Prediction of the large strain mechanical behaviour of heterogeneous polymer systems by a multi-level approach

Shear band formation in heterogeneous tensile bars was studied using an accurate homogenization method that allows for a numerical coupling between the microscopic and macroscopic stress-strain behavior. The procedure is based on a classical homogenization theory, assuming local spatial periodicity of the microstructure, and supplies a consistent objective relation between the local macroscopic deformation and the microstructural deformation of a spatially periodic representative vol. element (RVE), representing the local microstructure. The method was used to predict the influence of the microstructure on localization phenomena in plane strain hour-glass-shaped polycarbonate specimen with different vol. fraction of non-adhering low-modulus rubbery particles. An irregular particle distribution seems to promote deformation spreading over the sample, which leads to enhancement of toughness of heterogeneous polymer systems by the addn. of easily cavitating rubbery particle

Predictive modelling of the properties and toughness of polymeric materials, Part I: Why is polystyrene brittle and polycarbonate tough?

The brittleness of polystyrene (PS) and the toughness but notch sensitivity of polycarbonate (PC) have been studied by the detailed finite element analyses of the stress and strain fields in a notched tensile bar with a minor defect. The defect represented a flaw or imperfection, generated during the test specimen prodn. The large-strain mech. responses of both materials were approximated by an accurate elasto-viscoplastic constitutive model with appropriate material parameters. It was assumed that failure occurs instantaneously once the dilative stress exceeds a certain crit. craze-initiation stress. The analyses show that the unstable post-yield mech. response of both materials results in localization of stresses and strains near the defect at a very low macroscopic strain (0.16%). As a result, a strong dilative stress concn. is formed just below the surface of the defect. For the polystyrene specimen, the crit. stress is reached at the defect. For the polycarbonate, however, the effect of the stress concg. defect was counteracted by a higher craze-initiation stress and stronger strain hardening. The PC craze-initiation resistance, however, did not suffice to overcome the dilative stress concn. raised by the notch ti

Prediction of the large-strain mechanical response of heterogeneous polymer systems : local and global deformation behaviour of a representative volume element of voided polycarbonate

The mechanical behaviour of voided polycarbonate has been predicted by using a detailed finite element model of the microstructure and an accurate elasto-viscoplastic model for the glassy polymeric matrix material. On the microstructural level a spatially periodic plane strain matrix with irregularly distributed voids has been considered. The voids represent low-modulus non-adhering rubbery particles under negative pressure. The constitutive model for the homogeneous parts of the material reflects the typical yield and post-yield behaviour of glassy polymers: strain rate and history dependent yield, intrinsic strain softening and subsequent strain hardening. The finite element simulations show that the irregular void distribution causes a radical change in deformation behaviour. In particular the macroscopic strain softening disappears. This transformation in macroscopic behaviour originates from the arbitrary order in which local shear bands between the randomly distributed voids are formed and subsequently harden. In the averaged overall mechanical response the individual unstable yield and post-yield behaviour of the local shear bands is evened out, resulting in an overall stable macroscopic deformation behaviour. This mechanism is believed to be primarily responsible for the toughness enhancement of heterogeneous polymer systems through the addition of easily cavitating rubbery particle

Deformation and toughness of amorphous polymers : numerical evaluation of heterogeneous systems

This paper addresses the use of the Multi-Level Finite Element Method to analyze the heterogeneous deformation of two-phase polymer blends. Two important length scales are considered: the heterogeneous RVE (representative volume element) and that of the continuous scale. Analyses like these not only improve our understanding of the phenomena that occur on the different scales, but also give directions towards improvement of existing materials