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Research Papers

Displacement and Stress Fields in a Functionally Graded Fiber-Reinforced Rotating Disk With Nonuniform Thickness and Variable Angular Velocity

[+] Author and Article Information
Y. Zheng, H. Bahaloo, D. Mousanezhad, A. Vaziri

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

H. Nayeb-Hashemi

Department of Mechanical and
Industrial Engineering,
Northeastern University,
Boston, MA 02115 
e-mail: hamid@coe.neu.edu

1Corresponding author.

Contributed by the Materials Division of ASME for publication in the JOURNAL OF ENGINEERING MATERIALS AND TECHNOLOGY. Manuscript received October 27, 2016; final manuscript received February 20, 2017; published online April 19, 2017. Assoc. Editor: Vikas Tomar.

J. Eng. Mater. Technol 139(3), 031010 (Apr 19, 2017) (10 pages) Paper No: MATS-16-1307; doi: 10.1115/1.4036242 History: Received October 27, 2016; Revised February 20, 2017

Displacement and stress fields in a functionally graded (FG) fiber-reinforced rotating disk of nonuniform thickness subjected to angular deceleration are obtained. The disk has a central hole, which is assumed to be mounted on a rotating shaft. Unidirectional fibers are considered to be circumferentially distributed within the disk with a variable volume fraction along the radius. The governing equations for displacement and stress fields are derived and solved using finite difference method. The results show that for disks with fiber rich at the outer radius, the displacement field is lower in radial direction but higher in circumferential direction compared to the disk with the fiber rich at the inner radius. The circumferential stress value at the outer radius is substantially higher for disk with fiber rich at the outer radius compared to the disk with the fiber rich at the inner radius. It is also observed a considerable amount of compressive stress developed in the radial direction in a region close to the outer radius. These compressive stresses may prevent any crack growth in the circumferential direction of such disks. For disks with fiber rich at the inner radius, the presence of fibers results in minimal changes in the displacement and stress fields when compared to a homogenous disk made from the matrix material. In addition, we concluded that disk deceleration has no effect on the radial and hoop stresses. However, deceleration will affect the shear stress. Tsai–Wu failure criterion is evaluated for decelerating disks. For disks with fiber rich at the inner radius, the failure is initiated between inner and outer radii. However, for disks with fiber rich at the outer radius, the failure location depends on the fiber distribution.

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Figures

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Fig. 1

Schematic diagram of tapered disk with nonuniform thickness, where a and b are the inner and outer radii, respectively, and the disk is rotating around the z-axis by a variable angular velocity

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Fig. 2

Schematic diagram of unidirectional fiber-matrix composite, where the fibers are aligned with direction 1 (circumferential direction), and direction 2 (radial direction) is perpendicular to direction 1

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Fig. 3.

An element of the disk with all in-plane tractions presented in a polar coordinate system located at the center of the disk, where r and θ are the radial and angular coordinates

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Fig. 4.

Comparison between our FDM results and analytical solutions by Tang [22], presented for radial displacement, and radial and hoop stresses versus normalized radial coordinate

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Fig. 5

(a)–(c) Comparison between our FDM results and finite element analysis results, presented for radial displacement, radial stress, and hoop stresses versus normalized radial coordinate

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Fig. 6

(a) and (b) Fiber volume fraction distribution along the disk radius for disks with a fiber-rich at the outer and inner radii, presented for different values of gradient index, n, compared to a homogenous disk with the same volume

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Fig. 7

(a) and (b) Radial displacement along the disk radius for disks with fiber-rich at the outer and inner radii, presented for different values of gradient index, n, compared to a homogenous disk with the same volume

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Fig. 8

(a) and (b) Circumferential displacement along the disk radius for disks with fiber-rich at the outer and inner radii, presented for different values of gradient index, n, compared to a homogenous disk with the same volume

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Fig. 10

(a) and (b) Circumferential stress along the disk radius for disks with fiber-rich at the outer and inner radii, presented for different values of gradient index, n, compared to a homogenous disk with the same volume

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Fig. 11

(a) and (b) Shear stress along the disk radius for disks with fiber-rich at the outer and inner radii, presented for different values of gradient index, n, compared to a homogenous disk with the same volume

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Fig. 9

(a) and (b) Radial Stress along the disk radius for disks with fiber-rich at the outer and inner radii, presented for different values of gradient index, n, compared to a homogenous disk with the same volume

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Fig. 12

(a) and (b) Tsai–Wu failure criterion, along the disk radius for disks with fiber-rich at the outer and inner radii, presented for different values of gradient index, n

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Fig. 13

The effect of disk deceleration on the Tsai–Wu failure index for disks with fiber-rich at the outer radius and gradient index, n = 1

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Fig. 14

(a)–(c) Maximum radial, hoop, and shear stress distributions for disks under various angular deceleration

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