Contents lists available at ScienceDirect Engineering Fracture Mechanics journal homepage: www.elsevier.com/locate/engfracmech Experimental study and optimization of fracture properties of epoxy-based nano-composites: Effect of using nano-silica by GEP, RSM, DTM and PSO A. Dadrasi a, ⁎ , Gh.A. Farzi b , M. Shariati c , S. Fooladpanjeh a , V. Parvaneh a a Department of Mechanical Engineering, Shahrood Branch, Islamic Azad University, Shahrood, Iran b Department of Material and Polymer Engineering, Hakim Sabzevari University, Sabzevar 9617976487-397, Iran c Faculty of Engineering, Department of Mechanical Engineering, Ferdowsi University of Mashhad, Mashhad, Iran ARTICLEINFO Keywords: Fracture toughness Silica nano-particles Gene expression programming Response surface method Particle swarm optimization ABSTRACT The main purpose of this study was to examine, modelling and optimization the fracture toughness and the fracture energy of bisphenol-A epoxy resin reinforced by silica nano-particles. Three different approaches including Gene Expression Programming (GEP), Response Surface Method (RSM) and, Decision Tree Method (DTM) have been employed to predict the effects of particle size and the weight fraction of nano-particles on the mentioned parameters. Three sizes ofthenano-particleswiththemeandiametersof17nm,25nmand65nmupto6wt%havebeen used. The two general series of the nano-composites consisting of unimodal and bimodal particle sizesystemshavebeeninvestigated.ExperimentalandmodellingresultsshowedthattheYoung’s modulus, the fracture toughness and the fracture energy increased in all composites by the ad- dition of the silica nano-particles and also by increasing the silica weight percent. In addition, it was observed that the particle size had no considerable effect on the properties. Mixed use of particles with different sizes in a composite also showed a negligible synergy effect on the Young’s modulus and the fracture characteristics. The addition of these nano-particles did not have a significant effect on the yield strength of composites. Moreover, the best modelling ap- proach is selected and optimized values resulted by Particle Swarm Optimization (PSO). The fracture surface was examined to understand the role of nanoparticles on toughening mechan- isms by SEM. 1. Introduction Several researchers are interested in studying polymers and this is due to their unique characteristics such as light weight, low cost and often flexible nature though some of their properties need to be strengthened by addition of certain fillers. Inorganic particles are frequently used to improve the mechanical properties of the polymers such as the Young’s modulus, the yield strength, the fracture toughness and the fracture energy [1–5]. The efficiency of fillers in each composite is related to the type of toughening mechanisms that they can induce. There are various toughening mechanisms which explain toughness increasing of reinforced epoxy by the particles in micron and nano size. The nano-particles have some unique features that the microparticles have not [6,7]. The toughening contributions have been divided into two main categories: in-plane process (such as crack tip pinning or bowing [8] and crack path deflection [9,10]) and out-plane process (such as debonding and plastic void growth [11,12]). https://doi.org/10.1016/j.engfracmech.2020.107047 Received 16 January 2020; Received in revised form 22 March 2020; Accepted 9 April 2020 ⁎ Corresponding author. E-mail address: ali.dadrasi@gmail.com (A. Dadrasi). Engineering Fracture Mechanics 232 (2020) 107047 Available online 16 April 2020 0013-7944/ © 2020 Elsevier Ltd. All rights reserved. T