Deformation and failure of polymer glasses

This thesis is composed of six papers in the field of deformation and failure of polymer glasses. Prediction of deformation and failure behaviour of polymers has become very important. In the last two decades considerable effort is addressed to the development of 3D constitutive models that were able to capture the visco-elastic and post-yield behaviour of glassy polymers. The compressible Leonov model, as developed in our group, proved to be a suitable model which provides an adequate description of this behaviour, including rate- and temperature-dependent yield, strain softening and strain hardening. However a failure criterion is still lacking. Previous studies indicated that macroscopic deformation behaviour is dominated by the intrinsic post-yield behaviour. Improving the ductility should hence focus on avoiding! r localisation of strain by elimating strain softening and promoting the contribution of the strain hardening. Although it is quite well established that strain hardening originates from the contribution of the entangled polymer network, the high strain hardening modulus compared to the rubber-modulus and its temperature dependence requires further investigation. The physical origin of strain softening is less well known, although it is reported that strain softening can be altered by thermal treatments and can even be eliminated by mechanical rejuvenation. The limited resistance to void nucleation and the build-up of high dilative stresses under certain loading conditions, show that decreasing strain softening and increasing strain hardening are not sufficient to achieve tough deformation behaviour. To circumvent these problems heterogeneity should be introduced in the structure to relieve the build-up of high hydrostatic stresses. For materia! ls like polycarbonate and polyamide this results in a transition from crazing to shear yielding. For polystyrene this is only the case if the thickness of the ligaments within the structure are sufficiently small. The concept of a critical thickness suggests that an absolute length-scale is encountered. An absolute length-scale of the same order of magnitude as is found in mechanical tests, is also reported in polymer physics where a Tg-depression is found in thin polystyrene films. In chapter 2 the influence of the network density on the strain hardening modulus is investigated. An increase in network density of polystyrene, achieved by cross-linking and blending with polyphenylene oxide results in a proportional increase in strain hardening modulus. It is discussed that the maginitude of the strain hardening modulus and its negative temperature dependence might orginate from the time-scale of the stress-induced segmental mobility and tha! t, on this time-scale, the secondary interactions still play a significant role. The transient deformation behaviour of mechanically rejuvenated polstyrene in studied in chapter 3. Although the recovery of yield stress and strain softening is independent of the molecular weight, the time to re-embrittlement proves to increase with increasing molecular weight. This is rationalised by the fact that the tensile strength of the material, and hence the recovered yield stress at which this strength is exceeded in a localised plastic zone, depends on the molecular weight. The post-yield behaviour dominates the macroscopic deformation behaviour of amorphous polymers. In chapter 4 it is shown that polycarbonate with its moderate strain softening and strong strain hardening results is stable neck growth during deformation. By annealing the strain softening increases, leading to more severe localisation of strain and even brittle failure. The deformatio! nmode can be be predicted in a straight-forward manner using a stability analysis. The pronounced strain softening and weak strain hardening of polystyrene lead to extreme localisation of strain and explain that standard polystyrene can never be ductile. Elimination of strain softening by mechanical rejuvenation inhibits localisation of strain and results in (temporary) ductile deformation behaviour. Additional finite element simulations illustrate the route to improve ductility. Since a failure criterion was still lacking in the finite element simulations employing the compressible Leonov model, micro-indentation experiments are used to generate crazes in a reproducible way. By evaluation of the local stress and strain distribution by finite element simulations, a critical hydrostatic stress of 40 MPa was found in polystyrene (provided that this event is preceded by plastic deformation) as a criterion for void nucleation. This criterion prov! ed to be independent of thermal history and strain rate but proved to increase with network density. By means of micro- and nano-indenations on polystyrene the influence of an absolute length-scale, as reported in other areas of polymer science, is investigated. For large indenters and indentation depth the experiments compare well to the length-scale independent finite element simulations, using bulk properties. For the smallest indenter (2.2 ??m) and shallow indentation depth (100 nm) the resistance to indentation is much less than expected from the simulations, indicating that the mechanical properties near a free surface in polystyrene might differ from the bulk properties. Using the criterion for void nucleation, as identified in chapter 5, brittle-to-ductile transitions (BDTs) were predicted by the deformation of a representative volume element (RVE). By increasing the temperature in the RVE, the overall stress level lowers in such a ! way that at 70ÆC the critical level of 40 MPa is not exceeded anymore in the simulations and hence a transition from crazing to shear yielding is achieved in polystyrene. The length-scale which is encountered experimentally and numerically in chapter 6 was incorporated in the RVE by assuming a gradient of increased temperature near free surfaces. At an interparicle distance of less than approximately 15 nm the critical value of 40 MPa is not exceeded anymore and crazing is hence inhibited. Both brittle-to-ductile transition compare well to experimental observations.