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Strain-Rate Effect on the Stress and Strain Concentration in a Visco-Plastic Plate With An Elliptic Hole

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Abstract

The stress and strain concentration in some component has been a significant topic for structural safety assessment. However, the evaluation of the stress and strain concentration based on the widely existing solutions for linear elastic material under static loading would lead to remarkable errors when the material undergoes the dynamic loading, since the coupling effect induced by the nonlinearity of the stress–strain relationship and the strain-rate strengthening could be of significant influence. Here we analyzed the strain-rate dependent concentration of stress and strain for a visco-plastic plate with an elliptic hole subjected to dynamic loading. The three-dimensional stress and strain are calculated by finite element analyses based on a rate-dependent Johnson–Cook model in which the material constants are set according to a typical visco-plastic standard 45 carbon steel. Our results show that both the plastic stress and strain concentration factors significantly depend on not only the strain but also the strain rate. With the increment of the remote strain rate, the stress concentration monotonically increases, while the strain concentration shows decreasing tendency.

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Abbreviations

\( \sigma_{\infty} \) :

Remote stress applied on the specimen, see Fig. 1

Fig. 1
figure 1

The a rate-dependent plastic stress–strain curves at different strain rates obtained by Eq. (1) based on the Hu et al. (2003) and b the geometries of the model

Full size image
\( \varepsilon_{\infty} \) :

Remote strain applied on the specimen, see Fig. 1

\( \sigma_{\text{net}} \) :

Net mean stress for cross-section at y = 0, see Eq. (2)

\( \varepsilon_{\text{net}} \) :

Net mean strain for cross-section at y = 0, see Eq. (2)

\( \sigma_{yy} \) :

Opening stress at the root of hole, see Eq. (2)

\( \varepsilon_{yy} \) :

Opening strain at the root of hole, see Eq. (2)

\( K_{\sigma} \) :

Stress concentration factor, see Eq. (2)

\( K_{\varepsilon} \) :

Strain concentration factor, see Eq. (2)

\( \left({K_{\sigma}} \right)_{\max} \) :

Maximum stress concentration factor

\( \left({K_{\varepsilon}} \right)_{\max} \) :

Maximum strains concentration factor

\( \left({K_{\sigma}} \right)_{\text{mp}} \) :

Stress concentration factor in the mid-plane

\( \left({K_{\varepsilon}} \right)_{\text{mp}} \) :

Strain concentration factor in the mid-plane

\( \left({K_{\sigma}} \right)_{\text{surf}} \) :

Stress concentration factor at the free surface

\( \left({K_{\varepsilon}} \right)_{\text{surf}} \) :

Strain concentration factor at the free surface

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Acknowledgements

The authors gratefully acknowledge the financial support by the China Postdoctoral Science Foundation (2018M630513), National Natural Science Foundation of China (Grant Nos. 11302067, 11572140).

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Authors and Affiliations

  1. Jiangsu Key Laboratory of Advanced Food Manufacturing Equipment and Technology, School of Mechanical Engineering, Jiangnan University, Wuxi, 214122, China

    Yanqiu Chen, Jin Zhang, Peishi Yu & Junhua Zhao

  2. China Ship Scientific Research Center, Wuxi, 214082, China

    Jian Wu & Weibo Wang

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  1. Yanqiu Chen
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  2. Jin Zhang
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  3. Peishi Yu
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  4. Jian Wu
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Correspondence to Peishi Yu or Junhua Zhao.

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Chen, Y., Zhang, J., Yu, P. et al. Strain-Rate Effect on the Stress and Strain Concentration in a Visco-Plastic Plate With An Elliptic Hole. Int J Steel Struct 20, 1256–1267 (2020). https://doi.org/10.1007/s13296-020-00356-y

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