带有两个共线裂纹载流薄板的温度场及热应力强度因子

TEMPERATURE FIELD AND THERMAL STRESS INTENSITY FACTORS OF A CURRENT-CARRYING PLATE WITH TWO COLLINEAR CRACKS

采用复变函数的方法,给出带有两个等长度共线穿透裂纹的无限大载流薄板在瞬间电流作用下,裂纹尖端附近产生的温度场的表达式,得到温度在裂纹尖端的奇异特征。在通入垂直于裂纹的均匀电流作用下,由于裂纹的存在,裂纹尖端出现绕流现象,产生焦耳热,瞬时高温形成点热源。通过点热源在金属薄板内形成的温度场,可以导出裂纹尖端产生的热应力强度因子表达式。将其与外载荷产生的应力强度因子叠加,可建立通电状态下的断裂判据。算例分析表明,点热源在裂纹尖端附近产生的热应力强度因子为负值,可以部分抵消无穷远处施加的拉应力产生的应力强度因子的作用,进而达到止裂的目的。文中建立带有两个等长度共线穿透裂纹载流薄板的热应力强度因子的概念。其研究结果对工程结构实施电磁热效应裂纹止裂具有理论意义和实用价值。

By means of complex function, the temperature field near the crack tip in a current-carrying infinite plate with two same penetrated collinear cracks under the action of transient pulse current was provided. Singularity character of the temperature around crack tip was obtained. When sending an even electric current down the plate vertical to the crack line, the electric current was detoured near the crack tips for the existing of cracks and Joule heats was produced. The instantaneous high temperature formed the point heat source. The expressions of thermal stress intensity factors near the crack tips were calculated through the temperature field in the plate formed by point heat source. The fracture judge rule under the station of electric current-carrying was built through adding the thermal stress intensity factors to the stress factors caused by tension. The example showed that the value of thermal stress intensity factors near the crack tips caused by point heat source was minus and this could counteract parts of stress intensity factors intension caused by tension loaded in distance and the crack extension could be arrested. The concept of thermal stress intensity factors in a current-carrying plate with two same penetrated collinear cracks was built in this article. The results of study in this work have theoretical meaning and practical value to the application of the dectromagnetic thermal effects on crack prevention used in the structure of engineering projects.