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Research Papers

Elasto-Plastic Stresses in a Functionally Graded Rotating Disk

[+] Author and Article Information
Babak Haghpanah Jahromi, Hamid Nayeb-Hashemi

Department of Mechanical and Industrial Engineering,  Northeastern University, Boston, MA 02115

Ashkan Vaziri1

Department of Mechanical and Industrial Engineering,  Northeastern University, Boston, MA 02115vaziri@coe.neu.edu

1

Corresponding author.

J. Eng. Mater. Technol 134(2), 021004 (Mar 27, 2012) (11 pages) doi:10.1115/1.4006023 History: Received April 04, 2011; Revised January 30, 2012; Published March 26, 2012; Online March 27, 2012

A numerical method based on the extension of the variable material property method was developed to obtain the elasto-plastic stress field in a functionally graded (FG) rotating disk. The method was applied to estimate the stress field in a metal–ceramic functionally graded solid disk. To establish the validity of the proposed method, results were compared with finite element results. Unlike uniform rotating disks, where yielding starts from the disk center, plasticity in FG disks can originate at any point. The effect of different metal–ceramic grading patterns as well as the relative elastic moduli and densities of the ceramic and metallic constituents on the developed stresses were studied. Reinforcement of a metal disk with ceramic particles, in both elastic and plastic regimes, can significantly influence the mechanical response of the disk such as the stress distribution and the critical angular velocities corresponding to the onset of plasticity in the disk and plastic disk. Disks with increasing ceramic content from inner to outer radius showed a more uniform von Mises stress distribution for a fixed value of total ceramic content. In contrast, disks with decreasing ceramic content from inner to outer radius had the lowest outer edge displacement for a fixed value of total ceramic content.

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Copyright © 2012 by American Society of Mechanical Engineers
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Figures

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Figure 1

(a) Schematic of a thin rotating disk and the bilinear stress–strain curve of the disk material (metal). (b) Distribution of radial and tangential stresses in an all metal rotating disk at ω = 150 and 200 rad/s. For the angular velocity ω = 150 rad/s, the disk deforms plastically at the inner part and is elastic close to the outer edge. For ω = 200 rad/s, the disk deforms plastically along its radius. The radius of the disk is 120 cm and the metal density is considered 104 kg/m3 .

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Figure 2

Distribution of (a) radial, (b) hoop, and (c) von Mises stresses for a FG metal–ceramic rotating disk subjected to ω = 400 rad/s for different reinforcement distributions. The radius of the disk is 120 cm.

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Figure 3

(a) Distribution of von Mises stress in a FG rotating disk with n = 1 and different values of fo . (b) von Mises stress induced in the FG rotating disk with fo  = 1 and different values of n. The disk is rotating at ω = 400 rad/s.

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Figure 4

(a) Distribution of von Mises stress in a FG rotating disk with n = 1 and different values of fi . (b) von Mises stress induced in the FG rotating disk with fi  = 1 and different values of n. The disk is rotating at ω = 400 rad/s.

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Figure 5

(a) Effect of relative density of ceramic and metal, ρc /ρm , on the distribution of von Mises stress in a FG rotating disk subjected to ω = 200 rad/s. (b) The locus of elastic and plastic regions in a FG disk at different angular velocities for three values of ρc /ρm . (c) Relative density of ceramic and metal, ρc /ρm , versus the angular velocities developing incipient and full plasticity in a FG disk. The ceramic volume fraction varies according to fc (r) = (r/R) in these sets of results.

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Figure 6

(a) Effect of relative stiffness of ceramic and metal, Ec /Em , on the distribution of von Mises stress in a FG rotating disk subjected to ω = 200 rad/s. (b) The locus of elastic and plastic regions in a FG disk at different angular velocities for three values of Ec /Em . (c) Relative stiffness of ceramic and metal, Ec /Em , versus the angular velocities developing incipient and full plasticity in a FG disk. The ceramic volume fraction varies according to fc (r) = (r/R) in these sets of results.

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Figure 7

(a) Effect of relative stiffness of ceramic and metal, Ec /Em , on the distribution of von Mises stress in a FG rotating disk subjected to ω = 200 rad/s. (b) The von Mises stress distribution in a rotating disk with Ec /Em  = 0.1 subjected to four different angular velocities. (c) The locus of elastic and plastic regions in a FG disk at different angular velocities for three values of Ec /Em . (d) Relative stiffness of ceramic and metal, Ec /Em , versus the angular velocities developing incipient and full plasticity in a FG disk. The ceramic volume fraction varies according to fc (r) = (1 − r/R) in these sets of results.

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Figure 8

(a) The normalized outer edge displacement versus the average ceramic volume fraction for FG disks of radially increasing volume fraction with different reinforcement coefficients fo according to Eq. 7. (b) The normalized outer edge displacement versus the average ceramic volume fraction for FG disks of radially decreasing volume fraction with different reinforcement coefficients fi according to Eq. 8. The disks are subjected to ω = 400 rad/s.

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