Effect of the molecular structure of ethene–propene and styrene–butadiene copolymers on their compatibilization efficiency in low‐density polyethylene/polystyrene blends

The effect of the molecular structure of styrene–butadiene (SB) block copolymers and ethene–propene (EPM) random copolymers on the morphology and tensile impact strength of low‐density polyethylene (LDPE)/polystyrene (PS) (75/25) blends has been studied. The molecular characteristics of SB block copolymers markedly influence their distribution in LDPE/PS blends. In all cases, an SB copolymer is present not only at the interface but also in the bulk phases; this depends on its molecular structure. In blends compatibilized with diblock copolymers, compartmentalized PS particles can also be observed. The highest toughness values have been achieved for blends compatibilized with triblock SB copolymers. A study of the compatibilization efficiency of SB copolymers with the same number of blocks has shown that copolymers with shorter PS blocks are more efficient. A comparison of the obtained results with previous results indicates that the compatibilization efficiency of a copolymer strongly depends both on the blend composition and on the properties of the components. The compatibilization efficiency of an EPM/SB mixture is markedly affected by the rheological properties of the copolymers. The addition of an EPM/SB mixture containing EPM with a higher viscosity leads to a higher improvement or at least the same improvement in the tensile impact strength of a compatibilized blend as the same amount of neat SB. © 2007 Wiley Periodicals, Inc. J Appl Polym Sci, 2008     

Modeling and numerical analysis of counter-current dialyzer at steady state

A mathematical model of a continuous counter-current dialyzer in the case of the transport of one component, which is based on the mass balance and balance of transported component, has been presented. It enables users to calculate the component recovery yield if parameters of the dialyzer (height, dimensions of compartments), parameters of the membrane (thickness, partition coefficients, diffusivity of the component in the membrane, flux of solution through the membrane), parameters of liquids in both the compartments (density, viscosity, diffusivity of the component) and parameters of streams entering the dialyzer (component concentration, volumetric liquid flow rate) are specified.     

Application of the reaction kinetics and dispersion model to gas-solid reactors for removal of sulfur dioxide from flue gas

The conversions of a reactive, micro-grained limestone were studied in terms of exposure time and concentration of sulfur dioxide in the flue gas. The rates of the sulfation reaction were correlated as a function of the conversion of calcium oxide to sulfate and concentration of sulfur dioxide in the gas phase. In comparison with active sodium carbonate the sulfation of limestone particles proceeds at the rate which is substantially lower than the sulfation rate of soda particles.The empirical kinetic equation developed in this study is further applied in a two-phase dispersion model of simplified non-ideal flow behavior of the gas and solid in the reactor. The model can serve a rational basis for the conceptual design of a suitable contacting apparatus. Numerical solutions of the model equations outline possibilities and limitations of the dry lime process for the removal of sulfur dioxide from hot flue gas.     

Stability and post-critical growth of a system of cooling or shrinkage cracks

When a system of parallel equidistant cooling cracks propagates into an elastic halfspace, it reaches at a certain depth of the cracks a critical point of instability, and the equilibrium path of the system bifurcates. Further extension of equally long cracks is unstable and impossible. The stable post-critical path consists of extension of every other crack upon further cooling, initially with a crack jump at constant temperature, while the intermediate cracks stop growing and gradually diminish their stress intensity factor until it becomes zero. This represents a second critical state at which these intermediate cracks suddenly close over a finite length at no change in temperature and at constant length of the leading cracks. Subsequently, as the cooling front further advances, the leading cracks grow at equal length until they again reach a critical state, at which every other crack stops growing, and the process in which the crack spacing doubles is repeated. In this manner, the spacing of the opened cooling cracks fluctuates around roughly the one-half value of the cooling penetration depth.The instability is determined by the sign of the second variation of the work needed to create the cracks, which leads to positive definiteness conditions for a matrix consisting of partial derivatives of the stress intensity factors with regard to crack lengths, subjected to admissibility conditions for the eigenvector of crack length increments. The first initial state of crack arrest is characterized by the vanishing of the diagonal element of the matrix, while the second critical state of crack closing is characterized by the vanishing of the determinant of this matrix.The critical states and the postcritical crack growth are calculated numerically by finite elements. The solution is applied to the cooling of a hot granite mass, the cracking of which is important for one recently proposed geothermal heat extraction scheme. The solution is also of interest for drying shrinkage cracks, especially in concrete.

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Résumé Lorsque un système de fissures équidistantes parallèles survenant lors d'un refroidissement se propage dans un demi espace élastique, il atteint à une certaine profondeur de fissuration un état critique d'instabilité et le chemin d'équilibre du système bifurque. Une extension ultérieure de fissures de longueurs égales se présente comme instable est impossible. Le chemin post-critique stable correspondra à une extension de toute autre fissure correspondant à un refroidissement ultérieur, et ce à l'origine avec un resaut de la fissure à temperature constante, tandis que les fissures intermédiaires cessent leur croissance et voient leur facteur d'intensité de contrainte graduellement diminuer jusqu'à la valeur nulle. Ceci correspond à un deuxième état critique pour lequel les fissures intermédiaires se ferment brusquement sur une longueur finie sans que ne se produise un changement de température, et à longueur constante des fissures principales. Par après lorsque le front de refroidissement continue d'avancer, les fissures principales croissent d'une longueur égale jusqu'à ce qu'elles atteignent à nouveau un état critique, état pour lequel les autres fissures cessent de croître et pour lequel le processus d'espacement des fissures est répété. De cette manière, l'espacement de fissures s'ouvrant lors du refroidissement fluctue autour d'une valeur correspondant sensiblement à la moitié de la valeur de la pénétration de refroidissement.L'instabilité est déterminée par le signe de la deuxième variation du travail nécessaire pour créer les fissures, ce qui conduit à des conditions positives non définies pour une matrice comportant les dérivées partielles des facteurs d'intensité d'entaille par rapport aux longueurs de la fissure, l'ensemble étant sujet aux conditions d'admissibilité de l'eigenvector pour des accroissement de longueurs de la fissures. Le premier état initial de l'arrêt de la fissure est caractérisé par la disparition de l'élément diagonal de la matrice tandis que le deuxième état critique de fermeture de la fissure est caractérisé par la disparition du déterminant de cette matrice.Les états critiques et la croissance post-critique de la fissure sont calculés de façon numérique par des éléments finis. La solution est appliquée au refroidissement d'une masse granitique à haute température dont la fissuration est importante, dans le cadre d'un schéma d'extraction de la chaleur géothermique proposé récemment. La solution est également intéressante à appliquer dans le cas de fissures procédant d'une contraction due au séchage, et ce en particulier dans le cas du béton.

     

Sampling analysis of concrete structures for creep and shrinkage with correlated random material parameters

The latin hypercube sampling method, which represents the most efficient way to determine the statistics of the creep and shrinkage response of structures, has previously been developed and used under the assumption that the random parameters of the creep and shrinkage prediction model are mutually independent. In reality they are correlated. On the basis of existing data, this paper establishes, by means of the method of maximum likelihood, the joint multivariate probability distribution of the random parameters involved, tests the hypothesis of mutual dependence of parameters on the basis of the χ²-distribution, and generalizes the latin hypercube sampling method to the case of correlated multinormal random parameters. The generalization is accomplished by an orthogonal matrix transformation of the random parameters based on the eigenvectors of the inverse of the covariance matrix. This yields a set of new random parameters which are uncorrelated (independent) and can be subjected to the ordinary latin hypercube sampling, with samples of equal probabilities. Numerical examples of statistical prediction of creep and shrinkage effects in structures confirm the practical feasibility of the method and reveal a good agreement with the scatter observed in some previous experiments.     

Size Effect on Strength of Floating Sea Ice under Vertical Line Load

The size effect on the nominal strength of a floating ice plate subjected to a vertical uniform line load is analyzed. The cracks produced by the load, which are parallel to the load line, are treated as softening inelastic hinges. The problem is one dimensional in the direction normal to the load line, equivalent to a beam on elastic foundation provided by buoyancy of ice in water. The softening moment-rotation diagram of inelastic hinges is simplified as linear and its dependence on structure size (ice thickness) is based on the energy dissipated by fracture. For thick enough plates, no two hinges (on one side of the line load) can soften simultaneously, in which case a simple analytical solution is possible. In that case, the load-deflection diagram has multiple peaks and troughs and consists of a sequence of spikes that get progressively sharper as the plate thickness increases. In terms of a dimensionless nominal strength, the effect of a finite fracture process zone at ice surface leads to an up-and-down size effect plot, such that each load peak decreases with the size at first but then asymptotically approaches a rising asymptote of the type (thickness)1/4 (which implies a reverse size effect, caused by buoyancy). The energy dissipation when the crack in the hinge gets deep causes a strong monotonic size effect, such that the dimensionless troughs between two spikes, in the case of thick enough plate, decrease asymptotically as (thickness)?1/2. For thin enough plates, more than one hinge soften simultaneously and, in the asymptotic case of vanishing ice thickness, the plasticity solution, which has no size effect, is approached. In the intermediate size range with hinges softening simultaneously, the exact solution is complicated and only approximate formulas for the size effect are possible. They are constructed by asymptotic matching.     

Improved prediction model for time-dependent deformations of concrete: Part 7—Short form of BP-KX model,statistics and extrapolation of short-time data

For structures that do not have a high sensitivity to creep or for preliminary design of any structures, practising engineers demand a short formula for predicting the material creep properties. Such a formula is given in the present addendum to a previous six-part paper. It is based on optimal fitting of the previously published log-double power law to the formulae of the BP-KX model. A simple formula giving directly the compliance function rate is also presented. Finally, a simple method of improving the predictions on the basis of short-time measurements is described, and tables giving the statistics of the deviations of the prediction formulas of the simplified model and its short form from the data in the literature are presented.     

Effect of cracking in drying and shrinkage specimens

The significance of cracking and microcracking caused by nonuniform drying shrinkage of test specimens is analyzed. To assure that no cracks are produced by drying in load-free specimens, one must lower the environmental humidity gradually and sufficiently slowly, and use very thin specimens (about 1 mm thick). Graphs for the maximum admissible rate of change of environmental humidity, calculated from both linear and nonlinear diffusion theories, are provided. The spacing and width of parallel cracks due to drying are estimated from fracture mechanics considerations. In normal size specimens the drying cracks are usually too narrow to be visible. Drying leads to discontinuous microcracking rather than continuous macrocracks and is represented better as strain softening than as an abrupt stress drop. Shrinkage cracking can increase drying diffusivity by several orders of magnitude.     

Formal verification of multitasking applications based on timed automata model

The aim of this paper is to show, how a multitasking application running under a real-time operating system compliant with an OSEK/VDX standard can be modeled by timed automata. The application under consideration consists of several non-preemptive tasks and interrupt service routines that can be synchronized by events. A model checking tool is used to verify time and logical properties of the proposed model. Use of this methodology is demonstrated on an automated gearbox case study and the result of the worst-case response time verification is compared with the classical method based on the time-demand analysis. It is shown that the model-checking approach provides less pessimistic results due to a more detailed model and exhaustive state-space exploration.