Vol. 15, No. 5, 2020

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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
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