Numerical investigations on a yarn structure at the microscale towards scale transition

Abstract

Since the beginning of the last decade, few examples of multifilament models for dry fabrics have been presented in literature. This work deals with the simulation of a single yarn subjected to transverse impact. Inspired by the models previously developed by other authors, a revisited form of Discrete Element Method has been adopted to perform microscopic analyses in a more efficient computational environment. Transverse impact analysis onto a single KEVLAR KM2 yarn has been performed using this approach. Truss elements have been adopted to discretize yarn filaments instead of heavy computational 3D finite elements. A good agreement with literature results has been achieved with an important reduction of computational resource. In the end, a proposed scale transition is discussed.

Introduction

Dry fabrics comprised of high performance materials as Kevlar, Spectra, Zylon and Twaron have been largely adopted in protection systems due to their high penetration resistance and high strength to weight ratio. Some of applications include protecting clothing and containment systems for jet engines.

The outstanding performances of these materials in impact applications are directly related to a large number of parameters which includes fibres mechanical behaviour, weaving type and fibres reciprocal interaction. The energy absorbed by a fabric during an impact could be attributed to a large number of phenomena as fabric acceleration, fabric deformation, friction dissipation by yarn-to-yarn or fiber-to-fibre interactions. All these aspects cannot be individually evaluated using experimental approaches, which are restricted to the evaluation of macroscopic phenomena as penetration or projectile residual speed.

Since their first applications, numerical simulations turned to be a powerful tool to understand and to evaluate mechanical behaviour of dry fabrics under ballistic impact.

Some models assumed the fabric as an homogeneous medium [1], [2], [3], [4] while others were based on a mesoscale representation of the structure [5], [6], [7], [8], [9], [10].

In the first case, the computational efficiency is preferred to the model accuracy. The discrete nature of the fabric here is not addressed and capturing phenomena as yarn pull-out, individual yarn breakage or inter-yarn friction dissipation becomes difficult or impossible.

In the second case, fabric architecture is explicitly modelled. Representing the yarn individually, it is possible to have a more realistic description of the failure mechanisms near the impact zone and evaluate the effect of yarns interaction.

More recently fibre-level modelling has been adopted for an entire fabric or a part of it [11], [12], [13], [14]. Since their high computational requirement, these last models are only justified when microscopic effects, as fibre–fibre interaction or yarn section rearrangement, would be tracked.

The original approach, denoted Digital Element Method, was developed by Wang et al. to simulate weaving processes [15], [16], [17]. This method was successively improved by different authors [18], [19] and finally extended to impact applications [11], [14]. In this specific approach, yarns are modelled as a group of “Digital Fibres”. The term “Digital” refers to the fibres section which is larger than reality.

Each “Digital Fibre” was discretized as a sequence of pin-joined trusses while their transversal behaviour was included in the contact model. Usually, a coarse discretization (few dozen of Digital Fibres) was adopted for each yarn.

This method shows considerable improvements in results and phenomena description compared to the mesoscale models, however it relies on some hypotheses that still have to be verified:

• an elastic equivalence between Digital Fibres and real fibres was established only in longitudinal direction and no information was provided concerning their transverse mechanical behavior as well as the mechanical contact law among fibres. However, it has been demonstrated that inter-fibres contact plays an important role during an impact [12];

• optimum number of Digital Fibers was obtained by a convergence study on the ballistic performance of the whole fabric. This equivalence could fall if the mechanical response of a single yarn is analysed, as the yarns resultant mechanical behaviour is influenced by their reciprocal interaction within the fabrics.

More recently Nilakantan and Sockalingam [13], [20], [21] approached the filament-level modelling in a more radical way. In these works, a single yarn submitted to transverse impact is analysed. Each fiber of the yarn was considered and modelled using 3D Finite Elements, in order to describe accurately their transverse behaviour. Contact, friction and material anisotropy were considered too. The role of different parameters as fibres transversal stiffness, shear modulus and friction on yarn ballistic performance was exploited. The high computational time, given by the large number of degrees of freedom involved in the simulation, is one of the major drawback of this method. In this work, the same test performed by Nilakantan is reproduced using a revisited version of the Discrete Element Method (DEM) [22]. As in Digital Element Method, each fibre is discretized as a pin-joined sequence of truss elements. However, three main points differentiate it from the works by Wang:

• contact is evaluated using a particle-based approach;

• the multifilament analysis concerns a single yarn instead of a fabric;

• all the 400 fibres are explicitly modeled.

Results of the simulation are then compared to those presented by Nilakantan [13], in order to validate the proposed approach. In the final part a multiscale approach based on the Digital Element Formulation is presented. A comparison between the proposed real scale model and its equivalent “Digital Fibres” model is finally discussed.