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Stress analysis for a lip-shaped crack in a thermoelectric plate under combined electrical and thermal loadings

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Abstract

This study focuses on analyzing a slanted lip-shaped crack within a thermoelectric plate that experiences both a temperature gradient and an electric potential gradient. Based on the electrically insulated and thermally permeable crack model, we derive analytical solutions for the thermoelectric field and the associated thermal stress field in the cracked thermoelectric material by employing the complex variable method. Subsequently, we evaluate the stress intensity factors at the tips of the lip-shaped crack. Under the impact of thermoelectric loading, both mode-I and mode-II stress intensity factors occur at the tips of a slanted lip-shaped crack. Numerical examples are provided to demonstrate the influence of crack width, crack angle and thermal conductivity of the filling medium on the stress intensity factors at the crack tip.

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Abbreviations

\({\varvec{j}}_{{\textbf {e}}}\) :

Electric current density vector

\({\varvec{j}}_{{\textbf {u}}}\) :

Energy flux vector

\({\varvec{q}}\) :

Heat flux vector

\(\delta \) :

Electric conductivity

\(\kappa \) :

Thermal conductivity

s :

Seebeck coefficient

\(\gamma \) :

Peltier coefficient

T :

Temperature function

\(\phi \) :

Electric potential function

\(\mu \) :

Shear modulus

\(\lambda \) :

Thermal expansion coefficient

\(\nu \) :

Poisson’s ratio

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

Mode-I stress intensity factor

\(K_{\text{ II }}\) :

Mode-II stress intensity factor

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Acknowledgements

The authors are grateful for the support from the Natural Science Foundation of Jiangsu Province (Grant No. BK20210787), Qinglan Project of Yangzhou University and a Project Funded by Key Laboratory of Construction Hydraulic Robots of Anhui Higher Education Institutes (Grant No. TLXYCHR-O-21YB04).

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Authors and Affiliations

  1. College of Architectural Science and Engineering, Yangzhou University, Yangzhou, 225127, Jiangsu, China

    Chuanbin Yu & Chaofan Du

  2. Key Laboratory of Construction Hydraulic Robots of Anhui Higher Education Institutes, Tongling University, Tongling, 244000, Anhui, China

    Shichao Xing

  3. Key Laboratory of Additive Manufacturing of Tongling City, Tongling University, Tongling, 244000, Anhui, China

    Shichao Xing

  4. State Key Laboratory of Mechanics and Control for Aerospace Structures, Nanjing University of Aeronautics and Astronautics, Nanjing, 210016, China

    Cun-Fa Gao

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  1. Chuanbin Yu
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  2. Chaofan Du
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  4. Cun-Fa Gao
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Contributions

CY performed the formal analysis and wrote the first draft of the manuscript. CD contributed to the data presentation. SX and CG contributed to the conception and design of the study. All authors reviewed the manuscript.

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Correspondence to Chuanbin Yu.

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Yu, C., Du, C., Xing, S. et al. Stress analysis for a lip-shaped crack in a thermoelectric plate under combined electrical and thermal loadings. Z. Angew. Math. Phys. 75, 19 (2024). https://doi.org/10.1007/s00033-023-02155-x

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  • DOI: https://doi.org/10.1007/s00033-023-02155-x

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