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Modelling of textile composites - part one : geometrical parameters

 
By  : Piotr Szablewski
 

Technical University of Łdź

Department of Technical Mechanics and Informatics

ul. Żeromskiego 116, 90-924 Łdź, Poland

Phone: (48) (42) 636 14 29

E-mail: piotr.szablewski@p.lodz.pl


Abstract


This paper describes a simple sinusoidal geometrical model of textile composite. On the basis of this model it will be presented how to obtain certain geometrical parameters which fully characterize the geometry of composite structure. Using geometrical considerations it is possible to obtain from this model basic mechanical parameters very useful for further strength analysis. Such mechanical considerations and method for calculating mechanical parameters will be presented in future article.


On the basis of above‑mentioned theoretical considerations a special computer program was developed. The method of calculation presented in this paper can be applied to more complicated models of textile composites.


Key words: textile composites, textile mechanics, numerical methods, woven fabric, unit cell model.



1. Introduction


Textile composites represent a class of advanced materials which are reinforced with textile preforms for structural or load bearing applications. In general, composites can be defined as a select combination of dissimilar materials with a specific internal structure and external shape. The unique combination of two material components leads to singular mechanical properties and superior performance characteristics not possible with any of the components alone (see ref. [1], [2], [3]). The range of applications for composite materials appears to be limitless. Textile composites can be defined as the combination of a resin system with a textile fiber, yarn or fabric system. They may be either flexible or quite rigid. In this paper will be presented how to build a simple geometrical model of textile composite and how to get from this model certain geometrical and mechanical parameters, very useful for further strength analysis.


2. The geometrical model of textile composite


Let us consider a balanced plain weave textile composite in which the warp and fill yarns contain the same number of fibers n with all filaments having the same diameter , and with the warp and fill yarns having the same yarn packing density . The cross-sectional area of the yarns is given by .


The representative unit cell (RUC) is a rectangular consisting of two warp yarns interlaced with two fill yarns with resin matrix filling the remaining portion of the volume.


Its dimensions are and its thickness is denoted by H. The other parameters are denoted and shown in Figure 1. The thickness of the yarn along the centerline of the yarn path is denoted by t. If the fiber volume fraction specified for the unit cell is too small, it is necessary to add an additional resin layer of thickness to the unit cell. The geometry of the path of the warp or fill yarn is modelled using two assumptions: 1 - the centerline of the yarn path consists of undulation portions and straight portions, with the centerline of the undulating portions described by the sine function, 2 - the cross‑sectional area and the thickness of the yarn normal to its centerline are uniform along the arc-length of the centerline. The centerline of the warp yarn path in an undulating region is specified by


, . (1)


The trigonometric functions of the angle in terms of function are


, , . (2)

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