Time–temperature dependent brittle fracture of viscoelastic solids

The Griffith formulation is used to study fracture behavior of poly(methyl methacrylate) (PMMA) as a function of strain rate and temperature over the range 4.4 × 10^?5 ≤ ε ≤ 4.4 × 10^?2 in./in./sec and 25°C ≤ T ≤ T_g, T_g being the glass transition temperature. It is found that the transition from brittle to ductile failure occurs abruptly at a temperature T_f which is dependent on strain rate and is approximately the same as the glass transition temperature of the material. The Griffith brittle fracture criterion is found to apply below T_f for all strain rates. The brittle fracture behavior is shown to obey the time–temperature equivalence principle in the same way as the material's other viscoelastic properties, having the same shift function.     

Superposition of small shear deformations on large uniaxial extensions for viscoelastic materials

The equation for small amplitude torsional response superposed on a finite axial stretch history is derived for a material modelled by the BKZ constitutive equation. For the case of a uniaxial step stretch history, this equation contains a term generalizing the well known Rivlin result for nonlinear elasticity plus two additional terms. The equation is used to analyse a recent experiment which studies the relation between the period of free torsional oscillations, axial stretch and axial force in a material undergoing stress relaxation. It is shown that a 10% discrepancy which arises when the data is related by Rivlin's formula can be accounted for by the two additional terms associated with the BKZ formulation. Finally, an expression for the complex modulus for forced torsional oscillations is derived.     

Structural changes in polyethylene films at small deformations

Structural changes in PE films at deformation 2–7% under constant load were studied by molecular probe method. It was shown that at these conditions some structural rearrangements take place which involves more than 20% of polymer volume, only 2–3% being transformed in the state of three-dimensional ordering. The most part of ordering observed was connected with two-dimensional ordering in the AC plane of molecular folding, involving tie chains near the crystallites. The effect of relaxation process during deformation on structural rearrangements in PE films was also investigated.     

Structural and morphological changes in VPO solids during activation

The structural, morphological changes which occurred in the solid during the activation of the precursor were studied using a combination of techniques. For this purpose, aliquots of the same precursor were analyzed at selected points along the activation procedure. The structural changes were followed through DTA, XRD and ir spectroscopy, while the morphology was observed with SEM. The most critical steps of the activation strategy are the burning of the residual organic compounds retained by the precursor and the topotactic transformation of the (VO)HPO₄·1/2H₂O into the vanadyl pyrophosphate which is always present in the equilibrated catalysts. The time allowed for these processes to occur was found to correlate with the performance of the equilibrated catalyst.     

The orthotropic viscoelastic properties of Chinese fir wood during the temperature ramping process

Abstract

In this study, the orthotropic viscoelasticity of Chinese fir wood (Cunninghamia lanceolata [Lamb.] Hook) was investigated during the temperature ramping process. The storage modulus (E′) and loss modulus (E″) of longitudinal (L), radial (R), and tangential (T) specimens with six levels of moisture content (MC) ranging from 0.6 to 22.0% were determined form 20 to 280?°C. The change in E′ was influenced by the dual effects of temperature and MC; the loss of adsorbed water in the wood cell wall caused an increase in wood stiffness. The individual decline in E′ was affected by heating to different degrees and the heating exerted more influence on the transverse specimens and less contribution to the L specimens. Different relaxation processes of E′′ were observed in specimens with different MCs in the three main directions, indicating that the mechanical relaxation of wood was affected by its MC and microstructure. The β and γ-relaxation processes exhibited a conjointly circular arc shape in the transverse directions, which was attributed to the superposition of the transitions of lignin and hemicellulose. A higher α-loss peak temperature (α-T_LP) and intensity of the α-relaxation process were observed in the L specimens than the transverse specimens. The β-T_LP and γ-T_LP decreased with increasing MC in all orthotropic directions, whereas the individual decline in T_LP was affected differently by MC. In the β-relaxation process, the T_LP was more sensitive to MC changes in the L direction than in the transverse directions. In addition, the individual T_LP in the R and T directions was influenced by per unit adsorbed water to a similar degree for the β and γ-relaxation processes. These findings suggest that the difference in the orthotropic viscoelastic performance might cause some drying defects during the water loss process.     

The flow pattern of solids in a gravity column

Flow pattern of solids in a gravity column (150 mm diam.) with peripheral discharge was studied by measuring the residence time distribution (RTD) of coloured solids tracer in the exit stream. The data were used to calculate dispersion numbers and flow volumes by applying a dispersion model and a multiparameter model respectively. The results show that the flow pattern of solids in the upper 75% of the column height was plug and that this flow pattern was virtually unaffected by the flow rate in the range investigated (35 – 75 g/s millet seed). The flow pattern of the solids in the bottom section of the column is shown to be markedly mixed and to depend on the flow rate. The paper also notes the usefulness of RTD analysis in providing flow models of bulk flow equipment which can give supplementary design and operating information not available by traditional methods.     

Application of time‐temperature superposition to energy limit of linear viscoelastic behavior

The energy approach for evaluation of the limits of linear viscoelastic (LVE) behavior is considered. The approach of Foux and Bruller based on the Reiner‐Weissenberg dynamic theory of strength is developed for the temperature effect. Value of the stored energy at the limit of LVE is considered as the material characteristic independent on loading conditions and temperature. Time–temperature superposition principle is extended for the energy calculations. Curves of the stored energy calculated for different temperatures are shifted to each other in the logarithmic time axes similarly as creep compliance and relaxation modulus curves in creep and tension tests, respectively. Temperature is considered as a factor that accelerates transition form linear to non‐LVE at the same stored energy threshold. This is proved by example of polyvinylchloride by comparing temperature dependences of the stress limits of LVE determined in two independent test series: tensile creep and constant strain rate tests. © 2009 Wiley Periodicals, Inc. J Appl Polym Sci, 2009     

Heat transfer and kinetics in the low temperature pyrolysis of solids

New theory is developed to define the parameters controlling the pyrolysis rate of single particles. It is shown that the relative importance of internal and external heat transfer and of the intrinsic (first order) pyrolysis kinetics can be determined from the Biot number (hR/K) and, depending on the value of the Biot number, one of two Pyrolysis numbers defined by Py = (K/k?c_pR²) or Py′= (h/k?c_pR). On the basis of these groups four regions are defined, and appropriate and simple models of the kinetics of primary pyrolysis outlined. The models are tested against measurements of decomposition and temperature distributions in pyrolysing wood cylinders with diameters in the range 0.6–2.2 cm and at temperatures from 380 to 500°C. Good agreement with theory is found and it is concluded that, under these conditions, internal convection is unimportant and that with suitably large or small values of Bi, Py and Py′ very simple models are adequate. Some implications for reactor design are briefly discussed.     

The influence of suspended solids on oxygen transfer to organic liquids in a bubble column

Volumetric mass transfer coefficients (k_La), and gas holdups (ε_G) were studied for the oxygen transfer into organic slurries. Aluminium oxide, polyvinylchloride and polyethylene were used as solid particles in ligroin and tetralin. It was found that the presence of particles can affect the mass transfer remarkably. Solids with high densities can increase k_La in small concentrations for liquids with low density and viscosity. When the density difference is small or the liquid viscosity is high, the slurry behaves as a pseudohomogeneous phase. Successful correlations were proposed for k_La and ε_G as a function of the effective suspension viscosity.     

Influence of temperature on the flow properties of bulk solids

The flow behaviour of bulk solids depends upon a number of parameters. Shear tests are often used to determine the flow behaviour at room temperature. This paper aims to look at the influence of temperature on the flow behaviour of bulk solids. A newly developed ring shear test shows that the flow behaviour of some specific bulk solids depends upon the temperature.     

Transition to turbulent fluidization in a binary solids fluidized bed

This paper presents a study on the transition velocity from bubbling to turbulent fluidization in a binary solids fluidized bed. Experiments were carried out with two kinds of binary solids mixtures with FCC as fine particles and silica sands as coarse particles. The onset velocity to turbulent fluidization, U_c, determined by the measurement of pressure fluctuations, was found to increase with increasing the fraction of coarse/heavy solids. By introducing an equivalent particle diameter and an equivalent particle density, the results obtained in this study can properly be described by a general correlation of U_c proposed by Cai and co-workers (1989) for mono-density particles with relatively narrow size distribution.     

Observing changes in nonlinear viscoelastic properties occurring throughout the vulcanization process

Using a purposely modified Rubber Process Analyzer, a technique has been developed to record the complete torque signal during a vulcanization test, and to split it into a sequence of single oscillations, which are treated through Fourier transform calculations. Various EPDM‐based compounds were tested to investigate the capabilities of the technique. It was found that the progressive variation of the harmonic torque signal when vulcanization occurs reflects in singularities in the manner that all harmonic components vary during cure. Contrary to the main torque component (i.e., the torque amplitude) that exhibits a smooth variation as vulcanization proceeds, harmonic components exhibit sharp up and down changes at precise times that seem to be related to critical steps in the curing process. For instance, pair harmonic components passes through extremes (maximum or minimum) when scorch time is reached. Odd harmonic components show a singularity that is likely associated with the precise moment when the vulcanizing material passes from a still “liquid” state to an essentially “solid” one. This event does not coincide with the time for the maximum cure rate to be reached but occurs either before or after it, depending on the compound or the curing parameters. Such results support the view that rubber vulcanization presents some analogy with a nucleation process and underline the promising capabilities of the test technique. © 2006 Wiley Periodicals, Inc. J Appl Polym Sci 101: 1140–1150, 2006     

Mass transfer from suspended solids to a liquid in agitated vessels

A new fundamental approach to the formulation of mass transfer from suspended solids to a liquid in agitated vessels is presented. Influence of various dimensionless groups on mass transfer is studied using the water-banzoic acid system for experimental work.Results are compared with previous works in agitated vessels and a correlation is proposed:Sh = 0.046Re^0.283Ga^0.173U^?0.011(T/d)^0.019Sc^O.461     

Structural changes of fullerene by heat-treatment up to graphitization temperature

Structural changes of the C₆₀ and C₇₀ mixture during heat-treatment up to 2400 °C were studied by observing the carbonized disk of the fullerene with Raman spectroscopy, X-ray diffraction, FE-SEM, TEM, and AFM/STM. The fullerene lost its five-membered ring and its fcc crystal structure by heat-treatment at 800 °C, as revealed by the Raman spectra and X-ray diffraction, forming hexagonal planes which were randomly arranged by 1300 °C. Further heat-treatment allowed some stacking of layers which grow to dominate, reducing the randomly oriented planes. The graphitized temperature up to 2400 °C provided a very sharp peak at 26 °, suggesting formation of stable turbostratic layers. The TEM characterized turbostratic stacking of 3 to 4 layers. A series of observation under AFM/STM and TEM indicate the crystal of the fullerene, amorphous grain of the hexagonal planes, and the hollow sphere are all in the same range of size around 10–20 nm. Such microdomains induced micro-roughness as observed by FE-SEM on the surface of the carbon disk. Superstructure of hexagonal plane was observed on the surface. A kind of solid state carbonization of the fullerene is suggested to maintain the dimensions of its crystal into the spherical microdomain, even if its marked structural changes take place within the unit.     

Low temperature catalysts for oxidative coupling of methane

A simple review is given to the recent work of the oxidative coupling of methane at low temperature. Emphasis is laid on the different systems of low-temperature catalysts under conventional CH₄/O₂ co-feed conditions, and on the investigations of low-temperature oxidative coupling of methane in the presence of steam in the feed. Other approaches, e.g. oxidative coupling of methane at elevated pressure and moderate temperature, preparing ethylene by oxidative coupling reaction of methane on laser-activated solid surface, are also included.