A simple micromechanical model is developed to predict the onset of tear propagation at slit-like damage sites (i.e., a series of consecutive aligned yarn breaks) in biaxially stressed plain weave fabrics under increasing loading. A crucial aspect of the model is the treatment of the frictional slip of yarns near the damage site. Although the actual configuration of slipping regions is complex, the onset of tear propagation in large slits (i.e., more than, say, 35 breaks) is dominated by slip occurring on the first few intact yarns adjacent to the breaks. The assumptions in the mathematical model were motivated by both experimental observations and calculations for key configurations. Analytical results obtained for this simple model exhibit good agreement with experimental results, which are presented for a variety of fabrics with initial slits of 35 and 45 breaks.

The Onset of Tear Propagation at Slits in Stressed Uncoated Plain Weave Fabrics

A simple micromechanical model is presented for predicting the onset of tearing at slitlike damage sites in biaxially stressed coated plain weave fabrics. The stress concentration in the first intact yarn at the slit tip is determined as a function of increasing loading, and predictions for the onset of tearing are made under the assumption that tearing initiates through the rupture of the first intact yarn at a characteristic yarn breaking load. Extensive onset of tearing experiments on various coated nylon and polyester fabrics are presented, and the model is shown to capture the onset of tearing in these fabrics quite well over a range of slit lengths.

The Onset of Tearing at Slits in Stressed Coated Plain Weave Fabrics

The assumption of a constant friction force (simple slip assumption) on broken slipping yarns, which has been used in the micromechanical analysis of damage growth in stressed plain weave fabrics, is evaluated In this analysis, the frictional traction on slipping yarns is variable It starts from zero at the cut end of the yarn and approaches a constant value with exponential behavior, where the steepness of the approach depends on a parameter γ The stress concentration factor (SCF) is determined for various values of γ as a function of increased loading For values of γ that are expected to be physically realistic for most fabrics, the obtained SCF differs from that using the simple slip assumption by about 5%

Effect of Slipping Yarn Friction on Stress Concentration Near Yarn Breaks in Woven Fabrics

A micromechanical model has been developed that will allow the study of a slit-damaged braided fabric air-beam structure. As such, the relevant system of non-dimensional ordinary differential equations is derived and solutions are given for the stress concentration near the broken yarns. This knowledge will contribute to the prediction of damage growth and the ability to compare different fabric materials for their damage tolerance. A simplification of the analysis has been shown to be possible when a parameter, e, the ratio of yarn tensions due to inflation to the yarn stiffness is small, approaching zero. In such a case, the equations for the braided fabric can be reduced to those of the plain weave fabric, so that the stress concentrations are the same as those for woven fabrics. As it turns out, an important result of the present analysis is that the stress concentration factor is, in fact, independent of the parameter, e, and the helix angle of the braided fabrics. This means that much of what has been learned in the study of damage in woven fabrics can be used for braided fabrics.

A Micromechanical Model for Slit-damaged Braided Fabric Air-beams

A simple micromechanical model is used to study the onset of tear propagation at slit-like damage sites (i.e., a series of consecutive aligned yarn breaks) in biaxially stressed plain weave fabrics under increasing load. The method of treating the frictional slip of yarns near the damage site is critical to the success of the model. Although the actual configuration of slipping regions and rotation of yarns is complex, the onset of tear propagation in large slits (i.e., more than say 35 breaks) is dominated by slip occurring on the first few intact yarns adjacent to the breaks. Analytical results, relating the stress concentration in the intact yarn adjacent to the yarn break at the slit tip, versus the critical applied load at the onset of tear propagation exhibit good agreement with experimental results for a variety of fabrics with initial slits of 35 and 45 breaks. A parameter, /j,, that evolves from the work can provide a measure of damage tolerance for a class of such fabrics.

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T. A. Godfrey

Papers

Damage Analysis in Fiber Composite Sheets and Uncoated Woven Fabrics