Acta Polytechnica https://doi.org/10.14311/AP.2024.64.0487 Acta Polytechnica 64(6):487–500, 2024 © 2024 The Author(s). Licensed under a CC-BY 4.0 licence Published by the Czech Technical University in Prague ASSESSMENT OF THE EFFECTS OF UV-A EXPOSURE ON THE MECHANICAL STRENGTH OF OFFSHORE MOORING MULTIFILAMENTS Daniel Magalhães da Cruza,∗, Felipe Tempel Stumpfa, Jakson Manfredini Vassolera, Carlos Eduardo Marcos Guilhermeb a Federal University of Rio Grande do Sul (UFRGS), Graduate Program in Mechanical Engineering (PROMEC), Applied Mechanics Group (GMAp), 90050-170 Porto Alegre/RS, Brazil b Federal University of Rio Grande (FURG), Engineering School (EE), Stress Analysis Laboratory Policab, 96203-000 Rio Grande/RS, Brazil ∗ corresponding author: daniel.cruz@ufrgs.br Abstract. The offshore industry faces significant challenges in the dynamic energy and maritime domain, necessitating robust engineering solutions for mooring systems. This study investigates the impact of ultraviolet radiation A (UV-A) on the mechanical strength of high-strength multifilaments, crucial for offshore mooring. Five fibre types: Aramid, High-modulus polyethylene (HMPE), Liquid crystal polymers (LCP), Polyamide and Polyester, are exposed to UV-A for up to 28 days. Initial mechanical characterisation provides baseline data, while subsequent tests reveal varying degrees of degradation. Polyamide and polyester exhibit superior stability, while Aramid and HMPE show restrained degradation. LCP experiences substantial degradation. Mathematical modelling reveals distinct degradation patterns, emphasising the need for comprehensive understanding in ensuring the safety and efficiency of offshore operations. There are indications that degradation by ultraviolet exposure for Aramid, HMPE, polyamide, and polyester fibres, restricts the constitutive behaviour in terms of strength and extension, but without changing the shape of the curve. These findings provide valuable insights for the offshore industry and guidance future research and development efforts. Keywords: Tensile testing, mechanical characterisation, ultraviolet incidence, degradation, synthetic fibres, yarn break load, curve fitting modelling. 1. Introduction The offshore industry can be seen as one of the most challenging and dynamic sectors within the energy and maritime domain. With the continuous develop- ment of new technologies and techniques, operations in deep and ultra-deep waters are becoming increas- ingly feasible. However, the extreme environment re- quires robust engineering solutions, including reliable mooring systems that are pivotal for the safety and stability of offshore structures (especially for Floating Offshore Wind Turbines). A fundamental component of a mooring system is high strength multifilaments, which play a critical role in the station-keeping of floating structures that have to withstand adverse environmental conditions. In this context, offshore mooring systems have evolved considerably in recent decades, with one of the most notable changes being the transition from traditional steel wire cables to high-tenacity synthetic polymeric fibres. This revolutionary shift, initially proposed by Del Vecchio in the 1990s [1], introduced taut-leg mooring systems with synthetic fibres, mark- ing a significant innovation over conventional steel catenaries. Synthetic ropes offer several desirable prop- erties, including low weight, high strength, flexibility, low friction coefficient, and resistance to aggressive marine conditions [2–4]. Today, these polymeric mul- tifilaments, mainly polyester, are widely adopted in mooring systems, solidifying their role as an essential material for the offshore industry [5–12]. This technological novelty and the inherent char- acteristics of synthetic fibres have led to various ad- vancements in commercial, professional, and academic domains. These materials are extensively examined through analytical [13–17], numerical [18–26], and ex- perimental [4, 10, 12, 27–37] approaches due to their critical significance for the integrity and efficiency of offshore operations. Many studies have addressed the use of fibres for offshore mooring, covering a wide range of loading conditions, environmental settings, fibre types, stiffness analysis, and physical properties. A fundamental challenge in the offshore industry is the constant exposure to adverse environmental condi- tions, with ultraviolet (UV) radiation being a notice- able concern. These rays, particularly UV-A radiation, can significantly affect polymeric materials, including multifilaments used in mooring systems. A prolonged exposure to UV-A rays can lead to the degradation and weakening of polymers, thereby compromising their mechanical strength [38–40]. This potential degrada- tion threatens the integrity of mooring systems and, consequently, the safety of offshore operations. 487 https://doi.org/10.14311/AP.2024.64.0487 https://creativecommons.org/licenses/by/4.0/ https://www.cvut.cz/en D. M. da Cruz, F. T. Stumpf, J. M. Vassoler, C. E. M. Guilherme Acta Polytechnica Property Aramid HMPE LCP Polyamide Polyester Density [g cm−3] 1.44 0.97 1.40 1.14 1.38 Melting point [°C] 500 150 400 218 258 Glass transition [°C] 145 50 120 60 75 Modulus [N tex−1] 60 100 54 7 11 Tenacity [N tex−1] 2 3.5 2.29 0.84 0.82 Break strain [%] ∼4 ∼3.5 ∼4 18∼21 11∼13 Moisture [%] 1∼7 0 <0.1 5 <1 Table 1. General properties of high-performance synthetic fibres. Numerous studies have investigated the mechanical strength of polymeric fibres under ideal laboratory conditions [4, 9, 12, 29, 32–36, 41]. However, only a few studies have explored the impact of UV ex- posure on the strength of synthetic fibres. Most of the studies related to UV exposure have focused on composite matrices [42–44], glass fibres [45–47], and plant-based fibres [48, 49]. To the author’s knowledge, very few studies have directly addressed UV exposure in the offshore sector. Therefore, there is an urgent need for a comprehensive analysis to evaluate the ef- fects of UV-A radiation on the mechanical strength of multifilaments specifically designed for offshore moor- ing, with the aim of providing valuable insights for the industry. At the same time, it allows the charac- terisation of virgin fibres for each material, which can be compared with fibres from different sectors, such as surgical sutures [50–52], concrete and asphalt addi- tives [53, 54], mountaineering or rescue ropes [55, 56], and fishing lines [57, 58]. This article aims to investigate how exposure to UV-A affects the mechanical tensile strength and rup- ture characteristics of multifilaments used for making mooring ropes. The study is an exploratory one and uses custom-built UV exposure equipment. The re- search involves testing five types of fibres: Aramid, High Modulus Polyethylene (HMPE), Liquid Crystal Polymer (LCP), polyamide, and polyester. The UV exposure times range from one to twenty-eight days, with the filaments being removed every seven days for testing. This experimental study aims to deepen our un- derstanding of the mechanical degradation of moor- ing materials caused by exposure to UV-A radiation. Additionally, it seeks to investigate the impact of ul- traviolet radiation on isolated synthetic fibres. To complement the experimental findings, mathematical models are used to simulate and predict the behaviour of the materials being studied. These models serve as powerful tools to analyse complex phenomena by pro- viding a quantitative framework for interpreting data, identifying trends, and estimating parameters that describe the material behaviour. Their application contributes to a deeper understanding of the degra- dation processes and offers insights that can guide further research development and help with material selection for specific applications. The results of the study may act as a catalyst for further research in related areas. 2. Materials and methods 2.1. Materials All fibres investigated in the study are specific for manufacturing offshore mooring ropes and/or other marine applications. There was no authorisation to disclose the fibre codes or their manufacturers. In any case, it is important to highlight their main characteristics in general, as well as other prominent applications. Table 1, provides some information on the mechanical and physical properties of synthetic fibres in general as reported in the literature [33, 59, 60]. 2.1.1. Aramid Aramid fibres stand out due to their remarkable me- chanical properties. They are stronger than steel in terms of tensile strength. Furthermore, they ex- hibit good impact resistance while possessing a certain lightweight quality. This combination of strength, im- pact resistance, and lightness makes them ideal for applications such as bulletproof vests [61, 62]. Aramid has been used in mooring systems in the past, but its high cost compared to other fibres, and issues related to axial compression and abra- sion resistance hindered its continued use for mooring ropes [60, 63]. It is still used in other maritime ap- plications, particularly in lifting straps on ships and in applications where the fibre is exposed to high environmental temperatures. 2.1.2. High modulus polyethylene (HMPE) High-modulus polyethylene is renowned for its excep- tional tensile strength and lightness [3, 64, 65]. These fibres offer high specific tensile strength when com- pared to other typical materials, meaning they are strong for their weight. As shown in Table 1, their density is lower than that of water, giving them buoy- ancy and low moisture absorption. Their limitations are typically associated with higher temperatures and the creep phenomenon. There are studies in the literature that address the use of HMPE for mooring systems of Mobile Off- shore Drilling Units (MODU) [64, 65]. Additionally, there are studies focused on fibres designated as “Low 488 vol. 64 no. 6/2024 Assessment of the effects of UV-A exposure on the mechanical strength Creep” [37, 66]. Considering an entire mooring sys- tem made of HMPE, with its low elongation, would allow for even greater depths without compromising the platform offset. It is one of the most promising fibres, albeit with a higher specific cost [60]. Other applications of HMPE fibres include the manufacture of ballistic vests [67], mesh for lifting slings in load handling operations [68], among others. 2.1.3. Liquid crystal polymer (LCP) Liquid crystal polymer fibres are recognized for their high strength and rigidity. They can maintain their dimensional shape over a wide range of temperatures, making them ideal for applications requiring dimen- sional stability. These fibres can withstand high tem- peratures, making them valuable in heat-resistant applications. Their low thermal expansion is also im- portant, ensuring that the fibres maintain their struc- tural integrity under temperature variations, making LCP a strategic choice for components subjected to significant temperature changes [69]. LCP fibres are frequently used in applications where extended low creep elongation and/or abrasion resis- tance is needed for rope and cordage. Examples in- clude mooring tethers, tension ropes, actuator cables, for example, as used in robotics, and other specialty rope/cordage applications [70, 71]. 2.1.4. Polyamide Polyamide (PA), is renowned for its tenacity, elastic- ity, and wear resistance. It exhibits strong mechani- cal properties, including high abrasion resistance. As shown in Table 1, it has the highest elongation among the presented fibres. Due to its flexibility, polyamide is frequently used in products requiring elasticity, such as sportswear and stockings [72]. Polyamide fibre can absorb a high number of dy- namic loads, precisely because of its high elasticity, which is why it is also used in climbing, operation, and rescue ropes [73]. Its ability to absorb impacts (dynamic load) is discussed in the literature [32, 74]. In offshore mooring applications, polyamide stands out for Floating Offshore Wind Turbine (FOWT) sys- tems, as it effectively addresses the challenges posed by wave mechanics, tidal movements, winds, and waves [59, 75]. 2.1.5. Polyester Polyester (polyethylene terephthalate, PET) is renowned for its versatility and a wide range of desir- able properties. Its low cost and ease of processing also contribute to its extensive application across various sectors [60]. It is used in the textile industry for clothing, house- hold fabrics, curtains, among others, because of its durability, wear resistance, and ability to resist wrin- kling and fading [76]. In technical applications related to engineering, it is used in straps, various types of safety belts, and belts. In the offshore industry, it is the most commonly used fibre in mooring systems, with a considerable body of literature on its use in this application [5–12, 15, 18– 20, 29, 35, 36]. It is also interesting to highlight how the fibre has evolved over the years; decades ago, the linear tenacity of polyester was around 0.60 N tex−1, whereas today, this linear tenacity value has reached 0.85 N tex−1. 2.2. Ultraviolet exposure In the literature, several standards address UV expo- sure under related conditions, but there is no specific standard for ultraviolet exposure in high-performance synthetic fibres for the offshore industry. ASTM G155 [77] focuses on exposing non-metallic materials to UV radiation using xenon arc lamps that simu- late solar exposure. ASTM D4329 [78] tests the UV degradation resistance of plastics using fluorescent UV lamps, and ISO 4892 [79] provides broader methods for exposure to laboratory light sources, including UV light, for testing plastics. There are other spe- cific standards aimed at textile fibres, such as ASTM D5035 [80], which may be relevant for assessing the UV resistance of textile fibres. Due to the lack of a consolidated method for UV exposure of high-performance synthetic fibres for the offshore industry, a cost-effective custom equipment was designed, taking into account the overview from the mentioned standards. Geometrically, it has a rect- angular shape and is coated with aluminum foil (for light reflection). It features four ultraviolet lamps arranged on the top (lid) and four on the bottom. The samples are exposed at the geometric centre of the height, with a distance of 32 centimetres between the samples and the upper emission points and the same distance for the lower emission points. Figure 1 shows the equipment used. Regarding the lamps, UV-A ultraviolet lamps were used, which are particularly useful for comparing dif- ferent types of polymers. UV-A lamps have no wave- lengths shorter 295 nm and do not degrade materials as quickly as UV-B lamps. The specification of the lamp used is the “UVA-340” from Q-Lab [81], which provides the best possible simulation of sunlight in the critical short-wavelength region between 295–365 nm, with an emission peak at 340 nm and irradiance of 0.68–0.89 W m−2 nm−1, Figure 2 [81]. The sample groups for each fibre in relation to UV exposure time contain 10 specimens each and are shown in Table 2. The groups indicated as “0 days” will serve as reference data for mechanical testing and refer to the virgin condition (without UV exposure). In the case of HMPE and polyamide fibres, they have a smaller number of exposure groups due to material quantity limitations. The solution was to maintain a total exposure period of 28 days while sacrificing intermediate times (7 and 21 days). 489 D. M. da Cruz, F. T. Stumpf, J. M. Vassoler, C. E. M. Guilherme Acta Polytechnica Figure 1. Low-cost equipment for UV exposure for fibres. Figure 2. Wavelength of UVA-340 lamp from Q-Lab. 2.3. Mechanical characterisation The initial mechanical characterisation is performed on all fibres for linear density, tensile strength, and linear tenacity, with data constituting the reference baseline, conducted for virgin conditions without UV exposure. The remaining mechanical characterisation tests refer to the tensile tests performed on specimens after UV degradation. The linear density testing procedure is standardised by ASTM D1577 [82] and is performed according to ISO 139 [83]. The linear density test is conducted on 10 samples without UV exposure, with a length of 1 000 millimetres and a stabilisation time on a pre- cision scale of 9 minutes. The results are reported in terms of mass per unit length, with the standard unit being tex, representing the weight (in grams) for 1 000 metres of multifilament. The tensile test is standardised by ISO 2062 [84] and is performed according to ISO 139 [83]. This test, which leads to the fibres’ Yarn Break Load (YBL), requires an effective length of 500 millimetres, uniform Aramid HMPE LCP PA PET U V [d ay ] 0 0 0 0 0 7 - 7 - 7 14 14 14 14 14 21 - 21 - 21 28 28 28 28 28 Table 2. Ultraviolet exposure times for each fibre. Figure 3. Instron 3365 Equipment for Yarn Break Load tests. twist conditions of 60 turns per metre, with a con- stant extension rate of 250 millimetres per minute. The test is performed using Instron 3365 universal testing machine (Figure 3), capturing the force and extension data during the tensile test. This test will be performed for all conditions specified in Table 2. 490 vol. 64 no. 6/2024 Assessment of the effects of UV-A exposure on the mechanical strength Model Non-Linear Form Linear Form Linear - y = B + A · x Power y = B · xA ln y = ln B + A · ln x Exponential y = B · eA·x ln y = ln B + A · x Reciprocal y = (B + A · x)−1 y−1 = B + A · x Michaelis-Menten y = A · x · (B + x)−1 y−1 = A−1 + B · (A · x)−1 Table 3. Models used and their linearisation. Property Aramid HMPE LCP PA PET Linear density [tex] 344.80 185.40 178.50 280.10 339.60 Break strength [N] 631.53 569.98 416.49 198.07 261.15 Stress [MPa] 2 655.78 2 982.10 3 266.56 806.12 1 061.22 Break extension [mm] 20.36 17.01 21.03 87.67 67.90 Break strain [%] 4.07 3.40 4.21 17.53 13.58 Linear tenacity [N tex−1] 1.832 3.074 2.333 0.707 0.769 Table 4. Mechanical results of initial fibre characterisation (without UV exposure). The breaking force value can also be expressed in terms of stress. Due to the inherent difficulty in accu- rately determining the cross-section of a set of multifil- aments, the stress calculation (σ) is based on rupture force (F ), linear density (ρL), and material density or specific mass (ρ), as illustrated in Equation (1): σ [MPa] = F [N] × ρ [ g cm−3] ρL [g m−1] . (1) Densities represent the intrinsic physical properties of the material, and the density values indicated in Table 1 are used for this purpose. 2.4. Curve fitting In the evaluation of the experimental data, especially when characterising a quantity in relation to varying conditions – specifically, stress and/or strain in this case – associated with the increase in time under UV exposure, there is a natural inclination to pursue mathematical modelling of the behaviour. In this study, this type of determination can be a comparative criterion among different types of fibres under UV exposure. This mathematical parameterisation can be per- formed simply and effectively using the Least Squares Method (LSM), combined with the mathematical tech- nique of model linearisation. The LSM identifies the parameters of a model that minimise the sum of the squares of the differences between the observed values and those predicted by the model [85, 86]. For this study, we propose working with the following models: linear, power, exponential, reciprocal, and Michaelis- Menten, as listed in Table 3 along with their linearised expressions, using an open-source code available in the literature [87]. For linear fits, the criterion demonstrating the qual- ity of the fit is the coefficient of determination (R2), which ranges from 0 to 1, the closer it is to 1, the better the fit. The direct mathematical definition for the coefficient of determination is obtained through Equation (2): R2 = 1 − ∑ (yi − y′ i) 2∑ (yi − ȳ)2 , (2) where yi are the observed values, y′ i are the predicted values, ȳ is the mean of the yi values. 3. Results and discussion The linear density and initial mechanical results in terms of break strength, stress, break extension, break strain, and linear tenacity were obtained according to [82–84] and are presented in Table 4, for all the fibres under investigation. The values presented in Table 4 correspond to the initial condition (0 days of ultraviolet exposure). The overall results of different ultraviolet exposure conditions are presented in Table 5, including infor- mation on strength and extension for the YBL test. The values presented are the averages corresponding to the samples for each condition. Due to quantitative sample restrictions, the groups of 7 and 21 days of ultraviolet exposure were not performed for HMPE and polyamide. In the direct observation of the presented results, the LCP fibre values stand out. As the exposure times to ultraviolet radiation increase, the mechanical properties in the rupture test decrease substantially. Figures 4 and 5 show the evolution of the rupture force and extension along UV exposure time, respectively. When observing the obtained graphs, especially the rupture force versus ultraviolet exposure, it can be noted that polyamide and polyester samples exhibit 491 D. M. da Cruz, F. T. Stumpf, J. M. Vassoler, C. E. M. Guilherme Acta Polytechnica Property 0 days 7 days 14 days 21 days 28 days A ra m id Force [N] 631.53 603.31 559.21 516.69 503.60 Stress [MPa] 2 655.78 2 537.11 2 351.68 2 172.87 2 117.81 Extension [mm] 20.36 20.38 19.13 18.13 17.61 Strain [%] 4.07 4.08 3.83 3.63 3.52 H M PE Force [N] 569.98 - 529.83 - 499.19 Stress [MPa] 2 982.10 - 2 772.03 - 2 611.72 Extension [mm] 17.01 - 15.43 - 14.96 Strain [%] 3.40 - 3.09 - 2.99 LC P Force [N] 416.49 151.78 93.15 72.84 57.24 Stress [MPa] 3 266.56 1 190.40 730.55 571.31 448.97 Extension [mm] 21.03 10.97 7.84 6.26 5.22 Strain [%] 4.21 2.19 1.57 1.25 1.04 PA Force [N] 198.07 - 196.65 - 196.38 Stress [MPa] 806.12 - 800.35 - 799.26 Extension [mm] 87.67 - 84.36 - 85.12 Strain [%] 17.53 - 16.87 - 17.02 PE T Force [N] 261.15 248.13 251.72 249.94 242.55 Stress [MPa] 1 061.22 1 008.32 1 022.88 1 015.67 985.63 Extension [mm] 67.90 65.51 66.63 67.05 66.68 Strain [%] 13.58 13.10 13.33 13.41 13.34 Table 5. Mechanical results of rupture under ultraviolet incidence for all fibres. Figure 4. Break strength degradation due to ultravi- olet exposure for all fibres. the best stability against UV incidence. They show a decrease in mechanical behaviour but in a very restrained, almost minimal manner. On the contrary, for Aramid and HMPE samples, there was a more significant decrease in mechanical strength as compared to polyamide and polyester. For these materials, Aramid and HMPE, rupture elon- gation remain relatively constant even with the in- creased duration of UV exposure. Concerning rupture strength, the 28-day condition (maximum UV expo- sure in the study) represents a reduction of approxi- mately 20 % from the virgin rupture value for Aramid and 13 % for HMPE. Figure 5. Break extension degradation due to ultra- violet exposure for all fibres. The LCP is the material whose mechanical perfor- mance degrades the most under UV exposure. The same decrease in rupture force is reflected in rupture elongation with the increased duration of UV exposure for LCP fibres. After 28 days of UV exposure, the residual rupture value is 86 % lower than the initial condition (without UV exposure). Fibres exhibit varying orders of magnitude in terms of both rupture strength and rupture elongation. Nor- malising the results allows a comparison between dif- ferent fibres. The normalisation process involves di- viding all results obtained for different UV exposure durations of a particular fibre by its virgin rupture 492 vol. 64 no. 6/2024 Assessment of the effects of UV-A exposure on the mechanical strength Material Normalised Property 0 days 7 days 14 days 21 days 28 days Aramid Force [N N−1] 1.000 0.955 0.885 0.818 0.797 Extension [mm mm−1] 1.000 1.001 0.940 0.891 0.865 HMPE Force [N N−1] 1.000 - 0.930 - 0.876 Extension [mm mm−1] 1.000 - 0.907 - 0.880 LCP Force [N N−1] 1.000 0.364 0.224 0.175 0.137 Extension [mm mm−1] 1.000 0.522 0.373 0.298 0.248 Polyamide Force [N N−1] 1.000 - 0.993 - 0.991 Extension [mm mm−1] 1.000 - 0.962 - 0.971 Polyester Force [N N−1] 1.000 0.950 0.964 0.957 0.929 Extension [mm mm−1] 1.000 0.965 0.981 0.987 0.982 Table 6. Dimensionless mechanical rupture results under ultraviolet incidence for all fibres. Figure 6. Dimensionless break strength degradation due to ultraviolet exposure for all fibres. value (i.e. the rupture value without ultraviolet expo- sure). Consequently, all curves originate from a uni- tary value, and represent the evolution of behaviour with UV exposure in proportion to the reference con- dition (0 days). The normalised data are presented in Table 6, and plotted in Figure 6 for break strenght and Figure 7 for break extension. It can be observed that polyester and polyamide, both in terms of strength and extension criteria, are the most stable fibres under ultraviolet radiation. HMPE and Aramid show a slightly higher degradation, but still in a mild manner. In the case of LCP, the mechanical behaviour changes abruptly; the fibre undergoes significant degradation due to the ultraviolet exposure in terms of rupture force and elongation. The values presented in Table 6, along with the gen- eral graphical behaviour in Figures 6 and 7, allow for a potential interpretation that UV exposure decreases the rupture force for each fibre, similarly to the reduc- tion in rupture elongation. Thus, it is possible that when plotting the ratio of force to extension, this value remains approximately constant even with an increase Figure 7. Dimensionless break extension degradation due to ultraviolet exposure for all fibres. Figure 8. Force/extension ratio at break due to ultraviolet exposure for all fibres. in the UV exposure time. It is noteworthy that this force-to-extension ratio gives a unit of N mm−1, but it does not represent a direct or equivalent stiffness of the fibre, as these materials are viscoelastic and do not exhibit linearity in the stress-strain curve. Hence, Figure 8 is proposed, illustrating the ratio of rupture- 493 D. M. da Cruz, F. T. Stumpf, J. M. Vassoler, C. E. M. Guilherme Acta Polytechnica Model Parameter Aramid HMPE LCP Polyamide Polyester Linear A -4.89 -2.53 -11.39 -0.06 -0.51 B 631.36 568.39 317.78 197.87 257.78 R2 0.9768 0.9940 0.7188 0.8658 0.6814 Power A −1.13 × 10−2 −7.20 × 10−3 −1.13 × 10−1 −5.46 × 10−4 −3.70 × 10−3 B 560.05 525.16 118.19 196.83 250.53 R2 0.5487 0.8310 0.8510 0.9884 0.7586 Exponential A −8.70 × 10−3 −4.70 × 10−3 −6.72 × 10−2 −3.06 × 10−4 −2.00 × 10−3 B 633.21 568.70 306.57 197.87 257.77 R2 0.9786 0.9966 0.8974 0.8662 0.6830 Reciprocal A 1.55 × 10−5 8.89 × 10−6 5.33 × 10−4 1.55 × 10−6 7.97 × 10−6 B 1.60 × 10−3 1.80 × 10−3 2.70 × 10−3 5.10 × 10−3 3.90 × 10−3 R2 0.9791 0.9984 0.9965 0.8666 0.6843 Michaelis-Menten A 542.97 514.05 82.44 196.51 248.04 B −1.40 × 10−6 −9.81 × 10−7 −8.02 × 10−6 −7.84 × 10−8 −5.02 × 10−7 R2 0.4459 0.7835 0.5431 0.9778 0.7202 Table 7. Results for the mathematical models for all fibres. force to rupture-elongation [N mm−1] for each of the fibres over the course of the UV exposure time. As observed in Figure 8, with the exception of LCP, all other fibres indeed maintain an approximately con- stant force/extension ratio even with increasing UV exposure time. This implies that the degradation of mechanical rupture behaviour due to ultraviolet expo- sure is linear in relation to the constitutive behaviour of the material. In other words, for the studied dura- tions, it is evident that longer exposure to ultraviolet light leads to greater mechanical degradation. How- ever, Figure 8 demonstrates that, for most fibres, this degradation occurs simultaneously and similarly for both the force and extension. In this context, consid- ering a characteristic stiffness of the material (concept of derivative along the stress-strain curve), it is as if the degradation restricts the continuation of the test on the curve, anticipating the moment of rupture compared to the condition without UV exposure. The experimental results presented can be mathe- matically modelled as described in Section 2.4, both for the force and extension data. In this case, the mathematical modelling study is conducted only for the force data. Applying the methodology described earlier, the results are obtained and shown in Ta- ble 7 in terms of coefficients for each model and their respective coefficients of determination (R2). It is noteworthy that for all expressions/models, y refers to the force value in Newton, and x refers to the exposure time in day. The results pertaining to the coefficients of each model have been obtained. It is noteworthy that in Table 7, the best model for each fibre (having the high- est coefficient of determination, R2) is highlighted: in red for aramid, in green for HMPE, in blue for LCP, in magenta for polyamide, and in cyan for polyester. For Aramid, HMPE, and LCP fibres, the reciprocal model was the one that best fit the data within the range Figure 9. Reciprocal mathematical model for Aramid, force versus UV exposure time. addressed in this study. Meanwhile, for polyamide and polyester fibres, the best fit is achieved with the power model for the studied interval. For each fibre, the best-fitted equation can be high- lighted, along with the curve fitting of this model compared to the experimental data. Equation (3) and Figure 9 mathematically models the force versus UV exposure time for Aramid: y = 1 1.60 × 10−3 + 1.55 × 10−5 · x . (3) Similarly, for HMPE fibres, Equation (4) and Fig- ure 10 are obtained, also in a reciprocal model: y = 1 1.80 × 10−3 + 8.89 × 10−6 · x . (4) For LCP fibres, the reciprocal model is still used for modelling, and Equation (5) and Figure 11 are presented: y = 1 2.70 × 10−3 + 5.33 × 10−4 · x . (5) 494 vol. 64 no. 6/2024 Assessment of the effects of UV-A exposure on the mechanical strength Figure 10. Reciprocal mathematical model for HMPE, force versus UV exposure time. Figure 11. Reciprocal mathematical model for LCP, force versus UV exposure time. What is observed in the parameterisations made for Aramid, HMPE, and LCP with reciprocal models is that the curve fits very well to the data and exhibits certain homogeneity, where the decrease in rupture force is a gradual influence of the ultraviolet exposure throughout the entire study period. Now, for the polyamide fibre, the best model was the power model, Equation (6) and Figure 12 depicts these results: y = 196.83 · x−5.46×10−4 . (6) Similarly, the results for polyester are addressed (also a power model), in Equation (7) and Figure 13: y = 250.53 · x−3.70×10−3 . (7) In general, the behaviour of curves in the power model is naturally different from the behaviour of curves in the reciprocal model. Note that the ho- mogeneity of the decrease in value is not present for polyamide (Figure 12) and polyester (Figure 13), un- like the models for Aramid, HMPE, and LCP fibres. Figure 12. Power mathematical model for polyamide, force versus UV exposure time. Figure 13. Power mathematical model for polyester, force versus UV exposure time. It is worth noting that in the previously presented experimental data, polyamide and polyester fibres already showed better stability under UV incidence. What the mathematical model allows us to infer is that these fibres degrade substantially upon initial exposure to UV, after which the force values tend to remain stable even with increasing exposure time, or show only a minimal decrease in the force values. However, it is important to highlight a caveat regarding polyester. The mathematical model for polyester fibres is significantly limited across all types of curves. In Table 7, it can be observed that the coefficients of determination (R2) are substantially lower for all polyester models when compared to other fibres. Therefore, for this fibre, the model may not be the most suitable for predicting polyester failure under UV exposure. Nevertheless, in comparative terms, the best R2 provides an approximate representation of the behaviour (Figure 13). For a visual representation, all the obtained models for predicting degradation in terms of breaking force versus UV exposure time are shown in Figure 14, in 495 D. M. da Cruz, F. T. Stumpf, J. M. Vassoler, C. E. M. Guilherme Acta Polytechnica Figure 14. Mathematical models for all fibres, force versus UV exposure time. the same graph scale for all fibres. This plot allows for a general visualisation of the behaviours, for example, helping to perceive that the instantaneous degrada- tion of polyamide and polyester on first UV exposure in relation to the condition without UV (shown in Fig- ures 12 and 13, respectively) occurs on a small force scale, which when compared in the general view of all fibres becomes negligible, indicating strong stability to UV exposure of these fibres. 4. Conclusion In conclusion, the mechanical characterisation of aramid, HMPE, LCP, polyamide, and polyester fibres under different durations of ultraviolet (UV) expo- sure provides insights into their behaviour and degra- dation mechanisms. The initial mechanical results offer a baseline for comparison, demonstrating the properties of each fibre mentioned in the material descriptions. Regarding the impact of UV exposure on these fibres over different time intervals, it is notable that LCP fibres exhibit a substantial decrease in mechanical properties as UV exposure duration increases, without showing any stabilisation for the times tested. For the most extended period of UV exposure (28 days), there is an 86 % reduction in the reference value (0 days of UV exposure). Polyamide and polyester stand out for their stability against UV incidence, showing minimal degradation in both the rupture force and elongation. Aramid and HMPE, while exhibiting a more significant de- crease in rupture force, maintain relatively constant rupture elongation even with prolonged UV exposure. The normalisation of results allows a direct compar- ison between the different fibres, including viewing the reduction percentiles compared to the reference condition. The concept of force/extension ratio illustrates that, except for LCP, this ratio remains approximately con- stant for all fibres with increasing UV exposure time. This implies a linear degradation in mechanical rup- ture behaviour concerning the constitutive behaviour of the materials, as if UV degradation restricted the material’s stress-strain curve without changing its shape. This is verified for Aramid, HMPE, polyamide, and polyester when making linear coefficients for the data of the force/extension ratio. For these materials, values of -0.085, -0.005, 0.002, and -0.007 were found, respectively, and these values are close to zero, indi- cating a constant trend without a significant angular coefficient. For LCP, there is a considerable value of -0.283. The curve fitting of force data further elucidates the degradation patterns. The reciprocal model fits well for Aramid, HMPE, and LCP, indicating a gradual effect of UV exposure on rupture force. In contrast, the power model is more suitable for polyamide and polyester, suggesting an initial substantial degrada- tion followed by stable or minimally decreasing force values, coinciding with the fibres most resistant to UV incidence. In summary, the experimental and modelling results collectively contribute to a comprehensive understand- ing of how different fibres respond to UV exposure. For future studies, these effects should be investigated for larger structural elements, such as legs and sub- ropes used to manufacture offshore mooring ropes. Because ultraviolet exposure can be understood as a surface phenomenon, which, for larger structural elements, increases both the incidence area and the resistant section simultaneously. Acknowledgements This study was financed in part by the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior – Brasil (CAPES) – Finance Code 001. Thanks also to the funding agencies: CNPq, Finep, and FAPERGS. References [1] C. J. M. Del Vecchio. 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Desenvolvimento de código aberto em Octave para ajustes de funções através de linearização e MMQ [In Portuguese; Open source development in Octave for function adjustments through linearization and OLS]. E&S Engineering and Science 13(1):1–14, 2024. https://doi.org/10.18607/ES20241316896 500 https://doi.org/10.1520/G0155-21 https://doi.org/10.1520/D4329-21 https://doi.org/10.1520/D5035-11R19 https://doi.org/10.1520/D1577-07R18 https://doi.org/10.18607/ES20241316896 Acta Polytechnica 64(6):487–500, 2024 1 Introduction 2 Materials and methods 2.1 Materials 2.1.1 Aramid 2.1.2 High modulus polyethylene (HMPE) 2.1.3 Liquid crystal polymer (LCP) 2.1.4 Polyamide 2.1.5 Polyester 2.2 Ultraviolet exposure 2.3 Mechanical characterisation 2.4 Curve fitting 3 Results and discussion 4 Conclusion Acknowledgements References