Hyperelastic characterization of the interlamellar domain and interphase layer in semicrystalline polyethylene

The interphase layer in semicrystalline polyethylene (PE) serves as the transition between the crystalline lamellae and the amorphous domains and is recognized as the third constituent of PE. When PE undergoes large deformations, this interphase layer together with the amorphous phase behaves hyperelastically. Because of the metastable nature and nanometric size of the interphase and its intimate mechanical coupling to the neighboring crystal and amorphous domains, detailed characterization of its hyperelastic properties have eluded detailed experimental evaluation. To extract these properties, a combined algorithm is proposed based on applying the constitutive relations of an isotropic, compressible, hyperelastic continuum to the molecular dynamics simulation results of a PE stack from Lee and Rutledge (Macromolecules 2011, 3096–3108). The simulation element is incrementally deformed to a large strain, during which the stress–strain information is recorded. Assuming a neo‐Hookean model, the tensorial constitutive equation is derived. The hyperelastic parameters for the central amorphous phase, the interphase layer, and the interlamellar domain are identified with the help of the optimization notion and a set of nonnegative objective functions. The identified hyperelastic parameters for the interlamellar domain are in good agreement with the ones estimated experimentally and frequently used in the literature for the noncrystalline phase. The specifically developed sensitivity analysis indicates that the shear modulus is identified with a higher degree of certainty, in contrast to the bulk modulus. It is also revealed that the presented continuum mechanics analysis is able to capture the melting/recrystallization and rotation of crystalline chains that take place during the deformation. The evolutions of the boundaries of the hyperelastic elements are also identified concurrently with the hyperelastic parameters as the by‐product of the presented methodology. © 2013 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2013 , 51, 1692–1704     

Bubble shapes and orientations in low Re simple shear flow

We present measurements of shape and orientation of air bubbles in a viscous Newtonian fluid deformed by simple shear. The apparatus is a variation of the "parallel band" device developed by G. I. Taylor. Previous experimental studies on low viscosity ratio, low Reynolds number (Re < 1) bubble deformation have focussed on either small or large deformations (mostly small deformation) and have only qualitatively examined the orientation of bubbles except for small deformations. Our data set spans both the theoretical small deformation and high deformation limits. With these data we confirm theoretical relationships and assess the range of capillary numbers (Ca) over which theoretical relationships for shape and orientation of bubbles are appropriate. We also examine the geometry of deformed bubbles as they relax to a spherical shape once shear stresses are removed. Our data indicate that for extremely small Reynolds numbers and viscosity ratios, the small deformation theoretical relationship first developed by Taylor, is a good approximation for Ca<0.5. The large deformation results for both shape and bubble orientation derived by Hinch and Acrivos agree with our data for Ca>1 and Ca>0.5, respectively.     

Élaboration de nouvelles lois de comportement pour les élastomères : principe et avantages

A phenomenological study of deformed rubber in uniaxial tension, pure shear and equi-biaxial tension, leads to a generalized strain energy density representation for hyperelastic elastomeric material behaviour. A strain energy density function family is built with a new process. It is particularly well adapted for representing experimental data of different types of loading, and so, for a wide class of elastomers. Besides, parameter identification of this family of strain energy density functions is simple and fast.     

Stress–strain relations of crosslinked rubbers under different types of strain

Experimental data for the stresses and the deformations for crosslinked rubbers at uniaxial and symmetrical and asymmetrical biaxial extension and pure shear are given. Stressed states up to 100% extension are described by a single parameter, the highly elastic potential of Bartenev and Khazanovich. The classical statistical potential of Kuhn-James-Guth-Treloar is not in agreement with experimental data, as shear modulus G has different values for different types of stressed states.     

一种基于分子链统计理论的橡胶超弹性混合本构模型

橡胶材料因其独特的超弹性在实际中广泛应用,通过解析应力-应变关系可以为橡胶力学性能的工程应用提供理论指导。为了更准确地描述橡胶材料力学性能,提出一种适用于橡胶材料的超弹性混合本构模型。新模型基于Gaussian模型与八链模型,引入有关拉伸比的权重函数将二者耦合,在拉伸比较小的情况下,新模型退化成Gaussian形式,在拉伸比较大的情况下,新模型可以依靠权重函数改善八链模型在小变形区域的不足。针对取向硬化的应力-应变曲线、无取向硬化的应力-应变曲线、不同拉伸比应力-应变曲线三种力学特征曲线,从单轴拉伸、等双轴拉伸和纯剪切三类实验数据进行预测验证。结果表明,新模型同时保留了Gaussian模型在小变形范围和八链模型在大变形范围内的预测优势,且对拉伸比和应力应变曲线形式没有依赖性,均能给出高精度的预测结果,突破了Gaussian模型和八链模型的使用限制,为橡胶超弹性力学性能的预测提供了新的思路。     

Non-linear constitutive equations for viscoelastic behaviour of elastomers at large deformations

A non-linear theory of viscoelasticity for large deformation of elastomers has been developed. The concept of an internal variable stress which is governed by a rate equation, has been used to account for the viscoelastic behaviour of incompressible rubbers. Following a molecular approach the parameters of the model were extracted by the inverse Langevin approximation of rubber elasticity. Qualitative applications were made in the case of uniaxial elongation and simple shear deformations.     

Modified slotted shear test for a thin sheet of solid polymer under large deformations

A modified slotted shear test based on ASTM B831 is proposed and used for determining the mechanical behavior of a solid polymer at large deformations. The shear stress-strain response of a thin sheet of polytetrafluoroethylene was experimentally investigated and a V-notched rail shear test was carried out to validate the experimental results obtained with the proposed approach. Displacement and strain fields of the test specimens were estimated by the Digital Image Correlation method. The results indicate agreement between both tests for small deformations, while for large deformations significant discrepancies in shear stress-strain responses are observed. These discrepancies can be attributed to unwanted distortions of the gage section observed in the V-notched specimens. The modified slotted shear test provided a uniform shear strain distribution across the gauge section of specimens. In addition, the principal advantages of the proposed approach over V-notched rail shear test are a wide range of shear strains and absence of unwanted distortions.     

Mechanical response of three semi crystalline polymers under different stress states: Experimental investigation and modelling

The mechanical responses of high‐density polyethylene (HDPE), polypropylene (PP) and polyamide 6 (PA 6) were experimentally investigated for a wide range of stress states and strain rates. This was accomplished by testing numerous specimens with different geometries. The uniaxial compression of cylindrical unnotched specimens and the uniaxial tensile behaviour of dumbbell specimens at different strain rates, was determined. A series of biaxial loading tests (combined shear and tension/compression, pure shear, pure tension/compression) using a designed Arcan testing apparatus were also performed. Flat and cylindrical notched specimens with different curvature radii were additionally tested in order to explore a wider range of stress states. The Drucker‐Prager yield criterion was calibrated with a set of experimental data, for which analytical formulae for stresses are available, and then applied to predict the deformation behaviour under different stress states, prior to strain localization. The results of the numerical simulations show that the Drucker‐Prager model can capture the initial elastic range and the post‐elastic response very satisfactorily. For triaxial and biaxial stress states there is a good agreement, however some load‐displacement responses are only satisfactorily described. Deviations observed in the predicted and experimental results are very likely attributed to the third invariant stress tensor, which was not explored in the model calibration. The evolution of stress triaxiality and Lode angle parameters with equivalent plastic strain were extracted and analysed for several specimens. The results show a plastic yielding behaviour sensitive to the stress state, which can be attributed to different combinations of stress triaxialities and Lode angle parameters.     

Modelling of the simple shear flow of a flow-aligning nematic

The shear flow induced deformations of a nematic liquid crystal layer have been modelled numerically for the case of flow-aligning nematics. The director deviation from the plane of shear, which was predicted earlier for special surface orientation angles, has been confirmed. This deformation takes a form of director rotation about the axis perpendicular to the layer plane. As a result, transverse flow of the nematic arises. The rotation angle is close to pi at sufficiently strong shear stress, and the director is oriented at the usual flow alignment angle in a significant part of the layer. The director coming out of the shear plane should not be treated as a separate effect taking place during the flow, but rather as a way in which the usual flow-aligned structure is achieved.     

Semiclassical description of large multipole-deformed metal clusters

We use the semiclassical periodic orbit theory to describe large metal clusters with axial quadrupole, octupole, or hexadecapole deformations. The clusters are regarded as cavities with ideally reflecting walls. We start from the case of spherical symmetry and then apply a perturbative approach for calculating the oscillating part of the level density in the deformed case. The advantage of this approach is that one only has to know the periodic orbits of the spherical cavity, which makes the calculation very simple. This perturbative method is a priori restricted to small deformations. However, the results agree quite well with those of quantum-mechanical calculations for deformations that are not too large, such as typically occur for the ground states of metal clusters. We also calculate shell-correction energies. With this, it becomes possible to predict at least qualitatively the deformation energy of metal clusters.     

Stress relaxation of a polymer solution in double-step shear deformations: A separate evaluation of the stress components due to entangled segments of different orientations

When two shear deformations γ₁ and γ₂ are successively applied to an entangled polymeric system, a composite temporary network is formed. In this article a simple method is proposed for evaluating separately the contributions from the component networks of different deformations, γ₁ + γ₂ and γ₂, to the observed shear and normal stresses. The method is applied to literature data for a polystyrene solution. It is revealed that the entangled chain segments formed between the applications of two deformations relax very rapidly, while those formed prior to the first deformation do not relax for quite a long time. The result is in accord with the conjecture based on the tube model of entanglement that the chain ends lose their orientation as the chain creeps out of an oriented tube.     

Effects of bending and torsion rigidity on deformation and breakage of flexible fibers: a direct simulation study

To understand the various mechanisms of fiber deformation of flexible fiber suspensions, we carry out a direct simulation study to analyze the effect of fiber rigidity on fiber motion in simple shear flow. Such a study may be used to investigate the critical parameters controlling the breakage of flexible fibers during processing. We model the fiber as a series of rigid spheres connected by stiff springs. The stretching, bending, and torsional rigidities are determined by Young's modulus and shear modulus to realistically model the fiber rigidity. The model correctly predicts the orbit period of fiber rotation, T ?γ, as well as the trend of critical flow strength, η ?γ/E, versus fiber aspect ratio, r(p), at which breakage occurs in simple shear flow.     

Sorbitan tristearate layers at the air/water interface studied by shear and dilatational interfacial rheology

The shear and dilatational rheology of condensed interfacial layers of the water-insoluble surfactant sorbitan tristearate at the air/water interface is investigated. A new interfacial shear rheometer allows measurements in both stress- and strain-controlled modes, providing comprehensive interfacial rheological information such as the interfacial dynamic shear moduli, the creep response to a stress pulse, the stress relaxation response to a strain step, or steady shear curves. Our experiments show that the interfacial films are both viscoelastic and brittle in nature and subject to fracture at small deformations, as was supported by in-situ Brewster angle microscopy performed during the rheological experiments. Although any large-deformation test is destructive to the sample, it is still possible to study the linear viscoelastic regime if the deformations involved are controlled carefully. Complementary results for the dilatational rheology in area step compression/expansion experiments are reported. The dilatational behavior is predominantly elastic throughout the frequency spectrum measured, whereas the layers exhibit generalized Maxwell behavior in shear mode within a deformation frequency regime as narrow as two decades, indicating the presence of additional relaxation mechanisms in shear as opposed to expansion/compression. If the transient rheological response from stress relaxation experiments is considered, then the data can be described well with a stretched exponential model both in the shear and dilatational deformations.     

Collapse mechanisms and extreme deformation of particle-laden interfaces

Particle-laden interfaces are at the basis of many advanced materials, such as bijels and dry water. While the final properties of these materials can generally be controlled, their response to deformation during processing and use is still poorly understood. In particular, the dynamics of particle-laden interfaces in relevant flow conditions is receiving increasing attention. These conditions are typically highly dynamic and can involve unsteady flow or large deformations. This article gives an overview of the remarkable phenomena of particle-laden interfaces undergoing deformations of large amplitude and at high strain rate, in other words extreme deformation. Upon large-amplitude compression, a monolayer of particles can collapse by buckling or by expelling particles in the liquid. The criteria for buckling or expulsions, as well as recent experiments in highly dynamic conditions, are discussed, showing that these criteria can depend also on the rate of deformation. The emerging use of ultrasound-driven bubbles as an experimental platform for controlled deformation of particle-laden interfaces at high strain rate is also discussed. The ability to control the fate of particles at interfaces during dynamic deformation of droplets or bubbles ultimately underpins a variety of applications from controlled release to catalysis.     

Nonlinear rheology of complex fluid–fluid interfaces

Fluid–fluid interfaces stabilized by proteins, protein aggregates, polymers, or colloidal particles, tend to have a complex microstructure. Their response to an applied deformation is often highly nonlinear, even at small deformation (rates). The nonlinearity of the response is a result of changes in the interfacial microstructure. Most of the studies on interfacial rheology of complex interfaces currently available in the scientific literature, focus on the linear response regime. Since multiphase systems such as emulsions or foam are routinely exposed to large and fast deformations, characterization of the nonlinear response of complex interfaces is highly relevant. In this paper we review the recent work on nonlinear rheology of complex interfaces, both in shear and dilatational deformations. We also discuss several methods currently available for analyzing nonlinear interfacial rheology data, and recent progress in modeling nonlinear interfacial rheology, using nonequilibrium thermodynamic frameworks.     

Modeling hyperelastic behavior of rubber: A novel invariant‐based and a review of constitutive models

A constitutive phenomenological model completing the Gent‐Thomas concept is carried out to formulate laws governing the hyperelastic behavior of incompressible rubber materials. It is shown that the phenomenological Gent‐Thomas model (1958) and the constrained chain model (1992) give similar precise results at small to moderate deformation. On the other hand, comparisons of the outcome of the proposed model with that of the molecular model from the combined concepts of Flory‐Erman and Boyce‐Arruda (2000), and with those of the phenomenological models of Ogden (1982), Yeoh‐Fleming (1997), Pucci‐Saccomandi (2002) and Beda (2005) are made. Residual inconveniences raised by attractive continuum models in rubber elasticity literature have been successfully overcome. Results from both the statistical and phenomenological mechanics concepts are compared with the data of some useful classical materials (rubbers of Treloar, Rivlin‐Saunders, Pak‐Flory and Yeoh‐Fleming). The results permit one to see salient equivalence of the two theories for a more reliable prediction of stress‐stretch response for all states of any mode of deformation. A complete and exhaustive analysis of the Mooney plot that combines small and very large extension‐compression has been quite essential in assessing the validity of models. A method of identification of material parameters is presented and data of the simple tension suffice for the determination of the parameter values. It is shown that the ordinary identification procedures, such as the usual least squares, a very much used numerical method in materials investigation, can be unsuitable in some cases of hyperelastic modeling. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 1713–1732, 2007