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Effect of a Micro-crack on the Edge Macro-crack Propagation Rate and Path Under Mixed Loads

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Abstract

The solution of a half-plane containing a micro-crack and an edge macro-crack under mixed loads is presented based on the distributed dislocation technique. The complete stress field and stress intensity factors are obtained. The finite element model is established to simulate the macro-crack propagation path. The effect of a micro-crack on the macro-crack propagation is analyzed comprehensively. The results show that the shielding effect region is like two ‘petals’ under uniaxial tensile load and rotates with the change in micro-crack angle. For mixed loads, the shielding effect region rotates clockwise with the increasing ratio of applied loads \(\tau ^{\infty }/\sigma ^{\infty }\). It is like two ‘petals’ at \(\tau ^{\infty }/\sigma ^{\infty }\le 2\) and divides into two parts from the macro-crack tip at \(\tau ^{\infty }/\sigma ^{\infty }\ge 5\). The micro-crack has the attraction effect on the macro-crack propagation path. These results are useful for predicting the fracture or fatigue behaviors of materials containing micro-cracks.

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Abbreviations

a :

Half-length of the micro-crack

l :

Initial macro-crack length

\(\theta \) :

Micro-crack orientation

\(\alpha \) :

Micro-crack angle

d :

Distance between the macro-crack tip and the micro-crack center

\(\sigma ^{\infty }\) :

Uniform tensile load

\(\tau ^{\infty }\) :

Uniform shear load

\({\tilde{\sigma }}_{ij} \) :

Stress components contributed by the applied loads

\(\bar{{\sigma }}_{ij} \) :

Stress components contributed by distributed dislocations

\(x_{\mathrm{micro}} \) :

Horizontal ordinate of the micro-crack center

\(y_{\mathrm{micro}} \) :

Vertical ordinate of the micro-crack center

\(K_{\mathrm{eff}} \) :

Equivalent stress intensity factor

\(K_{\mathrm{eff}}^\infty \) :

Equivalent stress intensity factor for the case without micro-crack

\(K_{\mathrm{I}}^\infty \) :

Mode \(\mathrm{I}\) stress intensity factor for the case without micro-crack

\(K_{\mathrm{I}} \) :

Mode \(\mathrm{I}\) stress intensity factor at the macro-crack tip

\(K_{\mathrm{I}\mathrm{I}} \) :

Mode \(\mathrm{I}\mathrm{I}\) stress intensity factor at the macro-crack tip

\(b_x , b_y \) :

Components of Burgers vector

\(\mu \) :

Shear modulus

\(\kappa \) :

Kolosov constant

\(G(\xi ,x,y)\) :

Dislocation influence function

\(B(\xi )\) :

Dislocation density function

\(\beta \) :

Crack propagation direction

E :

Elasticity modulus

\(\nu \) :

Poisson’s ratio

\(\sigma _{\mathrm{von}} \) :

von Mises stress

\(\gamma \) :

Intersection angle between the micro-crack face and the line composed by the micro-crack center and macro-crack tip

SIF:

Stress intensity factor

ESIF:

Equivalent stress intensity factor

FE:

Finite element

FEM:

Finite element method

DDT:

Distributed dislocation technique

MCTSC:

Maximum circumferential tensile stress criterion

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (11472230) and Doctoral Innovation Fund Program of Southwest Jiaotong University (D-CX201836).

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  1. School of Mechanics and Engineering, Southwest Jiaotong University, No. 111, North 1st Section of Second Ring Road, Jinniu District, Chengdu City, 610031, Sichuan Province, China

    Xiaotao Li & Xiaoyu Jiang

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Correspondence to Xiaoyu Jiang.

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Li, X., Jiang, X. Effect of a Micro-crack on the Edge Macro-crack Propagation Rate and Path Under Mixed Loads. Acta Mech. Solida Sin. 32, 517–532 (2019). https://doi.org/10.1007/s10338-019-00099-2

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