There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

THE DESIGN AND ANALYSIS OF EXPERIMENTS. By Oscar Kempthorne. New York, John Wiley and Sons, Inc., 1952. 631 pp. $8.50. This book by a teacher of statistics (as well as a consultant for \"experimenters\") is a comprehensive study of the philosophical background for the statistical design of experiment. It is necessary to have some facility with algebraic notation and manipulation to be able to use the volume intelligently. The problems are presented from the theoretical point of view, without such practical examples as would be helpful for those not acquainted with mathematics. The mathematical justification for the techniques is given. As a somewhat advanced treatment of the design and analysis of experiments, this volume will be interesting and helpful for many who approach statistics theoretically as well as practically. With emphasis on the \"why,\" and with description given broadly, the author relates the subject matter to the general theory of statistics and to the general problem of experimental inference. MARGARET J. ROBERTSON

The Design and Analysis of Experiments

Intermolecular And Surface Forces

Nonlinear Oscillations: Exact Solutions and their Approximations

https://pureadmin.qub.ac.uk/ws/files/126683921/Edited_sudagar_R1.pdf

Electroless nickel, alloy, composite and nano coatings – A critical review

Loading-unloading behavior of a deformable sphere with a rigid flat under full stick contact condition is investigated for varying strain hardening. The study considers various tangent modulus using the finite element software ANSYS. Both the bilinear kinematic hardening and isotropic hardening models are considered. Numerical simulation reveals the qualitative similarity between kinematic and isotropic hardening regarding the variation of interfacial parameters during loading-unloading for various tangent modulus. It is found that the material with kinematic hardening dissipates more energy than the material with isotropic hardening during unloading. However for elastic perfectly plastic material, the loading-unloading behavior is insensitive to hardening model. DOI: 10.4018/ijseims.2013010102 14 International Journal of Surface Engineering and Interdisciplinary Materials Science, 1(1), 13-32, January-June 2013 Copyright © 2013, IGI Global. Copying or distributing in print or electronic forms without written permission of IGI Global is prohibited. the stress and strain. There occurs permanent change in shape on unloading. The behavior of materials that have been stressed beyond the elastic region is usually described with bilinear hardening using tangent modulus. Kogut and Etsion (2002) (KE Model) considered the elastic-plastic contact of a hemisphere and a rigid flat under frictionless contact condition during loading. They investigated the effect of tangent modulus by varying it up to 0.1E, E being the elastic modulus, and found the difference of resulting contact parameters with that of elastic perfectly plastic material to be less than 20%. Etsion et al. (2005) found that contact behavior was independent of the physical and geometrical properties of the sphere during unloading of an elastic-plastic loaded spherical contact with a rigid flat under perfect slip contact condition. They choose 2% isotropic linear hardening and observed a marginal variation of results with that of elastic perfectly plastic material. Kadin et al. (2007) studied the multiple loadingunloading of a deformable sphere against a rigid flat under frictionless contact condition. They observed slight additional hardening during the first unloading compared to the first loading. This hardening causes secondary plastic flow. They inferred that the incipient interference to cause secondary plastic flow increases with the increase in strain hardening. Shankar and Mayuram (2008) studied the elastic-plastic transition behavior in a hemisphere in contact with a rigid flat under frictionless contact condition accounting for the effect of realistic material behavior in terms of varying yield strengths and the isotropic strain hardening. They used three tangent modulus, 0.025E, 0.05E, and 0.1E and inferred that with the increase in tangent modulus, the transition from elastic-plastic to fully plastic state occurs in lower dimensionless interference ratio. Sahoo et al. (2010) considered the effect of strain hardening on interfacial parameters of deformable sphere with a rigid flat under frictionless contact condition during loading for a wide range of tangent modulus as high as 0.33E. They inferred that with the increase in strain hardening the resistance to deformation of a material is increased and the material becomes capable of carrying higher amount of load in a smaller contact area. Chatterjee and Sahoo (2010) analyzed the effect of strain hardening during unloading of an elastic plastic loaded sphere against a rigid flat under frictionless contact condition. They observed that higher tangent modulus (strain hardening) results lower residual interference when unloaded from a particular dimensionless interference; which in turn offers less resistance to full recovery of the original shape. Several researchers have considered full stick contact condition as well. Brizmer et al. (2006a) first analyzed the effect of full stick condition on the elasticity terminus of a spherical contact during loading. They found increasing differences in contact parameters with decreasing Poisson’s ratio compared to the perfect slip contact condition. Brizmer et al. (2006b) extended their study for the loading of an elastic plastic spherical contact both under full stick and perfect slip contact condition with 2% isotropic linear hardening and found that the interfacial parameters are insensitive to the contact condition and material properties of the deformable sphere. However they found the contact load and average contact pressure to be slightly affected by Poisson’s ratio for full stick contact condition. Zait et al. (2010a) performed the unloading of an elastic-plastic spherical contact under full stick contact condition with 2% isotropic linear hardening. They found a substantial variation in load-area curve during unloading under full stick contact condition compared to that of perfect slip contact condition. The effect of strain hardening can be studied by relating the size and shape of the yield surface to plastic strain in some appropriate way (Bower, 2008). Most of the elastic-plastic contact models available in the literature are based either on linear isotropic hardening or with elastic-perfectly plastic materials. Some finite element models have also been proposed to simulate multiple, cyclic loading-unloading using bilinear kinematic hardening. Zait et al. (2010b) used both isotropic and kinematic hardening during the study of multiple normal loading-unloading cycles of a spherical contact 18 more pages are available in the full version of this document, which may be purchased using the "Add to Cart" button on the product's webpage: www.igi-global.com/article/finite-element-based-unloadingelastic/75563?camid=4v1 This title is available in InfoSci-Journals, InfoSci-Journal Disciplines Engineering, Natural, and Physical Science, InfoSci-Healthcare Administration, Clinical Practice, and Bioinformatics eJournal Collection, InfoSci-Physical Sciences, Biological Sciences, and Engineering eJournal Collection. Recommend this product to your librarian: www.igi-global.com/e-resources/libraryrecommendation/?id=2

Finite Element Based Unloading of an Elastic Plastic Spherical Stick Contact for Varying Tangent Modulus and Hardening Rule

Electroless Ni-P coatings with hard Al2O3 composite particles are developed on mild steel specimens. The coating parameters viz. source of nickel ions, concentration of reducing agent and concentration of Al2O3 particles are used as coating parameters to minimize wear rate (wear depth in μm) and friction coefficient. As annealing temperature strongly affects hardness and wear resistance of coating, it is considered as fourth parameter. In the present study wear depth and friction coefficient are used as response variables. To convert multiple responses into single performance index, Weighted Principal Component Analysis (WPCA) is used. Taguchi L27 OA with four process parameters at three levels is used to conduct the experiments. ANOVA is used to find out the significance of each coating parameters and their interactions. Annealing temperature is found to be the most significant factor followed by concentration of composite particles. The surface morphology, composition and phase structure analysis are done with the help of SEM, EDAX and XRD respectively. Optimization of Friction and Wear Properties of Electroless Ni-P-Al2O3 Composite Coatings

Optimization of Friction and Wear Properties of Electroless Ni-P-Al2O3 Composite Coatings

Effect of Coating Bath Parameters on Properties of Electroless Nickel-Boron Alloy Coatings

The present research article deals with the study of corrosion behavior of Ni-P-TiO2 composite coating. The TiO2 composite coating is deposited on the mild steel substrate. Corrosion behavior of the TiO2 composite coatings after heat treatment at various annealing temperatures (300 °C, 400 °C, and 500 °C) is evaluated with the help of potentiodynamic polarization test using 3.5% NaCl solution. The electrochemical parameters, corrosion potential (Ecorr) and corrosion current density (Icorr), are optimized for maximum corrosion resistance using Taguchi based grey relational analysis. The coating parameters, namely, nickel sulphate, sodium hypophosphite, concentration of TiO2 particles and annealing temperature are considered as main design factors. The analysis of variance (ANOVA) revealed that the annealing temperature and concentration of TiO2 particles have significant influence on the corrosion behavior of the composite coating. The microstructure characterization of the coating is conducted using scanning electron microscopy, energy dispersive X-ray analysis and X-ray diffraction analysis. The Ni-P-TiO2 composite coating exhibits nodular structure with uniform incorporation of titanium particles and converts into the crystalline structure after heat treatment.

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Prasanta Sahoo

Papers

Finite Element Based Unloading of an Elastic Plastic Spherical Stick Contact for Varying Tangent Modulus and Hardening Rule

Optimization of Friction and Wear Properties of Electroless Ni-P-Al2O3 Composite Coatings

Effect of Coating Bath Parameters on Properties of Electroless Nickel-Boron Alloy Coatings

Effect of Heat Treatment and Bath Process Parameters on the Corrosion Behavior of Ni-P-TiO2 Composite Coatings

Design of experiments analysis of abrasive friction behavior of Al-TiB2 composites