obtain the stress-strain relationship in a fiber yarn through transverse impact testing because of immature dynamic experimental techniques for obtaining the stress-strain response six decades ago.…”

Dynamic Response of a Constrained Fibrous System Subjected to Transverse Impact. Part 2. A Mechanical Model.

“…Equations (1), (2), and (3) completely state the problem of traveling waves, in a bounded, elastic, ideally flexibl-. filament, when combined with appropriate boundary conditions.…”

“…1 Although there has been fairly extensive research into the properties of individual, unconstrained fiber components with transverse impact at ballistic velocities, 2 " 5 there has been a singular deficiency in defining how these properties translate into the system behawior, i.e., the constrained fiber including the boundary interactions.…”