Stress Distribution in Elastic Media Containing Hollow Fiber with Periodic Curvature

Year 2020, Issue: 19, 809 - 820, 31.08.2020

Reşat Köşker , İsmail Gülten

Abstract

In the present paper, stress distribution is studied in an infinite elastic body containining low concentration of periodical curved hollow fibers. Taking the low concentration of hollow fibers into account the interaction between them is neglected. So, the considered media is a single periodical curved hollow fiber with an infinite length embedded in an infinite elastic body. Moreover, it is assumed that the body is loaded at infinity by uniformly distributed normal forces which act along the hollow fiber. We suppose that on the inter-medium surfaces the completely cohesion conditions are satisfied. The investigations are carried out within the framework of the piecewise homogeneous body model with the use of the three-dimensional geometrical nonlinear exact equations of the theory of elasticity. In formulation and mathematical solution of the obtained boundary value problem, the boundary form perturbation method is used. In this study, numerical results are obtained in the framework of the zeroth and the first approximations for the normal stress and the self-equilibrium shear stresses on the contact surfaces between hollow fiber and matrix. The numerous numerical results related to the stress distribution in considered body and the influence of geometrical nonlinearity to this distribution are obtained and interpreted. Moreover, the influences of the geometrical and mechanical parameters of problem to these distributions are also analyzed.

Keywords

Hollow Fiber, Fibrous Composites, Stress Distribution, Periodic Curvature, Geometrical Non-linearity

Project Number

2014-07-03-DOP01

Periyodik Eğrilikli İçi Boş Lif İçeren Elastik Ortamda Gerilme Dağılımı

Abstract

Bu makalede, düşük yoğunluklu periyodik eğrilikli içi boş lifler içeren sonsuz elastik bir ortamda gerilme dağımılı incelenmiştir. İçi boş liflerin düşük yoğunluğu dikkate alındığında, aralarındaki etkileşim ihmal edilir. Dolayısıyla, dikkate alınan ortam, sonsuz bir elastik gövdeye gömülü sonsuz bir uzunluğa sahip tek bir periyodik eğrilikli içi boş liftir. Ayrıca, ortamın sonsuzda içi boş lif boyunca etkiyen düzgün dağılmış normal kuvvetlerle yüklendiği varsayılmaktadır. Ortamlar arası yüzeylerde ideal temas koşullarının sağlandığını düşünüyoruz. Araştırmalar, parçalı-homoje cisim modeli çerçevesinde elastisite teorisinin üç boyutlu geometrik doğrusal olmayan kesin denklemleri kullanılarak gerçekleştirilmiştir. Elde edilen sınır değer probleminin formülasyonu ve matematiksel çözümünde sınır formu pertürbasyon yöntemi kullanılmıştır. Bu çalışmada, içi boş lif ile matris arasındaki temas yüzeyleri üzerindeki normal gerilme ve kendi kendini dengeleyen kayma gerilmeleri için, sıfırıncı ve birinci yaklaşımlar çerçevesinde sayısal sonuçlar elde edilmiştir. Ele alınan cisimdeki gerilme dağılımı ve geometrik doğrusal olmamanın bu dağılıma etkisi ile ilgili çok sayıda sayısal sonuç elde edilmiş ve yorumlanmıştır. Ayrıca, geometrik ve mekanik problem parametrelerinin bu dağılımlara etkileri de analiz edilmiştir.

Keywords

İçi Boş Lif, Lifli Kompozitler, Gerilme Dağılımı, Periyodik Eğrilik, Geometrik nonlineerite

Supporting Institution

Yıldız Teknik Üniversitesi Bilimsel Araştırma Projeleri Koordinatörlüğü

Project Number

2014-07-03-DOP01

References

• AKBAROV, Surkay D. (2007). “Three-dimensional stability loss problems of the viscoelastic composite materials and structural members”. International Applied Mechanics. 43 (10):3-27.
• AKBAROV, Surkay D. (2012). Stability Loss and Buckling Delamination: Three-Dimensional Linearized Approach for Elastic and Viscoelastic Composites. Springer.
• AKBAROV, Surkay D. (2013). “Microbuckling of a Double-Walled Carbon Nanotube Embedded in an Elastic Matrix”. International Journal of Solids and Structures. 50: 2584- 2596.
• AKBAROV, Surkay D. KOSKER, Resat ve UCAN, Yasemen (2004). “Stress distribution in an elastic body with a periodically curved row of fibers”. Mechanics of Composite Materials. 40 (3): 191-202.
• AKBAROV, Surkay D. KOSKER, Resat ve UCAN, Yasemen (2006). “Stress distribution in a composite material with the row of anti-phase periodically curved fibers”. International Applied Mechanics. 42 (4): 486-493.
• AKBAROV, Surkay D. KOSKER, Resat ve UCAN, Yasemen (2010). “The Effect of the Geometrical Non-Linearity on the Stress Distribution in the Infinite Elastic Body with a Periodically Curved Row of Fibers”. CMC:Computers, Materials, & Continua. 17 (2): 77-102.
• AKBAROV, Surkay D. KOSKER, Resat ve UCAN, Yasemen (2016). “Influence of the interaction between fibers periodically located in a composite material on the distribution of stresses in it”. Mechanics of Composite Materials. 52 (2): 243-256.
• AKBAROV, Surkay D. ve KOSKER, Resat (2003). “On a stress analysis in the infinite elastic body with two neighbouring curved fibers”. Composites Part B: Engineering. 34 (2): 143-150.
• AKBAROV, Surkay D., GUZ, Aleksander N. (1985). “Method of Solving Problems in the Mechanics of Fiber Composites With Curved Structures”. Soviet Applied Mechanics. March: 777-785.
• AKBAROV, Surkay D., GUZ, Aleksander N. (2002). “Mechanics of curved composites (piecewise homogenous body model)”. International Applied Mechanics. 38 (12): 1415-1439.
• AKBAROV, Surkay D.-GUZ, Aleksander N. (2000). Mechanics of Curved Composites. Kluwer Academic Publishers.
• CORTEN, H. T., BROUTMAN, L. J., & KROCH, R. H. (1967). Modern Composite Materials. Micromechanics and Fracture Behavior of Composites. Addison-Wesley, Reading, Massachusetts.
• GUZ, Aleksander N. (1999). Fundamentals of the Three-Dimensional Theory of Stability of Deformable Bodies. Springer-Verlag. Berlin, Germany.
• GUZ, Aleksander N. (2003). “On one two-level model in the mesomechanics of compression fracture of Cracked Composites”. International Applied Mechanics. 39 (3):274-285.
• GUZ, Aleksander N. and DEKRET, V.A., (2008).” On two models in the three-dimensional theory of stability of composites”. International Applied Mechanics. 44 (8): 839-854.
• KASHTALYAN, M. Yu. (2005). “On deformation of ceramic cracked matrix cross-ply composites laminates”. International Applied Mechanics. 41 (1):37-47.
• KELLY, Anthony (1998), “Composite Materials: impediments do wider use and some suggestions to overcome these”, Proceeding Book ECCM-8, 3-6 June, Napoles-Italy, Vol. I, pp. 15-18.
• KOSKER, Resat ve AKBAROV, Surkay D. (2003). “Influence of the interaction between two neighbouring periodically curved fibers on the stress distribution in a composite material” . Mechanics of Composite Materials. 39 (2): 165-176.
• MALIGINO, A.R. & WARRIOR, N.A. & LONG, A.C. (2009). “Effect on inter-fibre spacing on damage evolution in unidirectional (UD) fibre-reinforced composites.”. European Journal of Mechanics - A/Solids., 28: 768-776.
• QİAN, D.; DİCKEY, E. C.; ANDREWS, R.; RANTELL, T. (2000): “Load transfer and deformation mechanisms of carbon nanotube-plytyrene composites”. Applied Physics Letters. 76 (20): 2868-2870.
• ZHUK, Y.A. and GUZ, I.A. (2007). “ Features of plane wave propagation along the layers of a prestrained nanocomposite”. International Applied Mechanics. 43 (4): 361-379.