Taguchi analysis of the tensile behaviour of unaged and hygrothermally aged asymmetric helicoidally stacked CFRP composites

Taguchi method was used to predict and optimize the effects of hygrothermal aging on the tensile behavior of asymmetric helicoidally stacked Carbon Fiber Reinforced Plastic (CFRP) composites. This research is in furtherance to the previous work, which dealt purely with experiments. MR70 12P carbon fiber epoxy prepreg sheets were manufactured into laminated composites comprising constant inter-ply pitch angles ranging from 0o to 30o. The composites were tested in tension as either dry unaged specimens or following hygrothermal aging in seawater at the constant temperatures of 40 oC and 60 oC for 2000 hrs. Optimizations were conducted based on Taguchi L18 orthogonal array considering two design parameters viz. inter-ply stacking angles and hygrothermal aging temperature. The result depicted that the combination of aging temperature (C) and stacking angles are major factors in determining the tensile behavior of composite materials (p = 0.011). The model explains 86.6% of tensile strength variability, with a predicted R-squared value of 93.04%. The model’s robustness is supported by the adjusted R-squared value of 77.6%. Analysis of variance shows that inter-ply stacking angles are the main significant factor affecting the tensile behaviors at a 95% confidence level. A confirmation test was carried out to validate the optimized results and it was found that there were improvements in S/N ratios from initial to optimal setting.

Abbreviations

Coeff: Coefficient; SE Coeff: Standard error Coefficient; T: T-Statistics; P: Probability value; Seq.: Sequential term; Adj. SS: Adjusted Sum of Square; Adj. Ms: Adjusted mean of Square; DF: Degree of Freedom; F: F-Statistics; UD: Unidirectional; H5: 5o; H10: 10o; H15: 15o; H20: 20o; H25: 25o; H30: 30o

Introduction

Helicoidal composite structures are found in mantis shrimps (Odontodactylus scyllarus) (Suksangpanya, et al. 2017) and crab carapaces [1], have an excellent combination of mechanical properties, including but not limited to toughness and impact resistance (Pinto, et al. 2016). Mantis shrimps are able to use their dactyl clubs to smash through the tough exoskeletal components of prey whilst retaining the integrity of their limbs (Wang, et al. 2014) [2], whereas crab carapace impact resistance is a result of combined structural hierarchy where helicoidal microstructures work alongside the macro-scale geometries of the carapace itself [3]. This architecture consists of stacked laminates of aligned fibres that are rotated by an angle relative to their neighboring laminates to form twisted (Bouligand) architectures with a variety of functions, such as thermal regulation and physical protection [1,4,5]. In order to reduce fracture, researchers have begun to focus more on the development of helical CFRP as an alternative to typical laminated composite structures [6,7]. Nwambu, et al. [8] previously investigated experimentally the tensile behavior of unaged and hygrothermally aged asymmetric helicoidally stacked CFRP composites. The result of the investigation revealed that both tensile modulus and tensile strength are found to be detrimentally affected by hygrothermal aging, and the extent to which aging affects these properties is a function of the inter-ply pitch angle. Based on the foregoing, there is a need to identify specifically the processing parameters with the highest effect. This will ensure better consistency and reproducibility of the inter-ply pitch angle and hygrothermally aged composite. Several previous studies have focused on experimental tests of mechanical properties of the composites especially tensile properties [9-11]. The correlation between the mechanical properties and the characteristic parameter, e.g., the composition of the composite and the operating conditions is of prime importance for designing proper composites in order to satisfy various functional requirements. optimization of characteristic parameters on mechanical properties of carbon fiber reinforced composites and optimal combination of parameters are of utmost importance [12]. For the optimization process, several studies have reported that the Taguchi method has shown a 95% confidence level compared to others such as the genetric algorithm, artificial neural network, and Taguchi method [13]. In the Taguchi method, a smaller number of tests is required and it can extract information more precisely and efficiently compared to other approaches. Furthermore. it will produce better consistency and reproducibility of results since it uses both a set of standard orthogonal arrays which can be used for many other experimental situations and a standard method for the analysis of results [12]. To date, there are no reports on the Taguchi analysis of the effects of hygrothermal aging on the tensile properties of asymmetric helicoidally stacked CFRP composites and this paper aims to fill this gap in knowledge.

Materials and experimental detailsn

Materials and composite fabrication

The materials and experimental techniques used are as stated in the previous work [14]. Unidirectional MR70 12P carbon fiber epoxy prepreg supplied from Mitsubishi Chemical Carbon Fiber and Composites and Toray E750 toughened epoxy resin was used to manufacture helicoidal CFRP composites. The Unidirectional (UD) plies were stacked using a constant increase in inter-ply pitch angle to form a laminated structure. Six different sample configurations were manufactured for conditioning and testing using the following inter-ply pitch angles in each configuration: 0o (unidirectional, UD), 5o (ID5), 10o (ID10), 15o (ID15), 20o (ID20), 25o (ID25), and 30o (ID30).

Experimental design based on the Taguchi method

The experimental procedure is designed with Taguchi’s L18 orthogonal array to reduce the experiment numbers. Each machining parameter level is set according to Taguchi’s L18 orthogonal array, based on the Taguchi experimental design method. The experimental observation is further transformed into a Signal-to-Noise (S/N) ratio using the MINITAB 14 software (Minitab user manual (2003)]. The S/N ratio for maximum load and stress values can be expressed as the “Higher is better” characteristic, which is calculated as a logarithmic transformation of the loss function. The S/N ratios determined from experimentally observed values are statistically studied by analysis of variance (ANOVA).

Results and discussion

Response surface regression of tensile strength (Mpa) versus ageing temp (C) and inter-ply angles.

The previous work [8] investigated the hygrothermally aged asymmetric helicoidal composite experimentally while this work statistically analyzed the experimental results to determine the best combination of processing parameters that can provide the optimal physical and mechanical conditions [12].

Based on this, Table 1 presents the estimated regression coefficients that provide insights into the complex relationship between fiber architecture, aging temperature, and material strength. The significantly negative coefficient for stacking angles (-111.7, p = 0.041) highlights the critical role of stacking angles in determining tensile strength. Selecting appropriate stacking angles is crucial for achieving desired tensile strength levels in CFRP composites according to previous literature [8] (Suksangpanya, et al. 2017). Considering the aging temperature effect, although the coefficient for aging temperature (-151.5) is negative, it’s not statistically significant (p = 0.128) at conventional significance levels. However, this suggests that aging temperature may still play a role in tensile strength, warranting further investigation. The significant interaction term “Stacking Angles * Stacking Angles” (p = 0.026) underscores the importance of considering squared stacking angles when optimizing tensile strength. In contrast, “Ageing temperature (C) * Stacking Angles” are major factors in determining the tensile behavior of composite materials (p = 0.011). Model Fit: The model explains 86.6% of tensile strength variability, with a predicted R-squared value of 93.04%. The model’s robustness is supported by the adjusted R-squared value of 77.6% [12].

In addition, Analysis of variance (ANOVA), as presented in Table 2, analyzed the tensile strength (MPa) in bioinspired asymmetric helicoidal Carbon Fiber-Reinforced Plastic (CFRP) composites which evaluates the influence of inter-ply stacking angles (0°, 0/90°, 5°, 15°, 10°, 20°, 25°, and 30°) and aging temperature on material strength. The “Regression” row in the ANOVA table indicates that the overall model shows statistical significance, with an F-statistic of 0.05 and a p - value of 0.115. This implies that the combined effects of stacking angles and aging temperature significantly affect tensile strength. The analysis categorizes effects into linear, square, and interaction terms. Among these, only the “Square” term is statistically significant (p = 0.044), indicating that squared stacking angles have an impact on tensile strength. Other terms, including “aging temp (C),” “Stacking Angles,” and interactions, are also statistically significant (p > 0.05).

Table 3 presents the predicted values resulting from the regression model, and it can be observed that these values are 95% certain to fall inside the lowest and highest conceivable values (i.e., the 95% Confidence Interval). The correlation factor (R) for the model predictions was 0.9304, indicating that regression model predictions are 93.04% correct which agrees with the work of Anmar, et al. [13].

As earlier predicted in Table 1 of response surface regression of tensile strength, the Figure 1 shows a perfect correlation between the actual values and the predicted values, which signifies that there is a very good agreement between the model predictions and experimental results [8].

Figure 1: Relationship between Actual versus Predicted value for %Yield.

Response surface regression of stiffness (GPa) versus ageing temp (C) and stacking angles

According to the Estimated Regression Coefficients for Stiffness (GPa) analysis as shown in Table 4, stacking angles significantly (p = 0.022), affected stiffness (26.270), indicating that the stiffness of the material changes as the stacking angle changes. In addition, the aging temperature coefficient (15.928), is statistically significant at standard levels. Stiffness is greatly impacted by interaction factors, such as squared stacking angles and interactions between stacking angles and aging temperature. The model’s predictive R-squared value is 94.8% (R-Sq(pred)), while its adjusted R-squared value is 83.2% (R-Sq(adj)), demonstrating robustness. The model explains 89.9% of stiffness variability (R-Sq).

As shown in Table 5, an F-statistic of 4.96 (p = 0.007) from the ANOVA indicates that the combined effects of stacking angles and aging temperature have a substantial impact on stiffness. The effects are broken down into linear, square, and interaction terms in the study of the main and interaction effects. Significant values are found for aging temp (C) and stacking angles (p 0.05), and squared stacking angles are also significant (p = 0.007). Stiffness is strongly influenced by interaction factors, such as the combination of aging temp (C) and stacking angles (p 0.01). Also, the comparatively small residual error implies that the model adequately accounts for the variations in stiffness.

In a nutshell, the analysis of variance (ANOVA) agreed with previous studies that stiffness in bioinspired asymmetric helicoidal CFRP composites is considerably influenced by stacking angles and aging temperature [6,8] (Pinto, et al. 2016). Interactions and squared stacking angles also affect stiffness variation. selecting the right stacking angle, and consideration of interactions are vital for achieving desired stiffness in composites.

Table 6 shows the predicted values obtained from the regression model for stiffness, and it was seen that the predicted values are 95 % certain to be within the lowest and highest possible values (i.e. 95% Confidence interval) which correspond to the report of Anmar, et al. [13] that the experimental and expected results are very close, with an error ratio not exceeding 5%. The model predictions gave a correlation factor (R) of 0.948 which implies that the model predictions are 94.8 % accurate.

Furthermore, Figure 2 presented that there was a perfect correlation between the actual values and the predicted values, which signifies that there is a very good agreement with the model predictions and experimental results of Nwambu, et al. [14-16].

Figure 2: Relationship between Actual versus Predicted value for stiffness.

Conclusion

Asymmetric helicoidally stacked Toray E750 carbon fiber reinforced toughened epoxy resin composites were optimized with the Taguchi method with an aim to determine the significant levels of stacking angles and ageing temperature on their properties under tensile loading in unaged and hygrothermally aged conditions. The following conclusions were drawn from the analysis. The stacking angles and ageing temperature show a linear correlation to the tensile strength of asymmetric helicoidally stacked carbon fiber reinforced toughened epoxy resin composites. It was established that Inter-ply stacking angles are critical factors affecting the extent of macromolecular mobility within helicoidally stacked continuous fiber CFRP composites. It was confirmed that ageing temperature has an 86% effect on the stiffness of asymmetric helicoidally stacked carbon fiber-reinforced toughened epoxy resin composites. Analysis of variance indicates that both inter-ply stacking angle and ageing temperature affect the tensile strength values at a 95% confidence level. The Taguchi optimization and experimental results are very close, with an error ratio not exceeding 5%. The result shows the Taguchi approach could be a very helpful tool for the design of experiments based on the processing parameters and control levels.

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