Studies on the growth of voids in amorphous glassy polymers

Abstract

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.

Localized plastic deformation in ternary polymer blends

“…It should be noted that by keeping the macroscopic strain ratio E 2 =E 1 constant, the present analyzes are different from earlier ones (e.g. Steenbrink et al, 1998;Socrate and Boyce, 2000) where one component of macrostrain is adjusted to keep T R constant. However, it is not clear which way of loading is more realistic and more suited for extracting information from the response of the blends.…”

“…Since then, a number of extensions have been suggested in the literature accounting for more general material behavior. Paying special attention to the effect of non-negligible elastic strains around growing voids in a glassy polymer, Steenbrink et al (1998) and Pijnenburg and Van der Giessen (2001) developed such a model showing much better agreement with cell calculations than the unmodified Gurson model. However, in view of the complexity of this model and of the error made in approximating the cavitated rubber particles as voids, we adopt here an alternative and computationally more convenient approach.…”

“…A usually made convenient assumption for these materials is to approximate the soft and cavitating rubber particles as voids. Unit cell models for periodic arrays of voids have been employed to investigate the evolution of shear band patterns in the thermoplastic matrix during void growth under various stress triaxialities (Steenbrink et al, 1998) or during macroscopic shearing as experienced by blends in the neighborhood of a moving crack tip (Pijnenburg et al, 1999). Three-dimensional (3D) unit cell calculations for porous PC were performed by Socrate and Boyce (2000) who also analyzed toughening implications in terms of peak values of hydrostatic stress in the matrix material.…”

Macroscopic yield in cavitated polymer blends

“…These models account for rate and temperature dependent¯ow, intrinsic strain softening upon yield, followed by progressive hardening. Such models have been used for International Journal of Solids and Structures 38 (2001) 3575±3598 www.elsevier.com/locate/ijsolstr instance to study the local deformations around pre-cavitated (Steenbrink et al, 1997(Steenbrink et al, , 1998Smit et al, 1999;Socrate and Boyce, 2000) or uncavitated rubber particles .…”

Micromechanical Modeling of Ferrite-Pearlite Steels Using Finite Element Unit Cell Models.

“…taining a second-phase particle can represent the entire twophase material under proper boundary conditions which insure macroscopic compatibility of the deformation field (i.e., no separation or overlapping of material at the boundary of two adjacent cells). This model was extensively applied for investigating the macroscopic and microscopic behavior of polymers [22][23][24] and metal-matrix composites. [25][26][27] The initial geometry of the SHA cell can be characterized by the parameters H 0 and R 0 as indicated in Fig.…”