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Search Results: 1 - 3 of 3 matches for " ?. Szparaga "
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On transition functions and nonlinearity measures in gradient coatings
J. Ratajski,?. Szparaga
Journal of Achievements in Materials and Manufacturing Engineering , 2012,
Abstract: Purpose: In this paper the influence of the shape of transition functions between the single layers of multilayer coating on the final internal stresses states in the coating was investigated. Additionally the degree of nonlinearity and asymmetry of postulated gradient layers was calculated.Design/methodology/approach: Physical and mathematical models of the layers were created basing on classical theory of elasto-plastic materials. Computer model of the object (coating + substrate) describing internal strains and stresses states in layers, after deposition process, was created using FEM method.Findings: New concepts of nonlinearity and asymmetry measurability of transition function were introduced. Using predefined measures the dependence between internal stresses fields in postulated class of gradient layers and values of nonlinearity and asymmetry were obtained.Research limitations/implications: There are an infinite number of possible measures of heterogeneity and nonlinearity of the transition layers. Also there are infinitely many functions with the same measures of asymmetry and nonlinearity, but different mathematical forms, thus a functions of the same measures value form a kind of class of abstraction. So it is convenient to consider specific representatives of the given class and expand the obtained results to remaining representatives which is laborious and ambiguous task.Practical implications: Proposed measures of gradient layers will become a significant components of the PC software in future, which will upgrade the designing process of hard, wear resistant coatings architecture.Originality/value: A class of monotonic and asymmetric transition functions, describing continuous physicochemical material’s parameters changes in each layer of K-layered coating was created. Also a new measures of nonlinearity and asymmetry of transition function were introduced.
Multi objective optimization of wear resistant TiAlN and TiN coatings deposite by PVD techniques
?. Szparaga,J. Ratajski,A. Zarychta
Archives of Materials Science and Engineering , 2011,
Abstract: Purpose: The goal of this paper is to determine, the optimal layer thickness of deposited coatings, in respect of thermal strain and stresses.Design/methodology/approach: For physical modelling purposes Cr, TiN and TiAlN layers were treated as a continuous medium, so the physical phenomena, occurring in the coating, are modelled based on a classical theory of stiffness. Computer model of the object (coating + substrate) describing strains and thermal stresses states in layers, after deposition process, was created using FEM method.Findings: The decisional objectives, based on various stresses fields in deposited coating, were defined. The set of optimal TiAlN and TiN layer thickness, in respect to created decision objectives was determined. Also method of optimal solutions set analysis, based on multidimensional, Euclidean metric was created.Research limitations/implications: There is a need to consider creation of a certain class of selection functions, as a standard, which will help to choose the optimal set of solutions - obtained in different multi objective optimization procedures. Of course, new and more detailed physical and mathematical models of the PVD processes are required.Practical implications: Proposed multi objective optimization procedure will become a component of the PC software in future, which will make design process of hard, wear resistant coatings architecture possible.Originality/value: Insertion of the base layer, below TiAlN and TiN tiers, was proposed, whose occurrence is reflected by the continuous change of the physical and chemical properties, across the coating thickness. Also method of optimal solutions set analysis, based on multidimensional, Euclidean metric was created.
Stratificational and antipodean properties of boundary states for N x N density matrices
S Kryszewski,M Zachcia?,Szparaga
Physics , 2007,
Abstract: We investigate the space of N x N dimensional density matrices. We show that there exist strata such that boundary states \rho_{p} with p zero eigenvalues lie on or outside the spheres with radii r_{p}=\sqrt{p/N(N-p)}. Moreover, we show that if in a certain direction there is a boundary state with q=N-p equal eigenvalues, then in the opposite (antipodean) direction exists a boundary state with p=N-q equal eigenvalues.
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