Heat conduction and thermal stress induced by an electric current in an infinite thin plate containing an elliptical hole with an edge crack

INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES

卷:47

Article

Hasebe, Norio¹  Bucher, Christian²  Heuer, Rudolf² 

[1] Nagoya Inst Technol, Dept Civil Engn, Showa Ku, Nagoya, Aichi 4668555, Japan

[2] Vienna Univ Technol, Dept Civil Engn, A-1040 Vienna, Austria

关键词: Electric current;    Joule heat;    Heat conduction;    Thermal stress;    Dislocation;    Stress intensity factor;    Edge crack;    Mapping function;    Elliptical hole;    Blowhole;   

DOI  :  10.1016/j.ijsolstr.2009.09.023

来源: Elsevier

【 摘 要 】

A uniform electric current at infinity was applied to a thin infinite conductor containing an elliptical hole with an edge crack. The electric current gives rise to two states, i.e., uniform and uneven joule heat. These two states must be considered to analyze the heat conduction problem. The uneven joule heat gives rise to uneven temperature and thus to heat flux, and to thermal stress. Using a rational mapping function, problems of the electric current, the joule heat, the temperature, the the thermal stress are analyzed, and each of their solutions is obtained as a closed form. The heat flux, distributions of the electric current, the joule heat, the temperature, the heat flux and the stress are shown in figures. The heat conduction problem is solved as a temperature boundary value problem. Solving the thermal dislocation and rotation terms appear, which complicates this problem. The solutions of stress problem, the joule heat, the temperature, the heat flux and the thermal stress are nonlinear in the direction of the electric current. The crack problems are also analyzed, and the singular intensities at the crack tip of each problem are obtained. Mode II (sliding mode) stress intensity factor (SIF) is produced as well as Mode I (opening mode) SIF, for any direction of the electric current. The relations between the electric current density and the melting temperature and between the electric current density and SIF are investigated for some crack lengths in an aluminum plate. (C) 2009 Elsevier Ltd. All rights reserved.

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