This article was downloaded by:[Indian Institute of Technology] On: 25 March 2008 Access Details: [subscription number 791119987] Publisher: Taylor & Francis Informa Ltd Registered in England and Wales Registered Number: 1072954 Registered office: Mortimer House, 37-41 Mortimer Street, London W1T 3JH, UK Journal of the Textile Institute Publication details, including instructions for authors and subscription information: http://www.informaworld.com/smpp/title~content=t778164490 Stress-strain characteristics of different spun yarns as a function of strain rate and gauge length A. Ghosh a; S. M. Ishtiaque b; R. S. Rengasamy b a Department of Textile Technology, Kumaraguru College of Technology, Coimbatore-641006, India. b Department of Textile Technology, Indian Institute of Technology Delhi, Hauz Khas, New Delhi-110016, India. Online Publication Date: 01 March 2005 To cite this Article: Ghosh, A., Ishtiaque, S. M. and Rengasamy, R. S. (2005) 'Stress-strain characteristics of different spun yarns as a function of strain rate and gauge length', Journal of the Textile Institute, 96:2, 99 - 104 To link to this article: DOI: 10.1533/joti.2004.0067 URL: http://dx.doi.org/10.1533/joti.2004.0067 PLEASE SCROLL DOWN FOR ARTICLE Full terms and conditions of use: http://www.informaworld.com/terms-and-conditions-of-access.pdf This article maybe used for research, teaching and private study purposes. Any substantial or systematic reproduction, re-distribution, re-selling, loan or sub-licensing, systematic supply or distribution in any form to anyone is expressly forbidden. The publisher does not give any warranty express or implied or make any representation that the contents will be complete or accurate or up to date. The accuracy of any instructions, formulae and drug doses should be independently verified with primary sources. The publisher shall not be liable for any loss, actions, claims, proceedings, demand or costs or damages whatsoever or howsoever caused arising directly or indirectly in connection with or arising out of the use of this material. Downloaded By: [Indian Institute of Technology] At: 13:32 25 March 2008 Stress–strain characteristics of different spun yarns as a function of strain rate and gauge length A. Ghosh1, S. M. Ishtiaque2 and R. S. Rengasamy2 1 2 doi:10.1533/joti.2004.0067 Department of Textile Technology, Kumaraguru College of Technology, Coimbatore-641006, India Department of Textile Technology, Indian Institute of Technology Delhi, Hauz Khas, New Delhi-110016, India Abstract: The influence of strain rates and gauge lengths on the characteristics of the stress–strain curves of ring, rotor, air-jet, and open-end friction spun yarns is investigated. A modified form of Vangheluwe’s model is used in describing the stress–strain characteristics of spun yarns. The proposed model can fairly well replicate these characteristics. Key words: Stress-strain, gauge length, strain rate, relaxation time, Maxwell element, non-linear spring, catastrophic. fact that the mechanical properties of spun yarns are timedependent phenomena because of the visco-elastic nature of textile yarn. Vangheluwe (1992) has shown that the tensile curve of a range of spun yarns (cotton, viscose, and polyester/cotton blends) can be reasonably predicted with a model based on a Maxwell element. Hence, in the second part of this paper, an attempt has been made to fit the stress–strain curves of various spun yarns using Vangheluwe’s proposed model describing the tensile curve of spun yarns with a modification. INTRODUCTION The tensile properties of yarns play a phenomenal role in the processability and quality of the end products. However, the values of yarn tenacity and breaking strain represent only about the terminal point of the stress–strain curve. In many situations, knowledge of the full course of the stress–strain curves is more desirable, since it provides the whole information about the behavior of stresses under various levels of strains. The behavior of the stress–strain curve of spun yarns is not only a function of the nature and structural arrangement of the constituent fibres in the yarns; the variation of rate of straining and gauge length also play a key role in defining the characteristics of stress–strain curves. Stress–strain curves are widely described in the literature for continuous filament yarns (Hearle and Thakur, 1961; Hearle, 1969; Furter, 1985; Realff et al., 2000). However, the reported information for spun yarns on this aspect is very limited (Chattopadhyay, 1999; Vangheluwe, 1992). The influence of testing parameters on the stress–strain characteristics of spun yarns (Rengasamy et al., 2004) and tensile failure of spun yarns as a function of yarn structure and testing parameters (Ghosh et al., 2004) are reported. The first part of this paper reports on the influence of various levels of strain rate and gauge length on the stress– strain curves of various spun yarns. It is an established EXPERIMENTAL Ring, rotor, air-jet, and open-end friction yarns having yarn count of 31.7, 30.6, 28.1, and 32.6 tex, respectively, were spun from viscose fibres. To study the stress–strain curves, these yarns were conditioned at 65% RH and 25°C for 24 hours and, subsequently, tensile tests were performed at strain rates of 0.1, 1, and 10 per min, at a constant gauge length of 500 mm. An Instron tensile tester was used for the lower strain rates, and an Uster Tensorapid tester was employed for the higher strain rate (10 per min). The yarns were also tested at gauge lengths of 50 and 500 mm at a constant strain rate of 1 per min in the Instron tensile tester. For each set of experiments, 100 tests were conducted. A typical stress–strain curve having tenacity and breaking strain close to the average values was selected. The strain rate u was calculated from the following expression Corresponding Author: Dr R. S. Rengasamy Dept of Textile Technology, Indian Institute of Technology, Hauz Khas New Delhi 110016, India Tel: 0091 11 2659 1418 Fax: 0091 11 2658 1103 Email: rsr60@hotmail.com © The Textile Institute 0138 u= v l 99 (1) JOTI 2005 Vol. 96 No. 2 pp. 99–104 6 where v is the rate of extension or speed of testing in mm/min and l is the test length in mm. The unit of strain rate is min–1. 10/min Stress (cN/Tex) 5 INFLUENCE OF STRAIN RATE AND GAUGE LENGTH ON STRESS–STRAIN CURVES The stress–strain curves of the different spun yarns tested at various levels of strain rates, namely 0.1, 1, and 10 per min at a constant gauge length of 500 mm, are depicted in Figures 1 to 4. The results show that there are outstanding 1/min 4 3 2 0.1/min 1 0 0 1 2 3 4 5 6 7 Strain (%) 8 9 10 11 12 20 Figure 4 Stress–strain curves of open-end friction spun yarn at different strain rates. 10/min Stress (cN/Tex) 16 1/min differences among different spun yarns in their stress– strain behavior. This can be explained in terms of their structural differences. In addition, the strain rates have significant influence on the stress–strain responses. At a constant gauge length (500 mm), a sharp and sudden fall in stress value is observed after the yarn attains its peak stress, for ring, rotor, and air-jet yarns at strain rates of 10 per min and 1 per min. However, for the open-end friction spun yarn, the stress falls off slowly with increasing strain, giving the peak a rounded-off shape. The roundedoff portion of the stress–strain region indicates that the breakage of fibres during yarn extension expands over a wide range of strain, or, in other words, the yarn breaks under a non-catastrophic mode of failure. At a slower strain rate (0.1 per/min), the ring spun yarn shows mostly catastrophic failure, the rotor spun yarn shows nearly noncatastrophic failure, while the air-jet and open-end friction spun yarns show non-catastrophic failure. The change of the failure mechanism of yarns from non-catastrophic to catastrophic mode with an increase in strain rate is due to the effect of impact loading, which is responsible for the simultaneous breakage of fibres at the same load. But open-end friction spun yarn fails under non-catastrophic mode even at a higher rate of straining, since there is a lack of cohesiveness of fibres in the yarn. At slow strain rates, the yarn failure is non-catastrophic, as more time is available for the fibres to slip apart. The non-catastrophic mode of yarn failure at slow strain rates is more pronounced for air-jet and open-end friction spun yarns because of reduced fiber interlocking in their structures. For every yarn, the curves shift towards the stress axis with an increase in the strain rate. This phenomenon can be ascribed to the shorter time available for yarn rupture hardly allowing for stress relaxation in the fibres at the high strain rate. Figures 5 to 8 depict the stress–strain curves of the different spun yarns tested at two different gauge lengths, 50 mm and 500 mm, at a constant strain rate of 1 per min. At this constant strain rate, all yarns show catastrophic failure at 500 mm gauge length except the open-end friction spun yarn, but all the experimental yarns tested at a gauge 12 8 0.1/min 4 0 0 2 4 6 8 Strain (%) 10 12 14 Figure 1 Stress–strain curves of ring spun yarn at different strain rates. 14 12 10/min Stress (cN/Tex) 10 1/min 8 6 0.1/min 4 2 0 0 2 4 6 8 Strain (%) 10 12 14 Figure 2 Stress–strain curves of rotor spun yarn at different strain rates. 12 10/min 10 Stress (cN/Tex) Downloaded By: [Indian Institute of Technology] At: 13:32 25 March 2008 A. Ghosh, S. M. Ishtiaque and R. S. Rengasamy 1/min 8 6 0.1/min 4 2 0 0 1 2 3 4 5 6 7 8 Strain (%) 9 10 11 12 13 Figure 3 Stress–strain curves of air-jet spun yarn at different strain rates. JOTI 2005 Vol. 96 No. 2 100 doi:10.1533/joti.2004.0067 © The Textile Institute 16 7 6 Stress (cN/Tex) Stress (cN/Tex) 12 500 mm 8 50 mm 4 5 50 mm 4 3 500 mm 2 1 0 0 4 8 12 Strain (%) 16 20 24 0 0 Figure 5 Stress–strain curves of ring spun yarn at different gauge lengths. 2 4 6 8 10 12 14 Strain (%) 16 18 20 22 Figure 8 Stress–strain curves of open-end friction spun yarn at different gauge lengths. 12 be adequate to cause sharp and instantaneous breaks. The stress–strain curves of air-jet spun yarns shows a definite stick–slip phenomenon and this phenomenon is more pronounced at lower rates of straining. The stick– slip phenomenon for air-jet spun yarn can account for its distinct structural characteristics. Air-jet spun yarn consists of a majority of fibres in an almost untwisted state in the core and a surface layer of fibres wrapped around the core. An occasional slippage of core fibres inside the wrapper fibres is likely to take place for air-jet yarn under increasing axial tension. But the stick–slip phenomenon is not observed for other yarns. Stress (cN/Tex) 10 8 50 mm 6 4 500 mm 2 0 0 2 4 6 8 10 12 14 16 18 Strain (%) 20 22 24 26 Figure 6 Stress–strain curves of rotor spun yarn at different gauge lengths. 10 THEORETICAL MODEL FOR STRESS–STRAIN CURVES OF SPUN YARNS 9 8 Stress (cN/Tex) Downloaded By: [Indian Institute of Technology] At: 13:32 25 March 2008 Stress–strain characteristics of different spun yarns as a function of strain rate and gauge length Vangheluwe (1992) investigated the influence of strain rates on the stress–strain curves of ring and rotor spun yarns using a visco-elastic model based on a Maxwell element. In her model, a nonlinear spring is placed in parallel with a Maxwell element (Fig. 9). The behavior of the nonlinear spring was assumed as 50 mm 7 6 5 500 mm 4 3 2 1 σ2 = D ε 2 0 0 2 4 6 8 10 12 14 16 18 20 Strain (%) 22 24 26 where σ2 and ε are the stress and strain of the nonlinear spring, and D is the spring constant (cN/tex). Vangheluwe obtained a good correlation with the experimental stress– strain curves. In her proposed model, she simply assumed that the stress is directly proportional to the square of the Figure 7 Stress–strain curves of air-jet spun yarn at different gauge lengths. length of 50 mm show non-catastrophic failure. The value of peak stress at 50 mm gauge length is higher than that of 500 mm gauge length. The difference in the characteristics of the stress–strain curves at short and long gauge lengths can be attributed to the fact that the storage of elastic energy in a yarn under axial tension is a linearly increasing function of gauge length and the energy stored in a specimen of longer gauge length is sufficient to complete the breakage. Therefore, rupture of yarns tested at the longer gauge length occurs under a catastrophic mode of failure (Hearle, 1969). On the other hand, energy stored in a yarn is low at short gauge length and may not © The Textile Institute doi:10.1533/joti.2004.0067 (2) E σ2 = D ε 2 η Figure 9 Vangheluwe’s model for describing the tensile curve of spun yarns. 101 JOTI 2005 Vol. 96 No. 2 strain for the nonlinear spring. However, in this present study, the following behavior of the nonlinear spring is being assumed σ2 = D ε n dk from the points to the experimental line. Using ‘genetic algorithms’ with MATLAB (version 6.5) coding, the sum of the square of the vertical distances dk is minimized and the values of A, B, D, and n are calculated for different spun yarns at strain rates of 0.1/min and 10/min. The experimental and fitted stress–strain curves for different spun yarns at strain rates of 0.1/min and 10/ min are shown in Figures 11 to 14. The actual curves are shown by the solid lines and the corresponding fitted curves are shown by dotted lines. Generally, a good correlation between the fitted and experimental curves was obtained. For all the yarns, the curve shifts towards the stress axis when the tensile test is executed at higher strain rates. Thus, the initial modulus increases with the rate of straining. Also, at certain levels of strain, the stress shows a greater value for higher strain rates compared to lower ones. (3) where n > 0. A schematic representation of the modified model is depicted in Fig. 10. E σ2 = D ε n η Figure 10 Modified Vangheluwe’s model for describing the tensile curve of spun yarns. 18 10/min strain rate 16 The second-order differential equation governing the stress–strain behavior of the Maxwell element is given by 14 Stress, cN/tex 12 δ 2 ε = 1 δ 2 σ + 1 ⋅ δσ (4) E δt2 η δt δt2 where σ and ε are the stress (cN/tex) and strain of the Maxwell element respectively, E is the spring modulus (cN/tex), and η is the viscosity (cN-s/tex) of the dashpot in the Maxwell element. The theoretical relationship between stress and strain of a spun yarn tested at a constant rate of extension is obtained by the solution of Equations 3 and 4, which is written as σ = A (1 – e – E ⋅ε η u) + Dε n σ = A (1 – ) + Dε 0.02 0.04 0.06 0.08 Strain 0.10 0.12 0.14 (5) 12 10/min strain rate 10 (6) n 0 Figure 11 Experimental and fitted stress–strain curves for ring yarn at different strain rates. By replacing the expression of τ in Equation 5, we have – ε e uτ 6 0 where A is a constant and u is the strain rate (min ). A Maxwell element can be characterized by its relaxation time τ, which is given by η E 0.1/min strain rate 8 2 –1 τ= 10 4 Stress, cN/tex Downloaded By: [Indian Institute of Technology] At: 13:32 25 March 2008 A. Ghosh, S. M. Ishtiaque and R. S. Rengasamy 8 0.1/min strain rate 6 4 (7) 2 According to the ISO 2062, a pre-tension of 0.5 cN/tex has to be given to the yarn while clamping in the tensile tester. At this pre-tension, strain in the yarn is zero. Therefore, a correction is made for the pre-tension in Equation 7. Thus, Equation 7 becomes σ = 0.5 + A (1 – e–Bε) + Dεn 0 0.02 0.04 0.06 0.08 Strain 0.10 0.12 0.14 Figure 12 Experimental and fitted stress–strain curves for rotor yarn at different strain rates. (8) where B = 1/u τ. Equation 7 can be fitted on the experimental tensile curve using a least square method, i.e. by minimizing the sum of squares of vertical distances JOTI 2005 Vol. 96 No. 2 0 Table 1 shows the values of the parameters A, B, D, and n of the modified Vangheluwe’s model for different spun yarns at two levels of strain rates. In Table 1, the 102 doi:10.1533/joti.2004.0067 © The Textile Institute 10 the strain rate and spinning technologies. Therefore, Equation 8 can be rewritten in the following form 10/min strain rate 9 σ = 0.5 + 1.28 (1 – e–Bε) + Dε2/3 8 Stress, cN/tex 7 6 5 4 2 1 0 0 0.02 0.04 0.06 Strain 0.08 0.10 0.12 Figure 13 Experimental and fitted stress–strain curves for air-jet yarn at different strain rates. 6 10/min strain rate 5 4 0.1/min strain rate 3 2 1 0 0 0.01 0.02 0.03 0.04 0.05 Strain 0.06 0.07 0.08 (9) The values of B depend on the strain rate u and relaxation time τ. As at high rate of straining the relaxation time τ reduces considerably, the values of B thus increases. It is observed from Table 1 that at all strain rates, the values of B and D are highest for ring spun yarns followed by rotor, air-jet, and open-end friction spun yarns. This trend is exactly similar to the tenacity of the above spun yarns. It can be expected that the value of the spring constant of the nonlinear spring D is higher for the stronger yarn. It is also evident from Table 1 that at all strain rates the value of relaxation time τ is lowest for ring spun yarn followed by rotor, air-jet, and open-end friction spun yarns. A better structural integrity and higher degree of fibre interlocking of fibres in ring spun yarns produce a shorter relaxation time τ under tensile loading as compared to the other yarns. Thus the values of B, which is an inverse measure of relaxation time τ, are higher for ring yarn followed by other yarns in the above sequence. Theoretically, the spring constant D should be independent of the strain rate. However, it is observed that D is not independent of the strain rate. The influence of strain rate on D as compared to the relaxation time τ is relatively smaller. During the tensile loading in a yarn, there are many processes contributing to the relaxation in fibres and yarns, and each process has a different relaxation time (Vangheluwe, 1992). 0.1/min strain rate 3 Stress, cN/tex Downloaded By: [Indian Institute of Technology] At: 13:32 25 March 2008 Stress–strain characteristics of different spun yarns as a function of strain rate and gauge length 0.09 CONCLUSIONS At high rates of straining (10 per min and 1 per min), ring, rotor, and air-jet yarns show catastrophic failure and open-end friction spun yarn shows mostly non-catastrophic failure. At a low strain rate (0.1 per min), ring yarn shows mostly catastrophic failure, rotor yarn shows nearly noncatastrophic failure, and air-jet and open-end friction spun yarns show non-catastrophic failure. The stress–strain curve shifts towards the stress axis with an increase in the strain rate for all yarns. At a high gauge length (500 mm), ring, rotor, and air-jet spun yarns exhibit catastrophic failure. On the other hand, non-catastrophic failure is observed for all the yarns tested at the lower gauge length of 50 Figure 14 Experimental and fitted stress–strain curves for open-end yarn at different strain rates. relaxation time τ is also calculated from the values of the parameter B and strain rate u. It is appreciated that the relaxation time is notably higher for the lower strain rate than that of the higher strain rate. A higher relaxation time obviously causes more stress relaxation, which is responsible for the decrease in stress at certain levels of strain for yarns tested at the lower strain rate as compared to these tested at the higher strain rate. It is evident from the Table 1 that the values of A and n are independent of Table 1 Parameters of the modified Vangheluwe’s model as a function of the strain rate Parameters A B D (cN/Tex) n τ (sec) © The Textile Institute Ring yarn Rotor yarn Air-jet yarn OE friction yarn Strain rate Strain rate Strain rate Strain rate 0.1/min 10/min 0.1/min 10/min 0.1/min 10/min 0.1/min 10/min 1.28 52.06 47.69 2/3 11.52 1.28 68.82 61.73 2/3 0.087 1.28 40.82 31.69 2/3 14.69 1.28 61.9 37.34 2/3 0.096 1.28 20.95 27.79 2/3 28.64 1.28 27.73 33.55 2/3 0.216 1.28 10.95 18.13 2/3 54.79 1.28 14.47 21.43 2/3 0.414 doi:10.1533/joti.2004.0067 103 JOTI 2005 Vol. 96 No. 2 Downloaded By: [Indian Institute of Technology] At: 13:32 25 March 2008 A. Ghosh, S. M. Ishtiaque and R. S. Rengasamy mm. The stress–strain curve of air-jet spun yarn has kinks indicating stick–slip phenomenon. It is possible to describe the tensile curve of spun yarn using the modified Vangheluwe’s model. The model can simulate the stress–strain characteristics of spun yarns with a reasonable degree of accuracy. Yarns as a Function of Structure and Testing Parameters, Communicated to Textile Res. J. HEARLE, J. W. S. and THAKUR, V. M., 1961. The Breakage of Twisted Yarns, J. Textile Inst., 52, T149–T163. HEARLE, J. W. S., 1969. Structural Mechanics of Fibres, Yarns and Fabrics, Vol. 1, Wiley-Interscience, New York. REALFF, M. L., PAN, N., SEO, M., BOYCE, M. C. and BACKER, S., 2000. A Stochastic Simulation of the Failure Process and Ultimate Strength of Blended Continuous Yarns, Textile Res. J. 70, 415–430. RENGASAMY, R. S., Ishtiaque, S. M., Ghosh, A. and Patnaik, A., 2004. The Influence of Strain Rate and Gauge Length on the Stress–Strain Characteristics of Staple Yarns Representing Different Spinning Systems, in Proc. 83rd TIWC, Shanghai, China, 411–414. VANGHELUWE, L., 1992. Influence of Strain Rate and Yarn Number on Tensile Test Results, Textile Res. J. 62, 586–589. REFERENCES CHATTOPADHYAY, R., 1999. The Influence of the Strain Rate on the Characteristics of the Load–Elongation Curves of Ringspun and Air-jet Spun Yarns, J. Textile Inst,. 90, 268–271. FURTER, R., 1985. Strength and Elongation Testing of Single and Ply Yarns, The Textile Institute, Manchester. GHOSH, A., ISHTIAQUE, S. M. and RENGASAMY, R. S., 2004. Analysis of Spun Yarn Failure Part I: Tensile Failure of JOTI 2005 Vol. 96 No. 2 104 doi:10.1533/joti.2004.0067 © The Textile Institute