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

Part of: Elastic materials Special kinds of problems 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:[email protected] (G. S. Dui)
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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 

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