均匀热流下导热裂纹Ⅱ型温度应力强度因子的解析解  

ANALYTICAL SOLUTION OF MODE Ⅱ THERMAL STRESS INTENSITY FACTOR FOR AN UNINSULATED CRACK UNDER UNIFORM HEAT FLOW

作　　者：陈星烨[1] 唐雪松[1] 

机构地区：[1]长沙理工大学土木与建筑学院,湖南长沙410114

出　　处：《工程力学》2012年第12期34-39,共6页Engineering Mechanics

基　　金：湖南省科技厅科技计划项目(2011FJ3235);教育部博士点基金项目(200805360002)

摘　　要：研究含中心裂纹无限大板受远场均匀热流作用,热流密度方向与裂纹有一夹角的情况。当垂直于裂纹面方向有定量热流穿过裂纹时,采用复变函数理论,得出了温度、应力与位移场解析解。利用位移单值条件,确定出温度应力强度因子的解析表达式。针对铝合金LY12材料进行了数值计算,研究了裂纹导热情况与热流方向对温度场及温度应力强度因子的影响。研究表明:该文给定的温度边界条件下,只产生Ⅱ型温度应力强度因子,不产生Ⅰ型温度应力强度因子。热荷载可等效为一个远场均匀作用的剪应力。Ⅱ型温度应力场取决于热流密度沿垂直裂纹面方向的分量,平行于裂纹方向的热流分量对温度应力场没有影响。An infinite plate with a central crack is subjected to remotely and uniformly applied heat flow. There is an angle between the heat flow and the crack. When a constant heat flow normal to the crack passes the crack surfaces, the analytical solutions of temperature, thermal stress and displacement fields are obtained using the complex function theory. The thermal stress intensity factor is determined from the unique condition of displacement field. Numerical simulation is performed for the aluminum alloy LY12 material. The effects of heat conduction property of crack and the direction of the heat flow on the temperature field and the thermal stress intensity factor are discussed. The result shows that only mode II thermal stress intensity factor is induced while the mode I thermal intensity factor vanishes under the given thermal boundary condition. Thermal loading can be equivalent to a uniformly and remotely applied shear stress. Mode II thermal stress field only depends on the component of remote heat flow normal to the crack surface, while the component of heat flow parallel to the crack line has little influence on the thermal stress field.

关 键 词：热弹性力学 复变函数解法 Ⅱ型裂纹 导热裂纹 温度应力强度因子 解析解 

分 类 号：O346.1[理学—固体力学]