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New Physically Consistent Yield Model to Optimize Material Design for Functionally Graded Vessels

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Abstract

The purpose of this research is to acquire an optimum design of FGMs for cylindrical and spherical vessels such that the whole material contributes to the load bearing. To do so, a reasonable yield strength profile for FGM is proposed and used in the material tailoring equation. In conjunction with equilibrium and compatibility equations as well as considering stress boundary conditions, a nonlinear ODE in terms of inclusion volume fraction is constituted and solved via applying initial conditions. For verification, a FE simulation made by ABAQUS software is performed that shows good agreement between the simulation and analysis results.

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Abbreviations

\( a,b \) :

Internal and external radii, respectively

\( P_{a} ,P_{b} \) :

Internal and external pressures, respectively

\( T_{a} ,T_{b} \) :

Internal and external temperatures, respectively

\( E \) :

Elastic modulus

\( V \) :

Poisson’s ratio

\( k \) :

Thermal conductivity

\( \alpha \) :

Coefficient of expansion

\( S_{\text{y}} \) :

Yield stress

A :

Coefficient of yield strength function

A ′ :

Fraction coefficient of yield strength function

\( B \) :

Exponent of yield strength function

\( \zeta \) :

Volume fraction of inclusion phase

\( \zeta_{0} \) :

Volume fraction of inclusion phase at the inner radius

\( \sigma_{\text{r}} ,\sigma_{\theta } \) :

Radial and circumferential stresses, respectively

\( \varepsilon_{\text{r}} ,\varepsilon_{\theta } \) :

Radial and circumferential strains, respectively

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Authors and Affiliations

  1. Mechanical Engineering Department, College of Engineering, Iowa State University, Iowa, USA

    Mohammad Saber Hashemi

  2. School of Mechanical Engineering, College of Engineering, University of Tehran, Tehran, Iran

    Amir Akbari

  3. Mechanical Engineering Department, College of Engineering, University of Tehran, Tehran, Iran

    Ali Parvizi

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  1. Mohammad Saber Hashemi
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Correspondence to Amir Akbari.

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Hashemi, M.S., Akbari, A. & Parvizi, A. New Physically Consistent Yield Model to Optimize Material Design for Functionally Graded Vessels. J Fail. Anal. and Preven. 20, 470–482 (2020). https://doi.org/10.1007/s11668-020-00844-7

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