Special Issue Honoring Professor Fazil Erdogan’s Contributions to Mixed Boundary Value Problems of Inhomogeneous and Functionally Graded Materials

Crack Initiation in Functionally Graded Materials Under Mixed Mode Loading: Experiments and Simulations

[+] Author and Article Information
Alpay Oral, Gunay Anlas

Department of Mechanical Engineering, Bogazici University, 34342 Bebek, Istanbul, Turkey

John Lambros

Department of Aerospace Engineering, University of Illinois, Urbana-Champaign, Urbana, IL 61801

Note that although it is feasible to obtain different mode mixities for the homogeneous case, it is virtually impossible for the FGM case, which would require testing of FGMs with exactly the same material property variation, but different loading conditions.

J. Appl. Mech 75(5), 051110 (Jul 11, 2008) (8 pages) doi:10.1115/1.2936238 History: Received June 29, 2007; Revised December 31, 2007; Published July 11, 2008

In this work, quasistatic crack initiation under mixed mode loading in planar (two-dimensional plane stress) functionally graded materials (FGMs) is studied. The goal of this work is to directly compare experiments and simulations so as to evaluate the applicability of the maximum tangential stress (MTS) criterion in predicting crack kinking in FGMs. Initially, crack initiation in the homogeneous material, which forms the basis of our FGM—polyethylene—is studied. The (generalized) maximum tangential stress is applied through the use of finite elements to determine crack initiation angles in the same graded configurations studied experimentally. Computational results of fracture parameters (stress intensity factors and T-stress), and crack initiation angles are compared to experimental results and good agreement is obtained. It is seen that the MTS criterion is applicable to FGM crack initiation prediction if the inherent material gradient length scale is larger than the fracture process zone.

Copyright © 2008 by American Society of Mechanical Engineers
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Figure 1

Geometry, loading, and elastic modulus variation for three FGM specimens used in Ref. 4: (a) Case I, symmetric loading and nonsymmetric property gradient; (b) Case II, nonsymmetric loading and property gradient; and (c) Case III, symmetric gradient and nonsymmetric loading

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Figure 2

Photograph of the final crack path for (a) Case I, (b) Case II, and (c) Case III from the experiments of Abanto-Bueno and Lambros (4)

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Figure 3

Typical finite element mesh used for (a) complete model and (b) near crack tip. (c) Shows the local coordinate system at the crack tip. All quantities must be rotated into this coordinate system.

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Figure 4

Edge cracked specimen geometry for homogeneous material (V0 is the applied displacement), H=90mm, W=70mm, h=45mm, a=33mm, and ϕ=π∕3

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Figure 5

Variation of σθθ with angle around the crack tip for specific radial directions obtained numerically for the FGM in Case II

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Figure 6

Close-up photograph showing initial crack kinking for Case III FGM

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Figure 7

Contours of (a) ux and (b) uy for Case III (solid lines and values in boxes are experimental results, and dashed lines, and values without boxes are numerical results)

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Figure 8

Contours of σθθ for (a) Case I, (b) Case II, and (c) Case III (solid lines and values in boxes are experimental results, and dashed lines and values without boxes are numerical results)




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