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Research Papers: Design and Analysis

A Global Limit Load Solution for Plates With Embedded Off-Set Elliptical Cracks Under Combined Tension and Bending

[+] Author and Article Information
Rongsheng Li, Yuebao Lei

College of Mechanical Engineering,  Zhejiang University of Technology, Hangzhou 310032, China

Zengliang Gao1

College of Mechanical Engineering,  Zhejiang University of Technology, Hangzhou 310032, Chinazlgao@zjut.edu.cn

1

Corresponding author.

J. Pressure Vessel Technol 134(1), 011204 (Dec 01, 2011) (9 pages) doi:10.1115/1.4004819 History: Received July 24, 2010; Revised November 24, 2010; Published December 01, 2011; Online December 01, 2011

A global limit load solution is derived in this paper for embedded off-set elliptical cracks in a plate under combined tension and bending, based on the net-section collapse principle. The new limit load solution is validated using 3D elastic-perfectly plastic finite element (FE) limit analyses. The results show that the limit load solution developed in this paper is conservative and close to the elastic-perfectly-plastic FE results. The global limit load solution is then compared with the limit load solution based on the rectangular crack assumption, showing that the difference between the two solutions is negligible as the ratio of crack length to the plate width is less than 0.25. However, the difference may become significant when the ratio approaches one.

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Figures

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Figure 1

Schematic illustration of a plate with an embedded elliptical crack

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Figure 2

Assumed stress distribution at crack plane for plastic collapse: (a) Shallow crack and (b) deep crack

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Figure 3

Illustration of definitions for shallow and deep cracks for a given β: (a) Pure tension (λ = 0), (b) pure bending (λ = ∞), and (c) combined tension and bending (0 < λ < ∞)

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Figure 4

Typical mesh used in the FE analyses (a/c = 0.4, a/t = 0.2, c/W = 0.4, and k = 0.2)

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Figure 5

Load–load point displacement curve obtained from a FE analysis for a/t = 0.2, k = 0.1, and c/W = 0.3 under pure tension

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Figure 6

Equivalent plastic strain contour at the on-set of plastic collapse (a/t = 0.2, k = 0.1, c/W = 0.3): (a) Small ligament yielding and (b) global yielding

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Figure 7

Comparison of the normalized limit load values between present work and the FE results for pure tension (λ = 0): (a) k = 0, (b) k = 0.1, and (c) k = 0.2

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Figure 8

Comparison of the normalized limit load values between present work and the FE results for pure bending (λ = ∞): (a) k = 0, (b) k = 0.1, and (c) k = 0.2

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Figure 9

Comparison of the normalized limit load values between present work and the FE results under combined tension and bending: (a) λ = 0.2, k = 0, (b) λ = 0.2, k = 0.1, (c) λ = 0.2, k = 0.2, (d) λ = 0.5, k = 0, (e) λ = 0.5, k = 0.1, and (f) λ = 0.5, k = 0.2

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Figure 10

Effect of normalized crack offset, k, on the normalized limit loads: (a) c/W = 0.2, a/t = 0.3 and (b) c/W = 0.5, a/t = 0.3

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Figure 11

Comparison of the limit load solutions between rectangular crack and elliptical crack assumptions: (a) k = 0, (b) k = 0.1, and (c) k = 0.2

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