Search results for: Aluminum matrix composites

Authors: Ebregbe David, Deng Weibo

Abstract:

The traditional second order statistics approach of using only the hermitian covariance for non circular signals, does not take advantage of the information contained in the complementary covariance of these signals. Radar systems often use non circular signals such as Binary Phase Shift Keying (BPSK) signals. Their noncicular property can be exploited together with the dual centrosymmetry of the bistatic MIMO radar system to improve angle estimation performance. We construct an augmented matrix from the received data vectors using both the positive definite hermitian covariance matrix and the complementary covariance matrix. The Unitary ESPRIT technique is then applied to the signal subspace of the augmented covariance matrix for automatically paired Direction-of-arrival (DOA) and Direction-of-Departure (DOD) angle estimates. The number of targets that can be detected is twice that obtainable with the conventional ESPRIT approach. Simulation results show the effectiveness of this method in terms of increase in resolution and the number of targets that can be detected.

Keywords: Bistatic MIMO Radar, Unitary Esprit, Non circular signals.

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Authors: Yongxin Yuan, Hao Liu

Abstract:

In this paper, we first give the representation of the general solution of the following least-squares problem (LSP): Given matrices X ∈ Rn×p, B ∈ Rp×p and A0 ∈ Rr×r, find a matrix A ∈ Rn×n such that XT AX − B = min, s. t. A([1, r]) = A0, where A([1, r]) is the r×r leading principal submatrix of the matrix A. We then consider a best approximation problem: given an n × n matrix A˜ with A˜([1, r]) = A0, find Aˆ ∈ SE such that A˜ − Aˆ = minA∈SE A˜ − A, where SE is the solution set of LSP. We show that the best approximation solution Aˆ is unique and derive an explicit formula for it. Keyw

Keywords: Inverse problem, Least-squares solution, model updating, Singular value decomposition (SVD), Optimal approximation.

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Authors: Ilija Plecas, Uranija Kozmidis-Luburic, Radojica Pesic

Abstract:

The leaching rate of 137Cs from spent mix bead (anion and cation) exchange resins in a cement-bentonite matrix has been studied. Transport phenomena involved in the leaching of a radioactive material from a cement-bentonite matrix are investigated using three methods based on theoretical equations. These are: the diffusion equation for a plane source an equation for diffusion coupled to a firstorder equation and an empirical method employing a polynomial equation. The results presented in this paper are from a 25-year mortar and concrete testing project that will influence the design choices for radioactive waste packaging for a future Serbian radioactive waste disposal center.

Keywords: bentonite, cement , radioactive waste, composite, disposal, diffusion

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Authors: H. Fazlinejad, A. Halvaee

Abstract:

In this study, characteristics of ATIG welds using ZnO flux on aluminum was investigated and compared with TIG welds. Autogenously AC-ATIG bead on plate welding was applied on Al1050 plate with a coating of ZnO as the flux. Different levels of welding current and flux layer thickness was considered to study the effect of heat input and flux quantity on ATIG welds and was compared with those of TIG welds. Geometrical investigation of the weld cross sections revealed that penetration depth of the ATIG welds with ZnO flux, was increased up to 2 times in some samples compared to the TIG welds. Optical metallographic and Scanning Electron Microscopy (SEM) observations revealed similar microstructures in TIG and ATIG welds. Composition of the ATIG welds slag was also analyzed using X-ray diffraction. In both TIG and ATIG samples, the lowest values of microhardness were observed in the HAZ.

Keywords: ATIG, active flux, weld penetration, Al 1050, ZnO.

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Authors: Fatemeh Panjeh Ali Beik

Abstract:

In the present work, we propose a new projection method for solving the matrix equation AXB = F. For implementing our new method, generalized forms of block Krylov subspace and global Arnoldi process are presented. The new method can be considered as an extended form of the well-known global generalized minimum residual (Gl-GMRES) method for solving multiple linear systems and it will be called as the extended Gl-GMRES (EGl- GMRES). Some new theoretical results have been established for proposed method by employing Schur complement. Finally, some numerical results are given to illustrate the efficiency of our new method.

Keywords: Matrix equation, Iterative method, linear systems, block Krylov subspace method, global generalized minimum residual (Gl-GMRES).

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Authors: Saliha Gachi, Mouloud Aissani, Fouad Boubenider

Abstract:

Friction Stir Welding (FSW) is a solid-state welding technique that can join material without melting the plates to be welded. In this work, we are interested to demonstrate the potentiality of FSW for joining the heat-treatable aluminum alloy 2024-T3 which is reputed as difficult to be welded by fusion techniques. Thereafter, the FSW joint is compared with another one obtained from a conventional fusion process Tungsten Inert Gas (TIG). FSW welds are made up using an FSW tool mounted on a milling machine. Single pass welding was applied to fabricated TIG joint. The comparison between the two processes has been made on the temperature evolution, mechanical and microstructure behavior. The microstructural examination revealed that FSW weld is composed of four zones: Base metal (BM), Heat affected zone (HAZ), Thermo-mechanical affected zone (THAZ) and the nugget zone (NZ). The NZ exhibits a recrystallized equiaxed refined grains that induce better mechanical properties and good ductility compared to TIG joint where the grains have a larger size in the welded region compared with the BM due to the elevated heat input. The microhardness results show that, in FSW weld, the THAZ contains the lowest microhardness values and increase in the NZ; however, in TIG process, the lowest values are localized on the NZ.

Keywords: Friction stir welding, tungsten inert gaz, aluminum, microstructure.

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Authors: Khairil Iskandar Othman, Zarina Bibi Ibrahim, Mohamed Suleiman

Abstract:

A parallel block method based on Backward Differentiation Formulas (BDF) is developed for the parallel solution of stiff Ordinary Differential Equations (ODEs). Most common methods for solving stiff systems of ODEs are based on implicit formulae and solved using Newton iteration which requires repeated solution of systems of linear equations with coefficient matrix, I - hβJ . Here, J is the Jacobian matrix of the problem. In this paper, the matrix operations is paralleled in order to reduce the cost of the iterations. Numerical results are given to compare the speedup and efficiency of parallel algorithm and that of sequential algorithm.

Keywords: Backward Differentiation Formula, block, ordinarydifferential equations.

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Authors: Ehsan Bashiri

Abstract:

A 7-step method (with 25 sub-steps) to assess risk of air pollutants is introduced. These steps are: pre-considerations, sampling, statistical analysis, exposure matrix and likelihood, doseresponse matrix and likelihood, total risk evaluation, and discussion of findings. All mentioned words and expressions are wellunderstood; however, almost all steps have been modified, improved, and coupled in such a way that a comprehensive method has been prepared. Accordingly, the SADRA (Statistical Analysis-Driven Risk Assessment) emphasizes extensive and ongoing application of analytical statistics in traditional risk assessment models. A Sulfur Dioxide case study validates the claim and provides a good illustration for this method.

Keywords: Criteria air pollutants, Matrix of risk, Riskassessment, Statistical analysis.

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Authors: A. R. Azrin Hani, R. Ahmad, M. Mariatti

Abstract:

Textile structures are engineered and fabricated to meet worldwide structural applications. Nevertheless, research varying textile structure on natural fibre as composite reinforcement was found to be very limited. Most of the research is focusing on short fibre and random discontinuous orientation of the reinforcement structure. Realizing that natural fibre (NF) composite had been widely developed to be used as synthetic fibre composite replacement, this research attempted to examine the influence of woven and cross-ply laminated structure towards its mechanical performances. Laminated natural fibre composites were developed using hand lay-up and vacuum bagging technique. Impact and flexural strength were investigated as a function of fibre type (coir and kenaf) and reinforcement structure (imbalanced plain woven, 0°/90° cross-ply and +45°/-45° cross-ply). Multi-level full factorial design of experiment (DOE) and analysis of variance (ANOVA) was employed to impart data as to how fibre type and reinforcement structure parameters affect the mechanical properties of the composites. This systematic experimentation has led to determination of significant factors that predominant influences the impact and flexural properties of the textile composites. It was proven that both fibre type and reinforcement structure demonstrated significant difference results. Overall results indicated that coir composite and woven structure exhibited better impact and flexural strength. Yet, cross-ply composite structure demonstrated better fracture resistance.

Keywords: Cross-ply composite, Flexural strength, Impact strength, Textile natural fibre composite, Woven composite.

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Authors: Abdul H, Jamil A, Imran U

Abstract:

Conflicts identification among non-functional requirements is often identified intuitively which impairs conflict analysis practices. This paper proposes a new model to identify conflicts among non-functional requirements. The proposed model uses the matrix mechanism to identify the quality based conflicts among non-functional requirements. The potential conflicts are identified through the mapping of low level conflicting quality attributes to low level functionalities using the matrices. The proposed model achieves the identification of conflicts among product and process requirements, identifies false conflicts, decreases the documentation overhead, and maintains transparency of identified conflicts. The attributes are not concomitantly taken into account by current models in practice.

Keywords: Conflict Identification, Matrix Maps, Non-functional Requirements, Requirements Analysis, Software Engineering

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Authors: Md. Mahmudul Hasan

Abstract:

OFDM systems are known to have a high PAPR (Peak-to-Average Power Ratio) compared with single-carrier systems. In fact, the high PAPR is one of the most detrimental aspects in the OFDM system, as it can cause power degradation (Inband distortion) and spectral spreading (Out-of-band radiation). In this paper, from the foundation of the PAPR analysis an effective method of PAPR reduction has been proposed based on Orthogonal Eigenvector Matrix (OEM) transform. Extensive computer simulations show that a PAPR reduction of up to 4.4 dB can be obtained without introducing in-band distortion or out-of-band radiation in the system.

Keywords: Orthogonal frequency division multiplexing (OFDM), peak-to-average power ratio (PAPR), Orthogonal Eigenvector Matrix (OEM).

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Authors: M. E. Ali Mohsin, Agus Arsad, Othman Y. Alothman

Abstract:

This study explains the influence of secondary filler on the dispersion of carbon nanotube (CNT) reinforced high density polyethylene (HDPE) nanocomposites (CNT/HDPE). In order to understand the mixed-fillers system, Montmorillonite (MMT) was added to CNT/HDPE nanocomposites. It was followed by investigating their effect on the thermal, mechanical and morphological properties of the aforesaid nanocomposite. Incorporation of 3 wt% each of MMT into CNT/HDPE nanocomposite resulted to the increased values for the tensile and flexural strength, as compared to the pure HDPE matrix. The thermal analysis result showed improved thermal stability of the formulated nanocomposites. Transmission electron microscopy (TEM) images revealed that larger aggregates of CNTs were disappeared upon addition of these two components leading to the enhancement of thermo-mechanical properties for such composites.

Keywords: Secondary filler, Montmorillonite, Carbon nanotube, nanocomposite.

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Authors: H. Soleimanimehr, M. J. Nategh , S. Amini

Abstract:

Development of artificial neural network (ANN) for prediction of aluminum workpieces' surface roughness in ultrasonicvibration assisted turning (UAT) has been the subject of the present study. Tool wear as the main cause of surface roughness was also investigated. ANN was trained through experimental data obtained on the basis of full factorial design of experiments. Various influential machining parameters were taken into consideration. It was illustrated that a multilayer perceptron neural network could efficiently model the surface roughness as the response of the network, with an error less than ten percent. The performance of the trained network was verified by further experiments. The results of UAT were compared with the results of conventional turning experiments carried out with similar machining parameters except for the vibration amplitude whence considerable reduction was observed in the built-up edge and the surface roughness.

Keywords: Aluminum, Artificial Neural Network (ANN), BuiltupEdge, Surface Roughness, Tool Wear, Ultrasonic VibrationAssisted Turning (UAT).

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Authors: Jin-Bao Zhao, Wei Deng

Abstract:

This paper aims at developing a multilevel fuzzy decision support model for urban rail transit planning schemes in China under the background that China is presently experiencing an unprecedented construction of urban rail transit. In this study, an appropriate model using multilevel fuzzy comprehensive evaluation method is developed. In the decision process, the followings are considered as the influential objectives: traveler attraction, environment protection, project feasibility and operation. In addition, consistent matrix analysis method is used to determine the weights between objectives and the weights between the objectives- sub-indictors, which reduces the work caused by repeated establishment of the decision matrix on the basis of ensuring the consistency of decision matrix. The application results show that multilevel fuzzy decision model can perfectly deal with the multivariable and multilevel decision process, which is particularly useful in the resolution of multilevel decision-making problem of urban rail transit planning schemes.

Keywords: Urban rail transit, planning schemes, multilevel fuzzy decision support model, consistent matrix analysis

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Authors: Abdul Rashid Husain, Mohamad Noh Ahmad, Abdul Halim Mohd. Yatim

Abstract:

In this paper, stabilization of an Active Magnetic Bearing (AMB) system with varying rotor speed using Sliding Mode Control (SMC) technique is considered. The gyroscopic effect inherited in the system is proportional to rotor speed in which this nonlinearity effect causes high system instability as the rotor speed increases. Also, transformation of the AMB dynamic model into a new class of uncertain system shows that this gyroscopic effect lies in the mismatched part of the system matrix. Moreover, the current gain parameter is allowed to be varied in a known bound as an uncertainty in the input matrix. SMC design method is proposed in which the sufficient condition that guarantees the global exponential stability of the reduced-order system is represented in Linear Matrix Inequality (LMI). Then, a new chattering-free control law is established such that the system states are driven to reach the switching surface and stay on it thereafter. The performance of the controller applied to the AMB model is demonstrated through simulation works under various system conditions.

Keywords: Active Magnetic Bearing (AMB), Sliding ModeControl (SMC), Linear Matrix Inequality (LMI), mismatcheduncertainty.

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Authors: Z. Sadeghi, M. R. Omidkhah, M. E. Masoomi

Abstract:

The purpose of this paper is to examine gas transport behavior of mixed matrix membranes (MMMs) combined with porous particles. Main existing models are categorized in two main groups; two-phase (ideal contact) and three-phase (non-ideal contact). A new coefficient, J, was obtained to express equations for estimating effect of the particle porosity in two-phase and three-phase models. Modified models evaluates with existing models and experimental data using Matlab software. Comparison of gas permeability of proposed modified models with existing models in different MMMs shows a better prediction of gas permeability in MMMs.

Keywords: Mixed Matrix Membrane, Permeation Models, Porous particles, Porosity.

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Authors: Ling Zhang, Feng Liu

Abstract:

A matrix is called a ray pattern matrix if its entries are either 0 or a ray in complex plane which originates from 0. A ray pattern A of order n is called spectrally arbitrary if the complex matrices in the ray pattern class of A give rise to all possible nth degree complex polynomial. Otherwise, it is said to be spectrally non-arbitrary ray pattern. We call that a spectrally arbitrary ray pattern A of order n is minimally spectrally arbitrary if any nonzero entry of A is replaced, then A is not spectrally arbitrary. In this paper, we find that is not spectrally arbitrary when n equals to 4 for any θ which is greater than or equal to 0 and less than or equal to n. In this article, we give several ray patterns A(θ) of order n that are not spectrally arbitrary for some θ which is greater than or equal to 0 and less than or equal to n. by using the nilpotent-Jacobi method. One example is given in our paper.

Keywords: Spectrally arbitrary, Nilpotent matrix, Ray patterns, sign patterns.

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Authors: M. Benachour, N. Benachour, M. Benguediab, A. Hadjoui

Abstract:

The knowledge of the nature of loading is very important in order to hold account on the total behavior such as vibration, shock, fatigue, etc. Fatigue present 90% of failure when loadings fatigues are very complex. In this paper a study of double through crack at hole for plate subjected to fatigue loading is presented. Various modes loading are studied where the applied load is the same one. The fatigue life is given where the effect of stress ratio is highlighted. This work is conducted on aluminum alloy 2024 T351 used for much aerospace and aeronautics applications. The fatigue crack growth behavior with constant amplitude is studied using the AFGROW code when Forman model is applied. The fatigue crack growth rate and fatigue life for different loading modes are compared with variation of others geometrical parameter such as thickness and dimensions of notch hole.

Keywords: Fatigue crack, mode loading, aluminum alloy

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Authors: G. Bal, D. Uygun

Abstract:

This paper describes the design and modeling procedure of a novel 5-phase segment type switched reluctance motor (ST-SRM) under simultaneous two-phase (bipolar) excitation of windings. The rotor cores of ST-SRM are embedded in an aluminum block as well as to improve the performance characteristics. The magnetic circuit of the produced ST-SRM is constructed so that the magnetic flux paths are short and exclusive to each phase, thereby minimizing the commutation switching and eddy current losses in the laminations. The design and simulation principles presented apply primarily to conventional SRM and ST-SRM. It is proved that the novel 5-phase switched reluctance motor under two-phase excitation is superior among the criteria used in comparison. The purposed model is particularly well suited for high torque and weight constrained applications such as automobiles, aerospace and military applications.

Keywords: Segmental Rotor Pairs, Two-phase Excitation, Commutation Switching, Aluminum Block.

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Authors: Kumar Neeraj, Ranjan Haldar

Abstract:

Polyaniline is an indispensible component in lightemitting devices (LEDs), televisions, cellular telephones, automotive, corrosion-resistant coatings, actuators etc. The electrical conductivity properties was found be increased by introduction of metal nano particles. In the present study, an attempt has been made to utilize platinum nano particles to achieve the improved electrical properties. Polyaniline and Pt-polyaniline composite are synthesized by electrochemical routes. X-ray diffractometer confirms the amorphous nature of polyaniline. The Bragg’s diffraction peaks correspond to platinum nanoparticles in Pt-polyaniline composite and thermogravimetric analyzer indicates its decomposition at certain temperature. The Scanning Electron Micrographs of colloidal platinum nanoparticles were spherical, uniform shape in the composite. The current-voltage (I-V) characteristics of the PANI and composites were also studied which indicate a significant decreasing resistivity than PANI-Platinum after introduction of pt nanoparticles in the matrix of polyaniline (PANI).

Keywords: Polyaniline, XRD and Platinum Nanoparticles.

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Authors: Dmitry D. Zakharov

Abstract:

The theoretical prediction of the acoustical polarization effects in the heterogeneous composites, made of thick elastic solids with thin nematic films, is presented. The numericalanalytical solution to the problem of the different wave propagation exhibits some new physical effects in the low frequency domain: the appearance of the critical frequency and the existence of the narrow transition zone where the wave rapidly changes its speed. The associated wave attenuation is highly perturbed in this zone. We also show the possible appearance of the critical frequencies where the attenuation changes the sign. The numerical results of parametrical analysis are presented and discussed.

Keywords: Surface wave, guided wave, heterogeneous composite, nematic coating.

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Authors: M. Sari Yilmaz, N. Karamahmut Mermer

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Coal fly ash is formed as a solid waste product from the combustion of coal in coal fired power stations. Huge amounts of fly ash are produced globally every year and are predicted to increase. Nowadays, less than half of the fly ash is used as a raw material for cement manufacturing, construction and the rest of it is disposed as a waste causing yet another environmental concern. For this reason, the recycling of this kind of slurries into useful materials is quite important in terms of economical and environmental aspects. The purpose of this study is to evaluate the Orhaneli and Tuncbilek coal fly ashes for utilization in some industrial applications. Therefore the mineralogical and chemical compositions of these fly ashes were analyzed by X-ray fluorescence spectroscopy, ourier-transform infrared spectrometer, and X-ray diffraction. The silicon (Si) and aluminum (Al) in the fly ashes were activated by alkali fusion technique with sodium hydroxide. The obtained extracts were analyzed for Si and Al content by inductively coupled plasma optical emission spectrometry.

Keywords: Extraction, Fly ash, Fusion, XRD.

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Authors: Samsiah Abdul Razak, Daud Mohamad

Abstract:

Molodstov-s soft sets theory was originally proposed as general mathematical tool for dealing with uncertainty problems. The matrix form has been introduced in soft set and some of its properties have been discussed. However, the formulation of soft matrix in group decision making problem only with equal importance weights of criteria, which does not show the true opinion of decision maker on each criteria. The aim of this paper is to propose a method for solving group decision making problem incorporating the importance of criteria by using soft matrices in a more objective manner. The weight of each criterion is calculated by using the Analytic Hierarchy Process (AHP) method. An example of house selection process is given to illustrate the effectiveness of the proposed method.

Keywords: Soft set, Soft Matrix, Soft max-min decision making (SMmDM), Analytic hierarchy process (AHP)

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Authors: Yiqin Lin, Liang Bao, Yimin Wei

Abstract:

In this paper we study numerical methods for solving Sylvester matrix equations of the form AX +XBT +CDT = 0. A new projection method is proposed. The union of Krylov subspaces in A and its inverse and the union of Krylov subspaces in B and its inverse are used as the right and left projection subspaces, respectively. The Arnoldi-like process for constructing the orthonormal basis of the projection subspaces is outlined. We show that the approximate solution is an exact solution of a perturbed Sylvester matrix equation. Moreover, exact expression for the norm of residual is derived and results on finite termination and convergence are presented. Some numerical examples are presented to illustrate the effectiveness of the proposed method.

Keywords: Arnoldi process, Krylov subspace, Iterative method, Sylvester equation, Dissipative matrix.

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Authors: Xu Zhao

Abstract:

Text categorization techniques are widely used to many Information Retrieval (IR) applications. In this paper, we proposed a simple but efficient method that can automatically find the relationship between any pair of terms and documents, also an indexing matrix is established for text categorization. We call this method Indexing Matrix Categorization Machine (IMCM). Several experiments are conducted to show the efficiency and robust of our algorithm.

Keywords: Text categorization, Sub-space learning, Latent Semantic Space

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Authors: Amal Kr Sarma, H Zeen Devi, N Nimai Singh

Abstract:

The Constraints imposed by non-thermal leptogenesis on the survival of the neutrino mass models describing the presently available neutrino mass patterns, are studied numerically. We consider the Majorana CP violating phases coming from right-handed Majorana mass matrices to estimate the baryon asymmetry of the universe, for different neutrino mass models namely quasi-degenerate, inverted hierarchical and normal hierarchical models, with tribimaximal mixings. Considering two possible diagonal forms of Dirac neutrino mass matrix as either charged lepton or up-quark mass matrix, the heavy right-handed mass matrices are constructed from the light neutrino mass matrix. Only the normal hierarchical model leads to the best predictions of baryon asymmetry of the universe, consistent with observations in non-thermal leptogenesis scenario.

Keywords: Thermal leptogenesis, Non-thermal leptogenesis.

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Authors: A.T.Z. Mahamat, A.M. A Rani, Patthi Husain

Abstract:

Copper based composites reinforced with WC and Ti particles were prepared using planetary ball-mill. The experiment was designed by using Taguchi technique and milling was carried out in an air for several hours. The powder was characterized before and after milling using the SEM, TEM and X-ray for microstructure and for possible new phases. Microstructures show that milled particles size and reduction in particle size depend on many parameters. The distance d between planes of atoms estimated from X-ray powder diffraction data and TEM image. X-ray diffraction patterns of the milled powder did not show clearly any new peak or energy shift, but the TEM images show a significant change in crystalline structure of corporate on titanium in the composites.

Keywords: ball milling, microstructures, titanium, tungstencarbides, X-ray

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Authors: Minto Rattan, Tania Bose, Neeraj Chamoli

Abstract:

The present paper investigates the effect of linear thermal gradient on the steady-state creep behavior of rotating isotropic disc using threshold stress based Sherby’s creep law. The composite discs made of aluminum matrix reinforced with silicon carbide particulate has been taken for analysis. The stress and strain rate distributions have been calculated for discs rotating at linear thermal gradation using von Mises’ yield criterion. The material parameters have been estimated by regression fit of the available experimental data. The results are displayed and compared graphically in designer friendly format for the above said temperature profile with the disc operating under uniform temperature profile. It is observed that radial and tangential stresses show minor variation and the strain rates vary significantly in the presence of thermal gradation as compared to disc having uniform temperature.

Keywords: Creep, isotropic, steady-state, thermal gradient.

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Authors: J. Ivorra-Martinez, L. Quiles-Carrillo, J. Gomez-Caturla, T. Boronat, R. Balart

Abstract:

The utilization of almond crop by-products to obtain Poly(3-hydroxybutyrat-co-3-hydroxyhexanoat) (PHBH)-based composites was carried out by using an extrusion process followed by an injection to obtain test samples. To improve the properties of the resulting composite, the incorporation of Oligomer Lactic Acid (OLA 8) as a coupling agent and plasticizer was additionally considered. A characterization process was carried out by the measurement of mechanical properties, thermal properties, surface morphology, and water absorption ability. The use of the almond residue allows obtaining composites based on PHBH with a higher environmental interest and lower cost.

Keywords: Almond shell, PHBH, composite, polymer.

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Authors: Guangbin Wang, Ning Zhang, Fuping Tan

Abstract:

In this paper, we present a preconditioned AOR-type iterative method for solving the linear systems Ax = b, where A is a Z-matrix. And give some comparison theorems to show that the rate of convergence of the preconditioned AOR-type iterative method is faster than the rate of convergence of the AOR-type iterative method.

Keywords: Z-matrix, AOR-type iterative method, precondition, comparison.

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