Here, we simulate accelerated thermal ageing of technical fabric and see how this ageing process influences the mechanical properties of the fabric.
Architectural fabric AF9032 has been subjected to artificial thermal ageing to determine changes of the material parameters of the fabric. The proposed method is based on the accelerated ageing approach proposed by Arrhenius. 300 mm x 50 mm samples were cut in the warp and fill directions and placed in a thermal chamber at 80 °C for up to 12 weeks or at 90 °C for up to 6 weeks. Then after one week of conditioning at ambient temperature, the samples were uniaxially tensioned at a constant strain rate. Experimentally, the parameters were determined for the non-linear elastic (linear piecewise) and viscoplastic (Bodner–Partom) models. Changes in these parameters were studied with respect to the ageing temperature and ageing period. In both cases, the linear approximation function was successfully applied using the simplified methodology of Arrhenius. A correlation was obtained for the fill direction between experimental results and the results from the Arrhenius approach. For the warp direction, the extrapolation results exhibited some differences. Increasing and decreasing tendencies have been observed at both temperatures. The Arrhenius law was confirmed by the experimental results only for the fill direction. The proposed method makes it possible to predict real fabric behavior during long term exploitation, which is a critical issue in the design process.
Polyester based architectural fabrics are commonly used for construction of hanging roofs1. Being relatively cheap with good mechanical properties, they can be employed in long-term exploitation (e.g., the hanging roof of the Forest Opera in Sopot – Poland). Unfortunately, weather conditions, ultraviolet radiation, biological reasons, and operational purposes (season pre-stressing and loosening2) can affect their mechanical properties. Hanging roofs made of AF9032 are typically seasonal structures subjected to high temperature (especially during sunny days in the summer), regular pre-tensioning and loosening. In order to properly design a hanging roof, fabric parameters must be determined not only at the beginning of exploitation, but also after several years of use.
Ageing analysis measures the ageing indicator and compares the initial and final values of the parameters to assess the impact of ageing. Cash et al.3 proposed one of the simplest methods by comparative analysis of 12 different types of roofing membranes. These membranes were exposed to outdoor weathering for 2 or 4 years. The authors used a rating system of several properties to assess fabric durability. In order to provide an analysis of polymer thermal ageing, the time-temperature superposition principle (TTSP) can be applied4. This principle states that the behavior of a material at low temperature and under low strain level resembles its behavior at high temperature and high strain level. The simple multiplicative factor can be used to relate the current temperature properties with the properties at the reference temperature. Graphically, it corresponds to the curve shift on the log time scale. Regarding the temperature, two methods are proposed to combine the shift factor and the ageing temperature: the Williams-Landel-Ferry (WLF) equations, and the Arrhenius law. Both methods are included in the Swedish standard ISO 113465 to estimate the lifetime and maximum operational temperature for rubber, or vulcanized and thermoplastic, materials. Recently, thermal ageing and Arrhenius methodology have been used in the cable lifetime prediction6,7, heating pipes8, and polymer glue PMMA4. An extension of the Arrhenius law is the Eyring law that takes into account other ageing factors (e.g., voltage, pressure, etc.)9. Alternatively, other studies propose and verify simple linear models for a description of ageing (e.g., biosensor ageing10). Although the Arrhenius method is commonly used, there is discussion on its relevance in the lifetime prediction of every material. Hence, the method must be used with care, especially in terms of initial assumptions and experimental conditions6.
Similar to most polymers, the polyester fabrics used in the current research exhibit two distinct transition phases defined by the melting temperature (Tm) and the glass transition temperature (Tg). The melting temperature (Tm) is the temperature when a material changes from its solid state to the liquid one, and the glass transition temperature (Tg) is the boundary between the glass and rubber states11. According to manufacturer's data, the AF9032 fabric is made from polyester threads (Tg = 100−180 °C12, Tm = 250−290 °C13) and PVC coating (Tg = 80−87 °C14,15, Tm = 160−260 °C16). The ageing temperature Tα should be selected below Tg. During sunny days, the temperature on the top surface of a hanging roof may even reach 90 °C; thus, two ageing temperatures (80 °C and 90 °C) are tested here. These temperatures are below the thread Tg and close to the coating Tg.
The performance of the accelerated ageing protocol on technical fabrics is presented in the current work. Artificial thermal ageing is used to predict changes of the material properties. The article illustrates appropriate laboratory testing routines and a way to extrapolate relatively short-term experimental results.
1. Accelerated thermal ageing experiments on technical fabric
2. Data preparation
3. Parameter identification of material models
4. Arrhenius extrapolation
NOTE: The Arrhenius law is based on an empirical observation that ambient temperature increase results in acceleration of a number of chemical reactions that may speed up the ageing process as well. The complete mathematical representation of the Arrhenius chemical reaction concept can be found elsewhere11,26. The Arrhenius law in a simplified form is called "the 10 degree rule"27. According to this rule, a surrounding temperature increase of about 10 °C theoretically doubles the rate of the aging process. Hence, the reaction rate f is defined as follows17:
where ΔT = T – Tref is the difference between the ageing temperature T and the service temperature Tref of a material.
5. Data representation
Figure 2 juxtaposes the stress-strain curves for the warp and fill directions of AF9032 fabric obtained at different ageing times, in the 80 °C temperature level for a strain rate of 0.001 s-1. The difference between the 1 h ageing period (reference test) and the rest of the ageing periods is clear. The ageing time does not seem to substantially affect the material response in the warp direction, as the stress–strain curves are highly repetitive, showing no important differences in the ultimate tensile strength (UTS). It stays contrary to the behavior observed for the fill direction, where the UTS is much lower in the case of artificially aged samples than in the unaged case. Moreover, the achieved stress–strain curves detect divergent trajectories when the strains exceed 0.06.
The results obtained at different temperature levels and the extrapolation of the results for a higher temperature level presented in one graph compress all the data concerning a particular parameter. If the curves representing evolution of the parameters in both temperatures over the ageing time fall into the same trajectory, it confirms that the obtained parameter values actually follow the Arrhenius equation. If the lines are parallel, it suggests that additional experiments are necessary to explain the observed phenomenon or that some correction coefficients should be introduced to the results at one temperature level to make results in both temperatures fall into one path.
Variation images of the PVC coating stiffness and fill ultimate strains over the ageing time are in Figure 3 and Figure 4, respectively. The experimental results at two temperature levels of 80 °C and 90 °C are presented in Figure 3a and Figure 4a. It was proven before24 that the first linear part of the experimental stress-strain curve of a simple tensile test (denoted here as EF0) corresponds to the stiffness of technical fabric covering made of PVC. The results obtained at the temperature level of 90 °C extrapolated in hours to 12 weeks (2000 hours) and recalculated to "real" years according to the Arrhenius simplified relation are drawn in the same graph in order to compare the results (Figure 3b and Figure 4b).
The evolution of stiffness of the PVC coating over ageing time is almost linear at temperature levels of 80 °C and 90 °C with a constant increment in time, much greater in 90 °C than in 80 °C. This phenomenon suggests that PVC subjected to relatively high temperature undergoes changes resulting in the growth of its stiffness, as an effect of accelerated ageing. This behavior is possibly caused by physical ageing, specific for polymer materials, like technical fabrics. The ultimate tensile strains values (εult) exhibit a decreasing trend over ageing time in the fill direction and temperature levels of 80 °C and 90 °C. For the warp direction, the UTS values show no significant variation over ageing time. On the other hand, the ultimate tensile strains (εult) decrease in 80 °C and grow in 90 °C.
The same procedure has been used to address the Bodner–Partom model parameters. Here, the hardening parameter m1 in the warp direction and the viscosity parameter n in the fill direction are presented in Figure 5 and Figure 6, respectively.
The final research results are sets of linear functions, which represent certain material parameters or fabric properties over ageing time. Following this, all the basic mechanical properties (stiffness, yield limit, ultimate tensile stress and strain) and Bodner–Partom model parameters (n, D0, D1, R0, R1, m1, m2) were identified, put together at temperature levels of 80 °C and 90 °C and analyzed by means of the Arrhenius extrapolation methodology29.
The approximation lines corresponding to the parameter trends throughout ageing time collapse to one line for UTS, εult, m1 in the case of fill direction. Other parameter approximation lines in ageing time exhibit parallel tendencies without collapse to one line.
In the case of warp direction, only the approximation lines of UTS, EW2 and m1 collapse into one line, while other parameters show neither clear tendency nor parallel character of the curves. All the parameter values in ageing time for the fill direction express parallel trends or collapse to one line. Thus, the approach of the Arrhenius simplified equation, shown in the present article, has been proven for that direction only.
Figure 1: Schematic representation of the piecewise linear model for AF9032 fabric. Please click here to view a larger version of this figure.
Figure 2: The impact in thermal ageing case at 80 °C on the stress–strain response in the warp and fill directions of AF9032 fabric, for the strain rate of 0.01 s-1. Please click here to view a larger version of this figure.
Figure 3: Stiffness of the PVC coating at different ageing times in hours (red and blue lines) (a); stiffness values obtained at 90 °C recalculated to time in years according to the Arrhenius simplified equation (blue lines) for the fill direction of AF9032 fabric (b). Please click here to view a larger version of this figure.
Figure 4: Ultimate strains of the PVC coating at different ageing times in (red and blue lines), experiments (a); ultimate strains values obtained at 90 °C recalculated to time in years according to the Arrhenius simplified equation (blue lines) in the fill direction of AF9032 (b). Please click here to view a larger version of this figure.
Figure 5: Bodner–Partom coefficient of isotropic hardening m1 at different ageing times in hours (red and blue lines), experiments (a); coefficient of isotropic hardening m1 values obtained at 90 °C recalculated to time in years according to the Arrhenius simplified equation (blue lines) in the warp direction of AF9032 (b). Please click here to view a larger version of this figure.
Figure 6: Bodner–Partom strain rate sensitivity parameter n at different ageing times in hours (red and blue lines) experiments (a); and strain rate sensitivity parameter n values obtained for 90 °C recalculated to time in years according to the Arrhenius simplified equation (blue lines) for the fill direction of the AF9032 (b). Please click here to view a larger version of this figure.
Inelastic strain rate | ![]() |
Cumulated inelastic strain rate | ![]() |
Additional equations | ![]() |
Isotropic hardening | ![]() |
Kinematic hardening | ![]() |
Material parameters | ![]() |
Table 1: Basis Bodner–Partom equations in uniaxial state.
Variable | Tref | T | ΔT | f | Calculation example for 4 weeks of therml ageing |
Formulation | – | – | T-Tref | 2(ΔT/10) | f*4/52 |
Unit | °C | °C | °C | [-] | [years] |
Resultados | 8 | 80 | 72 | 147 | 11.3 |
90 | 82 | 294 | 22.6 |
Table 2: Example calculations of the Arrhenius simplified equation.
Laboratory ageing time [weeks] | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | ||
Time according to Arrhenius [years] | 80 °C | 2.8 | (5.7) | 8.5 | (11.3) | 14.1 | (17.0) | 19.8 | (22.6) | 25.4 | (28.3) | 31.1 | (33.9) | |
90 °C | (5.7) | (11.3) | (17.0) | (22.6) | (28.3) | (33.9) | 39.6 | 45.2 | 50.9 | 56.6 | 62.2 | 67.9 | ||
( ) marks the ageing tests performed in the present study and used to identify parameters. |
Table 3: Extrapolation of ageing time recalculated with the Arrhenius equation at temperature levels of 80 °C and 90 °C.
This article incudes a detailed experimental protocol to simulate the laboratory accelerated experiments on polyester reinforced and PVC coated fabrics for civil engineering applications. The protocol describes the case of artificial thermal ageing only by the means of raising the ambient temperature. This is an obvious simplification of real weather conditions, as UV radiation and water influence play an additional role in material service ageing.
Generally, the conditions of accelerated ageing performed in the laboratory should be as close as possible to the true weather and service conditions of a tested material. For instance, materials used in aerospace or marine structures undergo hydrothermal ageing, when humidity and temperature primarily act upon the material durability30,31. Regarding the battery degradation level, two ageing factors are usually monitored: temperature and state of charge9. In electrical cable insulations, apart from temperature, different voltage and stress levels must be included, while performing accelerated laboratory ageing14. However, the thermal type of accelerated ageing is the most common one, thus it is easy to reflect it in the laboratory. The calibration of the obtained results with outdoor data of the service aged material creates a reliable tool to predict the future behavior of textile fabrics or other materials.
A drawback of the presented method is the number of samples tested. Because uniaxial tensile experiments with three different constant rates are conducted, two samples were tested in each material direction for each strain rate case. As the analysis has to cover both warp and fill directions of the fabric, tested at two temperature levels, with at least 5 ageing time intervals, a large number of samples is required. Fortunately, the results are very repetitive, displaying very similar tendencies; therefore, the obtained results are considered reliable even if two samples are tested in the same conditions only.
The procedure for conducting the uniaxial tensile tests with constant strain rates and with the video extensometer data registration is presented thoroughly. The European national standard1 does not require the use of an extensometer for testing technical fabrics. Therefore, the proposed protocol is more precise than the standard requirements; thus, the obtained data are more accurate.
The proposed protocol makes it possible to determine material parameters for fabrics in the future; therefore, it is a suitable tool in design. The method has been successfully validated during the research of the hanging roof of the Forest Opera in Sopot. The samples of the polyester reinforced, and PVC coated fabrics were collected from the roof after 20 years of operation. Samples of unaged material were also obtained from the same manufacturer. Both types of samples proceeded through the same laboratory experiments and parameter identification routines. Results were represented by the parameters of the piecewise linear and Bodner–Partom models. The trends observed in mechanical behavior of material from the Forest Opera resemble trends found in the case of thermal ageing. Thus, the results presented here have been confirmed by the tests of a fabric after 20 years of service28. Nevertheless, for other kinds of technical fabrics, some modifications of the proposed method may be required, thus the experimental protocol should be properly adjusted.
The authors have nothing to disclose.
The publication of this work was supported by the Faculty of Civil and Environmental Engineering at Gdansk University of Technology.
AF 9032 technical fabric | Shelter-Rite Seaman Corporation | ||
knife of scisors | |||
marker | pernament | ||
ruler | |||
Sigma Plot | Systat Software Inc. | v. 12.5 | |
Testing machine Z020 | Zwick Roell | BT1-FR020TN.A50 | |
TestXpert II program | Zwick Roell | v. 3.50 | |
Thermal chamber | Eurotherm Controls | 2408 | |
tubular spanner | 13 mm | ||
Video extensometer | Zwick Roell | BTC-EXVIDEO.PAC.3.2.EN | Instead of video extensometer, a mechanical one can be used |
VideoXtens | Zwick Roell | 5.28.0.0 SP2 |