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1

Elastic solutions based on the Mori-Tanaka scheme for pressurized functionally graded cylinder

Eker Mehmet, Yarımpabuç Durmu, Yıldırım Ali, Çelebi Kerimcan

Journal of Applied Mathematics and Computational Mechanics

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2020

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Vol. 19, nr 4

57--68

EN

In this paper, an elastic analysis of a thick-walled functionally graded cylinder subjected to internal pressure is examined. Material properties for the isotropic material are estimated to obey the Mori-Tanaka homogenization scheme through the thickness. The resulting two-point irregular boundary value problem is solved by the pseudospectral Chebyshev method that converts the boundary value problem to the system of equations, which can be solved by any appropriate decomposition method. Benchmark solutions are used to validate the method. The effect of the arbitrarily chosen volume fraction index is demonstrated for stress and displacement distributions. The effective stresses for different inner radius and volume fraction index are also discussed.

2

Determination of the optimal parameters of the structure of functional gradient materials using mathematical modelling approaches

Lyashenko B. A., Stotsko Z. A., Kuzin O. A., Kuzin M. O., Mikosianchyk O. A.

Journal of Achievements in Materials and Manufacturing Engineering

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2019

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Vol. 92, nr 1-2

13--18

EN

Purpose: Functioning of mechanical friction systems largely depends on the characteristics of the structure of their surface layers. By controlling these parameters, it is possible to significantly adjust the reliability and durability of parts under the conditions of contact interaction. Design/methodology/approach: he proposed approach, which is based on the principle of nonlocality of the operational properties of materials, allows determining the optimal microhardness values of the surface layers and the gradient of this parameter, at which the contact durability of friction pair elements significantly increases. Findings: It is established that by adjusting the ratios of the surface strength of materials and its gradient, it is possible to achieve a significant increase in the operational parameters of friction units. Practical implications: The engineering relationship considered in the work allows to establish functional distributions of microhardness in the structure of surface layers, at which their wear reaches minimum values. Originality/value: Mathematical approaches are proposed, which allow determining the parameters of the structure of the surface layers of parts to increase their durability under conditions of friction contact loads.

3

Zagadnienie zakrzywionej anizotropowej oraz funkcjonalnie gradowanej powłoki poddanej działaniu pola temperatury

Szubartowski D.

Zeszyty Naukowe Politechniki Rzeszowskiej. Mechanika

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2018

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z. 90 [298], nr 2

237--244

PL

Praca dotyczy problematyki zakrzywionej powłoki wykonanej z anizotropowego materiału o funkcyjnej gradacji. W rachunku wykorzystano koncepcję tensora krzywizny Riemanna-Christoffela wzbogaconą o wpływ pola temperatury przez obecność tensora właściwości termicznych. W ramach wykonanych obliczeń różnica wektora poddanego koneksji afinicznej wzdłuż infinitezymalnego czworokąta wyraża się, zależnie od drogi przejścia, sumą zarówno efektu geometrycznego, reprezentowanego tensorem krzywizny Riemanna-Christoffela, jak również efektu termicznego wyrażonego przez symbol krzywizny termicznej.

EN

This work concerns the problem of a curvilinear shell made of anisotropic material with functional gradation. The calculus is based on the concept of the Riemann-Christoffel curvature tensor enhanced by the influence of temperature field through the presence of a thermal tensor. Calculations comprise estimation of the difference of a vector subjected to the affine connection along the infinitesimal quadrangle expressed, correspondingly to the shifting path, by a sum of both the geometric effect, represented by the Riemann-Christoffel curvature tensor, as well as certain symbol of the thermal curvature.

4

Sterowanie rozpływem ciepła w wale kalandra z wykorzystaniem materiałów gradientowych

Turant J.

Zeszyty Naukowe Wyższej Szkoły Informatyki

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2013

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Vol. 12, Nr 1

81--89

PL

W pracy analizowano rozpływ ciepła w wale kalandra, którego elementy konstrukcyjne mogą być wykonane z materiałów gradientowych. Podstawowym problemem eksploatacyjnym kalandrów jest nierównomierność rozkładu temperatur wzdłuż powierzchni roboczej kalandra. Równomierność rozkładu temperatur może być regulowana poprzez wprowadzenie między elementami grzewczymi wału a jego powierzchnią roboczą warstwy materiału o zmiennym, odpowiednio dobranym, współczynniku przewodzenia ciepła. W ramach pracy przeprowadzono optymalizację współczynnika przewodzenia ciepła w tej warstwie zakładając, że warstwa ta zbudowana jest z mieszaniny dwóch materiałów o wyraźnie różnych własnościach przewodzenia ciepła. Na etapie optymalizacji wykorzystano hybrydowy algorytm zbudowany z szeregowo połączonego zmiennoprzecinkowego algorytmu ewolucyjnego i algorytmu Hookea-Jeewesa. Analiza zachowania się konstrukcji była przeprowadzana metodą elementów skończonych.

EN

In the paper the analysis of a heat flow in a calender shaft, which elements can be made of functionally gradient materials, is considered. The main operational problem of calenders is nonuniform temperature distribution along the working surface. The uniformness of temperature distribution may be controlled by introducing the layer, made of gradient materials with well defined thermal properties, which should be introduced between heating elements and working surface. As part of the work, the optimization process was performed to find the proper distribution of heat conduction coefficient in this layer, assuming that the layer is composed of a mixture of two materials having significantly different heat conduction properties. During optimization process hybrid algorithm, consisted with evolutionary algorithm combined, in series, with Hooke-Jeewes method was used. The analysis of the state of the calendar was done with finite element method.

5

Structure and properties of FGM manufactured on the basis of HS6-5-2

Matula G., Dobrzański L. A.

Journal of Achievements in Materials and Manufacturing Engineering

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2006

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Vol. 17, nr 1-2

101--104

EN

Purpose: It has been demonstrated in the paper structure and properties of tool gradient materials manufactured by powder metallurgy on the basis of high speed-steel HS6-5-2 type. Design/methodology/approach: Light microscope, SEM, image analysis, microhardness tests, density examination. Findings: Basing on the investigations of the HS6-5-2 type high-speed steels reinforced with ceramics particles fabricated with Powder Metallurgy it was found that density of sintered samples depend on reinforced particles, temperatures and atmosphere of sintering. Increasing of sintering temperature increase the density of sintering samples. Moreover the sintering under N2-10%H2 atmosphere produce samples with higher quality than using argon atmosphere and prevent of surface oxidation during sintering. Practical implications: The Powder Metallurgy gives the possibility to manufacturing tools gradient materials on the basis of high speed-steel which characterised very high hardness on the surface. Originality/value: In the paper the manufacturing of tool gradient materials on basis of high speed-steel reinforced with hard ceramics particles carried out in order to improve the tool cutting properties.