Composition optimization of PMMA base denture reinforced with different percentages of Nano Hydroxyapatite and alumina particles to obtain highest KIc and KIIc values using hybrid IWO/PSO algorithm

Composition of three-phase dental denture (Polymethyl methacrylate or PMMA + Nano Hydroxyapatite + Nano Alumina) was optimized using hybrid IWO/PSO algorithm to obtain the highest KIc and KIIc. First, initial fracture toughness tests were performed on nine groups of PMMA base dentures with different percentages of ingredients. Symmetric single edge notch beam and asymmetric three-point bend beam with inclined crack were used for KIc and KIIc testing, respectively. The initial design parameters were considered as: {75-100% PMMA, 0-10% Nano Hydroxyapatite and, 0-15% Nano Alumina}. As the initial guess values for starting the hybrid optimization algorithm, B-spline curves (as the cost function) were fitted to the experimental results of both modes I and II. Then the IWO/PSO algorithm was run to find the optimum composition and maximum fracture toughness value of each mode. The best KIc was found for the composition of {78.5% PMMA + 9% Nano Hydroxyapatide + 12.5% Nano Alumina}. Similarly, using the hybrid IWO/PSO algorithm the optimum composition of {83.4% PMMA + 8.7% Nano Hydroxyapatide + 7.9 % Nano Alumina} was obtained to gain the highest KIIc. The experimental fracture toughness values obtained from the proposed compositions via employing the hybrid algorithm were approximately 40% higher than the all tested nine groups of PMMA base dentures under both modes I and II. The fracture toughness ratio KIIc/KIc of the optimum mix-designs predicted by the hybrid algorithm was equal to 0.78 and showed good agreement with the experimental KIIc/KIc ratio. The fracture toughness for any desired mixed mode condition can also be predicted in-terms of the KIc and stress intensity factors and T-stress of the desired mode mixity.