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Acta Mechanica Sinica

, Volume 34, Issue 5, pp 936–948 | Cite as

Novel material tailoring method for internally pressurized FG spherical and cylindrical vessels

  • Fayyaz Nosouhi Dehnavi
  • Ali Parvizi
  • Karen Abrinia
Research Paper
  • 91 Downloads

Abstract

A new material tailoring method for spherical and cylindrical vessels made of functionally graded materials (FGMs) is presented. It is assumed that the FG material is composed of an Al–SiC metallic-matrix composite. A uniform ratio of in-plane shear stress to yield strength [\(\varphi \left( r \right) \)] is used as the design criterion to utilize the maximum capacity of the vessel. The aim is to find a distribution of SiC particles in the radial direction, i.e., \(f\left( r \right) \), that achieves a uniform index \(\varphi \left( r \right) =\hbox {const}.\) through the wall thickness of the internally pressurized spherical or cylindrical vessel. Both the Mori–Tanaka and rule-of-mixtures homogenization schemes are used to express the effective elastic module and Poisson’s ratio. Moreover, the strength of the composite is expressed based on the rule of mixtures. Besides, finite element simulation is carried out to verify the accuracy of the analytical solution. The effects of input parameters such as the internal pressure, strength of the SiC particles, ratio of in-plane shear stress to effective yield strength, and choice of homogenization scheme on the tailored distribution of the SiC volume fraction in the radial direction are also investigated.

Keywords

Material tailoring Sphere Cylinder FGM Mori–Tanaka Rule of mixtures 

List of symbols

ab

Inner and outer radius of sphere or cylinder, respectively

u

Radial displacement

c

Constant value of in-plane shear stress divided by effective yield strength

\(f\left( r \right) \)

Radial distribution of SiC particles

\(N_1 ,\,N_2 \)

Constants related to material properties based on Mori–Tanaka homogenization

\(C_1-C_9 \)

Constants related to material properties based on Mori–Tanaka homogenization

\(Z_1-Z_9 \)

Constants related to material properties based on Mori–Tanaka homogenization

\(P_a ,P_b \)

Internal and external pressure, respectively

E

Elastic modulus

K

Bulk modulus

Y

Yield strength

\(\mu \)

Shear modulus

\(\varphi \left( r \right) \)

In-plane shear stress divided by effective yield strength

\(\varepsilon _r ,\varepsilon _\theta ,\varepsilon _\varphi \)

Strains in radial, and first and second circumferential directions, respectively

\(\sigma _r ,\sigma _\theta \)

Radial and circumferential stress, respectively

v

Poisson’s ratio

\(\mathrm {p},\,\mathrm {m}\)

Subscripts denoting particle andmatrix, respectively

MT (MTHS)

Subscript (abbreviation) for Mori–Tanaka homogenization scheme

RM (RMHS)

Subscript (abbreviation) for rule-of-mixtures homogenization scheme

Notes

Acknowledgements

The work was supported by the Iran National Science Foundation (INSF).

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Copyright information

© The Chinese Society of Theoretical and Applied Mechanics; Institute of Mechanics, Chinese Academy of Sciences and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • Fayyaz Nosouhi Dehnavi
    • 1
  • Ali Parvizi
    • 1
  • Karen Abrinia
    • 1
  1. 1.School of Mechanical Engineering, College of EngineeringUniversity of TehranTehranIran

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