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Abstract

Coated fabrics can experience mechanical performance degradation due to environmental factors and long-term stress during service. Hence, studying the mechanical behaviors of these materials after aging is crucial. While PTFE (polytetrafluoroethylene)-coated fabrics are more commonly used than PVC (polyvinyl chloride)-coated fabrics, limited research exists on their performance after aging in practical engineering applications. PTFE-coated fabrics are primarily used in large-span fabric structures, where their mechanical performance under tensile-shear stress is crucial. This study aims to investigate the mechanical behaviors of PTFE-coated fabrics after practical aging under tension-shear stress. Test materials included decommissioned Saint-Gobain Sheerfill-II PTFE-coated fabrics, which had served for 23 years at Shanghai Stadium, and identical new fabrics. Monotonic tensile, central tearing, and cyclic tensile tests were conducted at seven different off-axis angles to compare the mechanical properties of aged fabrics with new fabrics, including tensile strength, tearing strength, modulus of elasticity, and ratcheting strain. Additionally, this study explored changes in failure mechanisms, tearing mechanisms, applicability of strength criteria, and suitability of the orthotropic model after aging. This provides a comprehensive understanding of the mechanical behaviors of aged PTFE-coated fabrics and valuable insights for engineering design.

Keywords

Aged PTFE-coated fabrics off-axis mechanical behaviors failure mechanism tearing mechanism strength criterion orthotropic model

Introduction

Coated fabrics with high-strength fibers and high-performance coatings are widely used in permanent outdoor structures like canopies, warehouses, and stadiums.¹ These fabrics are mainly made with either a PVC (polyvinyl chloride) coating or a PTFE (polytetrafluoroethylene) coating. They possess distinct mechanical properties due to different yarn fibers: polyester for PVC-coated fabrics and fiberglass for PTFE-coated fabrics. Coated fabrics are increasingly used in civil engineering due to their high strength, light weight, and cost-effectiveness.² Despite their advantages, prolonged exposure to environmental factors and continuous loads can cause these materials to age.^3,4

Yang⁵ reviewed the research on the mechanical properties and aging mechanisms of PVC-coated fabrics. Their evidence indicates that these properties degrade over time. FTIR (Fourier Transform Infrared Spectrometer) and SEM (Scanning Electron Microscope) analyses revealed that UV radiation intensity and temperature contribute to the breakdown of coating molecular chains. High temperatures cause yarn expansion and rupture, reducing the macroscopic mechanical properties of the coated fabrics. Current research on aging of coated fabrics is primarily conducted through artificial accelerated aging tests to simulate real environmental conditions and shorten the experimental period.⁶ Yu⁷ investigated the mechanical properties of PVC-coated fabrics at high temperatures (20°C to 170°C) using uniaxial tensile tests. Krimi⁸ conducted artificial accelerated aging tests on PVC and PTFE-coated fabrics and proposed a method for estimating their lifespan through extrapolation. Compared to intensive, controllable, and steady laboratory weathering conditions, the natural environment is mild, complicated, and changeable, which is indispensable for providing accurate and practical weathering data.⁹ The natural exposure test is very effective because it closely mimics real environmental conditions. Eischedt¹⁰ conducted a 10-years outdoor exposure test in various regions and found that air pollution is the primary factor affecting material durability. Razak¹¹ studied the surface properties of PVC and PTFE-coated fabrics, including stain resistance, discoloration, and coating condition, based on a 2-years outdoor exposure test. The research indicated that PTFE-coated fabrics generally had superior stain resistance, while PVC coatings showed more significant cracking and peeling. Based on the above, it is evident that most existing research focuses on the influence of environmental factors (e.g., UV radiation, humidity, temperature, etc.) on the aging properties of coated fabrics. However, these studies generally neglect the impact of stress conditions. Under applied load, the material’s microstructure changes, reducing yarn crimp and leading to irreversible deformation, thereby affecting mechanical properties.¹² Zhang¹³ proposed a simplified method combining cyclic tests and stress relaxation tests to study the long-term weather resistance of PVC-coated fabrics, considering the combined aging effects of environmental factors and load. This research indicates that long-term loading can decrease both tensile strength and tensile stiffness due to long-term fatigue effects on yarns. Field aging tests use experimental specimens from actual engineering structures, providing a more accurate reflection of material degradation under real environmental conditions and engineering loads.⁶ Nevertheless, field aging test cycles are excessively long and acquiring test specimens is relatively difficult, resulting in few published research papers on this type of aging test. Yang¹⁴ studied PVC-coated fabrics in China, ranging from 15 to 19 years old, along with a statistical analysis of mechanical indices and reliability changes. Zerdzicki¹⁵ investigated a 20-year-old PVC-coated fabric from the Sopot Forest Opera and studied the impact of aging on its constitutive model. The reviews are summarized in Table 1.

Table 1.

Literature review summary.

Refe-rence	Standard	Aging condition and duration	Key conclusions
7	BS ISO 2231:1989 DIN EN ISO 1421:2016	20°C、45°C、70°C、95°C、120°C、145°C and 170°C (prestress with 0、13.6、23.8 and 34.0 kN/m) Duration:120 min	The high-temperature experiments demonstrated that the maximum stress at 170°C decreased to 57%-59% of that at 20°C. Additionally, the constant application of external force increased stiffness and reduced the impact toughness of the material
8	NF EN 12310-1 NF EN 12311-1	pH = 13.5 Temperature = 50°C, 60°C and 70°C Duration:35 days to 60 days	This result confirmed the validity of Arrhenius lifetime estimation model for the two studied materials
10	US ATSM d-39-49	Natural conditions Duration:10 years	Apart from sunlight, air pollution was the primary factor affecting material durability
11	BS ISO 2231:1989 DIN EN ISO 1421:2016	Natural conditions. Aging time:10 years	PTFE-coated fabrics generally exhibited superior stain resistance, while PVC coatings show more pronounced cracking and peeling
13	DG/TJ08-2019-2007	Irradiation intensity:872 W/m², 63°C, rain/dry cycle: 18 min/102 min Duration:86, 172, 258, 344, 516 and 688 h	The load effect during the aging process could not be ignored. Long-term loading could decrease both tensile strength and tensile stiffness due to long-term fatigue effects of yarns
14	DG/TJ08-2019-2007 FZ/T01003-1991	Actual engineering applications Duration: 15 years in Zhengzhou, 16 years in Hangzhou and 19 years in Beijing	The materials lost some of their initial mechanical properties, especially the tensile strength, tearing strength and Young’s modulus. The reliability of the material changed after aging
15	ASTM D-4434:1985 DIN 16726:1983-05 ISO 1421:2001	Actual engineering applications Duration:10 years	Aging effects could impact the selected constitutive model

Due to the complexity and variability of natural environments, research under different climatic conditions is necessary to comprehensively reveal the intrinsic relationships between multi-scale degradation behaviors and their interactions with various weathering factors.⁸ In recent decades, researchers have conducted global studies in regions with characteristic climates. Figure 1 provides an overview of natural exposure and field aging tests conducted globally over the past decades. It details the materials used, maximum aging duration, and local climate types. This comprehensive analysis shows that the natural aging of coated fabric materials has been extensively studied, especially in locations like Beijing,¹¹ Zhengzhou,¹² Hangzhou,¹² Japan,¹⁶ Malaysia,¹¹ Poland,¹⁵ Germany,¹⁰ India,¹⁷ Portugal,¹⁸ and Miami, USA.¹⁰

Figure 1.

Aging research on coated fabrics around the world.

The basic mechanical properties of PTFE-coated fabrics are well described in these references 19–22. Due to its inert nature, strong UV resistance, non-aging characteristics, and long lifespan, PTFE-coated fabric has become the most reliable material for large-span fabric structures under harsh loading conditions.^23–26 PTFE-coated fabrics have been developed more recently than PVC-coated fabrics.² Because of their relatively recent development, only natural exposure tests have been conducted on PTFE-coated fabrics so far. As PTFE-coated fabric structures gain prominence, there is a pressing need for field aging tests on these materials. Such research will provide valuable insights, enrich the knowledge base on PTFE-coated fabrics, and enhance the design of more durable and reliable fabric structures. As the span of coated fabric structures expands, understanding their mechanical behavior under complex shear-induced stress becomes increasingly important.²³ Off-axis tests serve as the simplest method for examining complex stress situations.²⁷ Consequently, off-axis mechanical tests are gaining attention in the evaluation of new coated fabrics.^28,29 However, current research on the mechanical behavior of aged materials mainly focuses on changes in the warp and weft directions, overlooking broader aspects.^24,25 Additionally, the tearing resistance of aged coated fabrics is frequently assessed using the trapezoidal tearing method,^12,13 a technique originally developed for the apparel industry, which is not tailored for structural fabrics.²⁶ Consequently, the strength values derived from this method are rarely incorporated into design specifications. In contrast, the central tearing test aligns more closely with actual structural tearing in terms of stress distribution and crack opening shapes.³⁰ This test provides data on the tearing resistance of coated fabrics, which are more pertinent and directly applicable to real-world scenarios. Therefore, it is an appropriate method for investigating the tearing resistance of aged PTFE-coated fabrics and offers valuable insights for the design and assessment of fabric structures.

To address the research gaps, this study focuses on the off-axis mechanical behaviors of aged PTFE-coated fabrics, specifically Saint-Gobain Sheerfill-II. These fabrics were removed from Shanghai Stadium, the first large-span PTFE-coated fabric structure in China, which was dismantled after 23 years of service. Analyzing the mechanical performance of this aged fabric provides crucial insights for designing large-span fabric structures, particularly in understanding their longevity and durability under practical engineering conditions.

Experimentation

Materials and methodology

Shanghai Stadium (Figure 2),³¹ inaugurated in 1997, features a distinctive roof comprising 57 umbrella-like cable fabric units spanning a horizontal projection area of 37,000 m². This roof utilized Saint-Gobain Sheerfill-II PTFE-coated fabrics, marking China’s first use of fabric structures for large-span permanent buildings. This groundbreaking application laid the foundation for the widespread adoption of fabric architecture across the nation. After 23 years, coinciding with the stadium’s renovation for the World Cup, the iconic roof fabric structure was dismantled. The fabric investigated was removed from the western cantilevered portion of the stadium’s saddle-shaped roof, covering an area of 20 m² (Figure 2). Throughout its service life, it endured significant wind suction forces and underwent coupled weathering and mechanical aging. Table 2 shows the annual climate characteristics of Shanghai over the past 20 years.

Figure 2.

Shanghai Stadium.

Table 2.

Shanghai’s climatic characteristics.

Climate characteristics	Annual average value
Temperature	17.8°C
Relative humidity	73%
Precipitation	1166 mm
Sunshine duration	2784.81 h
Wind speed	14 km/h
Air quality index (AQI)	80

The material properties of Sheerfill-II PTFE-coated fabric are listed in Table 3.³² To comprehensively assess the off-axis mechanical behaviors of aged PTFE-coated fabrics after practical engineering application (hereafter referred to as “aged fabrics”), we analyzed new fabrics of the same model (hereafter referred to as “new fabrics”). Both aged and new fabrics were tested at seven different off-axis angles. These tests included uniaxial monotonic tensile, central tearing, and cyclic tensile tests to determine key mechanical properties such as tensile strength, tearing strength, elastic modulus, and ratcheting strain at various angles. Additionally, further in-depth studies on fracture and tearing mechanisms, the applicability of strength criteria, and the relevance of the orthotropic theoretical model are required. Since the aged and new fabrics originate from different batches, the comparison cannot yield definitive conclusions about the degradation behavior of aged PTFE-coated fabrics but provides directional insights.

Table 3.

Material properties of Sheerfill-II PTFE-coated fabrics.

Type	Tensile strength in warp (N/5 cm)	Tensile strengths in weft (N/5 cm)	Weight (kg/m²)	Thickness (mm)
Sheerfill-II	6875	4905	0.91	0.76

Figure 3 shows the dimensions of the test samples. For cyclic tensile tests, standard rectangular specimens measuring 50 mm in width and 200 mm in gauge length were employed for strain measurements. In the central tearing test, an initial crack of length 2a (25 mm in this study) was introduced at the center of each specimen. In the monotonic tensile tests, an improved rectangular specimen with winding clamps (Figure 4) was used to prevent slippage. The gauge length was 200 mm, and two extensometers fixed at both ends of the gauge length were used to measure deformation. Both new and aged fabrics were prepared into test specimens at various off-axis angles of θ (θ = 0°, 15°, 30°, 45°, 60°, 75°, and 90°), with the warp direction serving as the reference. The specimens were cut into dimensions suitable for the aforementioned tests (Figure 3).

Figure 3.

Specimen size (Unit: mm).

Figure 4.

Winding clamps.

Experiments

In this study, basic experimental conditions were kept the same. These conditions included maintaining a room temperature of 24 ± 0.5°C and a relative humidity of 65 ± 3%. The specific experimental parameters for the off-axis monotonic tensile test, central tearing test, and cyclic tensile test are detailed in the following subsections.

Off-axis monotonic tensile test

In each test, force was measured with a force sensor with an accuracy of ±1.0 N. Deformation was measured with extensometers attached to both ends of the specimen, with an accuracy of ±0.01 mm. The loading speed was set to 100 mm/min according to the DG/TJ08-2019-2019³³ standard. Each off-axis angle was tested five times. At least five repeated tests were conducted for each off-axis angle to obtain an average value, ensuring result reliability.

Off-axis center tearing test

According to Sun,²¹ as the crack length increases, coated fabrics transition from a strength-controlled fracture to a toughness-controlled fracture. This study focused on the impact of real-world aging on the fracture toughness of fabrics. Therefore, long cracks of 25 mm were selected for this study. At least five repeated tests were conducted.

Off-axis cyclic tensile test

Many studies agree that the fabric stress during the service life of practical fabric structures is generally less than one-fourth of the uniaxial ultimate tensile strength.³⁴ Therefore, in this study, the upper limit of stress amplitude for each off-axis angle was set to one-fifth of the tensile strength, corresponding to the respective off-axis angles of the new fabrics. The stress lower limit was set to the commonly used prestress value for PTFE-coated fabric structures, which is 4 kN/m²². In this study, a loading speed of 10 mm/min was selected based on ISO standards for uniaxial cyclic tests,³⁵ and 15 cycles were used according to ASTM standards for cyclic test duration.³⁶ At least three repeated tests were conducted.

Results and discussion

Off-axis monotonic tensile results

Off-axis tensile curve

Figure 5(a) and (b) show the typical off-axis load-displacement curves for new and aged PTFE-coated fabrics. As the off-axis angle ranged from 0° to 45° and reverted from 90° to 45°, both new and aged fabrics showed a consistent pattern: a gradual decline in tensile strength and an increase in elongation at break. This trend corroborates the conclusions drawn in this study.²⁸

Figure 5.

Off-axis monotonic tensile results. (a) Load-displacement curves (new) (b) Load-displacement curves (aged), (c) Relationship between tensile strength and off-axis angle.

The area beneath the load-displacement curve in the uniaxial tensile test of fabric specimens is referred to as fracture energy. Table 5 outlines the essential data points for these fabrics, including tensile strength, elongation at break, and fracture energy. The comprehensive experimental data clearly show that across all off-axis angles, the aged fabrics have lower strength, elongation at break, and fracture energy compared to the new fabrics.

Table 5.

Off-axis tensile test results.

Angle (°)	Tensile strength (N/5 cm)			Elongation at break (%)			Fracture energy (N·m)
Angle (°)	New	Aged	Retention rate (%)	New	Aged	Retention rate (%)	New	Aged	Retention rate (%)
0	6703	3928	58.6	5.29	5.05	95.5	23.74	15.81	66.6
15	3889	2992	76.9	15.12	7.48	49.5	39.69	20.07	50.6
30	3481	2319	66.6	33.05	21.76	65.8	59.22	41.85	70.7
45	3073	1751	57.0	36.88	27.06	73.3	56.17	38.35	68.3
60	3127	1813	58.0	34.23	25.96	75.8	53.79	38.15	70.9
75	3578	2690	75.2	21.43	19.92	93.0	53.07	44.22	83.3
90	5968	3471	58.2	9.58	5.90	61.6	21.17	11.38	53.8

Figure 5(c) shows the tensile strength of both new and aged fabrics, with error bars representing the standard deviation. The standard deviation indicates the variability in tensile strength data. Additionally, the coefficient of variation is shown. For the new fabrics, a notable decrease in strength was observed at lower off-axis angles, particularly at 15° and 75°. This decrease appears as a sharp drop; for example, the tensile strengths at 15° and 30° exhibit reductions of 42% and 6%, respectively, compared to those at 0° and 15°. This significant decline is associated with a shift in the fracture mode. As the off-axis angle increased, the extent of strength reduction diminished, reaching a minimum at 45°. The coefficient of variation in tensile strength of aged fabrics is notably higher than that of new fabrics, indicating that the aging process increases the variability of tensile strength. Therefore, relying solely on average tensile strength values as the evaluation index is deemed unscientific. Consequently, reliability calculations should be integrated into the durability design of fabric structures.

In contrast, the strength of the aged materials did not show a sharp decline with the change in fracture mode; rather, the reduction in strength was more gradual. For instance, the tensile strengths at 15° and 30° decreased by 24% and 17%, respectively, compared to those at 0° and 15°. This behavior and its implications are further explored in the subsequent subsection.

Fracture mechanism

Zhang²⁸ identified three primary failure modes for PTFE-coated fabrics under off-axis tension, as shown in Figure 6: In the warp and weft directions, failure predominantly occurred due to the breakage of the base fabric fibers, resulting in pure tensile failure. At an off-axis angle of 45°, the material experienced pure shear failure. This mode is characterized by high-strength yarns being pulled out from the coating, with failure occurring at the yarn-coating interface. At 45°, the tensile strength depends on the bonding strength of the interface. In tests at other angles, the failure was a mix of tensile and shear; the yarns at the edges were pulled out from the coating (shown as the blue debonding area), while the central yarns broke (shown as the red fracture area). The tensile strength in these instances correlates with the number of broken high-strength yarns at the center, representing the utilization rate of these yarns.²⁷ The higher the utilization rate (indicated by a larger red fracture zone), the higher the tensile strength.

Figure 6.

Tensile failure mode. (a) Pure tensile failure (b) Tensile shear mixed failure (c) Pure shear failure.

Figure 7 shows the fracture morphologies of new and aged fabrics at various off-axis angles after tensile testing. In mixed tensile-shear failure, aged fabrics exhibited fewer yarns pulled out compared to new fabrics, indicating a higher utilization rate of high-strength yarns. This is shown in Figure 7 by the smaller area of the red fracture zone, possibly due to changes in yarn properties and the interface induced by aging. Consequently, the strength reduction in aged fabrics was more gradual than in new fabrics.

Figure 7.

Tensile fracture morphologies.

Observations reveal significant differences in the fracture morphology of aged and new fabrics at 45°. In the fracture section of aged fabrics, all yarns are pulled out from the interface. Conversely, due to the influence of the coating on crack propagation, the fracture section of new fabrics presents a jagged appearance. Here, the center yarns are fractured, while the edges show yarns being pulled out from the yarn-coating interface. Compared to new fabrics, aged fabrics exhibit a significant decrease in their ability to resist pure shear. Consequently, assessing the safety factor of fabric strength due to aging should not rely solely on warp and weft tensile tests. For a comprehensive evaluation, especially in worst-case scenarios, the post-aging bonding strength at the interface must be considered to accurately calculate the safety factor.

Strength criterion

Strength criteria are essential for understanding material failure, especially under complex stress states. They are integral components of both theoretical research and practical engineering. These criteria are determined by the intrinsic properties of the materials as well as by factors such as aging and sustained stresses over time. A combined state of stress develops in an anisotropic material when the axes of anisotropic symmetry do not align with the directions of the applied loads. Off-axis testing is the simplest method to generate a complex stress state, and it can be used to investigate failure criteria.²⁸ To assess the predictive accuracy of various strength criteria for both new and aged fabrics, four widely recognized yet straightforward criteria were selected: Tsai-Hill,³⁷ Norris,³⁸ Yeh-Stratton,³⁹ and Hashin.⁴⁰ Using these criteria, we can gain insights into how effectively each one predicts the failure behavior of new and aged fabrics, providing valuable information for structural engineering design and analysis.

Tsai-Hill criterion

\frac{σ_{x}^{2}}{X^{2}} + \frac{σ_{y}^{2}}{Y^{2}} - \frac{σ_{x} σ_{y}}{X^{2}} + \frac{τ_{x y}^{2}}{S^{2}} = 1

(1)

Yeh-Stratton Criterion

\frac{σ_{x}}{X} + \frac{σ_{y}}{Y} - \frac{σ_{x} σ_{y}}{X^{2}} + \frac{τ_{x y}^{2}}{S^{2}} = 1

(2)

Norris Criterion

\frac{σ_{x}^{2}}{X^{2}} + \frac{σ_{y}^{2}}{Y^{2}} + \frac{τ_{x y}^{2}}{S^{2}} - \frac{σ_{x} σ_{y}}{X Y} = 1

(3)

Hashin Criterion

{(\frac{σ_{11}}{X})}^{2} + {(\frac{τ}{S})}^{2} = 1

(4)

where

X

and

Y

represent the tensile strengths in the warp and weft directions, and S is the shear strength.

σ_{x}

and

σ_{y}

stand for the normal stresses in the warp and weft directions, respectively, while

τ_{x y}

represents the shear stress.

It is possible to substitute $σ_{x} = σ_{θ} \cos^{2} θ$ ; $σ_{y} = σ_{θ} \sin^{2} θ$ ; and $τ_{x y} = σ_{θ} \cos θ \sin θ$ to obtain the strength criteria under an oblique angle. Taking the Tsai-Hill criterion as an example, the strength criterion under an oblique angle can be expressed as follows:

\frac{1}{σ_{θ}^{2}} = \frac{\cos^{4} θ}{X^{2}} + [\frac{1}{S^{2}} - \frac{1}{X^{2}}] \cos^{2} θ \sin^{2} θ + \frac{\sin^{4} θ}{Y^{2}}

(5)

where

θ

represents the off-axis angle, and

σ_{θ}

is the tensile strength in the

θ

direction.

The shear strength $S$ can be determined using the following formula:⁴¹

S = k \cdot \sin α \cdot \frac{X_{45}}{\sqrt{2}}

(6)

where

X_{45}

represents the tensile strength at 45°,

α

denotes the angle between the warp and weft yarns, ranging from 85° to 95°,⁴² and the coefficient

k

(0.7∼0.8) represents the efficiency of the conversion between oblique tensile strength and off-axis tensile strength. In this study,

k = 0.75

Figure 8 presents a comparative analysis of the experimental results for both new and aged fabrics, along with predictions made using various established strength criteria. Corresponding error values are shown in Table 6 and 7. For new fabrics, the Tsai-Hill, Norris, and Hashin criteria provided accurate predictions. However, significant deviations were noted at smaller off-axis angles, specifically at 15° and 75°. Conversely, the Yeh-Stratton criterion exhibited high accuracy at smaller off-axis angles but was less accurate at larger off-axis angles.

Figure 8.

Comparison of prediction results of several existing criteria with experimental data. (a) New coated fabrics (b) Aged coated fabrics.

Table 6.

Comparison of predicted and experimental values of new fabrics under several existing criteria.

$θ$ /°	Tsai-Hill		Yeh-Stratton		Norris		Hashin
$θ$ /°	Theoretical (N/5 cm)	Error (%)	Theoretical (N/5 cm)	Error (%)	Theoretical (N/5 cm)	Error (%)	Theoretical (N/5 cm)	Error (%)
0	6703	0	6703	0	6703	0	6703	0
15	4901	20.7	4134	5.9	4911	20.8	4828	19.5
30	3521	1.2	2892	20.3	3532	1.5	3469	0.3
45	3145	2.3	2584	18.9	3156	2.6	3145	2.3
60	3459	9.6	2843	10.0	3470	9.9	3403	8.1
75	4628	22.5	3943	9.0	4637	22.6	4566	21.4
90	5968	0	5968	0	5968	0	5968	0

Table 7.

Comparison of predicted and experimental values of aged fabrics under several existing criteria.

$θ$ /°	Tsai-Hill		Yeh-Stratton		Norris		Hashin
$θ$ /°	Theoretical (N/5 cm)	Error (%)	Theoretical (N/5 cm)	Error (%)	Theoretical (N/5 cm)	Error (%)	Theoretical (N/5 cm)	Error (%)
0	3928	0	3928	0	3928	0	3928	0
15	2825	5.9	2381	5.7	2831	5.7	2785	7.5
30	2011	15.3	1657	40	2018	14.9	1984	16.9
45	1793	2.4	1478	18.4	1799	2.7	1793	2.4
60	1975	8.2	1628	11.3	1982	8.5	1945	6.8
75	2663	1.0	2267	18.7	2668	0.8	2628	2.4
90	3471	0	3471	0	3471	0	3471	0

For aged fabrics, the Tsai-Hill, Norris, and Hashin criteria perform well at smaller off-axis angles but are less reliable at larger angles, resulting in greater errors. Interestingly, the Yeh-Stratton criterion, effective for new fabrics at small angles, is not accurate for aged fabrics. This disparity in predictive accuracy may stem from the more intricate failure modes observed in aged fabrics. This finding underscores the complexity of predicting the behavior of aged fabrics and emphasizes the need for criteria that accurately reflect changes induced by aging and long-term service.

Off-axis center tearing results

Load–displacement curve

Figure 9(a) and (b) illustrate the typical tearing load–displacement curves for both new and aged fabrics at various off-axis angles, with an initial crack length of 25 mm. These curves identify the tearing strength and displacement for each fabric, where the maximum load indicates the tearing strength and the corresponding displacement represents the ultimate tearing displacement. Table 8, provided alongside the figures, summarizes these values for various off-axis angles.

Figure 9.

Off-axial center tearing results. (a) Load-displacement curves (new) (b) Load-displacement curves (aged), (c) Relationship between tearing strength and off-axis angle.

Table 8.

Off-axis center tearing results.

Angle (°)	Tearing strength (N)			Tearing displacement (mm)
Angle (°)	New	Aged	Retention rate (%)	New	Aged	Retention rate (%)
0	1968	1340	68.1	9.03	6.38	70.7
15	889	855	96.2	11.79	7.77	65.9
30	1220	734	60.2	54.44	22.38	41.1
45	1002	893	89.1	63.11	40.17	63.7
60	1116	836	74.9	56.15	34.43	61.3
75	813	662	81.4	22.13	14.48	65.4
90	1816	1275	70.2	19.19	8.74	45.5

The tearing performance of the PTFE-coated fabrics showed significant anisotropy, but the overall characteristics of the curves remained consistent across various angles. As displacement increased, the load initially peaked and then showed local fluctuations before rapidly decreasing to a minimum value. Both new and aged fabrics can be categorized into two distinct failure modes based on their localized fluctuation characteristics. Progressive failure is characterized by an extended plateau stage after peak load with steady crack propagation and curve fluctuations. Brutal failure is identified by a sudden, overall collapse immediately after peak load, with little to no plateau stage, bypassing the stable crack propagation phase. Brutal failure typically involves larger displacement at failure compared to progressive failure. At various off-axis angles, the load associated with brutal failure is higher than that associated with progressive failure. For new fabrics, brutal failure was observed at 30°, 45°, and 60° off-axis angles, while progressive failure occurred at other angles. For aged fabrics, brutal failure was observed at 45° and 60° off-axis angles, while progressive failure occurred at other angles. A distinct variation in the failure modes of new and aged fabrics was noticeable at an off-axis angle of 30°.

Figure 9(c) provides a detailed analysis of the tearing strength variations in both new and aged fabrics influenced by the off-axis angle, with the standard deviation depicted as error bars. The coefficient of variation is also shown. This comparison reveals that the tearing strength and associated displacement at each off-axis angle were consistently lower for aged fabrics than for new ones. Moreover, the patterns of change for the two types of materials displayed distinct differences. For new fabrics, a notable decline in tearing strength was observed when transitioning from the warp and weft directions to smaller off-axis angles, specifically 15° and 75°. However, an interesting rebound in strength occurred at 30° and 60°, where local peaks in tearing strength were observed. At an off-axis angle of 45°, there was a slight fluctuation in strength, characterized by a minor decrease, yet the strength remained higher than at angles of 15° and 75°.

For aged fabrics, the strength does not recover at 30° but instead reaches its lowest value, indicating a change in the failure mode compared to new fabrics. This decrease was attributed to a shift in the failure mode from that observed in new materials, warranting further discussion. Notably, at 45°, aged materials exhibited a local peak in tearing strength.

Tearing mechanism

This section delves deeper into the findings of the previous subsection, using Figure 10 to illustrate the typical damage modes of the central tearing specimens and Figure 11 to show the fracture morphologies of new and aged fabrics.

Figure 10.

Central tearing damage model diagram.

Figure 11.

Fracture morphologies of center tearing specimens in different tensile directions.

In the warp and weft specimens (Figure 10(a)), the loading process caused inelastic deformation and slippage of the yarns, leading to a large deformation area (highlighted in blue in Figure 10(a)). The strain energy accumulated in this zone helps reduce stress concentration at the crack tip. Concurrently, two areas of stress concentration, termed delta zones (shown in red in Figure 10(a)), gradually emerged within the large deformation area. When the initial yarns in the delta zone fail due to intense stress concentration, the subsequent yarns take on the load, leading to an ongoing expansion of the delta zone until the specimen ultimately fails. This expanding delta zone correlated with fluctuations around the peak in the load curve. For specimens oriented along the warp and weft directions, the delta zone was fully developed, resulting in the breakage of all yarns within the cross-section of the crack, as shown in the red yarn fracture area in Figure 11.

As the off-axis angle increased, larger deformation zones arose due to shear deformation (Figure 10(b)), restraining the expansion of the delta zone and preventing it from reaching its full extent. When the delta zone reached a certain size, the yarns in the large deformation area, laden with significant strain energy, failed to support the transferred load, causing rapid yarn pull-out (shown as the blue debonding area in Figure 11). Approaching the off-axis angle of 45°, the debonding area progressively enlarged while the delta zone diminished, culminating in a shift from gradual to abrupt failure, as reflected by the sharp decrease following the peak of the curve. For new fabrics, at large off-axis angles of 30°, 45°, and 60°, the delta region was completely suppressed, causing all yarns in the cracked section to fail simultaneously, maximizing strength utilization. Consequently, at 45°, the tearing strength decreased due to an overall reduction in tensile strength. In contrast, for aged fabrics, the diminishing delta region at 45° leads to improved strength utilization and enhanced tearing strength.

The tearing morphologies reveal that the debonding areas in aged materials are smaller than in new materials, indicating a lower slippage capacity of yarns in aged fabrics. This results in smaller large deformation areas, larger delta zones, and more broken yarns. Particularly at an off-axis angle of 30°, the limited shear deformation capacity causes the delta zone to exceed the threshold for various failure modes, leading to a marked decrease in tearing strength compared to new materials.

The substantial reduction in the tearing strength of aged fabrics can be attributed to three primary factors: first, decreased yarn breakage strength; second, reduced slippage ability of the yarns, resulting in smaller large deformation areas and less effective stress concentration mitigation at the crack tip; and finally, a change in the failure mode at specific angles, where the most significant drop in tearing strength is observed in aged fabrics.

Off-axis cyclic stretching results

Cyclic tensile stress–strain curve

Typical off-axis cyclic tensile stress-strain curves are shown in Figure 12(a) and (b). Noticeable nonlinearity was observed at all seven off-axis angles. As the number of cycles increased, both the ratcheting strain and the elastic modulus increased slowly, with a larger proportion of this increase occurring in the initial cycles. As the off-axis angle approached 45°, the number of cycles required to reach a near-stable value increased. These characteristics were consistent for both new and aged fabrics. However, after 15 cycles of tensile stretching, the residual strain in aged fabrics was smaller at each off-axis angle compared to new fabrics.

Figure 12.

Off-axis cyclic stretching results. (a) Stress–strain curve (New) (b) Stress–strain curve (Aged), (c) Ratcheting strain differences (New) (d) Ratcheting strain differences (Aged), (e) Elastic modulus (New), (f) Elastic modulus (Aged).

Ratchet strain

Figure 12(c) and (d) show the progression of the ratcheting strain difference in both new and aged PTFE-coated fabrics relative to the number of loading cycles. The graphs reveal a noteworthy trend: as the cycle count increases, the ratcheting strain difference decreases and begins to stabilize. This change is most pronounced during the first and second cycles. For example, in new fabrics along the warp direction, the ratcheting strain difference was 0.022 in the first cycle but dramatically reduced to 0.0006 in the second cycle. The aged fabrics exhibited a more gradual change in ratcheting strain difference compared to new fabrics.

Although the low-cycle tests did not reach a definitive saturation value by the sixth cycle, the ratcheting strain difference in all tests stabilized below 0.2%. Based on this observation, it is reasonable to infer that the ratcheting strain in the fabrics tends to stabilize by the 15th cycle. Table 9 summarizes the ratcheting strain at different off-axis angles for both new and aged fabrics.

Table 9.

Ratchet strain of new and aged coated fabrics.

Angle (°)	Ratchet strain (%)
Angle (°)	New	Aged
0	2.47	1.9
15	3.52	2.46
30	19.12	10.6
45	24.92	16.28
60	22.94	14.69
75	9.48	6.12
90	6.8	3.5

The overall trend in the change in ratcheting strain is consistent for both new and aged fabrics, showing an increase at an off-axis angle of 45°. This trend highlights significant residual deformation accumulating in fabrics under real-world conditions, with the most substantial accumulation observed at 45°. In practical engineering applications, particularly in large-span fabric structures, high residual deformation indicates an increased risk of fatigue failure. Consequently, to mitigate the risk of fatigue damage in these structures, special attention must be given to areas experiencing high shear stress.

Modulus of elasticity

To achieve a more precise measurement of the elastic modulus during the cyclic tensile tests, the loading curve was segmented and analyzed using the least-squares method. This segmentation was based on the commonly used prestress of 4 kN/m for PTFE-coated fabric structures. Figure 12(e) and (f) show the variation in elastic modulus across different loading cycles. Notably, there was a significant increase in the elastic modulus during the initial cycles, followed by stabilization after several cycles. Compared to new fabrics, aged fabrics exhibit a less pronounced increase in elastic modulus and reach a near-stable state more quickly. This suggests that aging and prolonged stress result in more linear tensile behavior in fabrics.

Table 10 presents the measurements of the elastic modulus at various off-axis angles. The results indicate that the elastic modulus of aged fabrics is consistently lower than that of new fabrics at each off-axis angle, with the reduction magnitude varying across angles. The most pronounced difference was observed in the weft direction. At other off-axis angles, notably 75° (dominated by the weft yarn properties) and 45° (where pure shear deformation is predominant), the elastic modulus also decreased significantly. The variations in elastic modulus were less pronounced at other off-axis angles. In fabric structure design, it is crucial to consider the loss of elastic modulus and implement measures to mitigate the loss of fabric prestress.

Table 10.

Comparison of theoretical and experimental values of elastic modulus.

$θ$	New coated fabrics			Aged coated fabrics
$θ$	Theoretical (kN/m)	Experimental (kN/m)	Error (%)	Theoretical (kN/m)	Experimental (kN/m)	Error (%)
0	3203	3203	0	2937	2937	0
15	1521	1947	28	1475	1946	32
30	742	997	34	737	996	35
45	590	841	43	587	750	28
60	738	882	20	722	871	21
75	1497	1439	4	1378	1286	7
90	3081	3081	0	2529	2529	0

The PTFE-coated fabrics exhibited an anisotropic elastic modulus. In engineering design, orthotropic linear elastic models are commonly used for structural analyses. Consequently, this study compared the theoretical elastic modulus values derived from the orthotropic model with the actual values for both new and aged fabrics. This comparison aims to evaluate the applicability of the orthotropic model to PTFE-coated fabrics and examine the impact of aging on orthotropic behavior. The tensile orthotropic behavior should satisfy the following constitutive relationship:

\frac{1}{E_{θ}} = \frac{\cos^{4} θ}{E_{w}} + (\frac{1}{G_{w f}} - \frac{v_{w f}}{E_{w}} - \frac{v_{f w}}{E_{f}}) \cos^{2} θ \sin^{2} θ + \frac{\sin^{4} θ}{E_{f}}

(7)

where

E_{θ}

E_{w}

, and

E_{f}

represent the uniaxial elastic modulus in the

θ

, warp, and weft directions, respectively.

G_{w f}

v_{w f}

and

v_{f w}

represent the in-plane shear modulus and Poisson’s ratio, respectively.

Poisson’s ratio is essential for calculating the theoretical elastic modulus of composite materials, but it can be challenging to obtain. Given its stable mechanical characteristics, Poisson’s ratio is best determined from cyclic tensile tests. IIn this study, Digital Image Correlation (DIC) technology was used to obtain Poisson’s ratios for both new and aged fabrics at off-axis angles of 0°, 45°, and 90°. Images for the analysis were captured during the 15th cycle, as mechanical properties tended to stabilize at this stage.^40–42

Figure 13 shows the interface of the Ncorr⁴³ software used for image processing. The software calculates the displacement and coordinates for all points along the boundaries of the Region of Interest (ROI). It obtains the average lengths and average displacements of two vertical lines, denoted as $x_{1}$ , ${∆ x}_{1}$ , and $x_{2}$ , ${∆ x}_{2}$ , and the average lengths and average displacements of two horizontal lines, denoted as $y_{1}$ , ${∆ y}_{1}$ , and $y_{2}$ , ${∆ y}_{2}$ . Poisson’s ratio was then calculated using the following formula:

ε_{x} = \frac{∆ x_{2} - ∆ x_{1}}{x_{2} - x_{1}}

(8)

ε_{y} = \frac{∆ y_{2} - ∆ y_{1}}{y_{2} - y_{1}}

(9)

v = - \frac{ε_{x}}{ε_{y}}

(10)

where

ε_{x}

and

ε_{y}

represent the axial strain and transverse strain, respectively, and

v

represents the Poisson’s ratio.⁴⁴

Figure 13.

Methods for determination of Poisson ratio with DIC technique. (a) Horizontal direction (b) Vertical direction.

The shear modulus $G_{w f}$ for composite woven materials can be determined using the following formula:

G_{w f} = \frac{E_{45}}{2 (1 + v_{45})}

(11)

where

E_{45}

and

v_{45}

represent the elastic modulus and Poisson’s ratio at 45°, respectively.

Substituting the values yields shear modulus of 123.9 kN/m for new fabrics and 144.8 kN/m for aged fabrics. Practical aging results in an increase in the shear modulus of the fabrics.

Figure 14 compares the theoretical and actual values of the elastic modulus, while Table 10 summarizes the corresponding data and error values. At an off-axis angle of 75°, the actual elastic modulus closely matches the theoretical value. However, significant differences were observed at other off-axis angles, with the greatest discrepancy at 45°, where the error reached 43%. The accuracy of predicting the elastic modulus for both new and aged fabrics was similar at most off-axis angles. However, aged fabrics showed notably higher prediction accuracy at 45°, with an error of only 28%. This may be attributed to aged fabrics exhibiting a significantly lower degree of nonlinearity in tensile behavior at 45° compared to new fabrics.

Figure 14.

Experimental and theoretical elastic modulus against loading directions. (a) New coated fabrics (b) aged coated fabrics.

These findings suggest that aging does not reduce the applicability of the orthotropic model to fabrics. Due to the increased linearity at certain angles, the applicability of the model improves. Therefore, when using an orthotropic model for design in practical engineering applications, aging does not decrease the model’s suitability. However, this does not eliminate the impact of potential rotation of the orthogonal warp and weft yarns, which can influence the behavior of the fabrics and should be considered in design and analysis.

Conclusions

This study presented an in-depth analysis of the mechanical behaviors of Sheerfill-II PTFE-coated fabrics used in practical applications, focusing on the longest-serving decommissioned PTFE-coated fabrics in China. The findings indicate a general decrease in the fundamental mechanical properties at various off-axis angles for aged fabrics compared to new ones. In the monotonic tensile test, due to the increased utilization of high-strength yarns, the tensile strength of aged fabrics does not decrease as sharply with changes in failure mode as in new fabrics. It can also be observed that the prediction accuracy of different strength criteria for various off-axis angles shows significant differences between new and aged fabrics. In the tear test, a shift in the tearing failure mode at certain off-axis angles due to aging was observed, leading to a significant decline in tearing strength. In the cyclic tensile test, aged fabrics exhibit significant residual deformation. A downward trend was observed in the elastic modulus of aged materials across all off-axis angles, with the most notable reduction in the weft direction. Evaluating the applicability of the orthotropic model to aged fabrics revealed that the increased linearity of the tensile curve after aging enhances the model’s fit, especially at 45°.

Current research on the aging properties of coated fabrics, including PTFE-coated fabrics, primarily focuses on evaluating material performance. Integrating micromechanical models to examine the internal structures of aged fabrics has significant potential for advancing this field. This approach will bridge the gap between the evolution of mechanical properties and structural performance, extending its relevance at the structural level. To gain a more nuanced understanding of aging performance under complex stress states, biaxial testing is instrumental.

Footnotes

Declaration of Conflicting Interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) received no financial support for the research, authorship, and/or publication of this article.

ORCID iDs

Yueyang Yu

Yonghui Yang

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Comprehensive study of the off-axis mechanical behaviors of a Polytetrafluoroethylene‐ coated fabric after 23 Years of service at Shanghai stadium

Abstract

Keywords

Introduction

Experimentation

Materials and methodology

Experiments

Off-axis monotonic tensile test

Off-axis center tearing test

Off-axis cyclic tensile test

Results and discussion

Off-axis monotonic tensile results

Off-axis tensile curve

Fracture mechanism

Strength criterion

Off-axis center tearing results

Load–displacement curve

Tearing mechanism

Off-axis cyclic stretching results

Cyclic tensile stress–strain curve

Ratchet strain

Modulus of elasticity

Conclusions

Footnotes

Declaration of Conflicting Interests

Funding

ORCID iDs

References