In this article, response surface methodology (RSM) has been applied to simultaneously optimize the tensile and impact strength of polypropylene (PP)/nitrile butadiene rubber (NBR)/halloysite nanotubes (HNTs)/maleic anhydride (MA)‐grafted‐PP nanocomposites. Three levels of material parameters, including NBR (10, 20, and 30 wt%), HNTs (1, 3, and 5 wt%), and PP‐g‐MA (3, 9, and 15 wt%) as compatibilizers were used to design the experiments according to Box‐Behnken design. In order to investigate the morphology of nanocomposite samples, a scanning electron microscope was used. The model predicted that both the tensile strength and impact strength of nanocomposite were peaked between middle and high levels of HNTs content. There was also a peak for NBR loading in the main effect plot of impact strength. Two‐way interactions of all parameters were significantly affecting both responses. Based on RSM models using the desirability function, the optimum values of input parameters leading to optimized tensile strength and impact strength were predicted to be 17.87, 4.35, and 15 wt% for NBR, HNT, and PP‐g‐MA, respectively. Confirmation experiments were in good agreement with the predicted values.
The incorporation of second dispersed particulate phases in a polymer matrix enhances its mechanical properties. Because of the high surface to volume ratio of nanoparticles, the molecular structure of the matrix is altered at the nanoparticle/matrix interface and the volume of this perturbed region could be significant. These improved properties are produced by the interfacial interaction of the nanometric domains. In this research, epoxy matrix modified with three different sizes of nanosilica (12, 20, and 40 nm) and the effect of the interphase characteristics on the tensile properties of nanocomposites was investigated. At first, the theoretical values of the elastic modulus using a twophase mathematical model compared with the experimental data obtained from the nanocomposite samples and values between 8 and 10 nm were estimated for the interphase thickness. Afterward, considering the three-phase model, it takes into account that three different regions for interphase volume fraction, including single particles, polymer trapping, and agglomerated nanoparticles, and an equation for evaluation of interphase volume fraction are defined. Also, the interphase tensile modulus was considered continuously changing from the properties of nanoparticle to the polymer matrix properties. Finally, the overall tensile modulus of nanocomposites, which considers different key parameters including nanoparticle size, values for the interphase thickness (h), and interphase tensile modulus (E i), were calculated. The results were compared with the experimental ones of other studies and a good agreement was found. The smallest value of h as 6 nm for samples containing 12-nm diameter nanosilica and highest value of h as 8 nm for samples containing 40-nm diameter nanosilica is reported.
Response surface methodology (RSM) is used to study the mechanical and morphological properties of glass fiber (GF)/epoxy composites. The Box–Behnken method was used to design the experiments and quantify the effects of GF content, glass fiber length (GFL), and silica nanoparticles (SiO2). Each variable consisted of three levels: GF (5, 10, and 15 wt%), GFL (3, 6, and 9 mm), and SiO2 (0, 0.75, and 1.5 wt%). Tensile tests were performed to obtain the tensile strength and elongation at break of the samples, and morphology properties were studied by a scanning electron microscope (SEM). The results showed that at high levels of GF, the tensile strength, and elongation at break decreased up to 42% and 30%, respectively. Although increasing the GFL from 6 mm to 9 mm deceased tensile strength by 13%, the elongation at break increased by 7%. The presence of SiO2 at medium level in the composites decreased the elongation but enhanced the tensile strength by 10%. In addition, RSM was employed to develop the mathematical model between process variables. The developed models were validated by the analysis of variance. The R2 obtained from analysis of variance results and normal probability plots showed that the experimental data had a good agreement with those predicted by the models (above 0.95 for all responses).
In this paper, free vibration response of a hybrid composite plate was studied. Effects of some geometrical, physical and material parameters on response of the composite plates embedded with shape memory alloy (SMA) wires were investigated, which have not been reported in the literature thus far. Some of these parameters included important factors affecting free vibration response of the smart hybrid composite plates. The SMA wires were embedded within the layers of the composite laminate. First-order shear deformation theory (FSDT) was utilized to obtain the governing equations of hybrid composite plates. Transverse shear and rotary inertia effects of the plate were taken into consideration. For simply-supported boundary conditions, systematic closed form solutions were obtained by Navier's technique. It was established that dynamic behavior of the smart hybrid composite plate depended on various parameters such as volume fraction, temperature dependent recovery stress and tensile pre-strain of SMA wires and aspect ratio of the laminated hybrid plate.
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