CLC number: TG174

On-line Access: 2013-04-03

Received: 2012-10-17

Revision Accepted: 2013-01-03

Crosschecked: 2013-03-06

Cited: 3

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Xiao-guang Huang, Jin-quan Xu. 3D analysis for pit evolution and pit-to-crack transition during corrosion fatigue[J]. Journal of Zhejiang University Science A, 2013, 14(4): 292-299.

@article{title="3D analysis for pit evolution and pit-to-crack transition during corrosion fatigue",

author="Xiao-guang Huang, Jin-quan Xu",

journal="Journal of Zhejiang University Science A",

volume="14",

number="4",

pages="292-299",

year="2013",

publisher="Zhejiang University Press & Springer",

doi="10.1631/jzus.A1200273"

}

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%I Zhejiang University Press & Springer

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DOI - 10.1631/jzus.A1200273

**Abstract: **This paper presents a deterministic model to predict the pit evolving morphology and crack initiation life of corrosion fatigue. Based on the semi-ellipsoidal pit assumption, the thermodynamic potential including elastic energy, surface energy and electrochemical energy of the cyclically stressed solid with an evolving pit is established, from which specific parameters that control the pit evolution are introduced and their influence on the pit evolution are evaluated. The critical pit size for crack nucleation is obtained from stress intensity factor criterion and the crack nucleation life is evaluated by Faraday’s law. Meanwhile, this paper presents a numerical example to verify the proposed model and investigate the influence of cyclic load on the corrosion fatigue crack nucleation life. The corrosion pit appears approximately as a hemisphere in its early formation, and it gradually transits from semicircle to ellipsoid. The strain energy accelerates the morphology evolution of the pit, while the surface energy decelerates it. The higher the stress amplitude is, the smaller the critical pit size is and the shorter the crack initiation life is.

**
**

1. Introduction

A pit almost always initiates at some chemical or physical heterogeneity on the surface (Ma et al.,

In spite of the advances achieved in pit initiation, evolution and its transition to crack, the modeling of the pit evolution process is still an open question. In this paper, we focus on the thermodynamic framework of pit evolution during the corrosion fatigue process. Pit evolution is an irreversible thermodynamics process, and the variation of thermodynamic potential during pit growth may incite the diffusion on pit surface, which also affects the evolving morphology of the pit. A thermodynamic potential, including elastic energy, surface energy and electrochemical energy, is formulated for a 3D cyclically stressed solid with a corrosion pit varying in shape and volume, from which the actual evolving morphology is obtained. The critical pit morphology for crack nucleation and the corrosion fatigue crack nucleation life are also discussed in this paper.

2. Energetics of elastic solid with an evolving corrosion pit

According to the semi-ellipsoid assumption, the actual morphology can be indicated as the sequence of shape parameter

As the pit varies its morphology during corrosion fatigue, the semi-infinite elastic solid containing a semi-ellipsoidal pit subjected to remote cyclic stress stores an infinite amount of strain energy. Yet, the energy difference between the solid containing a semi-ellipsoidal pit and the solid without a pit subjected to the same stresses can be computed by the Eshelby inclusion theory (Eshelby,

When the initial pit grows to a random state, with the equivalent radius varying from

The surface area of the pit changes during the evolving process, leading to the variation of surface energy. The dimensionless coefficient

The surface area of the pit is written as

Let

According to the electrochemical mechanism of corrosion, the anodic potential of the corrosion electrochemical reaction can be expressed as

Assuming the anodic potential remains unchanged during pit evolution, the variation of electrochemical energy is

Thus, the variation of thermodynamic potential Δ

Here, only three leading terms are retained for small

The actual pit shape

From Eq. (

3. Corrosion fatigue crack nucleation

When the pit reaches a critical morphology that satisfies the threshold requirement for crack initiation, the pit is ready for ‘‘transition’’ into a crack, which essentially means that the kinetics of crack extension exceeds the pit growth rate at this moment, thus resulting in the crack taking over the damage mechanism.

According to the stress intensity factor criterion, the critical pit size at which a crack nucleates can be expressed in terms of the threshold driving force via the crack growth mechanism. According to the previous assumption of the pit, the semi-infinite elastic solid containing a semi-ellipsoidal surface is equivalent to an infinite plate consisting of semicircular surface flaws in 2D, and the expression for the stress intensity factor range Δ

Thus, the critical pit depth

Rewriting Eq. (

Integrating Eq. (

The corrosion fatigue crack nucleation life for corrosion fatigue is written as

Substituting

4. Results and discussion

The influences of

The sensitivity coefficients of

The strain energy fluctuates during every stress cycle, causing the fluctuation of shape parameter with

The predictions made from our model with respect to the crack initiation lives at different stress amplitudes are shown as open triangles in Fig.

5. Conclusions

The corrosion pit appears approximately as a hemisphere in its early stage of growth, and its morphology tends to transit from semicircle to ellipsoid with shape parameter gradually close to a stable value. The actual shape parameter of a pit can be seen as the outcome of the interaction between the variation in the elastic energy and surface energy; the strain energy accelerates the morphology evolution of the pit, while the surface energy decelerates it.

Stress amplitude has a significant effect on the critical pit size for crack nucleation and crack initiation life. The higher the stress amplitude is, the smaller the critical pit size is and the shorter crack initiation life is. The predictions of crack initiation life at different stress amplitude levels are found to be in fair agreement with the data available in the literature.

* Project supported by the National Natural Science Foundation of China (No. 10772116), and the Fundamental Research Funds for the Central Universities (Nos. 12CX04017B and 13CX02091A)

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