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Vector J-Integral Analysis of Crack Interaction With Pre-existing Singularities

[+] Author and Article Information
Lifeng Ma

Department of Engineering Mechanics, Xi’an Jiaotong University, Xi’an 710049, Chinamalf@mail.xjtu.edu.cn

Tian Jian Lu

Department of Engineering Mechanics, Xi’an Jiaotong University, Xi’an 710049, China and Department of Engineering, University of Cambridge, Cambridge CB2 1PZ, UKtjlu@mail.xjtu.edu.cn

Alexander M. Korsunsky

Department of Engineering Science, University of Oxford, Oxford OX1 3PJ, UKAlexander.korsunsky@eng.ox.ac.uk

J. Appl. Mech 73(5), 876-883 (Nov 21, 2005) (8 pages) doi:10.1115/1.2165243 History: Received June 17, 2005; Revised November 21, 2005

In this paper, the mechanics of a semi-infinite crack interacting with near crack-tip singularities (e.g., dislocations) in two-dimensional solids is investigated using the concept of potential energy release rate. The spontaneous relationship between the crack potential energy release rate and the well-known vector conservative integral Ji(i=1,2) is derived. It is demonstrated that J1 and J2 integrals are equally important in solving crack problems. This allows a more rational criterion to be proposed, based on the criterion of maximum energy release rate, to assess the so-called shielding/amplification effect on the crack tip due to the presence of the singularities. It is shown that the new criterion can not only assess the shielding/amplification effect under pure mode I or mode II remote loading, but also efficiently assess crack-singularity interaction under mixed mode remote loading. Simultaneously, it is found by re-examining the Ji integrals that there exists a simple but universal relation among the three values of the vector Ji integral corresponding separately to the contributions induced from the semi-infinite crack tip, the singularity, and the remote loading. Next, a multi-singularity-crack interaction model is addressed, and the closed-form solution is obtained. Finally, as an example, the problem of a single dislocation interacting with a main crack is solved to demonstrate the validity of the proposed model and the new criterion.

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Copyright © 2006 by American Society of Mechanical Engineers
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Figures

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Figure 1

Curve Γ: (a) surrounding a whole crack; (b) surrounding a crack tip

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Figure 2

A semi-infinite crack interacting with multisingularities

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Figure 3

A two-dimensional body containing a main crack and multisingularities

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Figure 4

Decomposition of multisingularity-crack interaction probelem

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Figure 5

Coordinates of the dislocation-crack system

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Figure 6

(a) Normalized G and KI(t) versus dislocation location angle θ0 under pure KI(∞) remote loading (case 1). (b) Normalized G and KII(t) versus dislocation location angle θ0 under pure KII(∞) remote loading (case 2). (c) Normalized G, KI(t) and KII(t) versus dislocation location angle θ0 under mixed mode remote loading KI(∞)=KII(∞)≠0 (case 3).

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