JOURNAL OF MATERIALS SCIENCE 28 (1993) 6799-6808 Dilatational bands in rubber-toughened polymers A. LAZZ E R I Materials Engineering Centre, University of Pisa, Via Diotisalvi 2, 56100 Pisa, Italy C. B. BUCKNALL SIMS, Cranfield Institute of Technology, Cranfield, Bedford MK43 OAL, UK A theory is advanced to explain the effects of rubber particle cavitation upon the deformation and fracture of rubber-modified plastics. The criteria for cavitation in triaxially-stressed particles are first analysed using an energy-balance approach. It is shown that the volume strain in a rubber particle, its diameter and the shear modulus of the rubber are all important in determining whether void formation occurs. The effects of rubber particle cavitation on shear yielding are then discussed in the light of earlier theories of dilatational band formation in metals. A model proposed by Berg, and later developed by Gurson, is adapted to include the effects of mean stress on yielding and applied to toughened plastics. The model predicts the formation of cavitated shear bands (dilatational bands) at angles to the tensile axis that are determined by the current effective void content of the material. Band angles are calculated on the assumption that all of the rubber particles in a band undergo cavitation and the effective void content is equal to the particle volume fraction. The results are in satisfactory agreement with observations recorded in the literature on toughened plastics. The theory accounts for observed changes in the kinetics of tensile deformation in toughened nylon following cavitation and explains the effects of particle size and rubber modulus on the brittle-tough transition temperature. 1. Introduction It has long been recognised that microscopic cavita- tion processes make an important contribution to the fracture resistance of rubber-toughened polymers, including both plastics and thermosets. Cavitation of toughened plastics was first reported in high-impact polystyrene (HIPS), which absorbs energy principally through multiple crazing of the polystyrene (PS) matrix [1]. It is clear from several transmission electron microscopy (TEM) studies that fibrillation of the PS to form crazes is accompanied by some- what coarser fibrillation of the rubber phase in the neighbouring particles [2-4], a process that enables the rubber particles to match the high strains in the surrounding matrix. Recently, Kramer et al. [5] used real-time X-ray measurements on HIPS to show that cavitation of the rubber particles actually precedes crazing of the matrix under tensile impact conditions, Cavities formed within the rubber particles can thus be seen as nuclei for craze growth, which occurs through the meniscus- instability mechanism proposed by Argon and Salama [63. Rubber particle cavitation is also of critical import- ante for toughening of plastics that are resistant to crazing. This was first recognised by Breuer et aL [7], who combined TEM with low-angle light scattering to study deformation mechanisms in ABS and rctbber- modified PVC. They observed X-shaped light-scatter- ing patterns, whieh are consistent with the formation of planar cavitated shear bands having their normals 0022-2461 1993 Chapman & Hall at about 35 ~ to the tensile axis. Fibrillation of a con- tinuous rubber phase in toughened PVC has been reported by Michler [8]. Cavitation of the rubber particles has also been seen in a number of other toughened polymers, notably epoxy resins containin~ CTBN rubber [9-11] and nylon-rubber blends [12]. Recently, Yee and Pearson have employed optical microscopy to observe particle cavitation in toughened epoxy resins [13] and shown that this precedes large-scale shear yielding of the matrix. Furthermore, Borggreve and Gaymans have shown that the brittle-tough transition in rubber- toughened nylon 6 shifts to higher temperatures when rubbers of increasing shear modulus (and hence in- creasing cavitation resistance) are used as toughening agents [14]: this work supports the view that particle cavitation is a prerequisite for extensive shear yielding of the matrix polymer under the severe conditions of the notched impact test. The same authors have shown that the brittle-tough transition temperature in toughened nylon decreases with decreasing particle size, but only down to a limiting diameter of about 0.2 I~m, below which the rubber particles appear to be very difficult to cavitate [15]. Direct TEM evidence of cavitation in toughened nylons has been published by Ramsteiner et al. [16,17], and comparable SEM observations have been made by Speroni et al. [18], Bucknall et aL [19] and Dijkstra [20]. Both Ramsteiner and Speroni showed that the voids were associated preferentially with shear bands. 6799