Step Strain Shear Research Articles

Coarse-grained model of entangled polymer melts in non-equilibrium

A coarse-grained model developed for entangled polymeric systems and calibrated to represent melts in equilibrium (Rakshit, Picu, J Chem Phys 125:164907(1)–(10), 2006) is used to model shear flows. The model is a hybrid between multimode and mean-field representations: chain inner blobs are constrained to move along the chain backbone and the end blobs are free to move in 3D and continuously redefine the diffusion path for the inner blobs. Therefore, contour length fluctuations and reptation are captured. Constraint release is implemented by tracing the position of chain ends and performing a local relaxation of the chain backbones once end retraction is detected. This algorithm takes advantage of the multi-body nature of the model and requires no phenomenological parameters other than the length of an entanglement segment. The model is used to study start-up and step strain shear flows and reproduces features observed experimentally such as the overshoot during start-up shear flow, the Lodge–Meissner law, the monotonicity of the steady state shear stress with the strain rate, and shear thinning at large $\dot {\gamma }$ . These simulations are performed in conditions in which using a fully refined model of the same system would have been extremely computationally demanding or simply impossible with the current methods.

Bread dough rheology in biaxial and step-shear deformations

We consider the use of a Lodge-type model with a damage function for the description of some bread dough rheology. The model has been reasonably successful in uniaxial elongation and shearing, and here, we investigate biaxial stretching, using a bubble method, and some step strain shear motions. The damage function, previously regarded as a function of the largest Hencky strain, is shown to be inadequate to describe biaxial stretching, and a modification is proposed. The sequence of step strains, with both reversing and steadily increasing steps, is reasonably well described by the model. The revised model can therefore describe small-strain motions, steady shearing, steady uniaxial and biaxial elongations, recoil, stress relaxation and step strain motions.

Experimental and Theoretical Study on Shear Flow Behavior of Polypropylene/Layered Silicate Nanocomposites

Polypropylene/layered silicate nanocomposites containing maleic anhydride grafted polypropylene were prepared by melt compounding and their rheological behavior was investigated in shear flow. Transient and steady shear flows were simulated numerically by using the K-BKZ integral constitutive equation along with experimentally determined damping functions under dynamic oscillatory and step strain shear flows. Nonlinear shear responses were predicted with the K-BKZ constitutive equation using two different damping functions such as the Wagner and PSM models. It was observed that PP-g-MAH compatibilized PP/layered silicate nanocomposites have stronger and earlier shear thinning and higher steady shear viscosity than pure PP resin or uncompatibilized nanocomposites at low shear rate regions. Strong damping behavior of the PP/layered silicate nanocomposite was predicted under large step shear strain and considered as a result of the strain-induced orientation of the organoclay in the shear flow. Steady shear viscosity of the pure PP and uncompatibilized nanocomposite predicted by the K-BKZ model was in good agreement with the experimental results at all shear rate regions. However, the model was inadequate to predict the steady shear viscosity of PP-g-MAH compatibilized nanocomposites quantitatively because the K-BKZ model overestimates strain-softening damping behavior for PP/layered silicate nanocomposites.

Experimental and modeling approaches of MR behaviors under large step strains

Rheological properties of MR fluids under large step strain shear are presented in this paper. The experiments were carried out using a rheometer with parallel-plate geometry. Under the large step strain shear, MR fluids behave as nonlinear viscoelastic properties, where the stress relaxation modulus, G( t, γ), shows a decreasing trend with step strain. The experimental results indicate that G( t, γ) obeys time-strain separability. Thus, a mathematical form based on finite exponential serials is proposed to predict MR behavior. In this model, G( t, γ) is represented as the product of a linear stress relaxation, G( t), and the damping function, h( γ), i.e. G( t, γ)= G( t) h( γ). G( t) is simply represented as a three-parameter exponential serial and h( γ) has a sigmoidal form with two parameters. The parameters are identified by adopting an efficient optimization method proposed by Stango et al. The comparison between the experimental results and the model-predicted values indicates that this mathematical model can accurately predict MR behavior.

Nonlinear rheological behavior ofmagnetorheological fluids: step-strain experiments

Relaxation experiments under simple step-strain shear wereperformed on MRF-132LD using a rheometer with parallel-plategeometry. The applied step strains vary from 0.01 to 100%, coveringboth the pre-yield and post-yield regimes. For small step-strainranges, the stress relaxation modulus G(t,γ) is independent ofstep strain, where magnetorheological (MR) fluids behave as linearviscoelastic solids. For large step-strain ranges, the stressrelaxation modulus decreases gradually with increasing step strain.Moreover, the stress relaxation modulus G(t,γ) was found toobey time-strain factorability. That is, G(t,γ) can berepresented as the product of a linear stress relaxation G(t) and astrain-dependent damping function h(γ). The linear stressrelaxation modulus is represented as a three-parameter solidviscoelastic model, and the damping function h(γ) has asigmoidal form with two parameters. The comparison between theexperimental results and the model-predicted values indicates thatthis model can accurately describe the relaxation behavior of MRfluids under step strains.

Shear and Extensional Properties of Three-Arm Polystyrene Solutions

Following the impressive advances in understanding the rheology of linear polymers using the basic Doi−Edwards model of reptation and its variants, rheologists are turning their attention to branched polymers. This is primarily motivated by a desire to understand the connection between chain topology and rheology. We examine the behavior of star polymers in shear and extensional flows. We use this study to illustrate the dramatic effect that the branch point has on both shear and extension. Data on steady and oscillatory shear and step strain shear are presented and analyzed using the Milner−McLeish model. Excellent agreement, using a consistent parameter set, is obtained between this theory and experiments. The filament-stretching rheometer is used to obtain the extensional viscosity of these solutions. The steady-state extensional viscosity shows strain rate softening at moderate strain rates and strain rate hardening at high strain rates. At low Weissenberg numbers (based on the longest relaxation time), the steady extensional stress depends on the number of chain entanglements. At the other extreme, at high Weissenberg number (based on the Rouse time), the steady-state stress depends only on the Weissenberg number. Qualitative similarities and some differences with linear polymers are noticed. The differences appear to be related to the different time constants for the longest relaxation times in these systems.