Damage accumulation in woven-fabric CFRP laminates under tensile loading: 2. Modelling the eect of damage on macro-mechanical properties F. Gao a , L. Boniface a , S.L. Ogin a, *, P.A. Smith a , R.P. Greaves b a Department of Materials Science and Engineering, University of Surrey, Guildford, Surrey GU2 5XH, UK b Composites and Ceramics Group, Rolls-Royce plc, PO Box 31, Derby DE24 8BJ, UK Received 3 October 1996; received in revised form 5 November 1997; accepted 4 December 1997 Abstract The relationship between the mechanical behaviour (i.e. Young's modulus, Poisson's ratio and residual strain) of CFRP woven fabric laminates and the damage sustained during quasi-static loading has been investigated in two, four- and six-layer laminates. The laminate thickness is found to be an important parameter in determining the eect of matrix cracking and delami- nations on the mechanical properties. The laminate behaviour has been modelled by a shear-lag analysis which takes into account delaminations at the crimp regions in the laminate where appropriate. Reasonable agreement is found between experiment and theory for the change in laminate properties as a function of damage accumulation. # 1999 Elsevier Science Ltd. All rights reserved. Keywords: A. Textile composites; B. Mechanical properties; C. Transverse cracking; C. Delamination 1. Introduction The damage mechanisms available to laminates based on woven fabrics are essentially the same as in non- woven ®bre-reinforced laminates, namely matrix crack- ing, delamination and ®bre fracture. In non-woven laminates, signi®cant progress has been made in under- standing the eect of accumulating damage on the laminate mechanical properties. For woven-fabric com- posites, the geometrical complexity of the damage, and the diculties inherent in its quanti®cation, have made progress in relating damage accumulation to property degradation much slower. In Part 1 of this work [1] we have presented qualita- tive and quantitative results on the accumulation of damage as a function of applied strain in woven fabric laminates consisting of two, four and six layers of woven cloth. Data were presented on the reduction in the normalised Young's modulus and Poisson's ratio with applied strain, as well as on the residual strain which is seen on unloading the laminate from progres- sively higher applied strains. In Part 2, we present models for the change in the measured parameters as a function of crack density and compare the values cal- culated from the models with the experimental data for the surface 0 dominated laminates (for details of mate- rials and nomenclature, see Part 1). 2. Analytical predictions and comparison with experimental data 2.1. Idealisation of the composite structure The predictions of the mechanical properties to be discussed here all utilise a one-dimensional shear-lag analysis originally derived for non-woven crossply laminates (e.g [2].). In order that such an analysis can be of use in discussing woven laminates, it is a necessary requirement that the woven composites are reduced to equivalent crossply laminates. Such a simpli®cation is possible because eight-harness satin fabrics have quite large intercrimp distances. A two-layer surface 0 dominated laminate can be visualised as in Fig. 1. Fig. 1(a) shows the real structure of a two-layer laminate viewed from the laminate edge. A surface 0 dominated laminate is shown such that the majority of the ®bre tows on the coupon surfaces lie parallel to the loading direction. Fig. 1(b) shows an idealisation of the laminate structure which brings the Composites Science and Technology 59 (1999) 137±145 0266-3538/99/$Ðsee front matter # 1999 Elsevier Science Ltd. All rights reserved PII: S0266-3538(97)00232-7 * Corresponding author.