Damage Growth in Prestressed Plain Weave Fabrics

Abstract

A simplified micromechanics approach is used to develop a mathematical model to predict damage growth in prestressed plain weave fabrics near sites where yams are broken. Stress concentration in the yams neighboring yarn breaks is determined as a function of increasing loading. An evaluation of the load redistribution around the damage region includes a determination of the frictional slip of broken yams. Consideration of equilibrium and deformation of constituent yams leads to linear differential equations for yarn displacements applicable to distinct regions where slipping does and does not occur. Slip frictional forces depend on yam normal contact forces at crossover points resulting from crimp interchange, Kawabata's model [12] is modified and used to motivate an analysis of frictional load transfer. The equations are nondimensionalized, and dimensionless parameters involving both geometry and material properties are identified.Biaxially stressed woven fabrics can be used for inflated fabric structures, parachute canopies, geotechnical structures, and numerous industrial applications. In many instances, fabrics are cut or punctured by accidental contact with a sharp edge or by impact with a moving object. Given sufficiently high biaxial tension in the region of the fabric surrounding the initial damage, the damage site provides a starting point for selfpropagating catastrophic tearing of the fabric. This situation is particularly untenable in gas-inflated fabric structures, where the tearing is accompanied by the sudden release of the stored energy of the compressed gas with explosive-like effects. Developing a model for damage growth in prestressed woven fabrics would significantly advance the state-of-the-art in selecting or designing new fabrics specifically for end-use as damage tolerant structural materials.A micromechanical analysis of damaged filamentary structures was first provided by Hedgepeth [10]. Although it was applied to fiber composite sheets, where the matrix transfers the load from broken to unbroken fibers by means of shear, he considered his shear lag model, where the fibers carry axial loads and the matrix is assumed to carry only shear, to apply to coated woven fabrics as well. In biaxially stressed uncoated woven fabrics, load transfer between yams of a given yam set is accomplished though a deformational stiffening effect involving the rotation of the tensioned crossing yarns in the fabric plane, while in the shear lag model, load transfer between neighboring yarns or fibers occurs through shearing of the coating or matrix. The ultimate transfer of the load to a given yarn arises through frictional contact at the cross-over point. This stress-induced shear stiffening effect has been noted by Christoffersen [ 4 ] and by Topping [ 18] . Christoffersen developed a finite deformation two-dimensional continuum model for a biaxially stressed ideal woven fabric (no slip occurs at yam cross-overs) and applied it to the problem of a slit parallel to a yarn direction. In our work, we incorporate...

A Micromechanical Model for Slit Damaged Braided Fabric Air-Beams

“…In contrast to the woven fabric case [3], we now have an oblique angle between the #1 and #11 yarns. As a result, it is necessary to consider the y-direction displacement of the cross-over points.…”

“…We consider the i, j th yarn cross-over point and its immediate neighbors in the braided fabric, as shown in Figure 2b. Equilibrium equations for the cross-over point i, j are easily derived using an approach similar to that taken previously with plain woven fabrics [3].…”

“…The equilibrium equations, where variations in the x (or j) direction have been averaged (smeared out) as in Reference [3], can be derived in a straightforward manner (details of the algebra is given in [4]). They are: , which is in fact the equation that results when modeling plain weave fabrics [3], implies that, for the case considered, where no slip occurs at the cross-over points, the braided fabric should develop stress concentrations similar to woven fabrics due to yarn breaks. This conclusion, as just indicated, was subject to the restriction that yarn tensions due to inflation are small compared to the yarn stiffness, so that the parameter e is small.…”

“…The tensile force in the #11 yarn consists of the initial tension, T, and the additional force due to the deflection of the yarn. If we consider the equilibrium of forces and moments of the #11 yarn in a manner similar to that done for the plain weave fabric configuration [3], i?, and R^ can be determined in terms of / and the x and y displacements of the #1 yarns n=l,-l. Products of displacement are neglected with respect to unity. The process is straightforward, and after much algebra, the results are, where.…”

“…Much work has already been done in studying damage growth in woven fabrics [1][2][3]5], where the yarns of the weave are oriented normal to one another. Determination of the stress concentration at the end of a slit in the yarns has been used to predict damage growth.…”