Abstract
Keywords
Introduction
The use of fiber-reinforced polymers (FRP) in structural applications has majorly been in the domain of structural retrofitting as they provide excellent tensile strength and confinement in case of columns. FRPs pose several benefits like light weight, high strength to weight ratio, ease of application, and reduction in retrofitting time. 1 Synthetic fibers like carbon and glass fibers are often used in FRPs employed for civil engineering works. 2 They are extremely strong, rigid, and resistant to chemical deterioration. 3 Additionally, synthetic fibers offer better thermal stability, 4 better toughness, and fatigue resistance as compared to the cellulose-based fibers counterparts. Although having good mechanical performance, synthetic fibers are not a sustainable approach towards using it on large scale. In applications where sustainability, weight reduction and cost effectiveness are of priority, natural fibers form a good alternative for the synthetic fibers. Natural fibers also reduce the wear on equipment processing them. 4
The mechanical performance of FRPs depends on the performance of fibers as well as the polymers. The epoxy serves as a host and matrix to the fibers which are the load carrying members in the composite. The function of epoxy is to protect the fiber and evenly disperse the load to the fibers. Epoxy polymers are widely used for manufacturing composites as epoxies provide a good resistance to most of chemical attacks, 5 and are also structurally good at transferring the loads to the fibers. Some epoxies gain strength in different stages. After 24 h of curing at room temperature, some thermosetting epoxies require a post curing process. Post-curing of epoxies is a process that involves subjecting epoxy materials to elevated temperatures after the initial curing process. This additional heat treatment enhances the mechanical, thermal, and chemical properties of the epoxy, ensuring it reaches its full potential. The specifics of post-curing, including temperature and duration, can vary based on the epoxy formulation and intended application. Post curing process improves strength, elevates the glass transition temperature, and reduces the residual stresses . 6 The post curing process needs to be optimized for achieving the best performance from the epoxy as under-curing may not achieve the complete cross linking of the polymers resulting in lower mechanical performance 7 and over curing may charr the composite disfiguring its aesthetic properties as well as degrading the mechanical performance. By under curing or over curing the polymerisation does not take place effectively, thus offering a lower mechanical strength of the composite. The post curing schedule for a certain epoxy system are generally provided by the supplier or manufacturer of the epoxy system. This schedule is however optimised for certain type of a synthetic fiber and may not be applicable to the fiber that we intend to work with, hence there is a need for determining the optimum post cure schedule for other fibers which are intended to be used in the structural application. Diego et al. 8 studied the post curing process of di glycidyl ether bisphenol acetate (DGEBA) and tri ethylene tetra amine (TETA) hardener and found that epoxy cured at moderate temperatures around 80o C to 90oC, which reduced the gel formation time, and a strong polymerisation was seen in the resin. Khalifa et al. 9 fabricated flax fiber composites and studied the effect of post curing temperature and time and the density of cellulose on the mechanical properties of the composite, it was ascertained that post curing is essential in increasing the cross linking and forming a strong polymer network. Seretis et al. 10 varied the post curing temperature and post curing time and developed a regression model for graphene nano platelet reinforced glass epoxy composite keeping the tensile strength and strain as response factor. This regression model was used to find the optimum temperature and time for post curing. Shubham et al. 11 studied the effect of post curing parameters of temperature and time on the inter laminar shear strength, aesthetics of the laminates was also given consideration and found that a post curing temperature of 140oC and post curing time of 6 h give a fairly good inter-laminar shear strength while retaining aesthetics. Andrew et al. 12 studied the effect of post cure temperature on bending response of repaired glass epoxy frp, it was seen that the post curing temperature significantly affected the response of the laminate and a optimum temperature of 50° determined. Sivasankaraiah et al. 13 investigated the effect of post curing temperature ranging from 40oC to 220oC for a fixed period of 6 h on the flexural performance of glass frp, the temperature played a significant role and was seen to increase the flexural strength from 40oC to 140oC and degrade from 140 to 220oC. Fernando et al. 14 developed a time-temperature-transformation (TTT) cure diagram which were crucial in determining the unreacted (48oC) and reacted system temperature (70oC).
Two important factors in post curing process are the post curing temperature and post curing time. The natural fibers depending on the lignin content are seen to mechanically degrade at higher temperatures, 15 hence the extent of temperature for post curing as suggested by the manufacturer of epoxy system may not be suitable for the natural fibers. It is also seen that higher the exposure time of natural fibers to high temperature more is the mechanical degradation. 16 The study initially focuses on the post curing of Ramie-Carbon hybrid composite at various combinations of temperatures and post curing time to achieve a maximum tensile strength and a trend is identified. Further a bio inspired based Particle swarm optimization is performed to identify the optimum in the range used for experimental purpose.
Methodology
Temperature-Time schematic.
Material selection
Mechanical properties of Ramie and Carbon fabric.
Epoxy resin properties. 19
Taguchi design of experiments
The Taguchi design of experiments is a powerful statistical technique that aims to optimize the performance of a process or system while minimizing variability and improving robustness. It offers several salient features that make it a valuable tool in engineering and industrial applications. One key feature of the Taguchi design is its use of orthogonal arrays to efficiently plan and conduct experiments. 20 Orthogonal arrays ensure that all factor combinations are evenly distributed, reducing the experiment trials required to determine the optimised settings. The L-orthogonal arrays, such as L9 or L16, are commonly used in Taguchi designs. 20 Signal to noise ratio (SNR) is another important aspect of the Taguchi method, it is used to calculate the quality of the output and its sensitivity to the noise factors. The SNR allows for the quantification of the effects of different factors on the response variable and helps identify the most significant factors for optimization. 21 There are different types of SNR measures, such as the smaller-the-better, the larger-the-better, and the nominal-the-best. 22 In this study the signal to noise ratio for tensile strength was kept as the-larger-the-better, as we expect the composites to have best performance in the tensile behaviour.
Laminate nomenclature.
Composite fabrication
The composites were prepared using a hand layup method, compacted using a hand roller and pressed under vice grip to consolidate the layers. A 5-layer Ramie fabric laminate is reinforced with four configurations of carbon layers (C0, C2, C4 and C6) viz. 0 layer (no carbon fabric used), 2, four and six layers respectively as described in Table 1. Figure 1(a)–(d) shows the variations of laminates that were fabricated. The laminate is thus composed of two cores, inner core consisting of natural fibers and outer core consisting of synthetic fibers. (a) 0 Carbon layer configuration (b) 2 Carbon layer configuration (c) 4 Carbon layer configuration (d) 6 Carbon layer configuration (e) Schematic of composite fabrication.
The fabric was first cut to a dimension of 200 x 270 mm, in the form of a layer sheet. A known weight of epoxy resin was prepared according to the ratio specified by the epoxy datasheet. A base coat was laid on the Teflon sheet resting on a firm base. The base coat is required to evenly coat the fabric from the bottom side. The carbon and natural fibers were sequentially layered, and hand compacted by the roller. The remaining weight of epoxy was noted. The composite was then subjected to a compacting pressure by vice grips as shown in Figure 2(b) and left for air curing for 7 days to complete the first stage of curing. The transition to post curing stage was accomplished by subjecting the epoxy to different post curing temperatures and post curing durations. Laminate fabrication (a) Laminate geometry (b) Consolidation of laminates (c) Marking for machining (d) CNC machining process (e) Testing of natural fiber laminates (C-0 configuration) (f) Testing of hybrid laminate.
Machining
The composite was wrapped in a masking-tape as shown in Figure 2(c), so as to prevent chipping of the edges while machining with a CNC machine. The laminate was machined to the required dimensions as specified by ASTM D 3039. The test coupon dimensions and the preparation for machining are as shown in the Figure 2(a).
Fiber volume fraction calculation.
Laminate properties.
Tensile testing of laminates
The test coupons were subjected to a tensile loading on a 50 kN capacity universal testing machine as shown in Figure 2(e)–(f). The grip length on either side of the test coupons was kept as 50 mm and the gauge length was 150 mm. The test was carried at a strain rate of 2 mm per minute. The test was carried until the fracture of the composite. A piece of emery cloth was required to wrap the grips of the machine in cases where slipping was inevitable. In case where emery cloth was insufficient to create the necessary grip, tabs made of glass frp were bonded to the gripping length of the laminates on both sides.
Results and discussion
From the tensile testing of composites, it was observed that, as the ratio of synthetic to natural fiber increased, the tension capacity of the composite increased proportionally. This is due to the high specific strength of carbon fibers. The sequence of failure was from inner to outer, as inner core was made of natural fibers and outer core of synthetic. Initially the load is taken by both (natural + synthetic) as a system. Subsequently delamination is seen between inner and outer core and the entire load is transferred to the outer core. This delamination can be attributed to local defects in the composite which develop during the hand layup process. The local defects like entrapped air while fabrication of laminate can lead to variation in the average weight and average thickness of laminate. This, in turn, affects the fiber volume fraction, requiring a normalization of fiber volume fraction to be performed, to compare the individual results. Table 6 shows the actual fiber volume fraction of all the laminates which are close to the value of 0.5, hence the fiber volume fraction of all laminates was normalised to a value of 0.5 in order to not deviate too far from the median. Since the stress of the laminate is directly proportional to the fiber volume fraction, the normalised stress is given by the equation (1). Strain and normalised stress values for (a) C0 configuration (b) C2 configuration (c) C4 configuration (d) C6 configuration.

The tensile stress for all laminates cured at 90 deg. post curing temperature showed a lower value as compared to other temperatures. This could be attributed to the over curing of natural laminate and under curing of synthetic laminates at 90o. At lower temperatures, the laminates with natural fiber showed a better performance in tension, which can be attributed to the degradation of natural fibers at higher temperatures as evident from the Figure 3(a). The trend showed that with increase in number of synthetic fiber layers, the post curing time for same temperature increased subsequently. As the curing temperature increased, the synthetic laminate was able to cure to a higher degree as seen in Figure 3(b)–(d), thus giving a better performance. For natural laminate, it was seen that the strength degraded as the temperature was increased from 60o to 150o due to degradation of natural fibers at higher temperatures. Maximum strength for natural fiber was achieved at 60o for 3 h.
Taguchi DOE results
The Taguchi DOE was analysed for normalised values of stress. The main effects plot ranked the significance of parameters on the tensile strength of the composite laminate as shown in Figure 4(a). It was seen that the number of layers was the most significant factor, followed by the temperature and followed by post curing time. (a) Main effect plot for Taguchi DOE (b) Multilinear equation fit (c) - (f) Time-Temperature variation for 0, 2, four and six layers of carbon fiber respectively.
A multilinear regression analysis was performed to fit the curve and predict the tensile strength, it yielded the following equation.
Where A = Temperature in degree Celsius, B = Time in hours, C = Number of Carbon layers.
Figure 4(c)–(f) shows that the strength of laminate is maximum and almost similar at two extreme ends of the temperature range taken for this experiment. However, the time for post curing is maximum (12 h) for the lower range of the temperature (60oC) and the post curing time is the least (3 h) for the higher range of the temperature (150oC).
Particle swarm optimization
A bio-inspired algorithm of particle swarm optimization was used for finding the optimum temperature and time in the range provided. The different combinations of temperature and time may produce local maximum for a particular number of carbon layers, however we intend to find the global maximum which shall give the optimum temperature and time.
Particle swarm optimization (PSO) is a computational optimization iterative technique that simulates the collective behaviour of a swarm of particles to solve optimization problems. PSO offers several salient features that make it a popular and effective technique in various fields of study.
PSO Control parameters.
The PSO was applied, and solution was checked for 0, 2, four and six layers of synthetic fibers. It was seen that the final solution was similar for all, the results for six layers are shown in Figure 5. The standard deviation and the swarm density curve show the convergence of particles towards the optimum value around the end of 16 iterations. The standard deviation at the beginning of iteration was as high as 40, as the particles were scattered around to search the potential solution. As the iterations increased, the particles tend towards the possible solution, the standard deviation decreased, and the swarm density increased. The particle trajectories show the swarming of particles towards the solution, the convergence curve shows the tensile strength obtained. (a) Particle trajectories (b) Swarm diversity (c) Convergence curve (d) Standard deviation curve.
The optimum value by particle swarm optimization was found to be at a temperature of 60oC for a curing period of 12 h, this is evident from the graphs shown in Figure 4(c)–(f).
Conclusions
The investigation focused on optimizing the post curing parameters, namely temperature and time, for Ramie-Carbon hybrid laminate fabrication. The L16 Taguchi design of experiment facilitated the selection of experimental combinations for laminate fabrication, followed by uniaxial tensile testing to evaluate performance. Conclusions drawn from the study, incorporating both uniaxial tensile testing outcomes and bio-inspired optimization techniques, are summarized as follows: 1. The primary influential factor affecting the tensile strength of the laminate, subsequent to the number of layers, is the post curing temperature, followed by the post curing time. 2. Notably, pure natural laminate exhibited maximum strength at lower temperatures (60°C for 3 h). Conversely, the hybrid laminate demonstrated comparable performance at lower temperatures (60°C) with extended curing times (12 h), as well as at higher temperatures (150°C) with shorter curing times (3 h). 3. An observed trend indicates that as the number of Carbon fabric layers increased, the laminate exhibited enhanced performance at higher temperature ranges. 4. The imposition of a narrow temperature range (60 to 150°C) aimed to mitigate the degradation of Ramie fiber at elevated temperatures. Considering future research endeavours, broader exploration encompassing a wider range of temperature, time, and diverse combinations of synthetic fabrics is warranted.
In conclusion, the findings underscore the critical role of post curing parameters in governing the mechanical properties of Ramie-Carbon hybrid laminates. Insights gleaned from this study contribute to advancing the understanding of laminate optimization techniques and provide valuable directions for future investigations in composite material science.
