均匀热流作用下含裂纹板I型温度应力强度因子的解析解

ANALYTICAL SOLUTION OF MODE I THERMAL STRESS INTENSITY FACTOR FOR CRACKED PLATE UNDER UNIFORM HEAT FLOW

研究一种新的温度边值问题。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。当裂纹面上维持一恒定温差时,采用复变函数理论,得出了温度场、温度应力场与位移场的解析解。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材料进行了相应数值计算,分析了热流密度大小与方向对温度分布与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I型温度应力强度因子,不产生II型温度应力强度因子。温度应力场取决于热流密度沿裂纹方向的分量,垂直于裂纹方向的分量对温度应力场没有影响。

A new thermal boundary value problem is investigated.An infinite plate with a central crack is subjected to remotely and uniformly applied heat flow,and there is an angle between the heat flow direction and the crack.When a constant temperature prevails on the crack surface,the analytical solutions of temperature,thermal stress and displacement fields are obtained by using the complex function approach in thermoelasticity.The thermal stress intensity factor is determined from the unique condition of the displacement field.Numerical computation was performed for the aluminum alloy LY12 material.The effects of magnitude and direction of heat flow on the temperature field and thermal stress intensity factor were discussed.The result shows that only mode I thermal stress intensity factor is induced while the mode II thermal intensity factor vanishes under the given thermal boundary condition.Thermal stress field only depends on the component of remote heat flow along the crack direction,while the component of heat flow normal to the crack surface has no influence on the thermal stress field.