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首页> 外文期刊>Journal of thermal stresses >HEAT CONDUCTION AND THERMAL STRESS ANALYSES OF A STRIP WITH SEMI-ELLIPTICAL NOTCH UNDER ELECTRIC CURRENT
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HEAT CONDUCTION AND THERMAL STRESS ANALYSES OF A STRIP WITH SEMI-ELLIPTICAL NOTCH UNDER ELECTRIC CURRENT

机译：电流下半椭圆形缺口条的导热及热应力分析

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摘要

An electric current is applied in a thin strip conductor with an edge crack or a semi-elliptical notch. The electric current gives rise to two states, i.e., uniform and uneven Joule heat. The Joule heat gives rise to the temperature, and thus the heat flux and also free thermal expansion. Using a rational mapping function, problems of the electrical current, the Joule heat, the temperature, the heat flux and the thermal stress are analyzed and their each solution is obtained as a closed form. The heat conduction problem is solved as a temperature boundary value problem. The distributions of the electric current, the Joule heat, the temperature, and the heat flux are shown in figures. After a free thermal expansion is obtained and a support condition is given, the stress components are calculated. The crack problems are analyzed for the problems of the electric current, joule heat, heat flux and stress. The expressions for intensity of the electric current, the heat flux and the Joule heat at the crack tip are derived. The exact expression of the temperature at the crack tip (notch tip) is also given. The notch problems are analyzed, and the approximate expressions of the concentration are given for each problem, of which error is a few percent. The relations between the electric current density and the melting temperature and between the electric current density and Joule heat are investigated for some crack lengths of aluminum strip. The intensity of the Joule heat relates to the creation of the blow hole.
机译：电流施加在带有边缘裂纹或半椭圆形缺口的薄带状导体中。电流产生两个状态，即均匀和不均匀的焦耳热。焦耳热会升高温度，从而引起热通量以及自由热膨胀。使用有理映射函数，分析电流，焦耳热，温度，热通量和热应力的问题，并以封闭形式获得它们的每个解。导热问题被解决为温度边界值问题。图中示出了电流，焦耳热，温度和热通量的分布。获得自由热膨胀并给出支撑条件后，计算应力分量。分析了裂纹问题中的电流，焦耳热，热通量和应力问题。推导了裂纹尖端处的电流强度，热通量和焦耳热的表达式。还给出了裂纹尖端（缺口尖端）的温度的精确表示。分析了缺口问题，并为每个问题给出了浓度的近似表达式，其误差为百分之几。对于铝带的某些裂纹长度，研究了电流密度与熔化温度之间的关系以及电流密度与焦耳热之间的关系。焦耳热的强度与气孔的产生有关。

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