Field intensity factors of three cracks originating from a circular hole in a thermoelectric material

Liu, Qing-Nan; Ding, Sheng-Hu

doi:10.2140/jomms.2020.15.605

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Field intensity factors of three cracks originating from a circular hole in a thermoelectric material

Qing-Nan Liu and Sheng-Hu Ding

Vol. 15 (2020), No. 5, 605–617

DOI: 10.2140/jomms.2020.15.605

Abstract

The fracture behavior of three cracks originating from a circular hole in a thermoelectric material is studied. The basic theory of thermoelectric materials is given under the condition of the impermeable boundary of the heat flux and electric current. By introducing the conformal mapping function, the infinite plane on the physical plane is mapped into the inner unit circle on the mathematical plane. The formulas of the relevant temperature and stress fields are derived, and the analytical solutions of the complex stress functions are obtained by the complex variable function method. According to Cauchy integral formula, the analytical expressions of the electric current intensity factor and the stress intensity factor for three cracks originating from a circular hole are obtained. The effects of the hole radius and the crack lengths on the electric current intensity factor and stress intensity factors were investigated.

Keywords

thermoelectric material, circular hole, three cracks, complex variable function, intensity factors

Milestones

Received: 3 July 2020

Revised: 10 August 2020

Accepted: 16 August 2020

Published: 30 November 2020

Authors

Qing-Nan Liu
School of Mathematics and Statistics Ningxia University Yinchuan, 750021 China

Sheng-Hu Ding
School of Mathematics and Statistics Ningxia University Yinchuan, 750021 China

Vol. 15, No. 5, 2020

Qing-Nan Liu and Sheng-Hu Ding

Abstract

Keywords

Milestones

Authors