Hostname: page-component-8448b6f56d-gtxcr Total loading time: 0 Render date: 2024-04-24T19:33:53.169Z Has data issue: false hasContentIssue false
  • English
  • Français

Elastic-Plastic Analysis for Functionally Graded Thick-Walled Tube Subjected to Internal Pressure

Part of: Special kinds of problems Elastic materials Material properties given special treatment

Published online by Cambridge University Press:  27 January 2016

Libiao Xin ,
Guansuo Dui ,
Shengyou Yang  and
Ying Liu
Libiao Xin
Affiliation:
Institute of Mechanics, Beijing Jiaotong University, Beijing 100044, China
Guansuo Dui*
Affiliation:
Institute of Mechanics, Beijing Jiaotong University, Beijing 100044, China
Shengyou Yang
Affiliation:
Institute of Mechanics, Beijing Jiaotong University, Beijing 100044, China
Ying Liu
Affiliation:
Institute of Mechanics, Beijing Jiaotong University, Beijing 100044, China
*
*Corresponding author. Email:gsdui@bjtu.edu.cn (G. S. Dui)
Get access

Abstract

The elastic-plastic response of the functionally graded thick-walled tube subjected to internal pressure is investigated by using the relation of the volume average stresses of constituents and the macroscopic stress of composite material in micromechanics. The tube consists of two idealized isotropic elastic-plastic materials whose volume fractions are power functions of the radius. As the internal pressure increases, the deformations of one phase and two phases from elastic to plastic are analyzed. In order to simplify the calculations we assume both materials with the same Poisson's ratio. By using the assumption of a uniform strain field within the representative volume element and the Tresca yield criterion, the theoretical solutions are obtained for the case of two elastic phases and the case of two plastic phases, and the function of the radial displacement is presented for the case with both elastic and plastic phases. The yield criterion of functionally graded material is given in terms of the yield stresses and volume fractions of constituents rather than Young's modulus and yield stress with different unknown parameters of the whole material in the existing papers. Finally we also discuss the position where the plastic deformation first occurs and the conditions for which material first yields in the tube.

Keywords

Functionally graded thick-walled tubeinternal pressureelastic-plastic solution

MSC classification

Secondary: 74B05: Classical linear elasticity 74E30: Composite and mixture properties 74M25: Micromechanics
Type
Research Article
Information
Advances in Applied Mathematics and Mechanics , Volume 8 , Issue 2 , April 2016 , pp. 331 - 352
Copyright
Copyright © Global-Science Press 2016 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1]Sobhy, M. and Zenkour, A. M., Thermodynamical bending of FGM sandwich plates resting on Pasternak's elastic foundations, Adv. Appl. Math. Mech., 7 (2015), pp. 116–134.CrossRefGoogle Scholar
[2]Birman, V., Mechanics and energy absorption of a functionally graded cylinder subjected to axial loading, Int. J. Eng. Sci., 78 (2014), pp. 18–26.Google Scholar
[3]Fu, Z. J., Chen, W. and Qin, Q. H., Boundary knot method for heat conduction in nonlinear functionally graded material, Eng. Anal. Bound. Elem., 35 (2011), pp. 729–734.CrossRefGoogle Scholar
[4]Fu, Z.J., Qin, Q. H. and Chen, W., Hybrid-Trefftz finite element method for heat conduction in nonlinear functionally graded materials, Eng. Comput., 28 (2011), pp. 578–599.CrossRefGoogle Scholar
[5]Fu, Z.J., Chen, W. and Qin, Q. H., Three boundary meshless methods for heat conduction analysis in nonlinear FGMs with Kirchhoff and Laplace transformation, Adv. Appl. Math. Mech., 4 (2012), pp. 519–542.Google Scholar
[6]You, L. H., Zhang, J. J. and You, X. Y., Elastic analysis of internally pressurized thick-walled spherical pressure vessels of functionally graded materials, Int.J. Pres. Ves. Pip., 82 (2005), pp. 347–354.CrossRefGoogle Scholar
[7]Tutuncu, N. and Ozturk, M., Exact solutions for stresses in functionally graded pressure vessels, Compos. Part B-Eng., 32 (2001), pp. 683–686.Google Scholar
[8]Shi, Z. F., Zhang, T. T. and Xiang, H.J., Exact solutions of heterogeneous elastic hollow cylinders, Compos. Struct., 79 (2007), pp. 140–147.Google Scholar
[9]Chen, Y. Z. and Lin, X. Y., Elastic analysis for thick cylinders and spherical pressure vessels made of functionally graded materials, Comput. Mater. Sci., 44 (2008), pp. 581–587.Google Scholar
[10]Hosseini, S. M. and Akhlaghi, M., Analytical solution in transient thermo-elasticity of functionally graded thick hollow cylinders (Pseudo-dynamic analysis), Math. Method Appl. Sci., 32 (2009), pp. 2019–2034.CrossRefGoogle Scholar
[11]Li, X. F. and Peng, X. L., A pressurized functionally graded hollow cylinder with arbitrarily varying material properties, J. Elasticity, 96 (2009), pp. 81–95.CrossRefGoogle Scholar
[12]Sofiyev, A. H. and Schnack, E., The stability of functionally graded cylindrical shells under linearly increasing dynamic torsional loading, Eng. Struct., 26 (2004), pp. 1321–1331.Google Scholar
[13]Wang, H. M. and Xu, Z. X., Effect of material inhomogeneity on electromechanical behaviors of functionally graded piezoelectric spherical structures, Comput. Mater. Sci., 48 (2010), pp. 440–445.CrossRefGoogle Scholar
[14]Nayak, P. and Mondal, S. C., Analysis of a functionally graded thick cylindrical vessel with radially varying properties, Int. J. Eng. Sci. Technol., 3 (2011), pp. 1551–1562.Google Scholar
[15]Tutuncu, N., Stresses in thick-walled FGM cylinders with exponentially-varying properties, Eng. Struct., 29 (2007), pp. 2032–2035.Google Scholar
[16]Sburlati, R., Analytical elastic solutions for pressurized hollow cylinders with internal functionally graded coatings, Compos. Struct., 94 (2012), pp. 3592–3600.CrossRefGoogle Scholar
[17]Nie, G. J., Zhong, Z. and Batra, R. C., Material tailoring for functionally graded hollow cylinders and spheres, Compos. Sci. Technol., 71 (2011), pp. 666–673.Google Scholar
[18]Timoshenko, S. P. and Goodier, J. N., Theory of Elasticity, McGraw-Hill, 1970.Google Scholar
[19]Chadwick, P., Compression of a spherical shell of work-hardening material, Int. J. Mech. Sci., 5 (1963), pp. 165–182.CrossRefGoogle Scholar
[20]Eraslan, N. A. and Akis, T., Elastoplastic response of a long functionally graded tube subjected to internal pressure, Turkish J. Eng. Env. Sci., 29 (2005), pp. 361–368.Google Scholar
[21]You, L. H. and Zheng, Z. Y., Elastic-plastic thermomechanical response of composite co-axial cylinders, J. Mater. Sci., 41 (2006), pp. 4901–4913.Google Scholar
[22]Akis, T., Elastoplastic analysis of functionally graded spherical pressure vessels, Comput. Mater. Sci., 46 (2009), pp. 545–554.Google Scholar
[23]Sadeghian, M. and Toussi, H. E., Axisymmetric yielding of functionally graded spherical vessel under thermo-mechanical loading, Comput. Mater. Sci., 50 (2011), pp. 975–981.CrossRefGoogle Scholar
[24]Sadeghian, M. and Toussi, H. E., Solutions to the problem of thermo-mechanical yielding in functionally graded material cylindrical vessels, J. Reinf. Plast. Comp., 32 (2013), pp. 1624–1633.Google Scholar
[25]Nayebi, A. and Sadrabadi, S. A., FGM Elastoplastic analysis under thermo mechanical loading, Int. J. Pres. Ves. Pip., 111-112 (2013), pp. 12–20.Google Scholar
[26]Xin, L., Dui, G., Yang, S. and Zhang, J., An elasticity solution for functionally graded thick-walled tube subjected to internal pressure, Int. J. Mech. Sci., 89 (2014), pp. 344–349.Google Scholar
[27]Xin, L., Dui, G., Yang, S. and Zhou, D., Solutions for behavior of a functionally graded thick-walled tube subjected to mechanical and thermal loads, Int. J. Mech. Sci., 98 (2015), pp. 70–79.Google Scholar
[28]Liu, B., Dui, G. and Yang, S., On the transformation behavior of functionally graded SMA composites subjected to thermal loading, Euro. J. Mech. A Solid., 40 (2013), pp. 139–147.Google Scholar
[29]Qu, J. M. and Cherkaoui, M., Fundamentals of Micromechanics of Solids, John Wiley & Sons, Inc., 2006.Google Scholar
[30]Erdogan, F., Fracture mechanics of functionally graded materials, Compos. Eng., 5 (1995), pp. 753–770.Google Scholar
[31]Mendelson, A., Plasticity: Theory and Application, Macmillan, 1968.Google Scholar