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Research Papers

Accounting for High Stress Gradient by a Modified Weibull Failure Theory

[+] Author and Article Information
S. Ekwaro-Osire1

Department of Mechanical Engineering,  Texas Tech University, Lubbock, TX 79409stephen.ekwaro-osire@ttu.edu

M. P. Khandaker, K. Gautam

Department of Mechanical Engineering,  Texas Tech University, Lubbock, TX 79409

1

Corresponding author.

J. Eng. Mater. Technol 130(1), 011004 (Dec 21, 2007) (8 pages) doi:10.1115/1.2806251 History: Received April 10, 2006; Revised September 03, 2007; Published December 21, 2007

A high stress gradient occurs in a component when the stress, due to external loading, rises asymptotically. The Weibull failure theory overestimates the probability of failure for components with high stress gradients generated due to the geometric irregularities, material mismatch, thermal mismatch, and contact loading. A modified Weibull failure theory is proposed in this paper. The method is based on the weight function method. The modified Weibull failure theory was applied to two specimens, and the results showed the ability of the proposed theory to handle high stress gradients. The theory considers variable equivalent stress intensity factors along the faces of cracks; hence, it considers the strength of a specimen to be dependent on the stress field.

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Figures

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Figure 1

Conditions leading to high stress gradients

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Figure 2

Weibull failure theory

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Figure 3

Modified Weibull failure theory

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Figure 4

Comparison of probability of failures for Weibull versus modified Weibull failure theory (ΔT=50°C)

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Figure 5

Comparison of Weibull and modified Weibull failure theories for notched specimen under far field loading

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Figure 6

Virtual crack configurations: (a) bimaterial specimen and (b) notched specimen

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Figure 7

Reference loadings for modified Weibull failure theory analysis: (a) distributed normal unit stress, ρ=1, (b) distributed shear unit stress, ρ=2, (c) unit point normal loads, ρ=3, and (d) unit point shear loads, ρ=4

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Figure 8

Reference loads used in the analysis of the virtual slanted crack: (a) base normal load, ρ=1, (b) base shear load, ρ=2, (c) midnormal load, ρ=3, and (d) midshear load, ρ=4

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