Cut resistance of textile fabrics A theoretical and an experimental approach

Indian Journal of Fibre & Textile Research Vol. 32, September 2007, pp. 306-311 Cut resistance of textile fabrics A theoretical and an experimental approach V K Kothari a, A Das & Sreedevi R Department of Textile Technology, Indian Institute of Technology, New Delhi 110 016, India Received 11 April 2006; accepted 8 September 2006 A simplified mathematical model to predict the cutting behaviour of textile fabrics has been developed. It has been tried to identify the forces involved in cutting a material with a reciprocating knife and also to derive an expression for the sliding distance, which is a measure of the cut resistance of the material. A series of 100% cotton woven fabrics with varying pick density and weave pattern (plain, matt, twill and honeycomb) and another series of fabrics with high performance fibres have been studied for their cut resistance properties. The plain weave has the maximum cut resistance, while the minimum cut resistance is exhibited by the honey comb weave. The cut resistance increases with the increase in picks/inch of the fabric. The study shows a very high cut resistance of the monofilament fabrics and the least cut resistance for para-aramid fabric along the warp direction, while the least cut resistance along the weft direction is exhibited by the HDPE fabric. Keywords: Cotton, Cut resistance, Cutting force, Fabric weave, High performance fabrics IPC Code: Int. Cl. 8 D03D 1 Introduction Cutting, which involves a normal and a sliding movement, is strongly controlled by friction between the blade and the cut material. That is, the total energy required to propagate a cut strongly depends on the coefficient of friction between the cutting edge and the material. However, this coefficient of friction depends on both the nature of the blade and the nature of the cut material, especially its surface roughness. It has been reported 1 that the type of deformation undergone by the fibre during the cutting process appears to be a very much plastic lateral compressive deformation, with the evidence of actual failure in either transverse tension or shear, and higher work of deformation means higher cut resistance. Hence, the greater is the work required to deform the material in the transverse compression, the higher is the energy dissipated which implies better cut resistance of the material. It has been reported 2 that an increase in the coefficient of friction increases or decreases the cut resistance of the material, depending on the thickness and the microstructure of the material to be cut. 3 Offermann et al. examined the mechanical cutting characteristics of yarns. They reported that the wires used in cut resistant cloths were not adequate, since these have high bending stiffness and poor comfort, a To whom all the correspondence should be addressed. E-mail: kotharivk@gmail.com/kothari@textile.iitd.ernet.in and broken wire can frequently cause injury. The course of the cutting force over the cutting path was determined exclusively by the stress/strain behaviour of the yarn. The moment of yarn breakage was determined by the resistance of the yarn to the tensile, compression and bending loads occurring in the cutting zone. The effects of different forms of cutting on most of the fibres are broadly similar in form. 4 A razor cut of cotton is clean, with a few grooves on the surface and perhaps some tearing. Tearing and squashing are much more apparent in a knife cut. The scissor cut of cotton is somewhat sharper, the razor cut of viscose rayon shows much less distortion of the fibre end than the knife cut. Differences between the clean cuts with a razor and the greater distortion of the knife and scissor cuts are shown by acetate fibres, acrylic fibres and wool. Cut resistance can be measured in various directions, i.e. in the weft direction, in the warp direction and also in various other directions as 45 to the warp and the weft. 5 The basic assumption behind this is that the exact motion of the tearing instrument at the time of tear is not known, so to get a more realistic picture the cut resistance is measured in various directions. A test procedure for evaluating the cut resistance of yarns under tension-shear loading conditions was described and demonstrated. 6 A knife blade was pressed transversely at a constant rate against a yarn gripped at its ends, the load-deflection relation was measured,

KOTHARI et al.: CUT RESISTANCE OF TEXTILE FABRICS 307 and the energy required to cut through the yarn was computed. The cut energy and strain to initiate cutting depend on the sharpness of the blade, the slicing angle, and the pre-tension in the yarn. The dependencies were explained by changes in failure mode of fibres within the yarn. One difficulty in making and using the cut resistant fibres and yarns is the abrasiveness of the filled fibres, which cause faster wear of the equipment used to process the fibre. 7 A method of producing the ply-twisted yarn useful in cut resistant fabrics has been developed. 8 The yarns were made by providing a first multifilament yarn of continuous organic filaments having a tensile strength of at least 4 g/den and a twist in a first direction of 0.5 to 10 turns/inch; providing a second yarn comprising 1-5 continuous inorganic filament(s); and ply-twisting each other by 2-15 turns/inch in a second direction opposite to that of the twist in the first yarn to form a ply-twisted yarn having an overall effective twist of +/-5 turns/inch. Different types of warp knitted structures were developed to improve cut resistance characteristics of fabrics. 9 Detailed overviews have been reported on various aspects of cut resistant textile products. 10,11 To predict the cut resistance of a material, it is important to understand the cutting phenomenon. Cutting behaviour of a material depends on many factors, such as type of cutting edge, type of material, type and magnitude of force, type of cutting action, etc. A simple mathematical model will help in understanding the cut resistance of textile materials. The present study is aimed at developing a simple mathematical model to predict the cutting forces and the distance slid to make a cut. A study on the effect of fabric constructional parameters and the type of high performance fibre on cut resistance of the fabrics has also been reported. The blade that is supplied with a normal and a tangential force is a large reservoir of energy. Energy is transferred from the blade to the fabric by means of frictional forces. The energy transferred is then converted to the permanent deformation of the fabric after overcoming the compressive and shear stresses of the fabric. The schematic representation of cutting force is shown in Fig. 1, where F N is the normal load; F t, the pretension; V, the velocity of blade; F f, the frictional force; F s, the separation force; t f, the thickness of material; and y, the current separation between the cutting edge and the base of the material. The free body and applied force diagrams during cutting are shown in Figs 2 and 3 respectively. Fig. 1 Schematic representation of cutting force Fig. 2 Free body force diagram 2 Theoretical Model 2.1 Forces Involved in Cutting To relate the cut resistance of a material to the properties of the material, it is essential to visualize the actual cutting process and the forces involved during cutting a material. In order to analyze the type of deformation and hence to derive an equation for the cutting force, the cutting process is related to the general wear of solids. In the present context, the wear is defined as an energy transfer process, as shown below: Fig. 3 Applied forces during cutting

308 INDIAN J. FIBRE TEXT. RES., SEPTEMBER 2007 2.2 Model to Determine the Cutting Force The cutting process, which is referred to as the moving of fibre material away from the fibre/blade contact point, involves the application of mechanical forces in the direction transverse to the fibre axis. An attempt has been made to develop a model to determine the actual force that is involved in cutting. The model is based on the following assumptions: The real area of contact increases proportionately to the load. The material undergoes plastic deformation on the application of load. The energy dissipated is proportional to the volume of wear. The frictional force is directly proportional to the load applied. The free body diagram (Fig. 2) shows the forces involved in cutting in three mutually perpendicular directions (i th, j th and k th ). If F 1 and F 2 are the two forces in i th and j th directions respectively, separated by an angle θ, then F 1 F 2 F 1 F2 = F1 F 2 sinθ (N) i.e., if F1 = F1 (i) and F2 = F2 (j) F 1 F2 = F1 F 2 sin(90) (i j) = F 1 F 2 (k) Now considering F2 = F N and F1 = F f (Figs 1, 2 and 3) F 1 F2 = FN Ff ( k) Which implies that the resultant force is in ( k th ) direction. But there are following two forces in (+k) direction: F S (+k) and Ft (+k) These two forces will balance the other two forces acting along i th and j th directions. F S + F t = F N F f or F S = F N F f F t 2.3 Equation for Sliding Distance Consider a uniform teflon sheet thickness t f which is presented to a cutting edge of thickness t b placed perpendicular to the sheet. Let a normal load F N be applied to the cutting edge and then allowed to slide over the material with a sliding velocity V. Assuming plastic deformation of the material on the application of normal load, as the smooth surface of the cutting edge which is hard approaches the smooth surface of the teflon sheet which is soft in nature, it compresses the material to a certain height. Hence, the normal approach will be given by (t f y), where y is the current separation between the cutting edge and the base of the material. When a hard surface slides over a soft surface, it tends to dig into the softer surface during sliding and produces a groove. The energy of deformation represented by the cut must be supplied by the friction force, which will therefore be larger than that when no such groove is formed. Hence, an additional component to the frictional force is involved. Following relationships have been used: Let the area, over which the shear force is applied to initiate sliding, be A H. Horizontal area of contact (A H ) = length of contact (cut) thickness of the blade edge Let the initial vertical area of contact after the normal load is applied, be A V. Initial vertical area of contact (A V ) = length of contact (t f y) During sliding, the penetrated area swept out is given by A V. A V = length of contact thickness of the material (t f ) Let the additional resistance of sliding, consisting of the need to displace an area A V during sliding, be A V P which is referred to as the ploughing term. Let F f be the frictional force, which is the tangential resistance to sliding. The F f involves two terms, a shear term and a ploughing term, as shown below: F f = A H S + A V P where S is the shear stress required to initiate sliding; and P, the yield stress of the material. But we know, F f = µ F N Therefore, A H S + A V P = µ F N Also, F N = A V P Therefore, µ = S/P + A V / A H The volume of wear (Q) = A H Depth of cut

KOTHARI et al.: CUT RESISTANCE OF TEXTILE FABRICS 309 Sample No. Weave Table 1 Specifications of 100% cotton fabrics Yarn linear density, tex Thread count/cm Cover factor Warp Weft Warp Weft Warp Weft Fabric Fabric thickness mm Fabric weight g/m 2 C 1 3/1 Twill 15 20 38 26 15.18 12.05 20.69 0.36 116.4 C 2 3/1 Twill 15 20 38 20 15.18 9.13 19.36 0.34 107.3 C 3 3/1 Twill 15 20 38 16 15.18 7.30 18.52 0.33 93.6 C 4 3/1 Twill 15 20 38 12 15.18 5.48 17.69 0.32 82.0 C 5 Plain 15 20 38 20 15.18 9.13 19.36 0.28 102.5 C 6 3/1 twill 15 20 38 20 15.18 9.13 19.36 0.34 107.3 C 7 2/2 matt 15 20 38 20 15.18 9.13 19.36 0.34 102.9 C 8 Honey comb 15 20 38 20 15.18 9.13 19.36 0.41 101.2 The amount of energy dissipated for a sliding distance (D) is E = F f D. Assuming that the energy dissipated is proportional to the volume of wear, i.e. F f D Q and, D µ Q F Q D= C F f f The sliding distance D is a measure of the cut resistance of the material and C is a constant, which is related to the transverse work of rupture of the material. 3 Materials and Methods 3.1 Fabric Samples Fabrics of different constructions and set made from 100% cotton yarn were selected for determining the cut resistance, so as to find the effect of weave pattern and fabric tightness on cut resistance. The types of weaves selected were plain, 3/1 twill, 2/2 matt and 8-end honey comb weaves. Out of this, the 3/1 twill weave was selected and fabrics of different picks/inch were constructed so as to observe the effect of fabric cover factor on cut resistance. To study the effect of fibre material on cut resistance, fabrics woven from kevlar, HDPE, nylon monofilament and nylon multifilament yarns were chosen. 3.2 Test Methods Counting glass was used to count the end and pick densities and an average of ten readings was taken. The linear density of the warp and weft yarns form fabric was determined using the Beesley balance. An average of five readings was taken. To determine the fabric weight per unit area, the fabric sample of 10cm 10cm was weighed on an electronic balance to Table 2 Specifications of selected high performance fabrics Sample Fabric type Weave Thread Fabric Fabric No. count/cm thickness weight Warp Weft mm g/m 2 HP 1 Nylon Plain 13 16 0.41 200 HP2 multifilament Nylon Plain 12 14 0.44 250 HP 3 camouflage HDPE 3/3 twill 51 21 0.70 330 HP 4 Para-aramid Plain 9 9 0.30 200 HP 5 100% nylon monofilament 3/3 twill 41 13 1.1 400 calculate the fabric weight in g/m 2. An average of 5 readings was taken for each sample. The thickness of a textile material as defined by the ASTM is the distance between the upper and lower surface of the material, measured under specified pressure of 20 g/cm 2. The thickness of the fabrics was measured by Essdiel thickness tester. The physical parameters of cotton and high performance fabrics are given in Tables 1 and 2 respectively. The measurement of cut resistance of various fabrics was carried out on an indigenously developed instrument. A strip of reference material (teflon) of 0.25 mm thickness and a strip of the fabric of dimensions 6 cm 2 cm are mounted adjacent to each other on the mandrel. The distance traveled by the mandrel to make a cut in the reference material and in the fabric was determined alternatively. Finally, the cut resistance of the fabric is expressed in terms of an index which is the ratio of the distance traveled by the mandrel to make a cut in the fabric to the distance traveled to make a cut in the reference material and is referred to as the cut resistance index (CRI). The speed of mandrel and the normal load during cutting for 100% cotton fabrics were 70 cm/min and 250 g respectively. For

310 INDIAN J. FIBRE TEXT. RES., SEPTEMBER 2007 high performance fabrics the normal load was kept at 750g. 4 Results and Discussion 4.1 Cut Resistance of Cotton Fabrics The effects of weave pattern on cut resistance index (CRI) of the 100 % cotton woven fabrics along the warp and weft directions are shown in Fig. 4. In the fabric samples C 5, C 6, C 7 and C 8 the only difference is the weave pattern and the yarn linear density, thread count and cover factors are same. The results reveal that the plain weave has the maximum cut resistance followed by the 2 2 matt weave and the 3/1 twill, while the honey comb weave exhibits the least cut resistance. The similar trend is observed both in warp as well as in weft directions. This can be attributed to the greater number of intersections per unit area of the plain weave which enables the cutting force to be shared by a greater number of threads and hence higher cut resistance. In a simpler way, this is because of the better stress propagation as more number of threads takes up and shares the cutting force. The honey comb weave has very poor cut resistance as compared to the other weaves because of its rough surface (special diamond and raised effect) which ultimately increases the friction between the cutting edge and the fabric, thus providing a better grip resulting in poor cut resistance. In general, the cut resistance index (CRI) of all the weaves in the warp direction is slightly higher than in the weft direction, as can be observed from Fig. 4. This can be attributed to the higher number of warp yarns as compared to the weft yarns per unit length. Figure 5 shows the impact of pick density on cut resistance in warp and weft directions. In the fabric samples C 1, C 2, C 3 and C 4 (Table 1) the weave pattern, yarn linear density and the warps per unit length are same and the only difference is the pick density. The cut resistance of the fabrics increases as the pick density increases. This can be attributed to the increased number of threads which has to take up the same cutting force as that by the other fabrics. 4.2 Cut Resistance of Different High Performance Fabrics The results on the cut resistance index (CRI) of the different high performance fabrics in warp and weft directions are shown in Fig. 6. The figure shows the highest cut resistance for the nylon monofilament fabric (HP 5 ) in both the warp and weft directions, while the lowest cut resistance is exhibited by paraaramid fabric (HP 4 ) in warp direction and the HDPE Fig. 4 Effect of weave pattern on cut resistance of 100% cotton fabrics Fig. 5 Effect of pick density on cut resistance of 100% cotton fabrics Fig. 6 Cut resistances of different high performance fabrics (HP 3 ) fabric along the weft direction. The high cut resistance of the monofilament fabric is mainly due to its very low compressibility, and hence when the normal load is applied there is no plastic deformation of the fabric and thus greater energy is dissipated in sliding to make a cut. This may also be due to less frictional force as lower contact area between the monofilaments and the cutting blades. The poor cut resistance of the HDPE fabric in the weft direction

KOTHARI et al.: CUT RESISTANCE OF TEXTILE FABRICS 311 may be attributed to the very low pick density compared to the end density. The cutting resistance in warp and weft directions of para-aramid fabric (HP 4 ) is found to be the same. This is because of the fact that the warp and weft densities of this fabric were the same. 5 Conclusions The present simplified mathematical model is able to predict the cutting force and the distance of slide during cutting process based on some assumptions. It is possible to predict the cutting force and distance slide by knowing some material-related and other parameters like normal load, pretension, velocity of cutting blade, frictional characteristics, thickness of the material, length of contact, etc. The study on the effect of weave pattern on cut resistance reveals that the plain weave has the maximum cut resistance, while the minimum cut resistance is exhibited by the honey comb weave. The study on the effect of fabric tightness on cut resistance shows that the cut resistance increases with the increase in picks/inch of the fabric. The study on the cut resistance of some of the high performance fabrics shows a very high cut resistance of the monofilament fabrics and the least cut resistance for para-aramid fabric along the warp direction, while the least cut resistance along the weft direction is exhibited by the HDPE fabric. References 1 Knoff W F, Text Asia, 33(2) (2002) 33. 2 Vu-Thi B N, Vu-Khanh T & Lara J, J Thermoplastic Compos Mater, 18(1) (2005) 23. 3 Offermann P, Pietsch K, Finkelmeyer S, Ulbricht V & Schirmacher F, Melliand Textilber, 84(5) (2003) 395. 4 Hearle J W S, Lomas B & Cook W D, Fibre Failure and Wear of Mater (Ellis Horwood Ltd., Chichester, UK), 1989. 5 Finkelmeyer S, Sonntag P, Hoffman G & Offermann P, Asian Text J, 6(7) (1997) 63. 6 Hyung S S, Erlich D C & Shockey D A, J Mater Sci, 38 (17) (2003) 3603. 7 Sandor R B, Carter M C, LaForce G, Gunilla E, Clear W F, Flint J A, Lanieve H L, Thompson S W, Oakley (Jr), Etheridge O, Kafchinski E R & Haider M I, US Pat 6,210,798 (to Honeywell International, Inc. Morristown, NJ), 2001. 8 Zhu R, US Pat Application No. 20040065072 (to Nanoamp Solutions, Inc.), 8 April 2004. 9 Hoffman G & Schwertfeger A, Melliand Textilber, 76(11) (1996) 991, E245. 10 Dietzel Y, Hoffmann G, Offermann P, Wehlmann J & Stoll M, Melliand-Textilber, 83(11-12) (2002) E165. 11 Bajaj P & Sriram, Indian J Fibre Text Res, 22(4) (1997) 274.