Model of shear of woven fabric and parametric description of shear resistance of glass woven reinforcements

Forming simulations of textile preforms require a description of the shear resistance of the preform plies. Experimental determination of the shear diagrams is time consuming, costly and requires highly qualified personnel. Typical glass rovings exhibit quite consistent behaviour, described by diagrams for bending, compression and tension, in function of linear density of the rovings. Based on these representative diagrams, a parametrical study of the shear resistance of glass preforms has been carried out, using a model, which accounts for different sources of the fabric resistance to shear: friction, compression of the yarns, yarn (un)bending, Possible simultaneous action of shear and (pre)tension is taken into account. The model (validated against experimental data) generates shear diagrams for plain, twill and 5-harness satin square fabrics. The diagrams were then processed to create analytical expressions of the shear diagrams: T = T0 + T1 tanaγ, where T is the shear force, γ is the shear angle, a, T0, and T1 are parameters, tabulated as functions of yarn linear density, fabric tightness and pretension. The value of a was found to be close to 2 in all the cases. The resulting family of shear diagrams was verified against experimental data.