Fonksiyonel Olarak Derecelendirilmiş Ti-6Al-4V ve Zirkonya Biyomalzeme Plakalarının Termomekanik Tepkisi

Year 2023, Volume: 4 Issue: 1, 224 - 243, 26.06.2023

Ramazan Özmen

https://doi.org/10.55546/jmm.1261024

Abstract

Bu makalede, termal yüke maruz kalan fonksiyonel olarak derecelendirilmiş malzemeli (FGM) gözenekli nanoplakaların serbest titreşim tepkilerini incelenmiştir. Geliştirilen matematiksel model, bir kayma deformasyonu, boyut ölçeği ve mikro yapı etkilerini içeren yüksek dereceli kayma deformasyonu (HSDT) ve yerel olmayan gerinim gradyanı (NGST) teorilerinden meydana gelmektedir. Çalışmada, düzgün, simetrik, asimetrik alt ve asimetrik üst dağılımı şeklinde kalınlık boyunca değişne dört farklı gözeneklilik modeli ele alınmıştır. Termal yükün etkileri de dahil olmak üzere FGM gözenekli nanoplakanın hareket denklemi Hamilton prensibi ile türetilmiş ve daha sonra Navier yöntemi kullanılarak analitik olarak çözülmüştür. Nanoplakanın serbest titreşim tepkileri için, yerel olmayan ve gerinim gradyan elastikiyetlerinin, sıcaklık artışının, gözeneklilik hacim fraksiyonunun ve dağılımının etkileri analiz edilmiştir.

Keywords

Gözeneklilik, Fonksiyonel Olarak Derecelendirilmiş Malzeme, Nanolevha, Lokal olmayan gerinim gradyan teorisi, Termal yük

Thermomechanical Response of Functionally Graded Ti-6Al-4V and Zirconia Biomaterial Plates

Abstract

This article studies the free vibration responses of functionally graded material (FGM) porous nanoplates exposed to thermal load. The developed mathematical model includes a shear deformation, size-scale, and microstructure influence by a high-order shear deformation (HSDT) and nonlocal strain gradient (NGST) theories. The study considers four different porosity patterns across the thickness: uniform, symmetrical, asymmetric bottom, and asymmetric top distributions. The equation of motion of the FGM porous nanoplate, including the effects of thermal load, is derived with Hamilton's principle, and then solved analytically by employing the Navier method. For the free vibration responses of the nanoplate, the effects of nonlocal and strain gradient elasticities, temperature rise, porosity volume fraction and its distribution are analyzed.

Keywords

Porosity, Functionally Graded Material, Nanoplate, Nonlocal strain gradient theory, Thermal load

References

• Aghababaei R., Reddy J.N., Nonlocal Third-Order Shear Deformation Plate Theory with Application to Bending and Vibration of Plates. Journal of Sound and Vibration, 326 (1–2), 277-289, 2009.
• Akavci S.S., An Efficient Shear Deformation Theory for Free Vibration of Functionally Graded Thick Rectangular Plates on Elastic Foundation. Composite Structures 108 (1), 667–676, 2014.
• Azeem P., B.M. R., Functionally Graded Materials (FGM) Fabrication and Its Potential Challenges & Applications. Materials Today: Proceedings (52) 413–418,2022.
• Barati M.R., Zenkour A.M., Analysis of Postbuckling Behavior of General Higher-Order Functionally Graded Nanoplates with Geometrical Imperfection Considering Porosity Distributions. Mechanics of Advanced Materials and Structures 26 (12), 1081–88, 2019
• Bendaho B., Belabed Z., Bourada M., Benatta M.A., Bourada F., Tounsi A., Assessment of New 2D and Quasi-3D Nonlocal Theories for Free Vibration Analysis of Size-Dependent Functionally Graded (FG) Nanoplates. Advances in Nano Research 7 (4), 277-292, 2019.
• Biçer, H., Reactive Sintering of Boron Carbide Based Ceramics by SPS. Journal of Materials and Mechatronics:A (JournalMM), 3(1), 129-136, 2022.
• Coskun S., Kim J., Toutanji H., Bending, Free Vibration, and Buckling Analysis of Functionally Graded Porous Micro-Plates Using a General Third-Order Plate Theory. Journal of Composites Science 3 (1), 15, 2019.
• Doan T. L., Le P.B., Tran T.T., Trai V.K., Pham Q.H., Free Vibration Analysis of Functionally Graded Porous Nanoplates with Different Shapes Resting on Elastic Foundation. Journal of Applied and Computational Mechanics 7 (3), 1593-1605, 2021.
• Eringen A.C., On Differential Equations of Nonlocal Elasticity and Solutions of Screw Dislocation and Surface Waves. Journal of Applied Physics 54 (9), 1983.
• Eringen, A.C., Suhubi E.S., Nonlinear Theory of Simple Micro-Elastic Solids-I. International Journal of Engineering Science 2 (2), 189–203, 1964.
• Esen I., Abdelrhmaan A.A., Eltaher M.A., Free Vibration and Buckling Stability of FG Nanobeams Exposed to Magnetic and Thermal Fields. Engineering with Computers, 38, 3463–3482, 2021a.
• Esen I., Alazwari M.A., Eltaher M.A., Abdelrahman A.A., Dynamic Response of FG Porous Nanobeams Subjected Thermal and Magnetic Fields under Moving Load. Steel and Composite Structures 42 (6), 805-26, 2022.
• Esen I., Daikh A.A., Eltaher M.A., Dynamic Response of Nonlocal Strain Gradient FG Nanobeam Reinforced by Carbon Nanotubes under Moving Point Load. The European Physical Journal Plus 136 (4), 458, 2021b.
• Esen I., Dynamic Response of a Functionally Graded Timoshenko Beam on Two-Parameter Elastic Foundations Due to a Variable Velocity Moving Mass. International Journal of Mechanical Sciences Volumes (153–154), 21-35, 2019.
• Esen I., Özarpa C., Eltaher M.A., Free Vibration of a Cracked FG Microbeam Embedded in an Elastic Matrix and Exposed to Magnetic Field in a Thermal Environment. Composite Structures (261),113552, 2021.
• Esen I., Özmen R., Free and Forced Thermomechanical Vibration and Buckling Responses of Functionally Graded Magneto-Electro-Elastic Porous Nanoplates. Mechanics Based Design of Structures and Machines, 1–38, 2022b.
• Esen I., Özmen R., Thermal Vibration and Buckling of Magneto-Electro-Elastic Functionally Graded Porous Nanoplates Using Nonlocal Strain Gradient Elasticity. Composite Structures (296) 115878, 2022a.
• Giannopoulos G.I., Kakavas P.A., Anifantis N.K., Evaluation of the Effective Mechanical Properties of Single Walled Carbon Nanotubes Using a Spring Based Finite Element Approach. Computational Materials Science 41 (4), 561–69, 2008.
• Huang X.L., Shen H.S., Nonlinear Vibration and Dynamic Response of Functionally Graded Plates in Thermal Environments. International Journal of Solids and Structures 41 (9–10), 2403-2427, 2004.
• Jalaei M.H., Thai H.T., Dynamic Stability of Viscoelastic Porous FG Nanoplate under Longitudinal Magnetic Field via a Nonlocal Strain Gradient Quasi-3D Theory. Composites Part B: Engineering 175, 107164, 2019.
• Ke L.L., Wang Y.S., Yang J., Kitipornchai S., Nonlinear Free Vibration of Size-Dependent Functionally Graded Microbeams. International Journal of Engineering Science 50 (1), 256-267, 2012.
• Kiani Y., Thermal Post-Buckling of FG-CNT Reinforced Composite Plates. Composite Structures 159, 299-306, 2017.
• Kong S., Zhou S., Nie Z., Wang K., The Size-Dependent Natural Frequency of Bernoulli-Euler Micro-Beams. International Journal of Engineering Science 46 (5), 427-447, 2008.
• Li L., Hu Y., Buckling Analysis of Size-Dependent Nonlinear Beams Based on a Nonlocal Strain Gradient Theory. International Journal of Engineering Science (97) 84–94, 2015.
• Li L., Hu Y., Nonlinear Bending and Free Vibration Analyses of Nonlocal Strain Gradient Beams Made of Functionally Graded Material. International Journal of Engineering Science (107), 77-99, 2016.
• Lim C.W., Zhang G., Reddy J.N., A Higher-Order Nonlocal Elasticity and Strain Gradient Theory and Its Applications in Wave Propagation. Journal of the Mechanics and Physics of Solids (78), 298-313, 2015.
• Najafi F., Shojaeefard M.H., Googarchin H.S., Nonlinear Dynamic Response of FGM Beams with Winkler–Pasternak Foundation Subject to Noncentral Low Velocity Impact in Thermal Field. Composite Structures (167) 132-43, 2017.
• Reddy J.N., Chin C.D., Thermomechanical Analysis of Functionally Graded Cylinders and Plates. Journal of Thermal Stresses 21 (6) 593–626, 1998.
• Reddy J.N., Nonlocal Theories for Bending, Buckling and Vibration of Beams. International Journal of Engineering Science 45 (2–8), 288-307, 2007.
• Reddy JN.,A Simple Higher-Order Theory for Laminated Composite Plates. Journal of Applied Mechanics 51 (4), 745–752, 1984.
• Şanlı, P., Gavas, M., Microstructure, Physical and Mechanical Properties of Al/SiC and Al/B4C Metal Matrix Composites Produced by Powder Metallurgy. Journal of Materials and Mechatronics: A (JournalMM), 2(2), 72-89, 2021.
• Talebizadehsardari P., Salehipour H., Shahgholian-Ghahfarokhi D., Shahsavar A., Karimi M., Free Vibration Analysis of the Macro-Micro-Nano Plates and Shells Made of a Material with Functionally Graded Porosity: A Closed-Form Solution.” Mechanics Based Design of Structures and Machines 0 (0), 1-27, 2020.
• Touloukian Y.S., Thermophysical Properties of High Temperature Solid Materials. Macmillan New York, 1967
• Zenkour A.M., A Comprehensive Analysis of Functionally Graded Sandwich Plates: Part 1-Deflection and Stresses. International Journal of Solids and Structures 42 (18-19) 5224–42, 2005.
• Zenkour A.M., Alghamdi N.A., Bending Analysis of Functionally Graded Sandwich Plates Under the Effect of Mechanical and Thermal Loads. Mechanics of Advanced Materials and Structures 17 (6) 419-32, 2010.
• Zhang C., Ji H., Xu H., Liang M., Huang J., Pei S., Li M., Interfacial Microstructure and Mechanical Properties of Ultrasonic-Assisted Brazing Joints between Ti–6Al–4V and ZrO2. Ceramics International 46 (6) 7733–7740, 2020.
• Zhang X., Zhang G., Li J., He X., Wang Y., Hang R., Huang X., Tang B., Chu P.K., Cellular Response to Nano-Structured Zr and ZrO2 Alloyed Layers on Ti-6Al-4V. Materials Science and Engineering (90) 523-530, 2018.
• Zhou X., Zhang M., Xu D., Geng S., Wang Q., Wang F., Microstructural Evolution, Corrosion Behavior and Cytotoxicity of Ti-6Al-4V/ZrO2 Composite Fabricated by Directed Energy Deposition for Implant Biomaterial.” Journal of Alloys and Compounds (892) 161820, 2022.