Sensibilidad a antifúngicos de las especies aisladas

The work presented in this thesis is aimed at characterising and modelling the geom- etry of textile fabrics and developing methods to predict the mechanical properties of fabrics at the micro and mesoscopic scales.

6.2.1 Geometric modelling

A generic method to define the geometry of all types of fabrics has been developed where geometry definition is split into two stages. The first stage consists of specifying the yarn centreline (or the yarn path) defined by a series of nodes on the centreline which are interpolated with a spline. In this way any desired path can be approximated and a higher degree of fit to the desired path can be obtained by increasing the number of points. However for the woven fabrics presented in this thesis it was found that only one point per cross-over was necessary to obtain a good fit to the real fabric.

The second stage is to define the cross-section of the yarn which can be done indepen- dently from the yarn path definition. Cross-sections are defined in two dimensions as parametric equations and a series of cross-sections defined in this way are presented: ellipse, power ellipse and lenticular. However any cross-section which can be defined

CHAPTER6: DISCUSSION AND CONCLUSIONS

as a parametric equation is suitable. The cross-sections can then be assigned at discrete points along the length of the yarn and interpolated between these points.

The geometric model defines the yarn surface and volume suitable for use in various numerical analysis techniques such as finite element analysis, boundary element anal- ysis, finite difference, etc. The geometric modelling algorithms have been implemented in the TexGen software package and this is used to create models of four woven fabrics presented in Chapter 3. Cross-section images of the fabrics were obtained using optical microscopy and scanning electron microscopy. Full three dimensional volumetric data of the fabrics were also obtained using microtomography. This data was used as both input and validation.

Difficulties were encountered in defining the boundary of the yarns in the cotton fabric due to the large number of stray fibres present. Other than this fundamental issue there were no limitations in representing the observed yarn shapes with the modelling tech- niques presented. The accuracy of the model is essentially determined by the accuracy of the input parameters. Features common to all the observed fabrics were identified and algorithms developed such that they are applicable to woven fabrics in general. More specifically an interference correction algorithm applicable to woven fabrics was developed and the location and magnitude of yarn rotations characterised.

6.2.2 Mechanical modelling

At the microscopic scale, an original numerical technique was developed for predict- ing the mechanical behaviour of tows. The method involves modelling fibres within a tow following the Euler-Bernoulli beam equations. The number of fibres that can be modelled in a yarn is limited by the computational requirements. Compaction of a tow was simulated by applying a linear transformation to the fibres contained within it. It was found that averaging results over a large number of small tow sections provides similar trends to experimental results. It is computationally cheaper to perform a large number of small scale simulations than a single large scale simulation hence the for- mer approach was adopted. Results were compared against experimental results and analytical models found in the literature. The pressure versus volume fraction curves of the simulation and experimental data were both found to fit closely to a power law hence showing that the trends are accurately predicted. Unfortunately the scale of the pressures predicted was found to be several orders of magnitude lower than experi- mental results. This is thought to be due to the assumption that the fibres are initially straight and consequently the inability to correctly model the longitudinal boundary conditions. However to the knowledge of the author there is currently no model able

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to accurately predict the scale of the compaction pressure without fitting parameters. The model was also used to simulate the shear behaviour of a polyester plain woven fabric. Results were compared against KES-f measurements of the modelled fabric. The shear response behaviour was decomposed into two parts, the first part caused by frictional sliding between fibres and the second part caused by elastic bending of the fibres. In contrast to the compaction simulation, the model showed very good predic- tive capabilities for the overall shear behaviour including hysteresis when compared against KES-f data. This is thought to be due to the accurate modelling of the longi- tudinal boundary conditions, as here a complete fabric unit cell was modelled with periodic boundary conditions.

At the mesoscopic scale, an explicit finite element analysis solver was implemented to predict the mechanical properties of fabrics under compression, tensile and in-plane shear deformations. The two Chomarat woven fabrics modelled using TexGen were simulated with the FE solver. It was found that very good agreement between FE results and experimental data can be obtained for compaction given an accurate trans- verse material model. Using yarn material properties obtained from McBride [88] a reasonably close fit to experimental data was found for the Chomarat 800S4-F1 fabric, however the material properties were found not to be suitable for the Chomarat 150TB fabric. The biaxial tensile behaviour of fabrics was found to follow trends presented by Boisse et al. [10]. However, the fabric shear behaviour could not be accurately mod- elled with the finite element method presented in this chapter due to the inability of the continuum elements to accurately represent the axial shear behaviour of yarns.

6.3

Conclusions

The conclusions gained from this thesis are summarised below.

• The geometry of any textile fabric can be represented in a generic way by speci- fying yarn path and yarn cross-sections independently.

• Characterisation of fabric geometry is difficult due to the large variability ob- served in measurement of fabric parameters. However given accurate input mea- surements an accurate geometric model of the fabric can be created.

• A number of assumptions about the path and shape of the cross-sections were made for 2D woven fabrics in general and validated against four different fabrics. Algorithms were implemented in TexGen to create 2D woven fabric geometric

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models using these assumptions with minimal input data. To avoid penetration between tows.

• Prediction of tow compaction behaviour involves modelling a complex system of fibre contacts and fibre bending. The numerical approach presented in this thesis shows promising trends.

• Fibre sliding is inevitable during shearing of fabrics and two possible distinct modes of sliding were identified: the sliding between fibres within a tow (intra- tow) and sliding between fibres between tows (inter-tow). For the polyester fabric modelled it was shown that only one mode occurs depending on the ratio of intra- tow coefficient of friction and inter-tow coefficient of friction.

• Prediction of fabric shear properties for low filament count tows where individual fibres were modelled showed good agreement with experimental results without any fitting parameters. It was shown that the force response could be separated into two components, the frictional forces between fibres caused by sliding and the internal stresses created by elastic deformation of the fibres due to bending. • A flaw in the use of solid continuum finite elements to model the behaviour of dry

fabrics where bending or axial shear of yarns plays a significant role was identi- fied. The internal fibre strains are not correctly represented by the continuum elements.