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RESEARCH PAPERS

Plastic Zone Coalescence and Edge Break Conditions of Internal Cracks in a Semi-infinite Sheet

[+] Author and Article Information
Toshihiko Nishimura

 Mitsubishi Heavy Industries, Ltd., Nagoya Aerospace Systems Works, 10 Oye-cho, Minato-ku, Nagoya 455-8515, Japantoshihiko̱nishimura@mhi.co.jp

J. Pressure Vessel Technol 129(1), 142-147 (Mar 29, 2006) (6 pages) doi:10.1115/1.2389031 History: Received March 27, 2006; Revised March 29, 2006

The problem of two cracks in a semi-infinite sheet is analyzed. The critical conditions when adjacent plastic zones just coalesced are obtained. Also, the conditions when a plastic zone just reached the sheet edge are obtained. Assuming the crack and plastic zones as a fictitious crack, the integral equations are formulated in terms of surface traction, nonsingular stress, and zero crack face displacement at the coalescent point or at the sheet edge. By solving the equations, critical remote stress, plastic zone sizes, and crack tip opening displacements are obtained. Numerical results are presented.

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Copyright © 2007 by American Society of Mechanical Engineers
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Figures

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Figure 1

Internal crack problems on a semi-infinite sheet. (a) Two cracks with attached plastic zones. (b) Single crack with attached plastic zone to free edge.

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Figure 2

Superposition for two cracks in a semi-infinite sheet

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Figure 3

Superposition for single crack in a semi-infinite sheet. (a) An infinite sheet due to surface traction. (b) A semi-infinite sheet due to induced traction.

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Figure 4

Normalized remote stress σ∕σys for Fig. 1 model

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Figure 5

Normalized outer plastic zone size R1−∕Ce1 for Fig. 1 model

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Figure 6

Normalized outer plastic zone size R2+∕Ce2 for Fig. 1 model

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Figure 7

Normalized inner plastic zone size R1+∕S for Fig. 1 model

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Figure 8

Normalized CTOD δ1−∕δo1− for Fig. 1 model

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Figure 9

Normalized CTOD δ1+∕δo1+ for Fig. 1 model

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Figure 10

Normalized CTOD δ2−∕δo2− for Fig. 1 model

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Figure 11

Normalized CTOD δ2+∕δo2+ for Fig. 1 model

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Figure 12

Normalized remote stress σ∕σys for Fig. 1 model

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Figure 13

Normalized plastic zone size R1+∕ce1 for Fig. 1 model

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Figure 14

Normalized CTODs δ1−∕δo1− and δ1+∕δo1+ for Fig. 1 model

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