Role of particle cavitation in rubber-toughened epoxies: II. Inter-particle distance R. Bagheri 1 , R.A. Pearson * Department of Materials Science and Engineering, Polymer Interfaces Center, Lehigh University, 5 East Packer Avenue, Bethlehem, PA 18015-3195, USA Received 17 December 1998; accepted 9 February 1999 Abstract Two types of conventional rubber modifiers and a series of hollow plastic micro-spheres were employed as toughening agents in a diglycidyl ether of bisphenol A (DGEBA) epoxy in Part I (Bagheri R, Pearson RA. Polymer 1996;37:4529) of this study. It was found that the rubber modifiers with different cavitation resistance and hollow plastic micro-spheres which act as pre-existing microvoids toughen epoxies in the same manner. The current study is composed to further examine the previous results in terms of the role inter-particle distance in rubber/microvoid toughened epoxies. It is shown that the fracture toughness in toughened blends goes through a ductile-to-brittle transition with inter-particle distance. The source of this transition is found to be a stress state change provided by voided particles. The ligament between neighboring particles, thus, experiences a transition from plane strain to plane stress state by decreasing the inter-particle distance. Interestingly, it is shown that the transition in toughened blends does not occur at a specific inter-particle distance as frequently proposed in literature, but varies with the size of the modifier. Therefore, there is an influence of particle size on yielding of the toughened epoxies that is responsible for the shift in transition.  1999 Elsevier Science Ltd. All rights reserved. Keywords: Toughened epoxies; Cavitation; Inter-particle distance 1. Introduction Rubber modification has been found as a very successful approach to overcome the inherent brittleness of many engi- neering polymers. Cavitation of rubber particles followed by plastic deformation of the matrix is believed to be the major toughening mechanism in many rubber-toughened polymers [1–4]. Researchers agree that cavitation alone is not a considerable source of toughening [4–7]. However, its importance on the plastic deformation of the matrix has been the subject of much debate [2,4,6,8]. Therefore, many investigations have been focused on the role of parti- cle cavitation in rubber-toughened polymers [8–21]. In addition, the discussion on the role of particle cavitation has yielded interests in studying the function of the pre- existing voids in toughening of polymers [4,9,10,22–25] since microvoids may play the same scenario that rubber particles do. Some studies, indeed, have shown that the microvoids are capable of toughening the polymer matrices [10,23,25]. In an earlier study [24], we employed a novel approach by incorporating hollow plastic micro-spheres in an epoxy resin to compare the function of pre-existing voids with that of rubber particles in toughening of the epoxy polymers. The results of that study revealed that the hollow plastic particles toughen the epoxy resin in the same manner that rubber particles do. Recently, in Part I of the current study [25], we investigated the concept of microvoid toughening of epoxies in more detail by incorporating different size and concentration of particles. The results of this study showed that micron and sub-micron size particles, no matter rubber or hollow, toughen epoxy polymers by promoting shear yielding in the matrix. Moreover, it is believed that the cavitation resistance of the rubbery phase does not play any role in the toughening mechanism as long as the particles can cavitate. The results of Part I [25] of this study also suggested an influence of the inter-particle distance on fracture toughness values obtained since at a given concentration of the modi- fier, the toughness was found to be highly dependent on the particle size. This part of the study, therefore, is dedicated to the issue of the role of inter-particle distance in rubber- toughened epoxies. The goal of this study is to further understand the process of rubber toughening and hence, provide a more clear picture of the role of particle cavitation Polymer 41 (2000) 269–276 0032-3861/00/$ - see front matter  1999 Elsevier Science Ltd. All rights reserved. PII: S0032-3861(99)00126-3 * Corresponding author. Tel.: + 1-610-758-3857; fax: + 1-610-758- 4244. 1 Current address: Department of Metallurgy and Materials Science, Sharif University of Technology, Azadi Avenue, Tehran 14584, Iran.