Non-linear Theory of the Biaxial Deformation of a Triaxial-weave Fabric

Abstract

A new theory predicting the biaxial tensile properties of a triaxial-weave fabric is presented. This theory is based on the plain-weave theory developed by Kawabata, Niwa, and Kawai in 1973 and improved by Kawabata in 1984. The basic structures of the fabric are (i) the thread-spacing of two warp threads and one weft thread, (ii) the weave-crimp shrinkage of the three threads, and (iii) the crossing angles between these threads. The yarn properties applied in this theory are the tensile properties, the lateral-compressional properties, the bending property, and the yarn-crossing-torque property. The biaxial tensile properties of the triaxial-weave fabric are then derived by solving an equilibrium equation of the forces acting at a thread-crossover point. The prediction and the experimental result coincide well over the wide range of deformation from the small-strain region to the finite-deformation region near breaking strain. The theoretical analysis shows that the yarn lateral-compressional properties have a significant effect upon the fabric tensile properties, and the effects of the yarn-bending and crossing-torque properties are negligibly small except for the very small-strain region. It is also shown that the tensile properties of the triaxial-weave fabric are much more isotropic than those of the ordinary woven fabric because of the symmetrical structure which appears for every 30° angle rotation of the fabric in the plane of the fabric, and it is demonstrated that the tensile properties of the triaxial-weave fabric are, in fact, almost completely isotropic.