Reliability analysis of stretchable workwear fabric under abrasive damage: influence of stretch yarn composition

ABSTRACT Movement comfort is an important performance parameter for workwear fabric. The lower value of load developed in the fabric at a certain extension level indicates lower stress on the skin and easier body movement. After repeated usage, there is a possibility of degradation in this movement comfort due to abrasion and cyclic loading. Measurement of the probability of successful performance of the workwear fabric in terms of movement comfort during usage is possible through reliability analysis. The present study is concerned with the reliability analysis of the body movement comfort of the workwear fabric under abrasive damage. The effect of composition and structure of different types of stretch yarn, i.e. cotton core spun, polyester core spun and polyester multifilament air-covered yarn, on this reliability has been studied. It is seen that after repeated cyclic loading there is a degradation in the movement comfort of the fabrics. The extent of degradation depends on the composition of the stretch yarn. Although the workwear fabric with the elastane contained cotton core spun weft yarn showed lower abrasion resistance, it showed the best reliability values in terms of movement comfort. Abrasive damage resulted in improvement in the level of movement comfort at higher levels of loading cycles.


Introduction
Comfort and durability are the key features of modern workwear fabrics. As regards body movement comfort, the garment fit cannot be loose for workwear fabric. Therefore, the load developed at a certain extension level of the fabric may be used as a criterion for judging its movement comfort. The lower value of load indicates less stress on the skin and easier body movement. Simple body movements such as bending the elbows or knees stretch the skin by as much as 20-45% (Hu and Lu 2015;Senthilkumar, Anbumani, and Hayavadana 2011;Tian et al. 2019). Strenuous movements involved even more stretch. However, the stretch imposed on the fabric depends on how close the fabric is to the skin. Thus, depending on the requirement of the level of stretch in the garment, there are two categories. The requirement of the stretch level below 30% is called comfort stretch and is relevant to apparel and workwear. Similarly, the requirement of the stretch level above 30% is called power stretch and is relevant to certain types of sportswear such as swimwear and compression garments.
To improve the stretchability of the fabric, the use of stretch yarn is very common. Various types of stretch yarns containing elastane filament in the core are used to provide such type of movement comfort in the fabric. Normally, the stretch yarns are used as weft during fabric manufacturing Mukhopadhyay 2022a, 2022b;Özdil 2008). The stretch yarn structure is mainly a core-sheath structure where staple fiber like cotton, viscose and polyester is used in the sheath and elastane filament is used as core. This core-sheath structure is commercially produced in a normal ringframe with some modification in the drafting zone. Nowadays, wrap spinning and air covering are the spinning technologies that have gained popularity to produce such stretch yarns due to their low cost of production (Senthilkumar, Anbumani, and Hayavadana 2011;Shaw and Mukhopadhyay 2022a).
When the workwear fabric is used by the consumer, the fabric undergoes abrasion through the process of wearing, surface rubbing, laundering, etc. Abrasion is the physical destruction of the fiber, yarn and fabric resulting due to the relative motion of the fabric with another surface (Abdullah et al. 2006). Abrasion not only results in the deterioration of the fabric's performance characteristics like strength but also affects the surface appearance of the fabric (Kaynak and Topalbekiroǧlu 2008).
Few recent studies Mukhopadhyay 2022a, 2022b) have considered the load developed at a lower level of tensile extension (20%) as a criterion to address the comfort of stretch fabric. It is seen that the structure and composition of the stretch yarn plays an important role in determining the load developed in the fabric at lower extension levels. In the studies (Mukhopadhyay and Prasad Shaw 2022;Shaw and Mukhopadhyay 2022b), the effect of abrasion on the extent of load developed in the stretch fabric has been investigated. Different types of stretch yarn with varying levels of elastane content were used as weft to provide the stretch in the fabric. It is found that the extent of increase in load after abrasion was significantly affected by the stretch yarn structure and composition. It must be added that in this study, the load developed in the fabric has been considered only for a single loading cycle. However, during actual usage, any fabric undergoes a large number of loading and unloading cycles throughout the life span of the garment. Such a large number of loading cycles or fatigue cannot be replicated in the laboratory setup. Nevertheless, if a fabric material is to be designed in which the comfort properties will last after repeated usage, then it is required to know the probability of its successful operation under the combined effect of abrasion and a large number of loading cycles (fatigue). Such probability can be measured by using reliability analysis (Kennedy and Louis 1967). Reliability is the probability that a system will perform its desired function under stated conditions. Reliability is also important as the average life alone cannot predict the failure rate at the end period of product life. A product or a system may have higher average life but also have higher failure rates. Thus, reliability analysis helps to determine the best raw material and process to make a product with better quality and life (Aggarwal 1993;Nenggan et al. 2009;Ramachandran et al. 2014;Singh, Mukhopadhyay, and Chatterjee 2017).
Thus, the present study investigates the effect of different types of stretch yarns, i.e cotton core spun, polyester core spun and polyester multifilament air-covered elastane yarn, on the rate of increase in the load developed in stretchable workwear fabric at a large number of loading cycles and then does the reliability analysis with the help of degradation and life data analysis. Further, the reliability values of unabraded and abraded workwear fabrics were compared to study the effect of abrasive damage on the durability of movement comfort of the fabric.

Material
Three different types of stretch yarn with 5% elastane content were produced. These stretch yarns have cotton staple, polyester staple and partially drawn polyester multifilament fiber as sheath/covering material. Table 1 shows the properties of the raw material used for producing the stretch yarn samples.
The polyester multifilament elastane yarn was produced by draw texturing and intermingling, whereas the staple cotton and staple polyester fibers were processed in a ring frame to produce elastane core-spun yarn. Core spun yarn was processed with a tex twist factor of 43 (T.M. 4.5) in the ring frame. The count of all three yarn samples was 24.6 tex (24 Ne). All the stretch yarns were used in the weft direction of the fabric. In the warp direction, an open-end yarn of 73.8 tex (8 Ne) was used. The raw material used for producing open-end yarn was cotton (30% clean cotton/55% noil/15% soft waste). The coding of the fabrics is done based on the type of elastane weft yarn ( Table 2).

Preparation of yarn
As shown in Figure 1, in the case of the core-spun, the elastane filament is fed to the nip of the front roller in the ring frame. The elastane filament is directed in such a way that it reaches the center of the roving fleece getting delivered from the front rollers. The draft of the elastane filament is adjusted so that the fineness corresponds to the content of the elastane filament in the yarn (Dhouib, El-Ghezal, and Cheikhrouhou 2006). The polyester multifilament elastane air-covered yarn was produced using Himson Engineering's Texturizing machine (HSS AX4 N). Two simultaneous processes are involved in the production of polyester multifilament air-covered elastane yarn. There is a sequence of draw texturing of partially oriented polyester multifilament and then intermingling the textured multifilament with the elastane filament. Air covering is a relatively cheaper method to produce elastane yarn due to low running cost. Intermingled sections of filaments are produced at regular intervals along the length of the yarn. An air nozzle is the main machine component of intermingling that generates airflow to create intermingled sections in the intermingled yarn ( Figure 2). Compressed air is blown on the filament at 90° to the direction of the yarn path through an outlet in the nozzle (Alagirusamy and Ogale 2004;Miao and Chun Christa Soong 1995;Pal, Gandhi, and Kothari 1996;Pinar and Özkan 2013). According to the requirement of the yarn count and the level of elastane, the draw ratio of polyester multifilament and draft for elastane filament is adjusted. Thus, the yarn structure of air-covered yarn is different from that of core-spun yarn. As seen in Figure 3, the corespun yarn has a sheath-core structure where the sheath fiber is twisted similar to a ring yarn while in air-covered yarn almost parallel bundles of multifiber are intermingled with the core filament at regular intervals.

Preparation of stretchable workwear fabric
Three types of fabric samples were produced from the three types of yarn samples (Table 2). These yarns were used as weft. The fabric samples were woven in Tsudakoma air-jet weaving machine (ZAX9200i). The fabric weave was 3/1 right-hand twill. The warp/cm and weft/cm on the loom were 29 and 21, respectively. As a warp, 73.8 tex (8 Ne) open-end dyed yarn was used. The same weaver's beam was used to produce all the different fabric samples. The fabric sample codes are listed in Table 2.
All the fabric samples after weaving were processed through singeing, wet finishing, sanforizing and calendaring. The nominal mass density of the fabric was 335 g/m 2 (range 332-337 g/m 2 ), and the average fabric thickness was 0.54 mm (range 0.52-0.56 mm).

Abrasion treatment
The fabric samples were abraded in M235 Martindale abrasion and pilling tester (SDL ATLAS). The abrasion movement was Lissajous in nature as per standard practice. Few modifications were done as per the requirement of the study in the standard method for abrasion resistance, i.e. ASTM D 4966. The fabric samples were abraded from the reverse side, i.e. where the elastane weft yarn is more prominent on the fabric surface. The present study is aimed at the investigation of the change in load developed in the fabric after abrasion concerning the variations in elastane weft yarn as well as the number of cycles of loading unloading. The position of the abradant and the fabric were interchanged. This modification was required to produce a larger abraded sample. This modification will help to produce a sample size that would be feasible for tensile testing. The diameter of the fabric sample was 140 mm and that of the abradant was 38 mm. Since the aerial density of the workwear fabric was high, in place of standard wool abradant, carborundum emery paper with 320 grit was used. The pressure was kept on the lower side, i.e. 9 KPa. After abrasion for 1200 cycles, the fabric was tested for change in the load developed in the fabric at a certain extension level during cyclic loading.

Tensile testing
The cyclic loading of the fabrics was done in Instron 3365 (Instron. Inc.) tensile testing machine. All the tensile loading was done in the weft direction of the fabric as the elastane yarn variables are inserted in the weft direction to produce horizontal stretch. The fabric was stretched to a 20% extension level in every loading cycle. The fabric holding jaw speed was 300 mm/min. The sample dimension was considered according to the abrasion tester fixture. When 140 mm diameter circular fabric is fixed in Martindale instrument, approximately 90 mm � 90 mm area of the fabric gets abraded. After abrasion, to test only the abraded portion of the fabric, the sample dimension was reduced to 45 mm � 90 mm ( Figure 4). The dimension of the unabraded fabric samples was also kept at 45 mm � 90 mm. The gauge length for the samples was kept at 50 mm.

Cyclic loading (fatigue) test
The cyclic tensile loading technique was first used by several researchers (Bunsell and Hearle 1971) to measure fiber fatigue. The fiber specimen was held between two clamps and one of them was subjected to a cycle of change of position. The disadvantage of this method was that slack develops in the specimen due to imperfect recovery and the specimen ceases to be subjected to tension during a large part of each cycle. Failure was observed only when the imposed extension is very large. During the present study, a similar observation of fabric growth was observed during the cyclic loading of the stretch workwear fabric that is similar to the experience of the previous researcher performing cyclic tensile loading of the fiber. As the fabric got permanent extension during the cyclic loading, the stress on the fabric got reduced drastically. Thus, for creating fatigue due to cyclic loading, the fabric must be in a taut condition. Therefore, to overcome the above problem, several researchers (Bunsell and Hearle 1971;Hearle and Vaughn 1970) had previously adopted techniques of cumulative extension cycling, which removes the slack at the end of each cycle and imposes a fixed extension on the specimens during the next cycle. This method makes it possible to cycle the fiber to failure. The researchers followed this principle in their tensile testing apparatus. Based on this method adopted by previous researchers, the cyclic loading of all the fabric samples was done intermittently in the tensile testing instrument both before and after abrasion in the present study. The samples were treated for 200 continuous loading cycles in the tensile testing instrument and then again re-fixed in the jaws in taut  The values of the Standard Deviation are given in the parenthesis.
condition (fixed pre-tension), then again treated for next interval of 200 continuous loading cycles. During cyclic loading, the fabric samples were extended upto 20% extension level. Five such intervals of cycles were run for each fabric sample. Five samples were tested for each fabric type. The values of the load developed at 20% extension level immediately after the treatment of 200 loading cycles were noted. The mean values of the load data before abrasion and after abrasion are given in Tables 3 and 4.

Microscopic Image
The surface damage due to abrasion was observed by an optical microscope (ALMICRO).

Mass loss
Mass loss was calculated using the formula:

Massloss % ð Þ= Mass of the fabric sample before abrasionÀ Mass of the fabric sample after abrasion
Mass of the fabric sample before abrasion � 100 Before testing the fabrics were kept in the laboratory for 24 h in standard atmospheric conditions (20°C ±2°C and 65 ± 2% relative humidity). All the interpretation has been done at a 95% level of significance.

Reliability analysis
The reliability analysis is done through the sequential process of degradation analysis and life data analysis. The degradation analysis is used by the manufacturer in the design of such products whose failure data cannot be obtained cost-effectively. The properties of such products cannot be tested in the laboratory for their failure under normal operating conditions. This analysis uses the degradation data of a product tested in the laboratory under normal conditions and then uses the data to estimate the failure time of the product. The estimation is done by extrapolating the failure behavior of the product by measuring and plotting the degradation data versus time/cycles. The plotted curve is then fitted with a suitable degradation model that fits the experimental data. This degradation model then becomes the basis of the subsequent life data analysis (Ramachandran et al. 2014;Singh, Mukhopadhyay, and Chatterjee 2017). In this study, the property that has been tested for the degradation analysis of the workwear fabric is the load developed at 20% extension in the fabric after large intervals of loading-unloading cycles both before and after abrasion. Life data analysis is an important tool to predict the longevity of a product and design a product with a longer life span. The purpose of life data analysis is to model the failure behavior of a product and then estimate the failure time of the process or the product. The life data points are commonly called time-to-failure data. Various statistical models like Weibull, normal, lognormal, and exponential are used to determine the reliability of the product through life data analysis. The Weibull distribution has been highly recommended by earlier researchers due to its flexibility to model various life data scenarios (Ramachandran et al. 2014;Singh, Mukhopadhyay, and Chatterjee 2017). Therefore, in the present study, the Weibull parameters have been calculated for analysis of the failure behavior of different types of workwear fabrics in terms of comfort loss. The values of the Standard Deviation are given in the parenthesis.
The probability density function for a three-parameter Weibull probability distribution function is where β > 0 is the shape parameter, η > 0 is the scale parameter and γ is the location or time delay parameter. γ is the estimate of the minimum possible time to failure of the specimen under test. In this study, the value of γ has been assumed as zero, because the minimum number of cycles for the failure of the fabric may be zero. The values of β depend on the shape of the degradation curve. β > 1 means an increasing rate of failure with time, β ¼ 1 means a constant rate of failure with time, while β < 1 means a decreasing rate of failure with time (Kennedy and Louis 1967;Muralidharan and Syamsundar 2012;Ramachandran et al. 2014). The Weibull reliability function is given by The following steps have been followed for the reliability analysis.
• Selection of the performance criteria (Increase in the value of load up to a critical point).
• Testing the fabric samples after different cycles of loading and unloading.
• Extrapolating the curve of performance data versus the number of cycles.
• Calculation of Reliability R(t) for different cycles of loading and unloading. microscopic image of the fabric ( Figure 5). Since the exposure of the weft yarn on the fabric surface is greater than the warp yarn, the surface damage behavior of the fabric is mainly affected by the response of the weft yarn to the abrasive damage. It is observed from the microscopic view that the types of abrasive damage to the fabric surface are different for different types of fabric. The fabric with the cotton core spun elastane weft yarn shows an apparent reduction in the diameter of the weft yarn after abrasion, which is the result of the scrapping off of the fiber from the yarn structure. In cases of fabric with polyester core-spun and polyester multifilament air-covered elastane yarn, the main phenomenon of abrasive damage is the fibrillation of the surface fibers in the fabric. The visual analysis of the type of abrasive damage is supported by the trend of the mass loss data ( Figure 6). The cotton core spun elastane weft fabric suffers maximum mass loss as the scrapping off of fiber is the main phenomenon of abrasive damage. It must be added that since cotton fiber in the sheath of the yarn is having relatively lower elongation, elasticity and work of rupture, the fabric with a cotton core spun elastane weft suffers maximum abrasive damage. On the contrary, the polyester fiber (staple and multifilament) has superior elastic properties making it a better fiber that can easily absorb and release the stress developed during abrasion. Thus, the fabric with the polyester core spun and polyester multifilament air-covered elastane weft suffers from lower mass loss due to abrasion. Table 3 shows the load developed in the fabric during 20% of its extension at various intervals of cyclic loading without abrasion. Table 4 shows the load developed in the fabric during 20% of its extension at various intervals of cyclic loading after abrasion. Both before and after abrasion, the load developed in the fabric increases as the number of cyclic loading increases. However, the rate of increase in the load is affected by the yarn structure, and composition as well as due to the effect of abrasion. The reason for such a change in the behavior of the fabric is discussed in subsequent sections.

Degradation analysis
In degradation analysis, the selection of performance criteria is important. It has been found in one of the recent studies (Shaw and Mukhopadhyay 2022a) that fabric without elastane, with similar fabric parameters as mentioned in this current study, tested under similar conditions had developed a load of 320 N at 20% extension. Therefore, it has been decided to keep 320 N as the critical value developed in the fabric during the cyclic loading at 20% extension. Thus, at this critical point, the stretch fabric will start behaving like normal fabric in terms of movement comfort. This point is referred to as the failure point of the fabric in the degradation analysis. In the current study, the degradation analysis is done by the extrapolation of the values of load data developed at different intervals of load cycles. The mean values of such load data are given in Tables 3  and 4. The extrapolation was done using exponential equations since it fitted the load data appropriately. The example of an exponential equation formed by the extrapolation of the load data is given in Table 5. These equations form the basis of the Life data Analysis. Figure 7a and 7b shows the degradation analysis curve, and Table 6 shows the mean number of loading cycles for failure both before and after abrasion. The failure data is obtained by the intersection points of the curves with the critical line of the load value (320 N) as shown in Figure 7a and 7b. The mean values of such failure data are shown in Table 6.
It is seen from Figure 7a that both before and after abrasion, the load increases with the number of loading cycles. Since the fabric is treated with cyclic loading in the weft direction, the elastane weft yarn plays a major role in defining such behavior. During initial intervals of loading cycles, the fabric gets some permanent growth resulting in the de-crimping of the weft yarn. However, after a large number of loading cycles, the weft yarn elongates and starts sharing the axial load. Thus, there is an increase in load developed for all the fabric types with an increase in the number of loading cycles.
The air-covered polyester multifilament weft yarn fabric behaves differently compared to the other two core-spun yarn elastane weft fabrics. The estimated time-to-failure data from Table 6 also suggests that the air-covered polyester multifilament weft yarn fabric reaches the failure point at a lower level of the loading cycle. The initial starting point in the degradation curve of the air-covered weft fabric is quite similar to that of polyester core spun weft fabric, but as the number of loading cycles increases, the rate of increase in load, i.e. the rate of deterioration in movement comfort is higher. It has already been discussed in the previous section 2.1.1 that there is a significant difference in the yarn structure of both the polyester core spun and polyester multifilament air-covered yarn (Figure 3). In the case of the polyester core spun yarn, the sheath/covering fiber is the staple polyester fiber, whereas in the case of the air-covered yarn, the covering fiber is a partially oriented polyester multifilament. In the case of polyester multifilament air-covered weft yarn, the partially oriented multifilament gets oriented due to the growth of the fabric developed during cyclic loading. As the level of multifilament orientation increases, the multifilament gets stiffer and the load developed during cyclic loading increases at a relatively higher rate as compared to the other core-spun weft yarn, where the sheath is cotton staple fiber or fully drawn polyester staple fiber.
Interestingly, from Table 6, it is also evident that after abrasive damage, the time to failure for all three fabrics improves. This means that after abrasive damage, a relatively larger number of loading cycles are required for all fabrics to reach the critical load value. The improvement is highest in the y is the value of load (N) developed at 20% extension; x is the number of loading cycles. case of cotton core spun elastane weft yarn. It is seen from the image analysis of abrasive damage ( Figure 5) and the mass loss data ( Figure 6) that the cotton core spun elastane weft fabric suffers maximum damage due to abrasion. It can be seen from Figure 5 that the abrasive damage in cotton core spun elastane weft is mainly due to the loss of surface fibers (apparent reduction in weft yarn diameter after abrasion). This fabric also suffers a maximum mass loss ( Figure 6) which inevitably supports a similar apprehension. As discussed earlier after a large number of repeated loading cycles, the fabric gets permanent growth (de-crimping) and the elastane yarn gets elongated and starts sharing the load. During the elongation of such twisted core-sheath yarn, there is a traverse force acting on the elastane core by the twisted sheath fibers. After abrasion, due to the loss of sheath or surface fiber from the yarn structure, the extent of the traverse force gets reduced and the elastane core comes into effect resulting in a decrease in the load developed. The reduction of the traverse force after abrasion may be due to the barber pole effect, i.e. uncovered core filament. Since the highest mass loss due to abrasion has been seen in the case of cotton core spun elastane weft fabric, the barber pole effect is supposed to be highest in such yarn. Therefore, the improvement in terms of the number of loading cycles to failure after abrasion is also highest for the fabric with a cotton core spun elastane weft. The improvement in terms of increase in the meantime to failure in the case of polyester core spun elastane weft fabric is intermediary, while the improvement in the case of polyester multifilament aircovered elastane weft fabric is minimum. In the case of the polyester core spun elastane weft fabric, the mass loss due to abrasion is relatively lower than the mass loss suffered by the cotton core spun elastane weft fabric. Thus, although there is a reduction in the traverse forces due to loss of surface fiber in polyester core spun elastane weft fabric but not to the extent of the fabric having cotton core spun elastane weft yarn. In the case of air-covered elastane yarn, no such traverse forces are acting on the core as there is intermingling rather than the twisting of sheath/covering fiber. Therefore, the gain in the meantime to failure is marginal.
However, if the trend of increase in load developed after cyclic loading before and after abrasion is analyzed comparatively from Tables 3 and 4, then, it can be seen that during initial cycle intervals (up to 200 cycles for cotton core spun fabric and 400 cycles for polyester core spun and polyester multifilament air-covered fabric), there is an increase in load due to abrasion for all the fabric types. As the number of cycles further increases then, there is a reduction in the level of load developed after abrasion in comparison to the unabraded fabric. This is because, during initial loading-unloading cycles, the fabric growth is minimum. The increase in the surface hairiness/fibrillation may create a hindrance to the inter-yarn movement during the initial phase of cyclic loading. However, when the fabric growth increases with a larger number of cumulative extension cyclic loading, the initial hindrances might have been overcome and the abraded yarn structure starts playing a significant role. The abraded yarn structure thus results in the reduction of traverse/cohesive force acting on the core filament due to inter fiber slippage. Thus, the reduction in this traverse/cohesive force results in a reduction in load development, i.e. improving the movement comfort.

Life data analysis
In the life data analysis, the cycles for failure for each type of fabric have been used to calculate the Weibull parameter ή and β using the median ranking method (Muralidharan and Syamsundar 2012). In life data analysis, the analysis of the failure behavior of the different types of fabric both before and after abrasion has been conducted. The values of β (shape parameter) and ή (scale parameter) are shown in Table 7.
The estimated value of β > 1 means that there is an increasing rate of failure concerning cycle intervals both before and after abrasion. The order of rate of failure for the corresponding β values of the unabraded stretch denim fabrics is given as Cotton core spun weft fabric > Polyester multifilament air-covered weft fabric > Polyester core spun weft fabric. The cotton core spun weft fabric has cotton staple fiber as a sheath fiber in the elastane weft yarn. Cotton is the least extensible among all the three types of sheath/covering material, resulting in the highest rate of failure of cotton core spun weft fabric. The rate of failure of polyester multifilament air-covered fabric is intermediary and that of polyester core spun weft fabric is the minimum. In both cases, the sheath/covering fiber is polyester that is relatively more extensible than cotton. However, in the case of polyester core spun fabric, during cyclic loading, there is a probability of inter-fiber slippage in the weft yarn structure resulting in the lowest rate of failure. In the case of polyester multifilament air-covered fabric, no such phenomena of fiber slippage are possible because of the continuous multifilament covering in the weft yarn structure. This order implies that the rate of failure in terms of movement comfort depends both on the stretch weft yarn structure and composition.
However, after abrasion, the order of rate of failure for the corresponding β values of the stretch denim fabric becomes as Polyester multifilament air-covered weft fabric > Polyester core spun weft fabric > Cotton core spun weft fabric. After abrasion, there is a change in the order of rate of failure of the fabrics indicating the significant role of the abrasive damage phenomena in deciding the movement comfort of the fabrics. The cotton core spun weft fabric showed improvement in failure rate due to abrasion, while the fabric made from polyester core spun weft and polyester multifilament air-covered weft are showing an increase in the rate of failure. The improvement in cotton core spun weft fabric is because, after abrasion, there is no significant increase in surface hairiness or fibrillation of surface fibers of the fabric due to abrasive damage ( Figure 5). However, in the case of polyester core spun and polyester multifilament air-covered fabric, there is a significant increase in the surface hairiness that is supposed to create a hindrance in the inter-yarn movement during fabric extension while cyclic loading. The ή value shown in Table 7 signifies the number of loading cycles by which 63.2% of the fabric samples are supposed to fail. Concerning the ή value, there is a difference in the number of cycles by which 63.2% of the fabric specimen will fail. The ή value is maximum for polyester core spun weft fabric followed by cotton core spun weft fabric and polyester multifilament air-covered weft fabric. Even though the cotton core spun weft fabric had the highest rate of failure (β value) but it has a higher ή value than polyester multifilament air-covered weft fabric. Since the load developed during the initial levels of loading cycles in the cotton core spun weft fabric was minimum (Table 3), it requires a relatively higher number of loading cycles (ή) to reach the failure point. Among the polyester core spun weft and polyester multifilament air-covered weft fabrics, the fabric having higher values of β has lower values of ή since both the fabrics have similar levels of load during initial levels of cyclic loading.
This implies that without abrasion, the fabric with a polyester core spun elastane weft yarn reaches its failure point after the highest number of loading cycles, while the fabric with polyester multifilament air-covered yarn reaches the failure point at the earliest. When the fabric undergoes extension during cumulative extension cyclic loading, the weft yarn starts sharing the load. The core-spun yarn structure has a staple fiber in the twisted form on the sheath and filament in the core. During gradual extension, there is a possibility of inter-fiber slippage in the case of core spun weft fabrics, which results in a relatively gradual rate of increase in the load developed in the fabric during cumulative extension cyclic loading. On the other hand, the fabric with polyester multifilament air-covered yarn suffers from a relatively higher rate of increase in the load developed during cumulative extension cyclic loading. This is because, in the case of air-covered yarn, the partially oriented multifilament is in the sheath of the yarn. When the fabric suffers growth, the air-covered weft yarn is extended and the partially oriented polyester filament sheath also gets elongated. Due to its elongation, the crystalline orientation of the partially oriented filament is supposed to improve. Therefore, with the increase in the orientation, the filament gets stiffer, i.e. increases the modulus and the load developed in the fabric increases at a relatively higher rate during cumulative extension cyclic loading.
It can be seen from Table 7 that the ή values have improved for all types of fabric due to abrasion; however, the β values have improved only for cotton core spun elastane weft fabric. An increase in the values of ή and a decrease in the values of β have been considered an improvement. After abrasion, the order of ή is highest for cotton core spun weft fabric followed by polyester core spun weft fabric and polyester multifilament air-covered weft fabric successively.

Reliability analysis
The calculation of Reliability R(t) for different cycles and different types of fabric before and after abrasion has been done using the formula from Equation (1). The values of ή and β from Table 7 are put in the equation to calculate Reliability R(t). The corresponding reliability data for different fabric types at different levels of cyclic loading both before and after abrasion is depicted in Table 8.
It can be seen from Table 8 that in the case of fabrics in an unabraded state, cotton core spun weft fabric reaches zero reliability of movement comfort at 1500 cycles, polyester core spun weft fabric at 1800 cycles and polyester multifilament air-covered weft fabric at 1300 cycles, respectively. After abrasion, the reliability of all the fabrics has improved. However, the highest level of improvement is in the case of cotton core spun weft fabric, and the least improvement is in the case of polyester multifilament air-covered weft fabric. In an unabraded state, the highest reliability of polyester core spun weft fabric is due to the lowest β values and highest ή values. Similarly, after abrasion, the lowest β values and highest ή values of cotton core spun weft fabric result in the highest reliability of movement comfort.
Both in unabraded states and abraded states, the reliability of polyester multifilament air-covered weft fabric approaches zero value at the earliest levels of cyclic loading. This means that the fabric with polyester multifilament air-covered elastane has a higher probability of behaving like a normal fabric as compared to the other two fabrics in similar life spans. This is because with the fabric growth during cyclic fatigue, the partially oriented multifilament sheath/covering will get stretched and elongated increasing the crystalline orientation of the multifilament. An increase in orientation increases the elastic modulus of the polyester multifilament, making the yarn and fabric stiffer. Thus, the stiffer fabric will start behaving like normal fabric, i.e. without elastane. It must be added that the reliability of the other two fabrics also deteriorated with time but not to the same extent as that of polyester multifilament air-covered weft fabric.
From Table 8, if reliability values of the unabraded fabrics are compared at both initial levels of cyclic loading and latter levels of cyclic loading, then the order changes after certain levels of cyclic loading. Initially, around 1000 cycles, the order is cotton core spun weft fabric > polyester core spun weft fabric > polyester multifilament air-covered weft fabric. After around 1400 cycles, the order of reliability becomes polyester core spun weft fabric > cotton core spun weft fabric > polyester multifilament air-covered weft fabric. Similarly, after abrasion, the order of reliability values of up to 1500 cycles is polyester core spun weft fabric > cotton core spun weft fabric > polyester multifilament aircovered weft fabric. However, after 1500 cycles, the cotton core spun weft fabric is providing maximum reliability values. Therefore, if the combined effect of large numbers of loading cycles and abrasive damage is to be considered, then the cotton core spun weft fabric proves to be the best among the three in terms of reliability of movement comfort even though having the least abrasion resistance in terms of mass loss. Since the cotton core spun elastane weft fabric suffers from maximum mass loss due to abrasion (Figure 6), the reduction in traverse forces in the weft yarn due to loss of sheath fiber is also maximum. Therefore, the possibility of inter-fiber slippage in the cotton core spun elastane yarn structure is maximum at similar levels of fabric growth during cyclic fatigue. Thus, the The shaded portion is depicting the poorest reliability region considering the minimum criteria of reliability as 0.90.
corresponding higher extent of reduction in axial load developed in weft yarn after abrasion results in higher reliability values at higher levels of loading cycles.

Conclusion
In this study, the effect of composition and structure of different types of stretch yarn, i.e. cotton core spun, polyester core spun and polyester multifilament elastane yarn, on the reliability of the movement comfort of the workwear fabric has been investigated. It is seen that the reliability of the workwear fabric in terms of its movement comfort is affected by the composition of stretch yarn, nature of abrasive damage and number of loading cycles. Based on the study, the following conclusions are drawn; There is an increase in load developed in the stretch workwear fabric as the number of cumulative extension loading cycles increases. The reliability of the workwear fabric in terms of movement comfort also reduces as the number of cumulative extension loading cycles increases. The extent of the increase in the load and reduction in the reliability of movement comfort with an increasing number of loading cycles depends on the structure of the elastane weft yarn. In the case of abraded fabrics, the type and extent of fabric surface damage due to abrasion also affects this rate of deterioration of movement comfort. Among the three types of fabric in the unabraded state, the fabric with the polyester core spun elastane weft yarn shows better reliability value concerning movement comfort. The reliability value of the cotton core spun elastane weft fabric is intermediatory and that of fabric having polyester multifilament air-covered elastane weft yarn is minimum.
The abrasive damage of the stretch workwear fabric deteriorates its movement comfort during initial loading cycles. However, in the long run, i.e., after a larger number of loading cycles, the abraded workwear fabric displays better reliability concerning the movement comfort than the unabraded fabric. This implies that although a certain extent of surface abrasion of the stretch workwear fabric is adversely affecting its movement comfort during the initial phase of its usage, in long run, there is no adverse effect of this abrasive damage on the movement comfort. On the contrary, it is seen that a certain extent of abrasion of the stretch workwear fabric decelerates the process of deterioration of movement comfort.
As regards the improvement due to abrasion in terms of mean time to failure and the reliability concerning the movement comfort, the cotton core spun elastane weft yarn shows maximum improvement. The extent of improvement in reliability is lower during initial loading cycles and relatively higher during larger loading cycles.
Among the three types of workwear fabrics, the cotton core spun elastane weft fabric showed minimum abrasion resistance as it suffered maximum mass loss during abrasion. However, considering the reliability values of both unabraded and abraded fabrics, it is better than polyester core spun elastane weft and polyester multifilament air-covered elastane weft fabrics in terms of movement comfort.
The mean time to failure and the reliability value concerning the movement comfort is lowest in the case of stretch workwear fabric having polyester multifilament air-covered yarn as weft both in the abraded and unabraded states. Although the workwear fabric with polyester multifilament air-covered elastane weft may be produced at a relatively lower cost, it will lose its comfort property at a faster rate during usage as compared to the fabrics having cotton and polyester core spun elastane weft.

Disclosure statement
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Funding
The author(s) reported that there is no funding associated with the work featured in this article.