Prediction of brittle-to-ductile transitions in polystyrene H.G.H. van Melick, L.E. Govaert * , H.E.H. Meijer Dutch Polymer Institute (DPI), Section Materials Technology (MaTe), Eindhoven University of Technology, P.O. Box 513, NL-5600MB Eindhoven, The Netherlands Abstract In this study it is attempted to predict brittle-to-ductile transitions (BDTs) in polystyrene blends, induced either by an increase in temperature or by a decrease in inter-particle distance. A representative, two-dimensional volume element (RVE) of a polystyrene matrix with 20% circular voids, is deformed in tension. During deformation a hydrostatic-stress based craze-nucleation criterion [1] is evaluated. The simulations demonstrate that crazes initiate at low temperatures while a transition from crazing to shear yielding (BDT) is found around 75 8C. The numerical results correlate well with tensile tests on similar heterogeneous polystyrene. The presence of an absolute length, as experimentally found, is more difficult to explain. Near a free surface a T g -depression is measured for polystyrene and also the resistance to indentation in polystyrene is lower than expected from bulk properties. Both observations are rationalised by an enhanced segmental mobility of chains near a free surface. As a consequence of these findings, an absolute length-scale could be incorporated in the numerical simulations. For simplicity, the length-scale is modelled by taking a temperature gradient over a thin layer near the internal free surfaces of the RVE. Deformation of the RVE with different absolute length-scales shows that indeed also the experimentally found brittle-to-ductile transition can be predicted if the ligament thickness between the inclusions (‘voids’) in polystyrene is below a critical value of ca. 15 nm. q 2002 Elsevier Science Ltd. All rights reserved. Keywords: Brittle-to-ductile transition; Polystyrene; Finite element simulations 1. Introduction Numerical prediction of strain localisation phenomena in glassy polymers has received substantial attention during the last decades. Following the work of Haward and Thackray [2], Boyce and co-workers [3–6] developed a model that was able to capture the post-yield behaviour of glassy polymers. Studies of the group of van der Giessen [7, 8] and our group [9–17] lead to the conclusion that the numerical simulation of plastic localisation in various loading geometries is now well established. However, failure, an important issue in the deformation behaviour, could not yet be predicted. The importance of failure prediction can be envisaged by taking the macroscopic deformation behaviour of poly- styrene as an example. Already in the apparent elastic region crack-like defects, so-called crazes, appear at the surface of a tensile bar under loading. The faces of these crazes are bridged by fibrillar material, which provides the crazes some load bearing capacity. From the highly stretched fibrils [18,19] it can be witnessed that on a local scale polystyrene is extremely ductile, but, due to its pronounced strain softening and weak strain hardening, the strain tends to localise in these small local zones that cannot be stabilised [20]. Kramer [21] recognised that the extreme localisation is even to be considered as a prerequisite event for the initiation of the crazes. His main conclusion was that the formation of a small, localised plastic deformation zone, within a relatively undeformed matrix, first leads to a build- up of tri-axial stresses. Subsequently, this deformation can either be stabilised provided that the polymer network is able to transfer sufficient load, or cannot be stabilised causing the localisation to evolve to extremes meanwhile building-up dilative stresses until, at a sufficiently high dilative stress (successive), nucleation of voids occurs. With ongoing deformation the voids coalescence into a void network and form a craze. Resistance to void nucleation is dependent on the network density of polymers [22–24]. This partly explains the craze- and defect-sensitivity of polystyrene that forms— due to its high chain stiffness—a low entangled network. Recently it was shown, by means of a combined experimental and numerical indentation study, that void nucleation, indeed preceded by plastic deformation, in 0032-3861/03/$ - see front matter q 2002 Elsevier Science Ltd. All rights reserved. PII: S0032-3861(02)00770-X Polymer 44 (2003) 457–465 www.elsevier.com/locate/polymer * Corresponding author. Tel.: þ 31-40-2472838; fax: þ 31-40-2447355. E-mail address: l.e.govaert@tue.nl (L.E. Govaert).