Applying the fuzzy theory method to predict the behavior of reinforced flax nonwoven and tire rubber composite

Abstract

This paper deals with the principal component analysis (PCA) optimization and fuzzy theory modeling techniques to evaluate and predict the main significant mechanical properties of the studied composite samples such as adhesion between the rubber matrix and the flax nonwoven structure, cyclic stress ( $C_{s\left(80\%\right)}$ ), elongation at break and breaking strength in two directions, longitudinal $\left(0°\right)$ and transverse $\left(90°\right)$ . In the studied experimental design of interest, the investigated input and output parameters were tested and reduced using the PCA technique with three input parameters: the size of tire rubber particles, the flax nonwoven areal density and the duration of thermo-press molding. Thus, a factorial design is applied to objectively study the contributions of the selected inputs on the mechanical behavior of the investigated composite samples. Subsequent to this, the developed fuzzy models are compared to predict the flax fiber-reinforced rubber composites’ performance based on the experimental results obtained by their mechanical characterization. Membership functions (Triangular, Trapezoïdal, Gaussian, Π-shaped, etc.) and fuzzy rules were constructed such that the fuzzy model can precisely predict the mechanical properties of the composites. The results show that the Π-shaped membership function gives a better fit of experimental findings because of its spline-based curve shape and is a product of the smf and zmf membership functions that represent polynomial-based curves. Although the Gaussian membership functions and bell membership functions achieve smoothness, they are unable to specify asymmetric membership functions compared to the Π-shaped membership function, which is important in certain applications. Furthermore, compared to the experimental properties, the studied theoretical performances of the reinforced flax/rubber composites can be accurately predicted in the desired field of interest. Hence, the significant coefficient of determination (R²) values relative to the breaking strength, $B_{s\left(MD\right)}$ and cyclic strength, $C_{s\left(80\%\right)}$ , are ranged from 90.1% to 96.6% and from71.4% to 77.6% respectively. Indeed, the theoretical models fit accurately the investigated data. By classifying the accuracy values of the best fuzzy models, a set of test case experiments were conducted so as to validate the theoretical findings. Three selected fuzzy membership functions (Gauss2mf, Gbellmf, and Gaussmf) seem accurate to evaluate and predict sufficiently the flax fiber reinforced rubber composite performance.