Evaluation of Physical and Mechanical Properties of Cotton Warps Under a Cyclic Load of Stretch-Abrasion

The specimens used in this study were cotton compact spun yarns in common use, and a total of four specimens were selected to compare with the physical and mechanical properties. The specifications of the specimens are shown in Table 1.

The fatigue cycle tests of warps were conducted using the WLS developed in our laboratory. Figure 1 presents the schematic diagram of the simulator. One end of the warp was fixed to the pre-tension weight, and the other end passed through the splitting roller, and then through the drop and induction device, smooth roll, reciprocating friction roll, and the oscillating friction roll. The reciprocating friction roll imparted flex abrasion and cyclic stresses to yarn. The oscillating friction roll imparted only flex abrasion to yarn. During the test, the reciprocating friction roll and the oscillating friction roll reciprocated once, and they produced a tensile, friction, and buckling effect on the yarn. The internal counter of the simulator recorded the fatigue cycle once. The number of cycles required to break yarn in trials was the index of the fatigue cycle. Besides the deflection, characteristics of the friction roll such as its surface roughness and material size and shape may also affect fatigue resistance.

Figure 1

The testing parameters of the WLS including the load amplitude, load speed, and pre-tension were set to 70 mm, 180 cycle/min, and 2.1cN/tex, respectively. The temperature and the relative humidity were (20 ± 3)°C and (65 ± 5)%, respectively.

To investigate the effect of the fatigue test on the tensile properties, the sized warps were worn for a certain number of cycles on the WLS equal to 5, 10, 20, 40, and 80% of their fatigue cycles tested based on failure. The warps that survived after the above-mentioned fatigue levels were collected and the tensile properties were further measured using an electronic single yarn strength tester model SHIMADZU AGS-X according to GB/T 3916-1997 with 250 mm/min speed and 250 mm specimen length. Thirty tests were conducted for each sample and the mean values were acquired. The temperature and the relative humidity were (20 ± 3)°C and (65 ± 5)%, respectively. Equations (1) and (2) show the calculation of SR and ER, respectively. They are defined as follows: (1) SR=S1S0×100% SR = {{{S_1}} \over {{S_0}}} \times 100\% (2) ER=E1E0×100% ER = {{{E_1}} \over {_0}} \times 100\% where SR is the strength retention in%, S₁ is the breaking strength of worn warp in cN, and S₀ is the breaking strength of unworn warp in cN; ER is the elongation retention in %, E₁ is the elongation at break of worn warp in millimeter, and E₀ is the elongation at break of unworn warp in millimeter.

The RH of warps causes the warp ends to cling together and even break off when weaving. Particularly critical is RH in staple fibers when they are woven on air-jet looms. Therefore, RH is an important parameter to evaluate the physical property of warps after fatigue load. The WLS was developed for abrading yarn. In this article, specimens endured different fatigue cycles to examine the development of RH. The abrasion areas of the worn warps are marked and obtained. We used a yarn examine machine model YG381 manufactured by Nantong Hongda Experimental Instrument Co. LTD (Nantong, China) to wind the worn warps evenly on it. The scanner model 9000F Mark2 manufactured by Canon China Co. LTD (Shanghai, China) provided a digital image of yarn. Finally, the images were processed, and the hairiness area index was extracted from them by the developed program through MATLAB R2014b [10]. A total of 30 tests were conducted for each sample. The mean values and the coefficient of variation (CV) acquired were used as data. The hair area index (H and H₁) was recorded. Hair area index (H or H₁) is a unit-less parameter defined as a ratio between the total area of single (i.e. looped and protruding) fibers S_F or S_F1 and the total area of core S_C [11]. It can be expressed by the following equation: (3) H=SFSC×100% H = {{{S_F}} \over {{S_C}}} \times 100\% (4) H1=SF1SC×100% {H_1} = {{{S_{F1}}} \over {{S_C}}} \times 100\% where H is the total hair area index in %, S_F is the total area of single fibers, S_C is the total area of the core; H₁ is the hair (3 mm or longer) area index in %, and S_F1 is the area of single fibers (3 mm or longer).

The influence of linear density on the statistical distribution of the yarns’ fatigue characteristic was investigated by the Weibull distribution. The collected data on SR, ER, and RH were analyzed statistically by a scatter plot. Regression fitting and R² were used to determine whether a response was significantly influenced by the independent parameters.

The behavior of Yarn fatigue follows a three-parameter Weibull distribution [12], which is given in Equation (5) as follows: (5) P(t)=1−exp[−(t−γη)β], for β>0;η>0;γ>0;t≥γ P(t) = 1 - \exp \left[ { - {{\left( {{{t - \gamma } \over \eta }} \right)}^\beta }} \right],\,{\rm{for}}\,\beta > 0;\eta > 0;\gamma > 0;t \ge \gamma where P(t) is the probability of cumulative fatigue; t is the lifetime in the number of cycles to rupture; γ is the minimum lifetime that the yarn will survive in; η and β are Weibull scale and shape parameter, respectively. β decides the shape of the distribution. P is calculated by (i−0.3)/(N+0.4) [13], where N is the total sample size and i is the ranking of a test based on the fatigue cycle data stored in ascending order.

By taking the logarithm twice, Equation (5) can be rewritten in a linear form. (6) ln[ln(11−P)]=βln(t−γ)−βlnη \ln \left[ {\ln \left( {{1 \over {1 - P}}} \right)} \right] = \beta \ln (t - \gamma ) - \beta \ln \eta

To evaluate the Weibull distribution model, a one-sample Kolmogorov–Smirnov (K–S) test was applied at a commonly adopted significance level (α = 0.01). The procedure of the goodness-of-fit test is as follows:

Determine the maximum deviation (D_n) between P₀ from P₀ = (i−0.3)/(N + 0.4) and P from the Weibull probability (Equation 5). (7) Dn=max|P0−P| {D_n} = \max |{P_0} - P|

The fitting of the Weibull distribution model is effective, and the mean value and variance of Weibull distribution can be calculated as follows: (9) μ=γ+(η−γ)Γ(1+1β) \mu = \gamma + (\eta - \gamma )\Gamma \left( {1 + {1 \over \beta }} \right) (10) S=(η−γ)[Γ(1+1β)−Γ2(1+1β)]12 S = (\eta - \gamma ){\left[ {\Gamma \left( {1 + {1 \over \beta }} \right) - {\Gamma ^2}\left( {1 + {1 \over \beta }} \right)} \right]^{{1 \over 2}}} where Γ(x) —is the gamma function, which can be obtained by looking up the table.

The fatigue characteristics of the yarn accompanied by strength and abrasion are of great importance for the weavability of warp. The Weibull distribution parameters of unsized and sized yarn samples in this article are given in Tables 2 and 3, respectively.

As for Figures 2(a) and 3(a), the Weibull statistical analysis of the fatigue cycle data yields three characteristic parameters for each group, that is, γ, β, and η. The results are summarized in Tables 2 and 3. The value of location parameter γ is the lower bound of the distribution, the minimum fatigue cycle that the yarn will survive [7]. The value of scale parameter η, which is the characteristic fatigue cycle and numerical close to the mean fatigue cycle, is found to be decreased with decreasing linear density irrespective of unsized and sized yarns. The shape parameter β is related to the coefficient of variations. All the fitting plots show acceptable linearity (R² > 0.919, except 11.6tex), signifying a reasonable Weibull distribution fitting. Furthermore, according to the values of D_n using a one-sample K–S test, the fatigue cycle of the yarn at four different linear densities irrespective of unsized and sized yarns all fit the Weibull distribution well at a level of 1%: all the D_n values are lower than that of the critical value (0.2305). As is well known, the twist imparted to the yarn affects the structure of yarn and the mechanical properties of the yarn. In automatic weaving, warp twist would also affect end breakage rate and consequently weaving efficiency. In general, increasing the twist and thus reducing the amount of loosely bound fiber on the yarn surface materially reduced the number of failures due to this factor. This is obviously due to the consolidation of the fiber assembly on account of the increase in helix angle, which causes an improvement in resistance to inter-fiber slippage during weaving stress. The twist level and linear density effects on the fatigue cycle of yarns are apparent, and the corresponding fatigue can be reasonably predicted from the three-parameter Weibull distribution model. The cumulative failure probability model (Figures 2(b) and 3(b)) is presented to predict the threshold values of the yarn fatigue cycle with different linear densities. All plots reveal a similar upward trend with increasing fatigue level, and yarns with different linear densities have different threshold values, which is a distinct indicator of the linear density dependence of the fatigue cycle. Therefore, the effect of linear density on the fatigue cycle cannot be ignored.

Figure 2

Figure 3

It can be also seen from Figure 2 that Weibull plots lie toward the far right of the plots for the yarn of 19.4 tex, followed by 14.5, 11.6, and 9.7 tex from right to left. This indicates the optimal fatigue property of the yarns of 19.4 tex as compared to that of the other three yarns, owing to the highest resistance to fatigue accompanied by stretch and abrasion. The higher the linear density of the yarn, the greater the number of fibers in the cross-section of yarn, and the harder it is to make it a failure. Nevertheless, after sizing, the improvement obtained in the weaving potential of yarn is substantially higher irrespective of linear density. These yarns exhibit similar trends after sizing, which are shown in Figure 3. Thus, it can be concluded that the fatigue characteristic of the yarn plays a dominant role in determining the weaving performance even in sized yarns.

Although the fatigue characteristic of yarn is of great importance for the warps, it is hard enough to establish weaving potential in terms of the characteristic fatigue cycle calculated by fitting a Weibull distribution because the actual tensile fatigue cycles of the yarn imposed on a loom can sometimes be far lower than these characteristic fatigue cycles. Therefore, understanding the gradual deterioration of yarn tensile properties as fatigue levels increase may yield useful information about the potential failure of yarn. Moreover, the breaking strength and breaking elongation of a warp are reduced by about 10% after weaving [14]. SR of a warp was a parameter that can reflect the ability to avoid damage from failure [15, 16]. In this experiment, with four sized yarn of different linear densities, the relationship between the SR and fatigue cycles as well as between ER and fatigue cycles was studied.

The variations in SR and ER with four sized warps of different linear densities are shown in Figure 4. As can be shown, both the SR and ER decrease generally with increasing fatigue cycles, as expected. Figure 4(a) shows that the SRs drop slightly in the first 5% of fatigue cycles, especially for 14.5tex yarn from 100% to 96.73%. This may be explained as follows. At the initial testing stage, a small amount of the size coating gets abraded, residual surface slurry maintained the structural integrity of warp and played a role in protecting fibers. Therefore, the reduction of yarn strength is not obvious. With the test progressing, the surface slurry was gradually worn off, and the exposed sheath fibers were worn directly by the load component. Cracks occurred on the surface of fibers and they damaged the structural integrity of the warps, which resulted in a decrease in the tensile properties [17]. Thus, the SR of yarns steadily declines from 100% to below 90.09% in the first 10% of fatigue cycles, except 14.5 tex yarn. Figure 4(a) also demonstrated that SR declined significantly from 20% to 40% of the fatigue cycle. The reason is that the warp was always kept in close contact with the load component and damaged after being worn for a certain amount of cycles. Once the relative movement between the warp and the load component occurred, the repetitive load between sheath fibers of warp and the load component would greatly reduce the cross-section and lead to a sharp decrease in tensile properties of warp [18, 19]. Moreover, in each fatigue cycle of the test, the testing area of warp alternated between straight and curved conditions, which caused bending and tensile fatigue. The indicator of ER shows a similar tendency, as shown in Figure 4(b). The results also reveal that the SR and ER of the yarn do not continuously decrease with increasing fatigue cycles but reach a threshold value at a 40% of fatigue cycle, after which they start to decline slowly. The authors observed a similar trend for cotton yarns [2, 6, 20]. Figure 4 also demonstrates a very strong relationship of quadratic polynomials between the tensile property and the fatigue cycle. The results of R² are all within the acceptable range. Therefore, in practical applications, the critical issue is to improve the surface performance of warp to reduce the influence of abrasion and stretch on its mechanical properties.

Figure 4

The RH of yarn is an important index to evaluate the physical performance of yarn. Reducing the RH generated during weaving can effectively avoid end-breakage caused by the adhesion between adjacent warps. The relationships between fatigue cycle and hair area index as well as between the fatigue cycle and hair area index (3mm or longer) are shown in Figure 5. According to the experimental results and observed morphology, typical images of worn warps at various fatigue cycles were obtained, as shown in Table 4.

Figure 5

As can be seen in Figure 5, under different fatigue cycles, H and H₁ indicate that the RH increases slightly with an increasing fatigue cycle in the first 5% of fatigue cycles for all samples mentioned above. This may be explained as follows. First, a thin layer of the size coating is abraded, the friction component had worn off the surface of sheath fibers and exposing surface fibers of yarns to abrasion to generate a small amount of hairiness. Similarly, RH has been found to increase gradually with the increase of the fatigue cycle from 5% to 20%. The presence of worn warp gradually progressed from slightly fuzzy to rough in this stage. Nevertheless, plucking of fibers from the yarn body due to cycle abrasion and stretch is likely to create higher RH in the sheath between 20% and 40% of the fatigue cycle. Therefore, the RH is almost twice the amount suffered by up to 40% of the fatigue cycle. It is especially obvious for the H of 19.4 tex yarn. There is a small amount of hairiness nodules to form hairballs as shown in Table 4. During the last testing stage, the uptrends of RH are moderate between 40% and 80% of the fatigue cycle. The reason is to be that with the continuous expansion of the yarn core, the number of fibers projecting from the yarn surface to form hairiness is limited [21, 22, 23]. The warp was very fuzzy and more sheath fibers were damaged, and the structure of the warp became looser. Similarly, the relationship of quadratic polynomials between the hairiness area index and fatigue cycle fits well. The results of R² are almost all above 95.50%. The uptrend of RH increasing with the fatigue cycle coincides with the downtrend of SR decreasing with fatigue life.