Studies on the growth of voids in amorphous glassy polymers

Numerical studies are presented of the localized deformations around voids in amorphous glassy polymers. This problem is relevant for polymer-rubber blends once cavitation has taken place inside the rubber particles. The studies are based on detailed finite element analyses of axisymmetric or planar cell models, featuring large local strains and recent material models that describe time-dependent yield, followed by intrinsic softening and subsequent strain hardening due to molecular orientation. The results show that plasticity around the void occurs by a combination of two types of shear bands, which we refer to as wing and dog-ear bands, respectively. Growth of the void occurs by propagation of the shear bands, which is driven by orientational hardening. Also discussed is the evolution of the local hydrostatic stress distribution between voids during growth, in view of possible craze initiation.

Void Growth in Glassy Polymers:Effect of Yield Properties on Hydrostatic Expansion

Void growth in plastically deforming glassy polymers is investigated by means of a simple spherical symmetric model. This type of void growth occurs in cavitated polymer-rubber blends and, at a smaller scale, during craze initiation. The study serves to provide approximate values for the stresses required for elastic-viscoplastic void growth under hydrostatic loading conditions. The constitutive model accounts for features such as rate and temperature dependent yield, intrinsic strain softening after yield, and subsequent hardening due to molecular alignment at large deformations. The separate effects of these features on void expansion and the stress distribution are studied. Due to the relatively large strain at yield for most glassy polymers, elastic effects play an important role even at macroscopic yield. Therefore, predictions of the maximum stress are significantly lower than those based on rigid-plastic behaviour, especially for low void volume fractions

On cavitation, post-cavitation and yield in amorphous polymer-rubber blends

The deformation behaviour of amorphous polymer-rubber blends is investigated in terms of an axisymmetric unit cell model containing an initially spherical rubber particle. The behaviour of the rubber is described by an incompressible non-Gaussian network theory, while for the matrix we adopt a recent large strain elastic-viscoplasticity model that incorporates the intrinsic softening upon yield and the subsequent progressive orientation hardening typical for amorphous glassy polymers. Guided by simple analytical estimates, cavitation of the rubber particle is interpreted in terms of the unstable growth of a pre-existing small void. It is shown that cavitation and yield are essentially coupled processes. On the macroscopic scale, both are softening mechanisms: If macroscopic yield takes place before the limit stress for cavitation is reached, cavitation is prohibited. Furthermore, and contrary to common belief, it is found from the interfacial stress history that, using realistic material parameters, the rubber particle continues to significantly affect plasticity in the matrix in the post-cavitation regime, i.e. after it has cavitated, so that cavitated particles cannot always be considered to be equivalent to particle-sized voids.

Shearing of particles during crack growth in polymer blends

Microstructural investigations below the fracture surface have revealed that the rubber particles in a number of polymer-rubber blends were deformed into remarkable S-like shapes. These shapes seem to have been largely ignored in previous microstructural studies of blends, but in fact cannot be explained from the known deformation states around a crack. We hypothesize in this paper that these shape changes develop as a consequence of macroscopic shearing of the blend as the crack front sweeps through the material. Large strain, finite element models for simple shearing of a blend are reported which demonstrate the evolution of round particles into S-shape ones for a range of material parameters, and thus support our hypothesis. The ‘microscopic’ localized deformation processes are identified, and the implications for the toughening mechanism in these blends is discussed.