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Research Papers

A Better Estimation of Plastic Zone Size at the Crack Tip Beyond Irwin's Model

[+] Author and Article Information
Y. J. Jia

AML, CNMM,
Department of Engineering Mechanics,
Tsinghua University,
Beijing 100084, China

M. X. Shi

Southwest Jiaotong University,
Chengdu 610031, China

B. Liu

e-mail: liubin@tsinghua.edu.cn
AML, CNMM,
Department of Engineering Mechanics,
Tsinghua University,
Beijing 100084, China

1Corresponding author.

Manuscript received November 20, 2012; final manuscript received January 2, 2013; accepted manuscript posted February 12, 2013; published online July 18, 2013. Editor: Yonggang Huang.

J. Appl. Mech 80(5), 051014 (Jul 18, 2013) (6 pages) Paper No: JAM-12-1525; doi: 10.1115/1.4023642 History: Received November 20, 2012; Revised January 02, 2013; Accepted February 12, 2013

Irwin's model on plastic zone at the crack tip is discussed in many fracture mechanics textbooks. However, we found in Irwin's model that the internal resultant force on the crack plane and the one applied in remote field are not strictly balanced. This imbalance leads to the error in the scenario of small scale yielding, and an improper finite plastic zone size (PZS) is predicted when the remote stress approaches the yielding strength. In this paper, an improved model is developed through surrendering some main assumptions used in Irwin's model and an infinite PZS is then predicted as the remote stress goes up close to yielding strength, which implies that this estimation can be applied to situations with large scale yielding. In small scale yielding cases, the new estimation of PZS agrees well with finite element simulation results. In addition, a more accurate quantitative relation between the PZS and the effective stress intensity factor is derived, which might help characterize fracture behaviors in engineering applications.

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References

Figures

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Fig. 1

Schematics of (a) an infinite plate with a central crack subjected to remote uniform stress without plastic yielding, and (b) Irwin's estimation on plastic zone size

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Fig. 2

Schematics of (a) an infinite plate with a central crack subjected to remote uniform stress with plastic yielding, and (b) the improved estimation on plastic zone size

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Fig. 3

Details of simulation model

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Fig. 4

(a) Theoretical and numerical predictions on the normalized plastic zone size versus σ∞/σys, (b) a zoom-in figure, and (c) relative error between our prediction rpnew and the Irwin's prediction rp_3Irwin

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Fig. 5

The normalized plastic zone size versus the effective stress intensity factor

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