Textured Polyester Fiber in Three-Dimensional (3D) Carpet Structure Application: Experimental Characterizations under Compression–Bending–Abrasion–Rubbing Loading

In this article, textured polyester fiber was used as pile yarn in three-dimensional woven carpet structures. The properties of developed polyester carpets under various mechanical loading were studied. A statistical method was used to analyze the experimental data. Regression models were proposed to explain the relationships between carpet pile height and density. The study showed that the bending rigidity and curvature of dry and wet polyester pile fiber carpets were influenced by pile height and pile density (indirectly weft density) in that the downward concave large bending curvature was obtained from very dense carpet structures. In addition, the average dry bending rigidity of the carpet was over eight times higher than the average wet bending rigidity of the carpet. The thickness loss (%) and resilience (%) for each recovery period of various polyester carpets were proportional depending on the pile density. It was broadly decreased when the pile density was increased due to the compression load carrying capacity per polyester fiber knot, which was higher in carpets having dense knots compared to sparse knots per area. On the other hand, the polyester pile density and height largely affected the carpet mass losses (%) of all textured polyester carpets under an abrasion load. The number of strokes received after completely fractured polyester pile yarns during a rubbing test were increased when the pile heights for each pile density were increased. Findings from the study can be useful for polyester carpet designers and three-dimensional dry or impregnate polyester fiber-based preform designers in particularly complex shape molding part manufacturing.

A digital camera (CANON PowerShot SX30 IS, Tokyo, Japan) was integrated with an in-house-developed flexure test instrument. It recorded the sample curvature end of the testing (Figure 2a) and the image was uploaded to the SnagIt drawing program to find the bending curvature ( Figure 2c) [82]. The bending curvature regression equations were determined using the image received from the drawing program. It was computed within MATLAB R2016a [83]. This was achieved using MATLAB's numerical integration and standard plotting tools. Bending length and bending rigidity for apparel and technical fabrics were computed following Equations (1)- (3).
where m is the fabric unit areal weight (g.m −2 ); l is the fabric length of overhang (apparel fabric, cm; technical fabric, m); c is the bending length (cm, m); G 1 and G 2 are the bending rigidity of apparel (mg.cm) and technical fabrics (mN.m), respectively; 9.81 is the gravitational constant (m.s −2 ). A digital camera (CANON PowerShot SX30 IS, Tokyo, Japan) was integrated with an in-house-developed flexure test instrument. It recorded the sample curvature end of the testing (Figure 2a) and the image was uploaded to the SnagIt drawing program to find the bending curvature (Figure 2c) [82]. The bending curvature regression equations were determined using the image received from the drawing program. It was computed within MATLAB R2016a [83]. This was achieved using MATLAB's numerical integration and standard plotting tools. Bending length and bending rigidity for apparel and technical fabrics were computed following Equations (1)-(3). l c= 2 where m is the fabric unit areal weight (g.m −2 ); l is the fabric length of overhang (apparel fabric, cm; technical fabric, m); c is the bending length (cm, m); G1 and G2 are the bending rigidity of apparel (mg.cm) and technical fabrics (mN.m), respectively; 9.81 is the gravitational constant (m.s −2 ).

Static Loading Test
A static loading test on face-to-face woven carpet samples was ordinarily carried out following BS 4939 [84] and ISO 3416 [85] test standards. The sample sizes of carpet for static loading were 10 cm × 10 cm. Before starting the test, sample initial thickness (h0) was measured. Later, it was uploaded in the test instrument where pressure on the sample was applied (7 kg/cm 2 , 0.687 MPa) via dead weight (10 kg). The samples under static loading were held 24 h (h). After that, the thickness loss on the sample was measured according to short (2 min and 1 h), medium (1 day and 3 days), and long (3 years) time periods. The test was repeated twice due to limited samples. Figure 3a-e shows the actual and schematic static loading instrument during testing of the carpet structure, and failed carpet samples.

Static Loading Test
A static loading test on face-to-face woven carpet samples was ordinarily carried out following BS 4939 [84] and ISO 3416 [85] test standards. The sample sizes of carpet for static loading were 10 cm × 10 cm. Before starting the test, sample initial thickness (h 0 ) was measured. Later, it was uploaded in the test instrument where pressure on the sample was applied (7 kg/cm 2 , 0.687 MPa) via dead weight (10 kg). The samples under static loading were held 24 h (h). After that, the thickness loss on the sample was measured according to short (2 min and 1 h), medium (1 day and 3 days), and long (3 years) time periods. The test was repeated twice due to limited samples. Figure 3a-e shows the actual and schematic static loading instrument during testing of the carpet structure, and failed carpet samples. The thickness loss and resilience of the carpet after prolonged heavy static load were determined using the following Equations (4)- (13). The relations are also presented in graphical form as exhibited in Figure 4 [46].  The thickness loss and resilience of the carpet after prolonged heavy static load were determined using the following Equations (4)- (13). The relations are also presented in graphical form as exhibited in Figure 4 [46].
where h 0 is the initial thickness (mm), h 1 is the thickness after 24 h compression (after 2 min recovery time) (mm), h 2 is the thickness after 1 h recovery time, h 3 is the thickness after 1 day (24 h) recovery time, h 4 is the thickness after 3 days recovery time, h 5 is the thickness after 3 years recovery time, TL is the thickness loss (%), TL 1h is the thickness loss after 1 h (%), TL 1d is the thickness loss after 1 day (%), TL 3d is the thickness loss after 3 days (%), TL 3y is the thickness loss after 3 years (%), R is the resilience (%), R 1h is the resilience after 1 h, R 1d is the resilience after 1 day (24 h), R 3d is the resilience after 3 days, and R 3y is the resilience after 3 years.
Polymers 2023, 15, x FOR PEER REVIEW 8 of 28 where h0 is the initial thickness (mm), h1 is the thickness after 24 h compression (after 2 min recovery time) (mm), h2 is the thickness after 1 h recovery time, h3 is the thickness after 1 day (24 h) recovery time, h4 is the thickness after 3 days recovery time, h5 is the thickness after 3 years recovery time, TL is the thickness loss (%), TL1h is the thickness loss after 1 h (%), TL1d is the thickness loss after 1 day (%), TL3d is the thickness loss after 3 days (%), TL3y is the thickness loss after 3 years (%), R is the resilience (%), R1h is the resilience after 1 h, R1d is the resilience after 1 day (24 h), R3d is the resilience after 3 days, and R3y is the resilience after 3 years. The abrasion properties of the polyester carpet structures were determined using the Martindale abrasion test method (ISO 12947-3) [86]. A Nu-Martindale Abrasion Test instrument (James H Heal, Halifax, UK) was used to evaluate the mass loss of carpet after  The abrasion properties of the polyester carpet structures were determined using the Martindale abrasion test method (ISO 12947-3) [86]. A Nu-Martindale Abrasion Test instrument (James H Heal, Halifax, UK) was used to evaluate the mass loss of carpet after abrasion in compliance with the TS EN ISO 12947-3 standards, as shown in Figure 5a-d.
Mass loss values were recorded at the end of each 5000-, 10,000-, 20,000-, 30,000-, 40,000-, and 50,000-abrasion cycle. Standard wool fabric was used for abrasion and the pile surface of the carpet samples were abraded under pressure (12 KPa). Thickness measurements were also performed, since the carpet sample had a thickness loss tendency after abrasion cycles, using a thickness gauge (Elastocon EV 07, Bramhult, Sweden) [71]. The experiment was repeated twice due to limited test materials.

Rubbing (Token) Test
To assess the rubbing behavior of the carpet sample according to the BS 2543 test standards, a crockmeter (Termal, Istanbul, Turkey) equipped with a metal token holder was employed [87]. The dry carpet's resistance to linear rubbing was evaluated using a metal token holder positioned at a 45° angle to the carpet pile surface. The areas of the carpet pile that exhibited deformations were identified through a visual assessment based on images captured using a digital camera. The dry carpet's resistance to linear rubbing was evaluated using a metal token holder positioned at a 45° angle to the carpet pile surface. The metal token utilized in the study had a diameter of approximately 29 mm, a thickness of 6 mm, and was made of copper [71]. The token rubbing test was employed to simulate carpet hand cleaning. In this method, a rectangular specimen was positioned on the rubbing area of the crockmeter, and a metal token holder, inclined at a 45° angle to the carpet pile surface, was used to rub the specimen under low pressure (9 N). Figure 6a-e show the token rubbing test instrument during the rubbing test on a carpet sample. The token rubbing test was conducted until a visually consistent level of deformation was observed across all samples. The results of the test were expressed in terms of the stroke number. In the context of this study, a stroke was defined as a single back-and-forth movement of the metal token holder along the surface of the carpet pile.

Rubbing (Token) Test
To assess the rubbing behavior of the carpet sample according to the BS 2543 test standards, a crockmeter (Termal, Istanbul, Turkey) equipped with a metal token holder was employed [87]. The dry carpet's resistance to linear rubbing was evaluated using a metal token holder positioned at a 45 • angle to the carpet pile surface. The areas of the carpet pile that exhibited deformations were identified through a visual assessment based on images captured using a digital camera. The dry carpet's resistance to linear rubbing was evaluated using a metal token holder positioned at a 45 • angle to the carpet pile surface. The metal token utilized in the study had a diameter of approximately 29 mm, a thickness of 6 mm, and was made of copper [71]. The token rubbing test was employed to simulate carpet hand cleaning. In this method, a rectangular specimen was positioned on the rubbing area of the crockmeter, and a metal token holder, inclined at a 45 • angle to the carpet pile surface, was used to rub the specimen under low pressure (9 N). Figure 6a-e show the token rubbing test instrument during the rubbing test on a carpet sample. The token rubbing test was conducted until a visually consistent level of deformation was observed across all samples. The results of the test were expressed in terms of the stroke number. In the context of this study, a stroke was defined as a single back-and-forth movement of the metal token holder along the surface of the carpet pile. The neat carpet sample and polyester pile mass loss of weight measurements were performed based on TS 251 [88] using an Ohaus Adventurer TM Pro AV812 (Ohaus Corp., Parsippany, NJ, USA) digital balance. The error in the measurement of weight was ±0.1 mg. The neat pile thickness, pile thickness after static loading and Martindale tests, and the neat carpet thickness were measured based on TS 7125 [89] and TS 3374 [90] using an Elastocon EV07 digital device, respectively. All mechanical tests were conducted in a standard laboratory atmosphere having a temperature of 23 °C ± 2 °C and relative humidity of 50 ± 10% [91]. A high-resolution digital camera (CANON PowerShot SX30 IS, Tokyo, Japan) was used to image the damaged surface of carpet samples after static loading and Martindale abrasion and token rubbing tests.

Statistical Model
Statistical modelling of some of the static loading (thickness loss and resilience) and abrasion (thickness loss) data on carpet samples was developed using "Design Expert" software. The best models on carpet were obtained, and the corresponding regression equations and regression curves were fitted. The analysis of variance (ANOVA) tables for static loading (thickness loss and resilience) and abrasion property, specifically the thickness loss, were measured, and the significance of the models was determined using pvalues smaller than 0.05. The ANOVA tables revealed significant interactions between the pile height (A) and density (B) in both the static loading and abrasion tests. These interactions were taken into account when developing the regression equations. The generated data were subjected to a normality test, which indicated that the data exhibited a distribution that was approximately aligned with the normality line and conformed to a normal distribution.

Carpet Structure Bending Results
Bending rigidity results on various carpet structures are presented in Table 3 and Figure 7a-d for both apparel fabric and technical fabric bending test methods. As shown in Table 3 and Figure 7a-b, the dry bending rigidity based on the apparel fabric test The neat carpet sample and polyester pile mass loss of weight measurements were performed based on TS 251 [88] using an Ohaus Adventurer TM Pro AV812 (Ohaus Corp., Parsippany, NJ, USA) digital balance. The error in the measurement of weight was ±0.1 mg. The neat pile thickness, pile thickness after static loading and Martindale tests, and the neat carpet thickness were measured based on TS 7125 [89] and TS 3374 [90] using an Elastocon EV07 digital device, respectively. All mechanical tests were conducted in a standard laboratory atmosphere having a temperature of 23 • C ± 2 • C and relative humidity of 50 ± 10% [91]. A high-resolution digital camera (CANON PowerShot SX30 IS, Tokyo, Japan) was used to image the damaged surface of carpet samples after static loading and Martindale abrasion and token rubbing tests.

Statistical Model
Statistical modelling of some of the static loading (thickness loss and resilience) and abrasion (thickness loss) data on carpet samples was developed using "Design Expert" software. The best models on carpet were obtained, and the corresponding regression equations and regression curves were fitted. The analysis of variance (ANOVA) tables for static loading (thickness loss and resilience) and abrasion property, specifically the thickness loss, were measured, and the significance of the models was determined using p-values smaller than 0.05. The ANOVA tables revealed significant interactions between the pile height (A) and density (B) in both the static loading and abrasion tests. These interactions were taken into account when developing the regression equations. The generated data were subjected to a normality test, which indicated that the data exhibited a distribution that was approximately aligned with the normality line and conformed to a normal distribution.

Carpet Structure Bending Results
Bending rigidity results on various carpet structures are presented in Table 3 and Figure 7a-d for both apparel fabric and technical fabric bending test methods. As shown in Table 3 and Figure 7a-b, the dry bending rigidity based on the apparel fabric test method of 2PES6-G 1 and 3PES6-G 1 was decreased by 12.67% and 108.63% compared to 1PES6-G 1 , respectively. Similar changes were obtained from remaining dry polyester carpet structures including 1PES9, 2PES9, 3PES9, 1PES12, 2PES12, and 3PES12 (Figure 7a). On the other hand, the polyester pile height probably indirectly affected the bending rigidity of carpet in that carpet areal density was incrementally increased when the pile height increased. The wet bending rigidity of 2PES6-G 1 and 3PES6-G 1 was decreased by 9.74% and 47.89% compared to 1PES6-G 1 , respectively. Similar trends were obtained from remaining wet carpet structures including 1PES9, 2PES9, 3PES9, 1PES12, 2PES12, and 3PES12 (Figure 7b). This indicated that the bending rigidity of polyester carpet samples from dry and wet cases exhibited similar results. The results from bending for apparel fabric showed that when the carpet weight (areal density, g/m 2 ) increased, the bending rigidity (mg.cm) decreased from loose to very dense carpet structures due to the increase in weft density. Moreover, the average dry bending rigidity of polyester carpet samples was 4.61 times higher than the average wet bending rigidity of samples due to water uptake increasing the carpet weight. As shown in Table 3 and Figure 7c,d, the dry bending rigidity, based on the technical fabric test method, increased by 21.95% and 47.26% for 2PES6-G2 and 3PES6-G2, respectively, compared to 1PES6-G2. Similar changes were observed in the remaining dry polyester carpet structures, including 1PES9, 2PES9, 3PES9, as well as 1PES12, 2PES12, and 3PES12 ( Figure 7c). On the other hand, it is likely that the pile height indirectly influenced the bending rigidity of the carpet, as the carpet's areal density increased incrementally with higher pile heights. The wet bending rigidities of 2PES6-G2 and 3PES6-G2 were increased by 18.78% and 50.34% compared to 1PES6-G1, respectively. Similar trends were nearly achieved from remaining wet carpet structures including 1PES9, 2PES9, 3PES9, and 1PES12, 2PES12, and 3PES12 (Figure 7d). This indicates that the bending rigidity of polyester carpet samples showed similar results in both dry and wet conditions. The bending results for technical fabric showed that as the carpet weight (areal density, g/m 2 ) increased, the bending rigidity (mN.m) also increased, moving from loose to very dense carpet structures.
This increase could be attributed to the larger sample size used for bending tests in technical fabric, with a sample width 12 times higher compared to the sample size used for bending tests in apparel fabric, where the sample size affects the bending stiffness. Furthermore, the average dry bending rigidity of polyester carpet samples was 8.11 times higher than the average wet bending rigidity of carpet samples, attributed to the increase in the weight of wet carpets. For future studies, the bending test for technical fabric can be simplified to determine the flexural properties of heavy three-dimensional dry or impregnated polymeric preforms, especially in complex shape molding for manufacturing specific parts.   Table 4. As shown in Table 3 and Figure 8a-h, the overhang lengths based on the apparel fabric test method of dry 2PES9-G1 and 3PES9-G1 carpet samples were decreased by 0.35% and 35.41% compared to 1PES9-G1, respectively. A similar tendency was found in the remaining dry carpet structures including 1PES6, 2PES6, 3PES6, and 1PES12, 2PES12, and 3PES12 (Table 3, Figure 8c). However, the pile height probably insignificantly affected the bending curvature of carpet in that carpet areal density was incrementally increased when the pile height increased (Figure 8c). The overhang lengths of wet 2PES9-G1 and 3PES9-G1 carpet samples were decreased by 2.2% and 29.92% compared to 1PES9-G1, respectively (Figure 8b). Nearly the same trends were obtained from rest of the wet polyester carpet structures including 1PES6, 2PES6, 3PES6, 1PES12, 2PES12, and 3PES12 (Table 3, Figure 8d). This indicated that the bending curvature of carpets from dry and  Table 4. As shown in Table 3 and Figure 8a-h, the overhang lengths based on the apparel fabric test method of dry 2PES9-G 1 and 3PES9-G 1 carpet samples were decreased by 0.35% and 35.41% compared to 1PES9-G 1 , respectively. A similar tendency was found in the remaining dry carpet structures including 1PES6, 2PES6, 3PES6, and 1PES12, 2PES12, and 3PES12 (Table 3, Figure 8c). However, the pile height probably insignificantly affected the bending curvature of carpet in that carpet areal density was incrementally increased when the pile height increased (Figure 8c). The overhang lengths of wet 2PES9-G 1 and 3PES9-G 1 carpet samples were decreased by 2.2% and 29.92% compared to 1PES9-G 1 , respectively (Figure 8b). Nearly the same trends were obtained from rest of the wet polyester carpet structures including 1PES6, 2PES6, 3PES6, 1PES12, 2PES12, and 3PES12 (Table 3, Figure 8d). This indicated that the bending curvature of carpets from dry and wet cases illustrated similar results. The results from bending curvature for the apparel fabric test showed that when the carpet weight (areal density, g/m 2 ) increased, the bending curvature (cm) decreased from loose to very dense carpet structures due to the increase in weft density. In addition, downward concave small bending curvature was obtained from very dense carpet structures. Further, the average dry bending curvature of carpet samples was 39.33% higher than the average wet bending curvature of carpet samples due to the increase in wet polyester carpet weight. Thus, large bending curvatures from all dry carpets were obtained compared to the wet carpets (Figure 8a-d

Carpet Structure Static Loading Results
Static loading (compression) results on the thickness (mm), thickness loss (%), and resilience (%) of various polyester pile carpet structures are presented in Table 5 and are illustrated in Figure 9a-d. In addition, Figure 10a-d illustrates various recovery period and resilience relations after static loading on dry carpet samples.
As shown in Table 5 and Figure 9a-d, the carpet thickness loss (%) of various recovery periods of all carpets almost linearly decreased. The average dry carpet thickness loss (%) under a vertical distributed load (compression) for various recovery periods including after 2 min, 1 h, 1 day, and 3 years of 2PES6 and 3PES6 were decreased by 0.45% and 12.53% compared to 1PES6, respectively. Similar results were roughly obtained from rest  As shown in Table 3 and Figure 8a-h, the overhang lengths based on the technical fabric test method of dry 2PES9-G 2 and 3PES9-G 2 carpets were increased by 1.99% and 12.05% compared to 1PES9-G 2 , respectively. Similar results were found from remaining dry carpet structures including 1PES6, 2PES6, 3PES6, 1PES12, 2PES12, 3PES12 (Table 3, Figure 8e). However, it is likely that the pile height had a minimal effect on the bending curvature of the carpet, as the carpet's areal density incrementally increased with higher pile heights (see Figure 8g). Compared to 1PES9-G2, the overhang lengths of wet 2PES9-G2 and 3PES9-G2 carpets exhibited increases of 10.58% and 12.26%, respectively (refer to Figure 8f). Similar trends were observed in the remaining wet carpet structures, including 1PES6, 2PES6, 3PES6, as well as 1PES12, 2PES12, and 3PES12 (see Table 3 and Figure 7h). This suggests that the bending curvature of carpets in both dry and wet conditions exhibited similar results. The results of the bending curvature test for technical fabric showed that as the carpet weight (areal density, g/m 2 ) increased, the bending curvature (cm) also increased, transitioning from loose to very dense carpet structures. This increase can be attributed to the higher weft density and the larger sample size used in the bending test for technical fabric, where the sample width was 12 times greater compared to the bending test for apparel fabric, where the sample size affects the bending curvature. In addition, loose carpet structures exhibited a downward concave small bending curvature, while very dense carpet structures exhibited a downward concave large bending curvature. Moreover, the average dry bending curvature of carpets was more than twice as high as the average wet bending curvature of carpets, attributed to the increase in wet carpet weight. Thus, it was found that all dry carpets exhibited larger bending curvatures compared to the wet carpets (see Figure 8e-h). It was concluded that bending via the technical fabric test can simplify for the determination of heavy three-dimensional dry or impregnate polymeric preforms' flexural properties, particularly for complex shape molding part manufacturing.
Regression equations of the bending curvature of the dry and wet form of carpets based on the apparel fabric and technical fabric bending tests were obtained using MATLAB R2016a [83]. This was achieved using MATLAB's numerical integration and standard plotting tools. Regression equations obeyed the polynomial function where n varied between 1.7630-0.7361 for apparel fabric and 0.9925-0.7570 for technical fabric. The coefficients of regression on the bending apparel and technical fabric test data were between 0.9999 and 0.9524, which was considered well fitted for the measured values (Table 4).

Carpet Structure Static Loading Results
Static loading (compression) results on the thickness (mm), thickness loss (%), and resilience (%) of various polyester pile carpet structures are presented in Table 5 and are illustrated in Figure 9a-d. In addition, Figure 10a-d illustrates various recovery period and resilience relations after static loading on dry carpet samples.
As shown in Table 5 and Figure 9a-d, the carpet thickness loss (%) of various recovery periods of all carpets almost linearly decreased. The average dry carpet thickness loss (%) under a vertical distributed load (compression) for various recovery periods including after 2 min, 1 h, 1 day, and 3 years of 2PES6 and 3PES6 were decreased by 0.45% and 12.53% compared to 1PES6, respectively. Similar results were roughly obtained from rest of the carpet structures including 1PES9, 2PES9, 3PES9, 1PES12, 2PES12, 3PES12, where when the pile density increases, the variation of thickness loss decreases for all polyester pile heights (Figure 9a-c). This is perhaps related to the increase in knots density, which affected polyester fiber-to-fiber friction (cohesion friction) and indirectly weft density. On the other hand, the thickness loss for each recovery period from loose to very dense carpets proportionally depended on the pile density. In general, it decreases as the pile density increases due to the compression load carrying capacity per knot. This capacity is higher in carpets with dense knots compared to those with sparse knots per unit area. In addition, the effect of pile heights on the carpet thickness loss for each recovery period was hardly significant from loose to very dense polyester carpets because of complex buckled pile yarn deformation mechanism under the constrained substrate, where critical structural parameters were considered as pile yarn specifications including linear density, knot density, polyester fiber-to-fiber friction, and twisted plied or untwisted textured forms [92]. As shown in Table 5 and Figure 10a-d, the carpet resilience (ability to recover from pile deformation or gain from total thickness loss, %) of various recovery periods of all carpets sharply increased. The average resilience (%) under static load (compression) for various recovery periods including after 2 min, 1 h, 1 day, and 3 years of 2PES6 and 3PES6 slightly decreased compared to 1PES6. Similar results were obtained from the remaining carpet structures, wherein an increase in pile density resulted in a decrease in resilience variation across all pile heights (refer to Figure 10a-c). This may be attributed to the increased density of knots and the structural weft density. On the other hand, the resilience for each recovery period from loose to very dense carpets depended on the pile density. Generally, it decreases as the pile density increases due to the strong resistance generated by carpets with dense knots per unit area. Furthermore, the impact of pile heights on the resilience of polyester carpet became marginally significant for each recovery period. As the pile height increased from loose to very dense carpets, the resilience of the carpet tended to decrease. This could be attributed to the time-dependent deformation mechanism of the polyester pile yarn under the constrained substrate, as well as the presence of complex residual stress and stress relaxation. These critical structural parameters include pile yarn specifications such as linear density, knots density, fiber-to-fiber friction, and the choice between twisted plied or untwisted textured forms. We plan to conduct further research on these aspects through generating load-displacement and stress-strain curves to elucidate the critical parameters of the carpet.  As shown in Table 5 and Figure 10a-d, the carpet resilience (ability to recover from pile deformation or gain from total thickness loss, %) of various recovery periods of all carpets sharply increased. The average resilience (%) under static load (compression) for various recovery periods including after 2 min, 1 h, 1 day, and 3 years of 2PES6 and 3PES6 slightly decreased compared to 1PES6. Similar results were obtained from the remaining carpet structures, wherein an increase in pile density resulted in a decrease in resilience variation across all pile heights (refer to Figure 10a-c). This may be attributed to the increased density of knots and the structural weft density. On the other hand, the resilience for each recovery period from loose to very dense carpets depended on the pile density. Generally, it decreases as the pile density increases due to the strong resistance generated by carpets with dense knots per unit area. Furthermore, the impact of pile heights on the resilience of polyester carpet became marginally significant for each recovery period. As the pile height increased from loose to very dense carpets, the resilience of the carpet tended to decrease. This could be attributed to the time-dependent deformation mecha- complex residual stress and stress relaxation. These critical structural parameters include pile yarn specifications such as linear density, knots density, fiber-to-fiber friction, and the choice between twisted plied or untwisted textured forms. We plan to conduct further research on these aspects through generating load-displacement and stress-strain curves to elucidate the critical parameters of the carpet.

Martindale Abrasion Results
Martindale abrasion results on carpet structure for different abrasion cycles, pile mass loss and thickness loss is presented in Table 6. Figure 11a-c shows various abrasion cycles and pile mass loss (%) relations after a Martindale abrasion test on the dry carpet samples. Furthermore, Figure 12 exhibits abrasion cycle (50,000) and carpet thickness loss (mm, %) relations after testing on carpets.
As shown in Table 6 and Figure 11a-c, when the pile density increased, the carpet mass losses (%) of all carpets increased. For instance, the average carpet mass losses (%) of 1PES9, 2PES9, and 3PES9 carpet samples were 1.23%, 4.59%, and 9.63% higher, respectively. This is because of the number of knots per area. At the same pile density, when the pile height increased, the carpet mass losses (%) of all carpets were nearly increased. For instance, the average carpet mass losses (%) of 1PES6, 2PES9, and 3PES12 carpets were 1.31%, 1.23%, and 1.52% raised, respectively. On the other hand, when the abrasion cycles were increased from 5000 cycles to 50,000 cycles, the average carpet mass losses (%) increased from 0.63% to 6.25%. Moreover, it was identified that the effect of substrate architecture on the carpet abrasion properties was insignificant.

Martindale Abrasion Results
Martindale abrasion results on carpet structure for different abrasion cycles, pile mass loss and thickness loss is presented in Table 6. Figure 11a-c shows various abrasion cycles and pile mass loss (%) relations after a Martindale abrasion test on the dry carpet samples. Furthermore, Figure 12 exhibits abrasion cycle (50,000) and carpet thickness loss (mm, %) relations after testing on carpets.   As shown in Table 6 and Figure 12, when the pile density increased, the carpet thickness losses (%) of all carpets were mainly increased after 50,000 abrasion cycles due to As shown in Table 6 and Figure 11a-c, when the pile density increased, the carpet mass losses (%) of all carpets increased. For instance, the average carpet mass losses (%) of 1PES9, 2PES9, and 3PES9 carpet samples were 1.23%, 4.59%, and 9.63% higher, respectively. This is because of the number of knots per area. At the same pile density, when the pile height increased, the carpet mass losses (%) of all carpets were nearly increased. For instance, the average carpet mass losses (%) of 1PES6, 2PES9, and 3PES12 carpets were 1.31%, 1.23%, and 1.52% raised, respectively. On the other hand, when the abrasion cycles were increased from 5000 cycles to 50,000 cycles, the average carpet mass losses (%) increased from 0.63% to 6.25%. Moreover, it was identified that the effect of substrate architecture on the carpet abrasion properties was insignificant.
As shown in Table 6 and Figure 12, when the pile density increased, the carpet thickness losses (%) of all carpets were mainly increased after 50,000 abrasion cycles due to more out-of-plane fibers being in contact at the abraded area. For example, the average carpet thickness losses (%) of 1PES9, 2PES9, and 3PES9 carpet samples increased by 9.33%, 21.32%, and 23.30% compared to the initial carpet thickness values, respectively. At the same pile density, when the pile height increased, the carpet mass losses (%) of all carpet samples were nearly increased. Similarly, the average carpet thickness losses (%) of 1PES6, 1PES9, and 1PES12 carpet samples were 8.30%, 9.33%, and 15.81% greater, respectively. more out-of-plane fibers being in contact at the abraded area. For example, the average carpet thickness losses (%) of 1PES9, 2PES9, and 3PES9 carpet samples increased by 9.33%, 21.32%, and 23.30% compared to the initial carpet thickness values, respectively. At the same pile density, when the pile height increased, the carpet mass losses (%) of all carpet samples were nearly increased. Similarly, the average carpet thickness losses (%) of 1PES6, 1PES9, and 1PES12 carpet samples were 8.30%, 9.33%, and 15.81% greater, respectively.

Token Rubbing Results
Token rubbing test results on carpet samples are presented in Table 7. Figure 13 exhibits token rubbing test results for various dry carpets. As shown in Table 7 and Figure  13, the number of strokes after the complete fracture of pile yarns increased as the pile heights for each pile density were increased. Comparable relationships were observed in both loose and dense carpet structures, with the exception of very dense carpet structures. Furthermore, it was discovered that the number of strokes after the complete fracture of pile yarns and the number of strokes at the onset of fractured pile yarns were proportional for almost all carpets.

Token Rubbing Results
Token rubbing test results on carpet samples are presented in Table 7. Figure 13 exhibits token rubbing test results for various dry carpets. As shown in Table 7 and Figure 13, the number of strokes after the complete fracture of pile yarns increased as the pile heights for each pile density were increased. Comparable relationships were observed in both loose and dense carpet structures, with the exception of very dense carpet structures. Furthermore, it was discovered that the number of strokes after the complete fracture of pile yarns and the number of strokes at the onset of fractured pile yarns were proportional for almost all carpets.

Statistical Modelling Results
A statistical model was applied to carpet thickness and resilience after some time period of static loading test data and abrasion thickness loss data generated from a Martindale test. The best models for carpet thickness and resilience and abrasion thickness loss were found using DESIGN EXPERT software [93]. Table 8 presents ANOVA for the models explaining carpet thickness, resilience, and abrasion thickness loss. Figure 14 illustrates the relationship between carpet thickness and pile height after a 3-day time period of static loading for various carpet pile densities. Figure 15a-c show the relationship between resilience and pile height after some time period of static loading for various carpet densities. Additionally, Figure 16 illustrates the relationship between carpet thickness loss and pile height after the abrasion test for various carpet densities.
As shown in Table 8 and Figure 14, the regression Equation (14) for carpet thickness (CT) was obtained from the ANOVA table where A is the pile height (mm), B is the density of the carpet (weft ends/10cm), and CT is the thickness of the carpet (mm) after 3 days of static loading. The coefficient of regression (R-squared) was 0.9919 and the mean absolute percent error was 1.28%. The general form of CT Equation (14) obeys the second-order polynomial function where pile height (A) is the main parameter before carpet density (B) of carpet thickness after static loading. The interaction graph of pile height and thickness after a 3-day time period of static loading was also fitted with the regression equations and exhibited in Figure 14.

Statistical Modelling Results
A statistical model was applied to carpet thickness and resilience after some time period of static loading test data and abrasion thickness loss data generated from a Martindale test. The best models for carpet thickness and resilience and abrasion thickness loss were found using DESIGN EXPERT software [93]. Table 8 presents ANOVA for the models explaining carpet thickness, resilience, and abrasion thickness loss. Figure 14 illustrates the relationship between carpet thickness and pile height after a 3-day time period of static loading for various carpet pile densities. Figure 15a-c show the relationship between resilience and pile height after some time period of static loading for various carpet densities. Additionally, Figure 16 illustrates the relationship between carpet thickness loss and pile height after the abrasion test for various carpet densities.  As shown in Table 8 and Figure 14, the regression Equation (14) for carpet thickness (CT) was obtained from the ANOVA table where A is the pile height (mm), B is the density of the carpet (weft ends/10cm), and CT is the thickness of the carpet (mm) after 3 days of static loading. The coefficient of regression (R-squared) was 0.9919 and the mean absolute percent error was 1.28%. The general form of CT Equation (14) obeys the second-order polynomial function where pile height (A) is the main parameter before carpet density (B) of carpet thickness after static loading. The interaction graph of pile height and thickness after a 3-day time period of static loading was also fitted with the regression equations and exhibited in Figure 14.
static loading. The interaction graph of pile height, density, and resilience after various time periods of static loading was also fitted with the regression equations and illustrated in Figure 15a As shown in Table 8 and Figure 16, the regression Equation (16) of carpet abrasion thickness loss (CTL) was obtained from the ANOVA table where A is the pile height (mm), B is the density of the carpet (weft ends/10cm), and CTL is the abrasion thickness loss of the carpet (mm) after Martindale abrasion testing. The coefficient of regression (R-

Conclusions
It was found that the bending rigidity (mN.m) based on the technical fabric test increased from loose to very dense carpet structures, probably due to the large size of the carpet samples in that the size of the sample affects the bending stiffness. Further, the As shown in Table 8 and Figure 15a-c, the regression Equation (15) for carpet resilience (CR) was obtained from the ANOVA table where A is the pile height (mm), B is the density of the carpet (weft ends/10cm), C is the recovery period (2 min, 1 h, 1 day, and 3 days), and CR is the resilience of the carpet (mm) after static loading. The coefficient of regression (R-squared) was 0.7144 and the mean absolute percent error was 6.19%. The general form of CR Equation (15) obeys the second-order polynomial function where the recovery period (C) is the main parameter before pile height (A) of carpet resilience after static loading. The interaction graph of pile height, density, and resilience after various time periods of static loading was also fitted with the regression equations and illustrated in Figure 15a As shown in Table 8 and Figure 16, the regression Equation (16) of carpet abrasion thickness loss (CTL) was obtained from the ANOVA table where A is the pile height (mm), B is the density of the carpet (weft ends/10cm), and CTL is the abrasion thickness loss of the carpet (mm) after Martindale abrasion testing. The coefficient of regression (R-squared) was 0.9199 and the mean absolute percent error was 21.71%. The general form of CTL Equation (16)

Conclusions
It was found that the bending rigidity (mN.m) based on the technical fabric test increased from loose to very dense carpet structures, probably due to the large size of the carpet samples in that the size of the sample affects the bending stiffness. Further, the average dry bending rigidity of polyester carpet was over eight times higher than the average wet bending rigidity of the carpet. The bending curvature (cm) increased from loose to very dense carpet structures due to the increase in weft density and the size of the samples. In addition, downward concave small bending curvature was obtained from loose carpet, whereas downward concave large bending curvature was obtained from very dense carpet. In addition, the average dry bending curvature of polyester carpet was higher than the average wet bending curvature of the carpet due to the increase in wet carpet weight. It was concluded that bending through the technical fabric test can simplify the determination of heavy three-dimensional dry or impregnate polymeric preforms' flexural properties.
The thickness loss (%) and resilience (%) for each recovery period from loose to very dense polyester carpets proportionally depended on the pile density. It generally decreased when the pile density increased due to compression of the load carrying capacity per knot, in which it was higher in carpets having dense knots compared to ones that had sparse knots per area. When the pile density increased, the carpet mass losses (%) of all carpets under abrasion load increased. At the same pile density, when the pile height increased, the carpet mass losses (%) of all carpet samples slightly increased. Additionally, after the number of strokes required to achieve completely fractured pile yarns in the rubbing test increased when the pile heights for each pile density increased.
For future studies, we will carry out more research on particular complex shape molding part manufacturing via generated load-displacement and stress-strain curves.