Leon Le Govaert

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 ).

A multi‐mode approach to finite, three‐dimensional, nonlinear viscoelastic behavior of polymer glasses

In this study a phenomenological constitutive model is proposed to describe the finite, nonlinear, viscoelastic behavior of glassy polymers up to the yield point. It is assumed that the deformation behavior of a glassy polymer up to the yield point is completely determined by the linear relaxation time spectrum and that the nonlinear effect of stress is to alter the intrinsic time scale of the material. A quantitative three‐dimensional constitutive equation for polycarbonate as a model polymer was obtained by approximating the linear relaxation time spectrum by eighteen Leonov modes, all exhibiting the same stress dependence. A single Leonov mode is a Maxwell model employing a relaxation time that is dependent on an equivalent stress proportional to the Von Mises stress. Furthermore, a Leonov mode separates the (elastic) hydrostatic and (viscoelastic) deviatoric stress response and accounts for the geometrical complexities associated with simultaneous elastic and plastic deformation. Using a single set of...

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.

A Constitutive Equation for the Elasto-Viscoplastic Deformation of Glassy Polymers

Constitutive equations for finite elastic-plastic deformation of polymers and metals are usually formulated by assuming an isotropic relation between the Jaumann rate of the Cauchy-stress tensor and the strain-ratetensor. However, the Jaumann-stress rate is known to display spuriousnon-physical behaviour in the elastic region. Replacing the Jaumann-stress rate by a Truesdell-stress rate results in an adequate description in the elastic region, but gives rise to a volume decrease during plastic flow intensile deformation. In this paper a ’’compressible-Leonov model‘‘ is introduced, in which the elastic volume response is rigorously separated from the elasto-viscoplastic isochoric deformation. This has the advantage that the model can be extended in a straightforward way to include aspectrum of relaxation times. It is shown that in the limit of small elastic strains, the compressible Leonov model reduces to the Jaumann-stress rate model, but diverges from the Truesdell-stress rate model. Finally, a comparison is made of the above mentioned models in ahomogeneous uniaxial tensile test and a homogeneous plane-stress sheartest, using polycarbonate (PC) as a model system. All models considered in this paper are ’’single mode‘‘ models (i.e. one relaxation time), and, therefore, cannot describe the full (non)linear viscoelastic region, northe strain-hardening or strain-softening response.

Strain-hardening behavior of polycarbonate in the glassy state

This paper presents an experimental characterization of the three-dimensional strain-hardening response of polycarbonate in the glassy state. Using a special mechanical conditioning technique, large homogeneous deformations were obtained in tension, compression, and shear. The experimental results are compared to a number of existing network models. It was found that the state-of deformation dependence of the strain-hardening response was adequately described by neo-Hookean behavior with a shear modulus G=26 MPa. Up to the deformations applied in this study, no sign of a finite extensibility of the entanglement network was observed.

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.

Evaluation of ductile fracture models for different metals in blanking

This study is focussed on the evaluation of ductile fracture methodologies, which are needed to predict product shapes in the blanking process. In an earlier publication [Goijaerts et al., J. Manuf. Sci. Eng., Trans. ASME 122 (2000) 476], two approaches were elaborated using local ductile fracture models. The first strategy incorporates the characterisation of a ductile fracture model in a blanking experiment. The second methodology is more favourable for industry. In this approach, instead of a complex and elaborate blanking experiment, a tensile test is used to characterise a newly proposed criterion, which was shown to predict accurately the ductile fracture for different loading conditions. In this paper, finite element simulations and experiments are performed on both tensile testing and blanking to evaluate the validity of both approaches with corresponding criteria for five different metals. In the blanking process, different clearances as well as different cutting radii of the tools are considered. In conclusion, it can be stated that the first approach gives very good results close to, or within the experimental error for all five materials. The second approach, the more favourable one for industry, yields good results that deviate slightly more over the range of metals. # 2001 Published by Elsevier Science B.V.

Hybrid composites based on polyethylene and carbon fibres Part 2: influence of composition and adhesion level of polyethylene fibres on mechanical properties

Abstract Combining high performance polyethylene (HP-PE) and carbon fibres as reinforcing elements in so-called hybrid composite structures results in a unique class of structural materials possessing high damping and impact resistance. Mechanical properties of unidirectional HP-PE/carbon-epoxy hybrids have been studied, emphasizing basic mechanical characterization such as tensile, compressive and shear strength, initial as well as long-term modulus, vibrational damping and impact response. This paper describes the influence of overall composition and adhesion level of the HP-PE fibres on the mechanical properties of such hybrids.

Prediction of Ductile Fracture in Metal Blanking

This study is focused on the description of ductile fracture initiation, which is needed to predict product shapes in the blanking process. Two approaches are elaborated using a local ductile fracture model. According to literature, characterization of such a model should take place under loading conditions, comparable to the application. Therefore, the first approach incorporates the characterization of a ductile fracture model in a blanking experiment. The second approach is more favorable for industry. In this approach a tensile test is used to characterize the fracture model, instead of a complex and elaborate blanking experiment. Finite element simulations and blanking experiments are performed for five different clearances to validate both approaches. In conclusion it can be stated that for the investigated material, the first approach gives very good results within the experimental error. The second approach, the more favorable one for industry, yields results within 6 percent of the experiments over a wide, industrial range of clearances, when a newly proposed criterion is used.