LLDPE’s grown with Metallocene and Ziegler–Natta catalysts: events in the melt and FTIR analysis

LLDPE samples synthesized with Ziegler–Natta (ZN) and Metallocene (MT) catalysts have been analyzed to investigate a potential catalyst-dependent morphology and to find an explanation for the difficult processing of MT. Slow calorimetry at v = 0.02 K/min and IR at RT and in the melt are used. The differences between MT and ZN are assigned to their different composition, MT not having the linear segments, which are present in ZN. Slow calorimetry is effectively a drawing process of the melt with chain orientation followed by decay. The later event, characterized by an endotherm, ΔH _network, occurs at higher temperatures for MT, the presence of a regular distribution of methyl groups slowing down the process. The rocking, gauche, bending and stretching regions of the IR spectra are analyzed. The nascent MT has more strained bands in the rocking region. The wagging region reveals the more homogeneous environment of MT through the maximum absorbance at 1,368 cm⁻¹. Decomposition of bands is made for the rocking and wagging regions. The orthorhombic crystallinity, α_c (FTIR), measures the sum of long- and short-range orthorhombic order, the latter being obtained by α_c (FTIR)-α_c (X-rays). The values of α_c (FTIR) for MT and ZN are very similar in conditions of equilibrium. The justifications for the molecular origin of ΔH _network are presented: (i) the slow relaxation of long chains strained and oriented in the melt measured by other techniques, (ii) The correlation, for gels of a linear sample, made in different solvents, between the maximum drawability, λ_max, and ΔH _network in a slow T-ramp. The range is 80–270 for λ_max and 40–120 J/g for ΔH _network. (iii) The comparison of two traces of the same sample, between 140 °C and 270 °C, show that comparable events in the melt appear in the integrated absorbance and in the slow calorimetry signal. Analysis on thin films of the little-studied CH₂ stretching region reveals that their extinction coefficient, ε, and the shape of the bands are highly sensitive to the sample history, ε diminishing by a large factor in slowly crystallized samples. Events in the slow T-ramp, followed by a fast crystallization, on the other hand, leads to materials with standard characteristics. Slow calorimetry traces display more events (endothermic and exothermic) for MT than for ZN, a finding consistent with more flow irregularities during processing. Equilibrium conditions and better processing could be reached for MT by extending time in the melt or using higher temperatures.     

Effects of grain sizes, shapes, and distribution on minimum sizes of representative volume elements of cubic polycrystals

In the literature the concept of representative volume element (RVE) was introduced to correlate the effective or macroscopic properties of materials with the properties of the microscopic constituents and microscopic structures of the materials. However, to date little quantitative knowledge is available about minimum RVE sizes of various engineering materials. In our recent paper [J. Mech. Phys. Solids 50 (2002) 881], a new definition of minimum RVE size was introduced based on the concept of nominal modulus. Numerical experiments using the finite element method (FEM) were then carried out for determining the minimum RVE sizes of more than 500 cubic polycrystals in the plane stress problem, under the assumption that all grains in a polycrystal have the same square shape––called the simple polycrystal model. The major finding is that the minimum RVE sizes for effective elastic moduli have a roughly linear dependence on crystal anisotropy degrees. The present paper takes into account the effect of grain sizes, shapes, and distribution on the minimum RVE sizes for real cubic polycrystals that are formed by crystallization processes. Similar roughly linear dependence is found again, with the slope about 19% lower than that in the simple polycrystal model. This finding is interesting and useful because numerical experiments on minimum RVE sizes for a large number of crystals are quite time-consuming and the simple polycrystal model reduces significantly the FEM pre- and post-processing works. This should be particularly true in numerically testing minimum RVE sizes for three-dimensional polycrystals and for nonelastic properties in future works. With a maximum relative error 5%, all the polycrystals tested have a minimum RVE size of 16 or less times the grain size.     

A comparative study of numerical solutions to non-linear discrete crack modelling of concrete beams involving sharp snap-back

Numerical problems are often encountered in modelling crack propagation in concrete beams using non-linear finite element (FE) analysis, especially when sharp snap-back behaviour in load-displacement relations occurs. This paper firstly identifies 16 arc-length control based numerical strategies based on extensive literature review. They are then used to carefully model the structural behaviour of a four-point single notched shear beam using discrete crack modelling approach in which cracks are represented by interface elements with bilinear softening constitutive laws. Based on extensive FE analyses, detailed comparisons of the merits and demerits of these numerical algorithms are then made. The results indicate that the effectiveness and efficiency of different algorithms may vary considerably from one to another, with the local arc-length based procedures in conjunction with tangential stiffness strategy and reversible unloading model being the most robust.     

High-strain-rate superplasticity of nanocrystalline aluminum alloy 1570

The structure and mechanical properties of nanocrystalline aluminum alloy 1570 obtained by means of severe plastic deformation have been studied. Being tested in a temperature range from 300 to 400°C, the alloy exhibits high-strain-rate superplasticity. At 400°C, the superplasticity is manifested in a very broad range of strain rates, extending from 5 × 10^?3 to 1 s^?1.     

A Recursive Frequency Estimator Using Linear Prediction and a Kalman-Filter-Based Iterative Algorithm

This paper proposes a new Kalman-filter-based recursive frequency estimator for discrete-time multicomponent sinusoidal signals whose frequencies may be time-varying. The frequency estimator is based on the linear prediction approach and it employs the Kalman filter to track the linear prediction coefficients (LPCs) recursively. Frequencies of the sinusoids can then be computed using the estimated LPCs. Due to the coloredness of the linear prediction error, an iterative algorithm is employed to estimate the covariance matrix of the prediction error and the LPCs alternately in the Kalman filter in order to improve the tracking performance. Simulation results show that the proposed Kalman-filter-based iterative frequency estimator can achieve better tracking results than the conventional recursive least-squares-based estimators.