An Analysis of Tearing Failure

Abstract

The tearing failure of materials depends very strongly on the conditions of use or testing which produce the non-uniform tensile stress which causes such failure. In the trapezoid tear test. the stress pattern is determined largely by variables at the disposition of the operator. The effect of these variables on the tearing strength and the relationship of the latter to the shape of the force-elongation curve have been determined. The tear load is given by an equation of the form where g is the modulus. h is the thickness. L o is the gauge length, α is the trapezoid angle. and E is the elongation of the material at break. The form of the term f ( E ) is determined by the shape of the force-elongation curve and has been calculated for the linear case and for cases yielding convex and concave curves.The validity of this equation has been evaluated with experiments on cotton and rayon fabries in which gauge length, trapezoid angle, thickness and elongation were varied The data are reasonably well tit by the equation using the form of f ( E ) calculated for a linear force-elongation curve. THE mechanical failure of materials is complicated and depends very strongly on the conditions of use or testing under which it occurs. This is particularly true of tearing failure. The characteristic feature of the tearing process is that it is ;i response to a non uniform tensile stress. If the stress pattern ran he denned, it is then possible in principle to relate the behavior of the material to its performance under a uniform stress, as in the usual tensile test.The stress pattern around a tear in a test sample is determined first of all by the geometry of the testing arrangement. In some cases, such as the tongue tear test used in textile testing, the stress application ;it the actual tear locus may also he determined largely lvy the preliminary response of the fabric through yarn slippage, trellis distortion 17 J. or the like. In other tests, these factors are less important and the stress pattern is controlled to a greater degree by variables at the disposition of the operator. The trapezoid tear test is of the latter sort and lends itself to analysis if the reactions normal to the straining direction are neglected. Tlte origin of the trapezoid tear test appears to he rather obscure The references cited hy ~{il1ard r 31 ] indicate that a test of this type was in use alout thr time of Wortd War I among workers studying the properties of aircraft fabrics. The acute angle of the trapezoid then used was larger than the angle in the· present standard tc>~t ( 1 ~ . The only theoretical study of the test seems to ht, that of llager, Gagliardi, and NValker r 21. whose analysis resulted in an equation relating tear strength to t'xtensibility and breaking strength The treatment of the trapezoid tear test giivrn in this paper is somewhat more detailed than that given by 1 i ager, Gagliardi, and Walker and leads to some new relations between the geometry of the test and the tear strength. In particular, the anKle:> of the trapezo...

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“…They described in detail the problem of tear strength, appropriate measurement methods, and the correlation relationships between the results obtained by different tear methods. Steele and Gruntfest [12] deduced general formulas to predict trapezoid tear strength of woven fabric and designed relevant experiments to confirm the effectiveness of the equations. The relationship among tear strength, dimension of the specimen, and fabric structural parameters were built up by the formulas.…”

Comparisons of trapezoid tearing behaviors of uncoated and coated woven fabrics from experimental and finite element analysis

“…Comparison results showed that tearing strengths obtained from two testing methods differed dramatically and single tongue tearing is much more satisfactory compared with trapezoid method. Steele and Gruntfest (1957) proposed a general equation to relate trapezoid tearing strength to mechanical properties of constituent yarns and geometrical size of tested sample. This formula is particularly suitable to predict the tearing strength for dense texture woven fabrics.…”