70 3-D textile reinforcements in composite materials 3.2.3 Micromechanical models Considering the actual importance of 2-D woven fabric composites in the family of structural composites,the mechanical analyses of these compo- sites are now extensively reviewed and presented.Most of the published data are related to stiffness properties of plain weave laminae.There are few publications on the internal stress distribution and on the damage and strength analysis problem of general woven fabric composites.The possible extension of the different micromechanical models to analyse 3-D woven fabric composites will be discussed.It should also be stressed here that in this rapidly evolving field of study any review will soon be incomplete.New results are always being presented or printed. Models of Ishikawa and Chou In the 1980s,an extensive amount of work on the thermo-mechanical mod- elling of 2-D woven fabric composites was done by Ishikawa and Chou. They developed and presented three analytical 1-D elastic models [11-13]. These models are known as the mosaic model,the fibre crimp model and the bridging model.The classical lamination theory forms the basic analyt- ical tool for these developments [14. The models of Ishikawa and Chou are labelled 1-D models because they only consider the undulation of the yarns in the loading direction.Notice the total absence of any geometric analysis.That is,the actual yarn cross- sectional shape or the presence of a gap between adjacent yarns is not con- sidered.Therefore,no predictions are made for the out-of-plane yarn orientation and the fibre volume fraction.Moreover,these models consider balanced closed weaves only,whereas in practice the fabric can be unbal- anced and open.Since the classical laminated plate theory is the basis of each model only the in-plane elastic properties are predicted.The elastic models were extended to analyse the thermal properties,hybrid fabrics and the knee behaviour under uniaxial tensile loading along the filling direction only.However,an extension to treat 3-D woven preforms is not useful because of the geometric simplifications and the limitation to predicting only in-plane properties. Models of N.Naik,Shembekar and Ganesh N.Naik and Shembekar have developed 2-D elastic models for a 2-D non- hybrid plain weave fabric composite [15].These models are essentially an extension of the 1-D models of Ishikawa and Chou.However,these 2-D models take into account the undulation of both warp and weft yarns,the presence of a possible gap between adjacent yarns,the real cross-section of3.2.3 Micromechanical models Considering the actual importance of 2-D woven fabric composites in the family of structural composites, the mechanical analyses of these compo￾sites are now extensively reviewed and presented. Most of the published data are related to stiffness properties of plain weave laminae. There are few publications on the internal stress distribution and on the damage and strength analysis problem of general woven fabric composites. The possible extension of the different micromechanical models to analyse 3-D woven fabric composites will be discussed. It should also be stressed here that in this rapidly evolving field of study any review will soon be incomplete. New results are always being presented or printed. Models of Ishikawa and Chou In the 1980s, an extensive amount of work on the thermo-mechanical mod￾elling of 2-D woven fabric composites was done by Ishikawa and Chou. They developed and presented three analytical 1-D elastic models [11–13]. These models are known as the mosaic model, the fibre crimp model and the bridging model. The classical lamination theory forms the basic analyt￾ical tool for these developments [14]. The models of Ishikawa and Chou are labelled 1-D models because they only consider the undulation of the yarns in the loading direction. Notice the total absence of any geometric analysis. That is, the actual yarn cross￾sectional shape or the presence of a gap between adjacent yarns is not con￾sidered. Therefore, no predictions are made for the out-of-plane yarn orientation and the fibre volume fraction. Moreover, these models consider balanced closed weaves only, whereas in practice the fabric can be unbal￾anced and open. Since the classical laminated plate theory is the basis of each model only the in-plane elastic properties are predicted. The elastic models were extended to analyse the thermal properties, hybrid fabrics and the knee behaviour under uniaxial tensile loading along the filling direction only. However, an extension to treat 3-D woven preforms is not useful because of the geometric simplifications and the limitation to predicting only in-plane properties. Models of N. Naik, Shembekar and Ganesh N. Naik and Shembekar have developed 2-D elastic models for a 2-D non￾hybrid plain weave fabric composite [15]. These models are essentially an extension of the 1-D models of Ishikawa and Chou. However, these 2-D models take into account the undulation of both warp and weft yarns, the presence of a possible gap between adjacent yarns, the real cross-section of 70 3-D textile reinforcements in composite materials RIC3 7/10/99 7:37 PM Page 70 Copyrighted Material downloaded from Woodhead Publishing Online Delivered by http://woodhead.metapress.com Hong Kong Polytechnic University (714-57-975) Saturday, January 22, 2011 12:30:11 AM IP Address: 158.132.122.9