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Research Papers: Materials and Fabrication

Evaluation of Two-Parameter Approaches to Describe Crack-Tip Fields in Engineering Structures

[+] Author and Article Information
Simon Kamel1

Department of Mechanical Engineering, Imperial College London, London SW7 2AZ, UKs.kamel@ic.ac.uk

Noel P. O’Dowd

Department of Mechanical and Aeronautical Engineering, Materials and Surface Science Institute, University of Limerick, Limerick, Irelandnoel.odowd@ul.ie

Kamran M. Nikbin

Department of Mechanical Engineering, Imperial College London, London SW7 2AZ, UKk.nikbin@ic.ac.uk

1

Corresponding author.

J. Pressure Vessel Technol 131(3), 031406 (Apr 21, 2009) (8 pages) doi:10.1115/1.3120266 History: Received September 26, 2007; Revised December 24, 2008; Published April 21, 2009

The application of two-parameter approaches to describe crack-tip stress fields has generally focused on Ramberg–Osgood (RO) power law material behavior, which limits the range of applicability of such approaches. In this work we consider the applicability of a J-Q or J-A2 approach (the latter is designated here as the J-A approach) to describe the stress fields for RO power law materials and for a material whose tensile behavior is not described by a RO model. The predictions of the two-parameter approaches are compared with full field finite-element predictions. Results are presented for shallow and deep-cracked tension and bend geometries, as these are expected to provide the expected range of constraint conditions in practice. A new approach for evaluating Q is proposed for a RO material, which, for a given geometry, makes Q dependent only on the strain hardening exponent.

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Copyright © 2009 by American Society of Mechanical Engineers
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Figures

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Figure 1

Q versus J/aσ0 for a range of values of (a) ε0 and (b) α, where Q is evaluated at the normalized distance r¯=2

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Figure 2

Variation of Q versus J/aε̂0σ̂0 for a range of values of ε0 and α, where Q is evaluated at the normalized distance r̂=0.004

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Figure 3

Normal stress distributions ahead of the crack tip for an M(T) geometry, a/W=0.1, and n=10, at a load P=1.2P̂0

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Figure 4

Normal stress distributions ahead of the crack tip for a SEN(B) geometry, a/W=0.4, and n=10, at a load P=1.6P̂0

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Figure 5

Error e versus normalized load for an M(T) geometry, a/W=0.1, and n=10

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Figure 6

Error e versus normalized load for a SEN(B) geometry, a/W=0.4, and n=10

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Figure 7

Angular variation of equivalent von Mises stress for M(T), a/W=0.1, at a load of 1.2P̂0

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Figure 8

ΔS′/ΔS versus normalized load P/P̂0 for (a) M(T), a/W=0.1, and (b) SEN(B), a/W=0.4, geometries

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Figure 9

True stress-strain curve for ×100 steel up to (a) 5% strain and (b) 20% strain

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Figure 10

Normal stress distributions ahead of the crack tip for an M(T) geometry, a/W=0.1, ×100 steel, at a load P=1.0P̂0

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Figure 11

Normal stress distributions ahead of the crack tip for a SEN(B) geometry, a/W=0.4, ×100 steel, at a load P=1.0P̂0

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