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Çift fazlı malzemelerin şekil değişimi davranışının sonlu elemanlar yöntemi ile parametrik analizi

Başlık çevirisi mevcut değil.

  1. Tez No: 55945
  2. Yazar: CENK UĞUR SERMET
  3. Danışmanlar: PROF.DR. AHMET ARAN
  4. Tez Türü: Yüksek Lisans
  5. Konular: Makine Mühendisliği, Mechanical Engineering
  6. Anahtar Kelimeler: Belirtilmemiş.
  7. Yıl: 1996
  8. Dil: Türkçe
  9. Üniversite: İstanbul Teknik Üniversitesi
  10. Enstitü: Fen Bilimleri Enstitüsü
  11. Ana Bilim Dalı: Belirtilmemiş.
  12. Bilim Dalı: Belirtilmemiş.
  13. Sayfa Sayısı: 111

Özet

ÖZET Günümüzde teknolojik açıdan önem taşıyan malzemelerin birçoğu çift fazlı malzemelerden oluşmaktadır. Çift fazlı malzemelerin özel liklerinin belirlenebilmesi ve bu özelliklerin iyileştirilebilmesi, yeni malzemeler geliştirilebilmesi ile daha ekonomik ve güvenli tasarımlar oluşturulabilmesi açısindan önem taşımaktadır. Bu özelliklerin belir lenmesinde sonlu elemanlar yöntemi iyi bir araç olarak karşımıza çıkar ve bu yöntemin kullanımı bilgisayar teknolojisinin de gelişimiyle gün geçtikçe yaygınlaşmaktadır. Bu çalışmada, ilk olarak çift fazlı malzemelerin mekanik özellikleri hakkında bilgi verilmiştir. Daha sonra, bu tür malzemelerin elasto- plastik özelliklerin belirlenmesinde kullanılacak olan sonlu elemanlar yöntemi ile bu yöntemle çözüm yapan Ansys 5.0 paket programı kısaca açıklanmış ve çift fazlı malzemelerin özelliklerini belirlemek için Ansys 5.0'da yapılacak bir çözümün hangi aşamalardan oluştuğu, bu aşamalarda ne gibi işlemler yapıldığı anlatılmıştır. Ansys 5.0 paket programı kullanılarak, ilk olarak programla elde e- dilen sonuçların deneysel verilere uygunluğu gösterilmiş, daha sonra parametrik analize geçilmiştir. Parametrik analizde, elastiklik modülü ve akma dayanımı sabit bir matriste, iki farklı elastiklik modülüne sahip sert fazlar için değişik hacim oranlarında çözümler yapılmıştır. Bu çö zümler mükemmel plastik matris ve pekleşen matris için ayrı ayrı gerçekleştirilmiştir. Çözümler sonucunda, çift fazlı malzemelerin elastiklik modülleri, mikro ve makro akma dayanımları, sınır gerilme, geometrik pekleşme, toplam pekleşme, matrisin pekleşme katsayısının çift fazlı malzemenin pekleşmesine katkısı ile ilgili sonuçlar elde edilmiş ve bu verilerin sert faz hacim oranı ve sert faz-matris elastiklik modülü oranı ile nasıl değiştiği irdelenmiştir. IX

Özet (Çeviri)

SUMMARY Nowadays, most technologically significant materials are double- phased. However, in order to produce new materials with economical as well as reliable designs can only be possible through the development of double-phased materials and their subsequent improvement. Within this context, the finite elements method comes across as the most appropriate tool to determine those properties. In addition, this method is more widely used thanks to the usage of computer technology. Many technologically important materials consist of two or more ductile phases. These materials include two-phase steels, two phases brasses and a-|3 titanium alloys. To improve the properties of the existing materials, or to design materials with improved properties, it is necessary to understand the deformation behavior of the two-phase materials in terms of the volume fraction, morphology and strength of the component phases. There is a lack of understanding in this area. This is due to the fact that whenever a two-phase material is subjected to stress, the component phases deform differently resulting in inhomogeneous stress and strain distributions. Many investigators have studies the stress-strain behavior of various two-phase materials. It has been shown that, in general, the law of mixture rule cannot be applied to model the the deformation behavior of two-phase materials. Whenever a two-phase materials consisting of two or more phases with different mechanical properties is subjected to stress, the phases react differently to the applied stress. This results in inhomogeneous stress and strain distributions. The inhomogeneities lead to constraints from each other at the two-phase interface. Stresses resulting from the constraints are different from the applied stress and are known as interaction stresses. The nature of inhomogeneities and the interaction stresses depend on the strength difference between the phases and the volume fraction per cent and morphology of the phases. It is necessary to understand the nature and magnitude of inhomogeneities either to ximprove the properties existing materials or to design new two phase materials with improved properties. A number of approaches have been used to predict the stress-strain behavior and stress-strain distribution of two-phase materials including the finite element method (FEM). The investigators showed that the stress-strain curve and strain distributions predicted by Finite Element Method closely correspond to those obtained experimentally, indicating that Finite Element Methoc is a viable method for modelling the deformation behavior of two-phase materials. The finite element method is a numerical procedure for solving the differential equations of physics and engineering. The method had its birth in the aerospace industry in the early 1950s and was first presented in the publication by Turner, Clough, Martin and Topp (1956). This publication stimulated other researchers and resulted in several technical articles that discussed the applicatin of the method to structural and solid mechanics. An important theoretical contribution was made in 1963 when Melosh showed that the finite element method was really a variation of the well known Raleigh-Ritz procedure. In structural problems, the method produces a set of linear equilibrium equations by minimizing the potential energy of the system. The connecting of the finite element method with a minimization procedure quickly led to its use in other engineering areas. The method was applied to problems governed by the Laplace or the Poiison equations because these equations are closely related ta the of a functional. The finite element method has advanced from a numerical procedure for solving structural problems to a general numerical procedure for solving a differential equation or a system of differential equations. This advencement has been accomplished in a period of 15 years and has been assisted by the development of high-speed digital computers, the need for a more accurate analysis of aircraft frames, and the national commitment to space exploration. The digital computers provided a rapid means of performing the many calculations involved. Space exploration provided money for basic research and stimulated the development of multiple purpose computer programs. The design of airplanes, missies, space capsules, and the like, provided application areas for the theory. XIThe fundemental concept of the finite element method is that any continuous quantity, such as temperature, pressure or displacements, can be approximated by a discrete model composed of a set of piecewice continuous functions defined over a finite number of sub domains. The piecewise continuous functions are defined using the values of the continuous quantity at a finite number of points in its domain. The more common situation is where the continuous quantity is unknown and we wish to determine the values of this quantity at certain points whitin the region. The costruction of the dicrete is most easily explained, however, if we assume that we already know the numerical value of the quantity at every point within the damain. We shall return to the more common situation shortly. The discrete model constructed as follows. 1- A finite number of points inthe domain is identified. These points are called nodal points or nodes. 2- The value of the continuous quantity at each nodal points is denoted as a variable which is to be determined. 3- The domain is divided into a finite number of sub domains called elements. These elements are connected at common nodal points and collectively approximate the shape of the domain. 4- The continuous quantity is approximated over each element by apolynominal that is defined using nodal values of the continuous quantity. A differential polynominal is defined for each element, but the element polynominals are selected in such a way that continuity is maintained along the element boundaries. This study firstly aims to explain the mechanical properties of double-phased materials. Secondly, the finite element method which will be used in the determination of the elasto-plastic properties and the Ansys 5.0 computer pechage programme which analysis it are briefly explained. Furthermore, various steps of Ansys 5.0 and their calculations are also explained. The Ansys 5.0 programme is primarily used to analyse the coherence of the results whit experimental data. That was fallowed by the parametric analysis whitin which a constant Young's Modulus and a contant yield strength are gothered in a matrix and two different xiiYoung's Modulus for hard phase are analysed for various hard phase volume percents. Those analyses are realized separetely for perfect plastic matrix and hardening matrix. As a result, a number of analyses namely, the Young's Modulus of double-phased materials, micro and macro yield strengths, limit stresses, geometrical hardening, total hardening, and the impact of the hardening matrix on the double-phased material hardening coefficient are obtained. Additionely, the results are used in the further analyses of the changes between the volume percent of hard phase and the Young's Modulus ratio of hard phase and matrix. As to the results of calculations of the analyses; 1- The peckage programs that can calculate via the usage of finite elements method can give precise results about the macro behaviour of doble-phased materials. 2- Less than 25 of the hard phase volume percent, an insignificant increase is observed for a double-phased material which consist of a soft matrix second phase hard particules. Interestingly, for volume percent over 25, the role of increase speeds up. Furthermore, while the increase in the Young's Modulus ratio of hard phase and matrix does not effect the Young's Modulus of the material up to 25 of hard phase volume percent, over the above percentage the effect becomes clearer. 3- Due to the stress accumulation, the increase in the equivalent stresses results in micro yielding in the matrix below the yield strength. The value of the micro yielding stresses decreases up to 15 of the hard phase volume percent. After this percentage, the micro yielding stresses stay constant up to 70 of hard phase volume percent and starts to increase over 70 %. In addition, the materials which consists of more rijid hard phase, have lower micro yielding strength for all hard phase volume percent. 4- Double phased materials with perfect plastic matrix start to micro yield at the overall stress values, which are lower than yield strength. However, for the deformation to continue, the overall stress has to be increased. The material deforms in perfectly plastic manner over a limit stress value. This is called geometrical hardening. The above-mentioned hardening remains constant between 15 and 20 of hard phase volume percent. The geometrical hardening exhibits a linear increase over 20 %. The limit stress increases slightly in a linear xiiifashion with the increasing hard phase volume percent. The aggrevation in the rigidity of the hard phase does not effect the limit stress. 5- Total hardening in the double-phased materials with hardening matrix is equal to the sum of the geometrical hardening and matrix hardening. Total hardening is increasingly aggrevated with the hard phase volume percent. The increase in the rigidity of the hard phase becomes more effective over 30 of hard phase volume percent. The contribution of matrix hardening on the double-phased material hardening is increasingly aggrevated in line with the increase in the total hardening with increasing hard phase volume percent. 6- The 0.1 % yield strength of the double-phased material with hardening matrix increases slightly up to 30 of hard phase volume percent. Upto that volume percent, an increase in the Young's Modulus ratio of hard phase and matrix does not effect significantly the yield strength. An increasing aggrevate in the yield strength can be observed and the effect of the Young's Modulus ratio of hard phase and matrix becomes visible with the increase in the hard phase volume percent. xiv

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