Mechanical modelling of solid woven fabric composites 75 Table 3.1.Stiffness reduction scheme for the UD yarn elements,according to Blackketter [27] Failure mode Mechanical property and degradation factors En E22 E33 G23 G31 G12 Longitudinal tension on 0.01 0.01 0.01 0.01 0.01 0.01 2 Transverse tension 022 1.0 0.01 1.0 1.0 0.2 0.2 3 Transverse tension oaa 1.0 1.0 0.01 1.0 0.2 0.2 Transverse shear t2a 1.0 0.01 0.01 0.01 0.01 0.01 5 Longitudinal shear ti3 1.0 1.0 0.01 1.0 0.01 1.0 6 Longitudinal shear t12 1.0 0.01 1.0 1.0 1.0 0.01 correct constituent stiffness/strength data and by applying an appropriate stiffness reduction scheme,it is possible to predict the stress-strain behav- iour of woven fabric composites.The same ideas could certainly be applied poo to analyse 3-D woven fabric composites.However,Blackketter does not discuss in detail the limitations of the finite element modelling technique (meshing or calculation time). Models of Whitcomb oo/ Whitcomb and coworkers [28-30]have studied the effect of the yarn archi- tecture on the predicted elastic moduli and stresses in plain weave com- posites.The work is restricted to linear elastic analysis.Three-dimensional finite element models were used.Only simple plain weaves were studied because these offer sufficient complexity for the task.A refined model of 8 the complete unit cell would require immense amounts of computer memory and calculation time.However,by exploiting the geometric and material symmetries in the simple unit cell,it was sufficient to analyse 1/32 of the size of the complete plain weave unit cell.Twenty node isoparamet- ric hexahedral elements were used.Two different yarn architectures were investigated.The first was the 'translated architecture'where the complete yarn is created by keeping the cross-section vertical along the yarn path. The second was the 'extruded architecture'wherein the yarn cross-section is always placed perpendicular to the yarn path.The extruded yarn archi- tecture requires a more complex mesh generation. Whitcomb and coworkers also analysed progressive failure of plain weave fabric composites under in-plane tensile loading using a 3-D finite element model.The mechanical loading was parallel to one of the yarn directions.Thermal loading or thermal residual stresses were not consid- ered.The effects of various characteristics of the finite element model on predicted behaviour were examined.There is no 'right'way to modelcorrect constituent stiffness/strength data and by applying an appropriate stiffness reduction scheme, it is possible to predict the stress–strain behav￾iour of woven fabric composites. The same ideas could certainly be applied to analyse 3-D woven fabric composites. However, Blackketter does not discuss in detail the limitations of the finite element modelling technique (meshing or calculation time). Models of Whitcomb Whitcomb and coworkers [28–30] have studied the effect of the yarn archi￾tecture on the predicted elastic moduli and stresses in plain weave com￾posites. The work is restricted to linear elastic analysis. Three-dimensional finite element models were used. Only simple plain weaves were studied because these offer sufficient complexity for the task. A refined model of the complete unit cell would require immense amounts of computer memory and calculation time. However, by exploiting the geometric and material symmetries in the simple unit cell, it was sufficient to analyse 1/32 of the size of the complete plain weave unit cell. Twenty node isoparamet￾ric hexahedral elements were used. Two different yarn architectures were investigated. The first was the ‘translated architecture’ where the complete yarn is created by keeping the cross-section vertical along the yarn path. The second was the ‘extruded architecture’ wherein the yarn cross-section is always placed perpendicular to the yarn path. The extruded yarn archi￾tecture requires a more complex mesh generation. Whitcomb and coworkers also analysed progressive failure of plain weave fabric composites under in-plane tensile loading using a 3-D finite element model. The mechanical loading was parallel to one of the yarn directions. Thermal loading or thermal residual stresses were not consid￾ered. The effects of various characteristics of the finite element model on predicted behaviour were examined. There is no ‘right’ way to model Mechanical modelling of solid woven fabric composites 75 Table 3.1. Stiffness reduction scheme for the UD yarn elements, according to Blackketter [27] Failure mode Mechanical property and degradation factors E11 E22 E33 G23 G31 G12 1 Longitudinal tension s11 0.01 0.01 0.01 0.01 0.01 0.01 2 Transverse tension s22 1.0 0.01 1.0 1.0 0.2 0.2 3 Transverse tension s33 1.0 1.0 0.01 1.0 0.2 0.2 4 Transverse shear t23 1.0 0.01 0.01 0.01 0.01 0.01 5 Longitudinal shear t13 1.0 1.0 0.01 1.0 0.01 1.0 6 Longitudinal shear t12 1.0 0.01 1.0 1.0 1.0 0.01 RIC3 7/10/99 7:37 PM Page 75 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