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Stress Distribution in Linear State in Four-Walled Carbon Nanotubes with Local Curvature

Yıl 2021, Sayı: 22, 167 - 175, 31.01.2021
https://doi.org/10.31590/ejosat.848831

Öz

Nanotubes, which have extremely high strength, are the most important structural elements of nanomaterials used in nanotechnological applications and are used in the production of nanocomposite materials. They enable composites to gain superior mechanical properties by being placed in matrix materials. When composite materials are being strengthened, the primitive curvature caused by structural reasons or technological processes causes self-balancing stresses to appear. The magnitude of these stresses can cause the safety limits of the material to be exceeded. Therefore, it is important for engineering to examine the mechanical behavior of materials under load in terms of theoretically. In this study, the composite material containing four-walled carbon nanotube with local curvature was investigated within the scope of the piecewise homogeneous body model using the geometrical linear exact equations of the three-dimensional elasticity theory. An approximate analytical method has been developed for the solution by using the boundary form perturbation method. The study covers the solution for the zero and first approximation of the solution method and it is sufficient. The research involves the analysis of normal and shear stresses at the intersection surface of the matrix material with the outer surface of the carbon nanotube (CNT) outer layer. In addition, ideal contact conditions between the carbon nanotube and the matrix were used. The results were investigated for the geometric linear case. Van der Waals forces occurring between carbon nanotube layers were taken into account and their effect on stresses was explained with numerical results. Numerical results regarding the effect of other problem parameters on the stress distribution are presented and discussed. In addition, it has been observed that the stress values change non-monotonously with the increase of nanotube outermost radius. Moreover, it has been found that increasing the ratio of elasticity constants significantly affects the stresses. The change of the parameter showing the oscillation frequency in the equation of the centerline of the carbon nanotube is also investigated and its effect on stresses is presented. Apart from this, as an important finding, it has been determined that increasing the number of walls in carbon nanotubes decreases the stress values.

Kaynakça

  • Akbarov, S.D. (2013). Microbuckling of a doublewalled carbon nanotube embedded in an elastic matrix. International journal of Solids and Structures, 50, 2584-2596
  • Akbarov, S.D. ve Guz, A.N. (1985). Method of Solving Problems in the Mechanics of Fiber Composites with Curved Structures. Soviet Applied Mechanics, 20(9), 777-790.
  • Akbarov, S.D. ve Guz, A.N. (2000). Mechanics of Curved Composites, Amsterdam: Kluwer Academic Publishers.
  • Akbarov, S.D. ve Kosker, R. (2001). Fiber Bucling in a Viscoelastic Matrix. Mechanics of Composite Materials, 37(4), 299-306.
  • Akbarov, S.D. ve Kosker, R. (2003a). On a Stresss Analysis in the Infinite Elastic Body with Two Neighbouring Curved Fibers. Composites Part B, 34, 143-150.
  • Akbarov, S.D. ve Kosker, R. (2003b). Influence of the Interaction Two Neighbouring Curved Fibers. Mechanics of Composite Materials, 39, 165-176.
  • Akbarov, S.D. ve Kosker, R. (2003c). Stress Distribution Caused by Anti-Phase Periodical Curving of Two Neighbouring Fibers in a Composite Materials. European Journal of Mechanics A/Solids, 22, 243-256.
  • Akbarov, S.D. ve Kosker, R. (2004). Internal Stability Loss of Two Neighboring Fibers in a iscoelastic Matrix. Internal Journal of Engineering Science, 42, 1847-1873.
  • Arefi, A. ve Nahvi, H. (2017). Stability analysis of an embedded single-walled carbon nanotube with small initial curvature based on nonlocal theory. Mechanıcs of Advanced Materials and Structures, 24(11), 962-970.
  • Breuer, O. ve Sundararaj, U. (2004). Big Returns From Small Fibers: A Review of Polymer/Carbon Nanotube Composites. Polymer Composites, 25(6), 630-645.
  • Coban, F. (2009). The stress distribution of infinite body containing a single locally curved and hollow fiber. (Yayımlanmamış Yüsek Lisans Tezi). Yıldız Teknik Universitesi, İstanbul.
  • Coban, F. (2016) Stress And Stabılıty Analysıs Of Double And Trıple-Walled Carbon Nanotubes Wıth Local Curvature. (Yayımlanmamış Doktora Tezi). Yıldız Teknik Universitesi, İstanbul.
  • Duan, H.L., Wang, J., ve Karihaloo, B.L. (2009). Theory of elasticity at the nanoscale. Advanced Applied Mechanics, 42(1), 1–68.
  • Guz, A.N. (1999). Fundamentals of the Three-Dimensional Theory of Stability of Deformable Bodies, Berlin: Springer-Verlag.
  • Guz, I.A. (2012). Continuum solid mechanics at nano-scale: how small can it go? Journal of Nanomaterials and Molecular Nanotechnology, 1 (1).
  • Iijima, S. (1991). Helical microtubules of graphitic carbon. Nature, 354, 56–58.
  • Kalamkarov, A.L., Georgiades, A.V., Rokam, S.K., Veedu, V.P. ve Ghasemi-Nejhad, M.N. (2006). Analytical and numerical techniques to predict carbon nanotubes properties. International Journal of Solids and structures, 43:, 6832-6854
  • Karličić, D., Kozić, P., Pavlović, R. ve Nešić, N. (2017). Dynamic stability of single-walled carbon nanotube embedded in a viscoelastic medium under the influence of the axially harmonic load. Composite Structures, 162, 227-243.
  • Mantazeri, A. ve Naghdabadi, R. (2009). Study the Effect of Viscoelastic Matrix Model on the Stability of CNT/Polymer Composites by Multiscale Modeling. Polymer Composites, 30(11), 1545-1551.
  • Ru, C.Q. (2001). Axially compressed buckling of a double walled carbon nanotube embedded in an elastic medium. Journal of Mechanics, Physics and Solids, 49, 1265–1279.
  • Shi, J.X., Natsuki, T., Lei, X.W. ve Ni, Q.Q. (2012). Buckling Instability of Carbon Nanotube Atomic Force Microscope Probe Clamped in an Elastic Medium, Journal of Nanotechnology in Engineering and Medicine. 3(2), 1-5.
  • Xiaohu, Y. ve Qiang, H. (2006). Investigation of Axially Compressed Buckling of a Multi-Walled Carbon Nanotube Under Temprature Field. Composite Science and Technology, 67, 125-134.
  • Yan Y, Wang W.Q. ve Zhang, L.X. (2010) Nonlocal effect on axially compressed buckling of triple-walled carbon nanotubes under temperature field. Applied Mathematical Modelling, 34, 3422–3429.
  • Zhang, M. ve Li, J. (2009). Carbon Nanotube in Different Shapes. Materials Today, 12(6), 12-18.

Yerel Eğrilikli Dört Duvarlı Karbon Nanotüplerde Lineer Durumda Gerilme Dağılımı

Yıl 2021, Sayı: 22, 167 - 175, 31.01.2021
https://doi.org/10.31590/ejosat.848831

Öz

Son derece yüksek mukavemete sahip olan nanotüpler, nanoteknolojik uygulamalarda kullanılan nanomalzemelerin en önemli yapısal elemanlarıdır ve nanokompozit malzemelerin üretiminde kullanılırlar. Kompozitlerin matris malzemelerine yerleştirilerek üstün mekanik özellikler kazanmalarını sağlarlar. Kompozit malzemeler güçlendirilirken, yapısal nedenlerden veya teknolojik işlemlerden dolayı oluşan ilkel eğrilik, kendi kendini dengeleyen gerilmelerin ortaya çıkmasına neden olur. Bu gerilmelerin büyüklükleri, malzemenin güvenlik sınırlarının aşılmasına neden olabilir. Bu nedenle malzemelerin yük altında mekanik davranışlarının teorik olarak incelenmesi mühendislik açısından önemlidir. Bu çalışmada, yerel eğrilikli dört duvarlı karbon nanotüp içeren kompozit malzeme, üç boyutlu elastisite teorisinin kesin geometrik nonlineer denklemleri kullanılarak parçalı homojen cisim modeli kapsamında incelenmiştir. Çözüm için sınır formu pertürbasyon yöntemi kullanılarak yaklaşık analitik bir metot geliştirilmiştir. Çalışma çözüm yönteminin sıfırıncı ve birinci yaklaşımı için çözümü kapsamaktadır ve yeterlidir. Araştırma, karbon nanotüpün (CNT) dış katmanının dış yüzeyi ile matris malzemesinin kesişim yüzeyindeki normal ve kayma gerilmelerinin analizini içerir. Ayrıca karbon nanotüp ile matris arasında ideal olmayan temas koşulları kullanılmıştır. Sonuçlar, geometrik lineer durum için araştırılmıştır. Karbon nanotüp katmanları arasında ortaya çıkan Van der Waals kuvvetleri dikkate alınmış ve gerilmeler üzerindeki etkisi sayısal sonuçlar ile açıklanmıştır. Diğer problem parametrelerinin de gerilme dağılımı üzerindeki etkisine ilişkin sayısal sonuçlar sunulmuş ve tartışılmıştır. Ayrıca nanotüp en dış yarıçapının artması ile gerilim değerlerinin monoton olmayan şekilde değiştiği gözlenmiştir. Bununla birlikte, elastisite sabitlerinin oranının artmasının gerilmeleri önemli ölçüde etkilediği tespit edilmiştir. Karbon nano tüpün orta çizgisinin denkleminde bulunan ve salınım frekansını gösteren parametreye göre değişim de araştırılmış ve gerilmeler üzerindeki etkisi sunulmuştur. Bunun dışında önemli bir bulgu olarak karbon nanotüplerde de duvar sayısının artmasının gerilme değerlerini düşürdüğü tespit edilmiştir.

Kaynakça

  • Akbarov, S.D. (2013). Microbuckling of a doublewalled carbon nanotube embedded in an elastic matrix. International journal of Solids and Structures, 50, 2584-2596
  • Akbarov, S.D. ve Guz, A.N. (1985). Method of Solving Problems in the Mechanics of Fiber Composites with Curved Structures. Soviet Applied Mechanics, 20(9), 777-790.
  • Akbarov, S.D. ve Guz, A.N. (2000). Mechanics of Curved Composites, Amsterdam: Kluwer Academic Publishers.
  • Akbarov, S.D. ve Kosker, R. (2001). Fiber Bucling in a Viscoelastic Matrix. Mechanics of Composite Materials, 37(4), 299-306.
  • Akbarov, S.D. ve Kosker, R. (2003a). On a Stresss Analysis in the Infinite Elastic Body with Two Neighbouring Curved Fibers. Composites Part B, 34, 143-150.
  • Akbarov, S.D. ve Kosker, R. (2003b). Influence of the Interaction Two Neighbouring Curved Fibers. Mechanics of Composite Materials, 39, 165-176.
  • Akbarov, S.D. ve Kosker, R. (2003c). Stress Distribution Caused by Anti-Phase Periodical Curving of Two Neighbouring Fibers in a Composite Materials. European Journal of Mechanics A/Solids, 22, 243-256.
  • Akbarov, S.D. ve Kosker, R. (2004). Internal Stability Loss of Two Neighboring Fibers in a iscoelastic Matrix. Internal Journal of Engineering Science, 42, 1847-1873.
  • Arefi, A. ve Nahvi, H. (2017). Stability analysis of an embedded single-walled carbon nanotube with small initial curvature based on nonlocal theory. Mechanıcs of Advanced Materials and Structures, 24(11), 962-970.
  • Breuer, O. ve Sundararaj, U. (2004). Big Returns From Small Fibers: A Review of Polymer/Carbon Nanotube Composites. Polymer Composites, 25(6), 630-645.
  • Coban, F. (2009). The stress distribution of infinite body containing a single locally curved and hollow fiber. (Yayımlanmamış Yüsek Lisans Tezi). Yıldız Teknik Universitesi, İstanbul.
  • Coban, F. (2016) Stress And Stabılıty Analysıs Of Double And Trıple-Walled Carbon Nanotubes Wıth Local Curvature. (Yayımlanmamış Doktora Tezi). Yıldız Teknik Universitesi, İstanbul.
  • Duan, H.L., Wang, J., ve Karihaloo, B.L. (2009). Theory of elasticity at the nanoscale. Advanced Applied Mechanics, 42(1), 1–68.
  • Guz, A.N. (1999). Fundamentals of the Three-Dimensional Theory of Stability of Deformable Bodies, Berlin: Springer-Verlag.
  • Guz, I.A. (2012). Continuum solid mechanics at nano-scale: how small can it go? Journal of Nanomaterials and Molecular Nanotechnology, 1 (1).
  • Iijima, S. (1991). Helical microtubules of graphitic carbon. Nature, 354, 56–58.
  • Kalamkarov, A.L., Georgiades, A.V., Rokam, S.K., Veedu, V.P. ve Ghasemi-Nejhad, M.N. (2006). Analytical and numerical techniques to predict carbon nanotubes properties. International Journal of Solids and structures, 43:, 6832-6854
  • Karličić, D., Kozić, P., Pavlović, R. ve Nešić, N. (2017). Dynamic stability of single-walled carbon nanotube embedded in a viscoelastic medium under the influence of the axially harmonic load. Composite Structures, 162, 227-243.
  • Mantazeri, A. ve Naghdabadi, R. (2009). Study the Effect of Viscoelastic Matrix Model on the Stability of CNT/Polymer Composites by Multiscale Modeling. Polymer Composites, 30(11), 1545-1551.
  • Ru, C.Q. (2001). Axially compressed buckling of a double walled carbon nanotube embedded in an elastic medium. Journal of Mechanics, Physics and Solids, 49, 1265–1279.
  • Shi, J.X., Natsuki, T., Lei, X.W. ve Ni, Q.Q. (2012). Buckling Instability of Carbon Nanotube Atomic Force Microscope Probe Clamped in an Elastic Medium, Journal of Nanotechnology in Engineering and Medicine. 3(2), 1-5.
  • Xiaohu, Y. ve Qiang, H. (2006). Investigation of Axially Compressed Buckling of a Multi-Walled Carbon Nanotube Under Temprature Field. Composite Science and Technology, 67, 125-134.
  • Yan Y, Wang W.Q. ve Zhang, L.X. (2010) Nonlocal effect on axially compressed buckling of triple-walled carbon nanotubes under temperature field. Applied Mathematical Modelling, 34, 3422–3429.
  • Zhang, M. ve Li, J. (2009). Carbon Nanotube in Different Shapes. Materials Today, 12(6), 12-18.
Toplam 24 adet kaynakça vardır.

Ayrıntılar

Birincil Dil Türkçe
Konular Mühendislik
Bölüm Makaleler
Yazarlar

Fatma Çoban Kayıkçı 0000-0003-4417-7740

Yayımlanma Tarihi 31 Ocak 2021
Yayımlandığı Sayı Yıl 2021 Sayı: 22

Kaynak Göster

APA Çoban Kayıkçı, F. (2021). Yerel Eğrilikli Dört Duvarlı Karbon Nanotüplerde Lineer Durumda Gerilme Dağılımı. Avrupa Bilim Ve Teknoloji Dergisi(22), 167-175. https://doi.org/10.31590/ejosat.848831