88 3-D textile reinforcements in composite materials 12 10 40 5060708090 12345678 0.2 0.4 0.6 E fibre(GPa) E resin(GPa) Fibre Fraction V 3.11 Predicted shear moduli for the benchmark composite:comparing results from an FEM study [24]and our CEM calculations(material: glass-epoxy plain weave.▲Gz=Gx(CEM:●Ggy(CEM;△Ga=Gzx 195650t1 (FEM);O Gxy(FEM). WV IL:OE variable on the 3-D elastic performance of the 2-D woven fabric compo- site.The proposed model can easily be extended to calculate the so-called 202 thermal concentration tensors for the computation of the effective thermal expansion constants [33].Moreover,the model can be generalized to 3-D preforms by simply extending the set of macro-cells. 3.4 Strength model 豆 3.4.1 Introduction Woven fabric composite components are subjected to a variety of loading conditions during their service life.Therefore,an understanding of the mechanical response of these materials to various loading conditions is necessary for the safe design of a component.The prediction of strength is certainly one of the outstanding problems in the analysis of fibre composites.This section presents a method to predict the micro-stress fields,the first cell failure and the ultimate strength of woven fabric composites. 3.4.2 The complementary energy stress model In order to predict strength accurately,a sufficiently detailed stress distri- bution must be available for composites subjected to arbitrary combina- tions of applied stresses.The need for computationally efficient predictive tools is clear when one considers the large range of fibres,matrices andvariable on the 3-D elastic performance of the 2-D woven fabric compo￾site. The proposed model can easily be extended to calculate the so-called thermal concentration tensors for the computation of the effective thermal expansion constants [33]. Moreover, the model can be generalized to 3-D preforms by simply extending the set of macro-cells. 3.4 Strength model 3.4.1 Introduction Woven fabric composite components are subjected to a variety of loading conditions during their service life. Therefore, an understanding of the mechanical response of these materials to various loading conditions is necessary for the safe design of a component. The prediction of strength is certainly one of the outstanding problems in the analysis of fibre composites. This section presents a method to predict the micro-stress fields, the first cell failure and the ultimate strength of woven fabric composites. 3.4.2 The complementary energy stress model In order to predict strength accurately, a sufficiently detailed stress distri￾bution must be available for composites subjected to arbitrary combina￾tions of applied stresses. The need for computationally efficient predictive tools is clear when one considers the large range of fibres, matrices and 88 3-D textile reinforcements in composite materials 3.11 Predicted shear moduli for the benchmark composite: comparing results from an FEM study [24] and our CEM calculations (material: glass-epoxy plain weave).
Gyz = Gzx (CEM); Gxy (CEM); Gyz = Gzx (FEM);  Gxy (FEM). RIC3 7/10/99 7:37 PM Page 88 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