Modeling of aerosol spray characteristics for synthesis of sensor thin film from solution

A model is developed of aerosol spray for synthesis of sensor film from solution. The synthesis technique considered involves atomization of a solution of mixed salts in methanol, spraying of solution droplets, droplet deposition on a heated substrate, evaporation and chemical reaction to produce mixed oxides, and subsequent film growth. The precise control of oxide nanoparticle size distribution and inter-particle spacing in the film is crucial to achieving high sensitivity. These in turn largely depend on the droplet characteristics prior to impingement on the substrate. This paper focuses on the development of a model to describe the atomization and spray processes prior to the film growth. Specifically, a mathematical model is developed utilizing computational fluid dynamics solution of the equations governing the transport of atomized droplets from the nozzle to the substrate in order to predict droplet characteristics in flight. The predictions include spatial distribution of droplet size and concentration, and the effect on these characteristics of swirling inlet flow at the spray nozzle.     

A coupled discrete droplet and SPH model for predicting spray impingement onto surfaces and into fluid pools

In this paper we detail the development of a combined DEM-SPH model for spray impingement into a pool of water or onto a flat surface on which a pool of water can build up. The spray is represented by discrete particles which can collide with solid objects, each other and also merge with liquid surfaces. The liquid pool dynamics are solved for using the SPH method. The proposed coupling allows momentum to be transferred from the discrete spray phase into the fluid phase in the pool. The performance of this coupled DEM-SPH method is evaluated by comparing to experiments performed for simple spray arrangements in which the pressure in the pool just above the solid surface is carefully measured by a probe that is moved systematically across the surface. A comparison of the simulated pressure distribution with those from the experiments shows very good agreement for the size of the high pressure region, the average pressure the pressure distribution within this region generated by the spray impingement for cases with one, two and three overlapping sprays. Collisions between spray droplets in the case of multiple sprays are found to have a small but noticeable effect on the details of the high pressures in the regions of overlap of the sprays.     

Anisotropy of torsional rigidity of sheet polymer composite materials

Wide application of polymer composite materials (PCM) in modern technology calls for detailed evaluation of their stress-strain properties in a broad temperature range. To obtain such information, we use the dynamic mechanical analysis and with the help of a reverse torsion pendulum measure the dynamic torsional rigidity of PCM bars of rectangular cross section in the temperature range up to 600 K. It is found that the temperature dependences of the dynamic rigidity of the calculated values of dynamic shear moduli are governed by the percentage and properties of the binder and fibers, the layout of fibers, the phase interaction along interfaces, etc. The principles of dynamic mechanical spectrometry are used to substantiate and analyze the parameters of anisotropy by which the behavior of a composite can be described in the temperature range including the transition of the binder from the glassy into a highly elastic state. For this purpose, the values of dynamic rigidity are measured under low-amplitude vibrations of the PCM specimens with a fiber orientation angle from 0 to 90°. It is shown that for unidirectional composites the dependence between the dynamic rigidity and the fiber orientation angle is of extreme character. The value and position of the peak depend on the type of the binder and fibers and change with temperature. It is found that the anisotropy degree of PCM is dictated by the molecular mobility and significantly changes in the temperature range of transition of the binder and reinforcement from the glassy into a highly elastic state (in the case of SVM fibers). The possibility of evaluating the anisotropy of composites with other reinforcement schemes, in particular, of orthogonally reinforced PCMs, is shown.Translated from Mekhanika Kompozitnykh Materialov, Vol. 35, No. 3, pp. 291–308, May–June, 1999.     

A fully meshless method for ‘gas – evaporating droplet’ flow modelling

A meshless method for modelling two-phase flows with phase transition is described. The method is based on consideration of three systems: viscous-vortex blobs, thermal-blobs and droplets; and can be applied for numerical simulation of 2D non-isothermal flows of ‘gas-evaporating droplets’ in the framework of the one-way coupled two-fluid approach. The carrier phase is viscous incompressible gas. The dispersed phase is presented by a cloud of identical spherical droplets, and, due to evaporation, the radius and mass of droplets are time dependent. The carrier phase parameters are calculated using the viscous-vortex and thermal-blob method; the dispersed phase parameters are calculated using the Lagrangian approach. Two applications have been considered: (i) a standard benchmark – Lamb vortex; (ii) a cold spray injected into a hot quiescent gas. In the latter problem three cases corresponding to three droplet sizes were investigated. The smallest droplets (of the three cases considered) are more readily entrained by the carrier phase and form ring-like structures; the flow shows better mixing. Larger droplets evaporate less intensively. The medium sized droplets collect into two narrow bands stretched along the jet axis. The largest droplets form a two-phase jet, which remains close to the jet axis. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Homogenization of Elastic Properties of Short Fiber Reinforced Composites Based on Discrete Microstructure Data

Since the microstructure of short fiber reinforced composites is inhomogeneous, the application of micromechanical models is useful, that take into account their characteristics like the fiber orientation and the aspect ratio of fibers. Two different methods are considered in this work: A two-step approach is utilized to get approximately the upper and lower bounds of the elastic properties. Furthermore, an approximation for the elastic properties is calculated by the self-consistence method. Both methods use discretely microstructural information including the length, the diameter and the orientation of each single fiber. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Application of a genetic algorithm to optimal lay-up of shells made of composite laminates

The orientation of fiber direction in layers and the number of layers of composites play the major role in determining the strength and stiffness. Thus, the basic design problem is to determine the optimum stacking sequence of the composite laminate. Many methods are available at present for the design optimization of structural systems. However, these methods are based on mathematical programming techniques involving the gradient search and the direct search. These methods assume that the variables are continuous. In this paper, a different search and optimization algorithm, known as a Genetic Algorithm (GA), has been successfully applied to obtain the optimum fiber orientation of multilayered shells, which considers the angle of fiber orientation as a discrete variable. The principle of GA is applied to obtain optimum layers and the orientation of fibers of stiffened shells for both the symmetric and antisymmetric orientations of fibers for dynamic analysis. Shells composed of two to nine layers without stiffeners, with one stiffener, and with two stiffeners for a single as well as different materials are analyzed and the maximum frequency for each population is computed using the FEAST-C software. Submitted to the 11th International Conference on Mechanics of Composite Materials (Riga, June 11–15, 2000). Published in Mekhanika Kompozitnykh Materialov, Vol. 36, No. 2, pp. 271–278, March–April, 2000.     

Skew products of interval maps over subshifts

We treat step skew products over transitive subshifts of finite type with interval fibers. The fiber maps are diffeomorphisms on the interval; we assume that the end points of the interval are fixed under the fiber maps. Our paper thus extends work by V. Kleptsyn and D. Volk who treated step skew products where the fiber maps map the interval strictly inside itself. We clarify the dynamics for an open and dense subset of such skew products. In particular we prove existence of a finite collection of disjoint attracting invariant graphs. These graphs are contained in disjoint areas in the phase space called trapping strips. Trapping strips are either disjoint from the end points of the interval (internal trapping strips) or they are bounded by an end point (border trapping strips). The attracting graphs in these different trapping strips have different properties.     

Predicting the elastoplastic response of fiber-reinforced metal matrix composites

This paper aims to investigate the effect of microstructure parameters (such as the cross-sectional shape of fibers and fiber volume fraction) on the stress–strain behavior of unidirectional composites subjected to off-axis loadings. A micromechanical model with a periodic microstructure is used to analyze a representative volume element. The fiber is linearly elastic, but the matrix is nonlinear. The Bodner–Partom model is used to characterize the nonlinear response of the fiber-reinforced composites. The analytical results obtained show that the flow stress of composites with square fibers is higher than with circular or elliptic ones. The difference in the elastoplastic response, which is affected by the fiber shape, can be disregarded if the fiber volume fraction is smaller than 0.15. Furthermore, the effect of fiber shape on the stress–strain behavior of the composite can be ignored if the off-axis loading angle is smaller than 30°.     

On Copositive Programming and Standard Quadratic Optimization Problems

A standard quadratic problem consists of finding global maximizers of a quadratic form over the standard simplex. In this paper, the usual semidefinite programming relaxation is strengthened by replacing the cone of positive semidefinite matrices by the cone of completely positive matrices (the positive semidefinite matrices which allow a factorization FF ^T where F is some non-negative matrix). The dual of this cone is the cone of copositive matrices (i.e., those matrices which yield a non-negative quadratic form on the positive orthant). This conic formulation allows us to employ primal-dual affine-scaling directions. Furthermore, these approaches are combined with an evolutionary dynamics algorithm which generates primal-feasible paths along which the objective is monotonically improved until a local solution is reached. In particular, the primal-dual affine scaling directions are used to escape from local maxima encountered during the evolutionary dynamics phase.     

Creep of Heat-Resistant Composites of an Oxide-Fiber/Ni-Matrix Family

A creep model of a composite with a creeping matrix and initially continuous elastic brittle fibers is developed. The model accounts for the fiber fragmentation in the stage of unsteady creep of the composite, which ends with a steady-state creep, where a minimum possible average length of the fiber is achieved. The model makes it possible to analyze the creep rate of the composite in relation to such parameters of its structure as the statistic characteristics of the fiber strength, the creep characteristics of the matrix, and the strength of the fiber-matrix interface, the latter being of fundamental importance. A comparison between the calculation results and the experimental ones obtained on composites with a Ni-matrix and monocrystalline and eutectic oxide fibers as well as on sapphire fiber/TiAl-matrix composites shows that the model is applicable to the computer simulation of the creep behavior of heat-resistant composites and to the optimization of the structure of such composites. By combining the experimental data with calculation results, it is possible to evaluate the heat resistance of composites and the potential of oxide-fiber/Ni-matrix composites. The composite specimens obtained and tested to date reveal their high creep resistance up to a temperature of 1150°C. The maximum operating temperature of the composites can be considerably raised by strengthening the fiber-matrix interface.     

Critical length and distribution of fibrous fillers and composites

The adhesion of UKN-01 carbon fibers to a PA-12 polymeric matrix is investigated by the method of testing single-fiber model composites. The distribution of critical fiber length is constructed from measurements of fragment lengths formed in the final stage of testing. Variation in the distribution of critical length is established as a result of surface treatment of the reinforcing fiber. A bimodal distribution corresponds to the initial carbon fiber, and a monomodal distribution to the treated fiber. This is explained by replacement of a physicomechanical type of interaction of the phase interface by a physicochemical interaction owing to electrochemical treatment of the fiber surface. Analysis of the results indicated that each type of interphase interaction has its own characteristic critical length. The selection of critical length has been confirmed for calculation of the interphase shear strength by the Kelly-Tyson formula.Uvikom, Moscow Oblast, Russia. Translated from Mekhanika Kompozitnykh Materialov, Vol. 33, No. 1, 98–103, January–February, 1997.     

Evolution of Mechanical Properties in Tissues Undergoing Deformation-Related Fiber Remodeling Processes

We consider a biological fibrous soft tissue in which fibers are distributed in all directions. The mechanical properties of the fibers evolve due to a continuous remodeling process. The model to describe these fiber properties is based on the strain energy density of the protofibers and a survival kernel which describes the deformation-related property changes. In particular, this study investigates the development of the fiber orientation density for different choices of the fiber creation rate and fiber dissolution rate models. It has been shown that the fiber orientation density depends on both the history of the deformation and the deformation state of the fibers at the time of their creation. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Model studies of stress-intensity factors near cracks interacting with fibers

The problem of determining the stress-intensity factors near cracks interacting with fibers is solved for the first time using data from optical-polarization measurements. Simplified models of composites are investigated — plates reinforced with single short fibers with cracks assigned on one of the ends of the fibers and tensioned in the direction of the fibers. The plates (dies) were fabricated from a photosensitive material, and the fibers were modeled by bars of steel, glass, and polymer. The stress-intensity factors were determined from Eq. (5) using data derived from optical-polarization measurements at several points by the nonlinear method of least squares. We investigated the influence exerted by several physical and geometric parameters on the stress-intensity factors. It was established that the stress-intensity factor K₁ near the end of a crack interacting with a fiber is higher than the factor K⁰ ₁ near a crack of corresponding length in the unreinforced plate. The ratio K₁/K⁰ ₁ depends on the mechanical properties of the fiber and die materials and the geometric dimensions of the crack and fiber. Despite the fact that these results were obtained using simplified models of composites, they are of interest for evaluation of the failure and serviceability of real composites.Scientific-Research Institute of Mechanics, M. V. Lomonosov Moscow State University, Moscow, Russia. Translated from Mekhanika Kompozitnykh Materialov, Vol. 32, No. 4, pp. 493–501.     

张量封闭模型与三维取向分布对纤维悬浮槽流稳定性的影响

应用3种不同的纤维方向张量封闭模型,数值模拟了纤维悬浮槽流的流动稳定性问题,从而研究封闭模型和纤维的三维取向分布对稳定性分析的影响．结果发现,采用3种不同封闭模型所得到的流动稳定特性与纤维参数之间的关系是相同的,但采用三维混合封闭模型时,由于纤维的取向与流向的偏差程度较大,所以纤维对流动的不稳定性具有最强的抑制作用．而采用二维混合封闭模型时,由于纤维在平面取向条件下,其轴线整体上趋于呈流向排列,使得对流体的作用削弱,导致纤维对流动不稳定性抑制的作用最弱．     

Investigation of the three-dimensional micromechanical behavior of woven-fabric composites

A three-dimensional representative volume-element model is presented to study the micromechanical behavior of woven-fabric composites. The effects of the fiber undulation zone and the fiber braid angle on the elastic modulus of the composites are taken into account in the unit cell. Based on isostrain and isostress assumptions, a standard homogenization procedure is used to calculate the effective elastic properties of woven-fabric composites, and all the final stiffness components are expressed in an explicit form. The results obtained by the model considered agree with published experimental results very well. The relationship between the geometric parameters, such as fiber width, thickness, volume fraction, etc., and the macromechanical behavior of the composites can be obtained by this model. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 42, No. 2, pp. 209–220, April–May, 2006.     

Evolution of the Fiber Density in Biological Tissues

An important challenge in the field of biomechanics is to understand and to model the properties of fibrous tissues. We consider a matrix-fiber composite for which the matrix microstructure and its mechanical properties are taken to be constant. The initial fiber distribution is assumed to be unstructured and the mechanical properties of the fibers evolve during deformation. Further we assume that the fiber creation rate is constant while the fiber degeneration is stretch-dependent. In particular, this study investigates the change of the fiber orientation density when a sudden simple shear is applied to the material. The fiber orientation density depends on the current deformation, the history of the deformation, and the deformation state of the fibers at the time of their creation. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Study of microbuckling of fiber-reinforced composite materials

On the basis of the theory of microbuckling of lamina-reinforced composites and formula predicting the critical composite stress for microbuckling in the shear mode _cs published in the literature, a FORTRAN program for study of the behavior of microbuckling of fiber reinforced composites has been developed. Some types of composite materials (reinforcement of different fibers and epoxy matrix) have been studied. Graphics and curves, accounting for the dependences of the compressive stress at failure _cs from the reinforcement volume k, specimen length L, and shear modulus of resin G_r have been obtained. The comparison of the theoretical diagrams presented here and experimental and theoretical results, published in the literature shows good agreement. The basic conclusion of the work presented here is that the study could be used for other fiber reinforced composites (with different mechanical properties of matrices and fibers).Institute of Mechanics, Bulgarian Academy of Sciences, Sofia, Bulgaria. Published in Mekhanika Kompozitnykh Materialov, Vol. 32, No. 4, pp. 531–538, July–August, 1996.     

圆管纤维悬浮湍流场中粒子运动的研究

利用从细长体理论出发得到的三维分段积分法和湍流简化方法模拟了大量纤维粒子在圆管湍流内的运动．统计了不同Re数下计算区域内的纤维的取向分布,计算结果与实验结果基本吻合,结果表明湍流的脉动速度导致纤维取向趋于无序,且随着Re数的增加,纤维取向的分布越来越趋于均匀．其后又考虑了纤维速度和角速度的脉动,二者都充分体现了流体速度脉动的影响,且纤维速度的脉动在流向上的强度大于横向,而其角速度的脉动在流向上的强度小于横向．最后统计了纤维在管道截面上的位置分布,说明Re数的增加加速了纤维在管道截面上的位置扩散．     

The simulation of electrified liquid jets

The simulation of a two-dimensional electrified liquid jet is described. A finite difference technique is coupled with a computational fluid dynamic code to solve Poisson's equation and the Navier-Stokes equations at the electrostatic fluid-flow interface. The dynamics of free-surface electrohydrodynamic fluid flow are simulated for a dielectric fluid in an electrostatics nozzle and a conducting two-dimensional jet. The fluid flow in a nozzle is compared with and without an applied electric field, and the effects of adding a grounded conducting cylinder to the configuration is demonstrated. A set of time sequence graphs are used to illustrate the breakup of a charged jet into droplets, and the influence of viscosity on jet formation and breakup is depicted.     

Temperature field of a layer of a fibrous composite material under conditions of external thermal radiation

On the basis of an expression for the scattering phase function of an individual fiber, relations modeling radiative properties of fibrous composites are obtained. We calculate the temperature state of a layer of such a material under condition of external thermal radiation. Dependences of temperature distributions on the volume fraction of fibers in the composite, their reflectance, and size are investigated. Translated from Matematychni Metody ta Fizyko-Mekhanichni Polya, Vol. 51, No. 1, pp. 185–193, January–March, 2008.