Stress-strain characteristics of different spun yarns as a function of strain rate and gauge length Corresponding Author

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 and tensile failure of spun yarns as a function of yarn structure and testing parameters are reported. The first part of this paper reports on the influence of various levels of strain rate and gauge length on the stressstrain curves of various spun yarns. It is an established 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.

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 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 .

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 differences among different spun yarns in their stressstrain 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.

Figure 1

Figures 5 to 8depict 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 Stress-strain curves of ring spun yarn at different strain rates. Stress-strain curves of rotor spun yarn at different strain rates. Stress-strain curves of air-jet spun yarn at different strain rates. Stress-strain curves of open-end friction spun yarn at different strain rates.

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. 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 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 stickslip 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. 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

Figure 9

Vangheluwe's model for describing the tensile curve of spun yarns.

THEORETICAL MODEL FOR STRESS-STRAIN CURVES OF SPUN YARNS

where σ 2 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 stressstrain curves. In her proposed model, she simply assumed that the stress is directly proportional to the square of the strain for the nonlinear spring. However, in this present study, the following behavior of the nonlinear spring is being assumed

where n > 0. A schematic representation of the modified model is depicted in Fig. 10. The second-order differential equation governing the stress-strain behavior of the Maxwell element is given by

Figure 10

Modified Vangheluwe's model for describing the tensile curve of spun yarns.

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

where A is a constant and u is the strain rate (min -1 ). A Maxwell element can be characterized by its relaxation time τ, which is given by

By replacing the expression of τ in Equation 5, we have

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

where B = 1/uτ. 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 d k 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 d k 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. Figure 12 Experimental and fitted stress-strain curves for rotor yarn at different strain rates. 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 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 the strain rate and spinning technologies. Therefore, Equation 8 can be rewritten in the following form σ = 0.5 + 1.28 (1 -e -Bε ) + Dε 2/3 (9)

Figure 11

Experimental and fitted stress-strain curves for ring yarn at different strain rates.

Figure 12

Table 1

Parameters of the modified Vangheluwe's model as a function of the strain rate

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).