Orientation dependent size effects in thermal buckling and post-buckling of nanoplates with cubic anisotropy

In this work, a continuum model is presented for size and orientation dependent thermal buckling and post-buckling of anisotropic nanoplates considering surface and bulk residual stresses. The model with von-Karman nonlinear strains and material cubic anisotropy of single crystals contains two parameters that reflect the orientation effects. Using Ritz method, closed form solutions are given for buckling temperature and post-buckling deflections. Regarding self-instability states of nanoplates and their recovering at higher temperatures, an experiment is discussed based on low pressurized membranes to verify the predictions. For simply supported nanoplates, the size effects are lowest when they are aligned in [100] direction. When the edges get clamped, the orientation dependence is ignorable and the behavior becomes symmetric about [510] axis. The surface residual stress makes drastic increase in buckling temperature of thinner nanoplates for which a minimum thickness is pointed to stay far from material softening at higher temperatures. Deflection of [100]-oriented buckled nanoplates is higher than [110] ones but this reverses at higher temperatures. The results for long nanoplates show that the buckling mode numbers are changed by orientation which is verified by FEM.     

不同管径聚乙烯管的旋转挤出

通过口模旋转挤出制备3种管径聚乙烯(PE)管,系统研究其结构与性能。结果表明,相较于传统挤出PE管内串晶平行与轴向,旋转挤出过程中聚合物熔体的流动是轴向牵引流动和环向拖曳流动的叠加,其方向偏离轴向,可诱导串晶偏离轴向排列,从而提高PE管的环向取向度,实现PE管的环向增强,抑制裂纹在PE管内沿轴向扩展。随PE管管径的增加,在相同旋转角速度下环向流动线速度增大,串晶偏离轴向的夹角增加,环向取向度更高,因而旋转挤出制备的大口径PE管具有更优的性能。     

Variation of fiber orientation in turbulent flow inside a planar contraction with different shapes

In this study, we have investigated the influence of shape of planar contractions on the orientation distribution of stiff fibers suspended in turbulent flow. To do this, we have employed a model for the orientational diffusion coefficient based on the data obtained by high-speed imaging of suspension flow at the centerline of a contraction with flat walls. This orientational diffusion coefficient depends only on the contraction ratio and turbulence intensity. Our measurements show that the turbulence intensity decays exponentially independent of the contraction angle. This implies that the turbulence variation in the contraction is independent of the shape, consistent with the results by the rapid distortion theory and the experimental results of axisymmetric contractions. In order to determine the orientation anisotropy, we have solved a Fokker–Planck type equation governing the orientation distribution of fibers in turbulent flow. Although the turbulence variation and the orientational diffusion are independent of the contraction shape, the results show that the variation of the orientation anisotropy is dependent on shape. This can be explained by the variation of the rotational Péclet number, Pe_r, inside the contractions. This quantity is a measure of the importance of the mean rate of the strain relative to the orientational diffusion. We have shown that when Pe_r < 10 turbulence can significantly influence the evolution of the orientation anisotropy. Since in contractions with identical inlet conditions the streamwise position where Pe_r = 10 depends on the shape, the orientation anisotropy is dependent on the variation of rate of strain in a given contraction. We demonstrate the shape effect by considering contraction with flat walls as well as three contractions with different mean rate of strain variation.     

Characterizing texture in polycrystalline materials by ultrasonic waves

A method for characterizing texture from measurements of ultrasonic wave velocities is proposed. In polycrystalline aggregates, ultrasonic wave velocities are strongly affected by orientation distribution coefficients (ODCs), which are usually used to describe the degree of preferred grain orientation in textured materials. In this work, velocities of longitudinal and transverse waves propagating into aluminum alloy 6061 were measured under pure shear, simple shear and uniaxial tension. From the measured ultrasonic wave velocities, the ODCs W₄₀₀ and W₄₂₀ were calculated to infer the deformation-induced texture. The predicted pole figures, obtained using ultrasonic velocities, were in good qualitative agreement with the finite element polycrystal model analyzed pole figures.     

Porous polycrystals built up by uniformly and axisymmetrically oriented needles: homogenization of elastic propertiesPolycristaux poreux constitués d'aiguilles orientées de façon uniforme ou axisymétrique : homogénéisation des propriétés élastiques

Porous polycrystal-type microstructures built up of needle-like platelets or sheets are characteristic for a number of biological and man-made materials. Herein, we consider (i) uniform, (ii) axisymmetrical orientation distribution of linear elastic, isotropic as well as anisotropic needles. Axisymmetrical needle orientation requires derivation of the Hill tensor for arbitrarily oriented ellipsoidal inclusions with one axis tending towards infinity, embedded in a transversely isotropic matrix; therefore, Laws' integral expression of the Hill tensor is evaluated employing the theory of rational functions. For a porosity lower 0.4, the elastic properties of the polycrystal with uniformly oriented needles are quasi-identical to those of a polycrystal with solid spheres. However, as opposed to the sphere-based model, the needle-based model does not predict a percolation threshold. As regards axisymmetrical orientation distribution of needles, two effects are remarkable: Firstly, the sharper the cone of orientations the higher the anisotropy of the polycrystal. Secondly, for a given cone, the anisotropy increases with the porosity. Estimates for the polycrystal stiffness are hardly influenced by the anisotropy of the bone mineral needles. Our results also confirm the very high degree of orientation randomness of crystals building up mineral foams in bone tissues. To cite this article: A. Fritsch et al., C. R. Mecanique 334 (2006).     

Melt shear rheology of carbon nanofiber/polystyrene composites

The rheological behavior and morphology of carbon nanofiber/polystyrene (CNF/PS) composites in their melt phase have been characterized both through experimental measurements and modeling. Composites prepared in the two different processes of solvent casting and melt blending are contrasted; melt-blended and solvent-cast composites were each prepared with CNF loadings of 2, 5, and 10 wt%. A morphological study revealed that the melt blending process results in composites with shorter CNFs than in the solvent-cast composites, due to damage caused by the higher stresses the CNFs encounter in melt blending, and that both processes retain the diameter of the as-received CNFs. The addition of carbon nanofiber to the polystyrene through either melt blending or solvent casting increases the linear viscoelastic moduli, G′ and G″, and steady-state viscosity, η, in the melt phase monotonically with CNF concentration, more so in solvent cast composites with their longer CNFs. The melt phase of solvent-cast composites with higher CNF concentrations exhibit a plateau of the elastic modulus, G′, at low frequencies, an apparent yield stress, and large first normal stress difference, N ₁, at low strain rates, which can be attributed to contact-based network nanostructure formed by the long CNFs. A nanostructurally-based model for CNF/PS composites in their melt phase is presented which considers the composite system as rigid rods in a viscoelastic fluid matrix. Except for two coupling parameters, all material constants in the model for the composite systems are deduced from morphological and shear flow measurements of its separate nanofiber and polymer melt constituents of the composite. These two coupling parameters are polymer–fiber interaction parameter, σ, and interfiber interaction parameter, C _I. Through comparison with our experimental measurements of the composite systems, we deduce that σ is effectively 1 (corresponding to no polymer–fiber interaction) for all CNF/PS nanocomposites studied. The dependence of CNF orientation on strain rate which we observe in our experiments is captured in the model by considering the interfiber interaction parameter, C _I, as a function of strain rate. Applied to shear flows, the model predicts the melt-phase, steady-state viscosities, and normal stress differences of the CNF/PS composites as functions of shear rate, polymer matrix properties, fiber length, and mass concentration consistent with our experimental measurements.     

Arc reversals of cycles in orientations of G vertex-multiplications

Ryser proved that any two tournaments with the same score sequence are $C_3$-equivalent while Beineke and Moon proved the $C_4$-equivalence for any two bipartite tournaments with the same score lists. In this paper, we extend these results to orientations of G vertex-multiplications. We focus on two main areas, namely orientations with the same score list and with score-list parity. Our main tools are extensions of the refinement technique, directed difference graph and a reduction lemma.     

Uniaxial deformation and orientation of ethylene–tetrafluoroethylene films

This study concerns the thermal and mechanical response of several commercial grades of ethylene – tetrafluoroethylene copolymer films. Differential scanning calorimetry was used to show that, although films have similar degrees of crystallinity and melting temperature, the melting endotherms and crystallisation exotherms differ between materials, suggesting small changes in composition between manufacturers. Films were deformed in tension at a range of temperatures and rates. Selected films were unloaded immediately after stretching, and measurement of the elastic recovery highlighted further differences between materials. Batches of films were pre-drawn uniaxially above the glass transition and immediately quenched. When these materials were subsequently re-drawn below the glass transition temperature, most of them exhibited much improved yield stress, modulus and tensile strength (improving by factors of 5, 5 and 4, respectively at a draw ratio of 3), but a reduced strain to failure. In most of the films, the pre-drawing, as well as the initial orientation of the films, is accounted for by a simple shift in the true strain axis. This is indicative of a material response dominated by entropic network stretch. It also suggests that, in the cases where strain superposition does not work, a different arrangement of crystalline lamellae may be present, limiting the extent to which improved properties can be achieved in some materials.     

Structural recovery mechanism after shear induced orientation of multiwalled carbon nanotube in polypropylene matrix

In this work the flow induced orientation and the governing mechanism of structural recovery of multi-walled carbon nanotube (MWCNT) filled polypropylene nanocomposites were investigated. A series of linear and nonlinear melt rheological measurements including stress growth and time sweep experiments were performed at different temperatures to study the structural breakdown, nanoparticles orientation, subsequent structural recovery and MWCNT loadings. The results showed that the structural recovery occurred in two stages. The first stage, initial agglomeration, showed a quick recovery which was independent of temperature, can be interpreted in terms of inter-particle van der Waals interactions. This structural recovery stage had major contribution in the storage modulus increment. The second stage of the recovery, secondary agglomeration, was slower and dependent on temperature, can be attributed to rotary diffusion of nanoparticles. This stage had minor contribution to the storage modulus increase. Storage modulus increment in both of these agglomeration was attributed to the increase of nanotube-nanotube contacts. Both of these stages were confirmed by transmission electron micrographs. These result were in a good agreement with those calculated using van der Waals and diffusion concepts.     

Transition from the hierarchical distribution to a homogeneous formation in injection molded isotactic polypropylene (iPP) with dynamic mold temperature control

There is an increasing demand to produce injection molded thermoplastic parts with high performance and more uniform microstructure. In this study, an injection mold with dynamic mold temperature control was developed to create a thermo-mechanical environment in which a high mold temperature and slow cooling rate were retained. Two-dimensional wide angle X-ray diffraction (2D-WAXD) and polarized optical microscopy (POM) studies were carried out to investigate the morphological distribution of isotactic polypropylene (iPP) through the depth. Due to the fast relaxation of polymer chains at a high temperature, the macroscopic orientated structure of iPP in conventional injection molding was eliminated, that is transited from the hierarchical morphology distribution to a more homogeneous formation. A homogeneous appearance without layer boundary was shown and many radial spherulites with loosely packed lamellae distributed uniformly throughout the sample.