van Hgh Melick

On the origin of strain hardening in glassy polymers

Abstract The influence of network density on the strain hardening behaviour of amorphous polymers is studied. The network density of polystyrene is altered by blending with poly(2,6-dimethyl-1,4-phenylene-oxide) and by cross-linking during polymerisation. The network density is derived from the rubber-plateau modulus determined by dynamic mechanical thermal analysis. Subsequently uniaxial compression tests are performed to obtain the intrinsic deformation behaviour and, in particular, the strain hardening modulus. At room temperature, the strain hardening modulus proves to be proportional to the network density, irrespective of the nature of the network, i.e. physical entanglements or chemical cross-links. With increasing temperature, the strain hardening modulus is observed to decrease. This decrease appears to be related to the influence of thermal mobility of the chains, determined by the distance to the glass-transition temperature ( T − T g ).

Localisation phenomena in glassy polymers: influence of thermal and mechanical history

The macroscopic deformation behaviour of amorphous polymers is dominated by localisation phenomena like necking and crazing. Finite element simulations show that the details of the intrinsic post-yield behaviour, strain softening and strain hardening, determine the severity of strain localisations. In order to perform these numerical simulations an accurate constitutive model is required. The compressible Leonov model is, for this purpose, extended to include temperature effects. Experimentally it is demonstrated that by a small increase in strain softening (by annealing of polycarbonate) or substantial decrease (by mechanical rejuvenation of polystyrene), transitions from ductile to brittle and, respectively, brittle to ductile can be realised. An analytical stability analysis is performed that predicts stable or unstable neck growth dependent on the ratio between yield stress and hardening modulus. The extensive simulations and experimental results lead to the conclusion that in order to macroscopically delocalise strain, and thus improve toughness, one has to reduce strain softening or enhance strain hardening, either by improving the intrinsic behaviour of polymers, or by creating an optimised micro-structure.

Kinetics of ageing and re-embrittlement of mechanically rejuvenated polystyrene

Pre-deforming polystyrene by rolling results in elimination of strain softening and induces ductile deformation behaviour in a subsequent tensile test. However, both yield stress and strain softening recover in time as a result of ageing, resulting in renewed brittle failure behaviour. The kinetics of this process is addressed in this paper. Although the process of recovery of yield stress and strain softening shows no molecular weight dependence, the time-scale of renewed brittle fracture after rejuvenation does. Any localisation of strain can only be stabilised if the molecular network can transfer sufficient load. For relatively low molecular-weight polystyrene, the load bearing capacity is already exceeded at short ageing times, whereas for higher molecular-weight grades this takes longer. Since the creep compliance and shift-rate of mechanically rejuvenated polystyrene shows a pronounced increase as compared to thermally rejuvenated polystyrene, the segmental mobility in the mechanically rejuvenated samples has increased, despite a lower free volume. This indicates that a new explanation for ageing should be postulated, which is discussed.

Temporary toughening of polystyrene through mechanical pre-conditioning

The post-yield behaviour of glassy polymers is governed by intrinsic strain softening followed by strain hardening. Intrinsic softening is the dominant factor in the initiation of plastic localisation phenomena like necking, shear band formation or crazing. Removal, or a significant reduction, of intrinsic softening can be achieved by mechanical or thermal pre-conditioning, and is known to suppress necking in tough amorphous polymers like polycarbonate and polyvinylchloride. Here, the effect of mechanical pre-conditioning on the macroscopic deformation of a brittle polymer, notably polystyrene, is studied. As a result of mechanical pre-conditioning, a 30% thickness reduction by rolling, the yield stress is decreased and the intrinsic softening drastically reduced, resulting in a more stable deformation behaviour yielding an increase in the macroscopic strain to break to approx. 20% as compared to 2% in the untreated samples. The effect observed is of a temporary nature, as, due to progressive ageing, the yield stress increases and intrinsic softening is restored on a time-scale of minutes. This indicates that the toughening is indeed caused by the removal of intrinsic softening, and not due to enhanced strain hardening related to molecular orientation induced by the rolling treatment.

A micro-indentation method for probing the craze-initiation stress in glassy polymers

Initiation of a localised plastic zone is numerically simulated using a constitutive model that incorporates an accurate description of the post-yield behaviour with the important phenomena of strain softening and strain hardening. Subsequent nucleation of voids in the deformation zone is detected using a hydrostatic stress criterion. This criterion is identified and validated. A micro-indenter with a sapphire sphere is used to produce indents that are later examined with an optical microscope. These observations lead to a critical force at which crazes are initiated in polystyrene. Combining these experiments with a numerical study shows that the loading part of indentation can be accurately predicted. A critical hydrostatic stress of 40 MPa is extracted from the numerical model by monitoring of the local stress field at the moment that the indentation force reaches the experimentally determined force level at which crazes were found to initiate. This criterion is validated by indentations on samples with different thermal histories, and at various loading rates. Finally, the influence of network density on the value of the hydrostatic stress criterion is investigated by indentation of blends of polystyrene and poly(2,6-dimethyl-1,4-phenylene-oxide). It is shown that the critical hydrostatic stress increases with network density.