含界面层圆形夹杂的平面热弹性问题

Plane thermoelastic problem for circular inclusion with interphase layer

研究了无穷远均匀拉伸条件下，含界面层圆形弹性夹杂的平面热弹性问题。运用Muskhelishvili复势理论的级数展开技术，将各区应力函数展开为合适的Taylor和Laurent级数，考虑边界上的力和位移连续性条件，将问题转化为线性方程组的求解，数值分析表明：总体上，软界面层可以有效的减小夹杂和基体的界面应力集中；硬界面层可以减小夹杂内的界面应力集中，但却增加了基体内的界面应力集中；此外，总体上，界面相热膨胀系数较基体相和夹杂相过高，不利于降低界面应力集中。

The plane thermoelastic problem for circular inclusion with interphase layer under the coupled action of uniformly mechanical loads and temperature loads is investigated. By applying the technique of series expansion in the complex potential theory established firstly by Muskhelishvili in conjunction with the boundary conditions, the stress potentials in the form of Taylor and Laurent series for every region are written, then the problem will be reduced to solve a set of linear algebraic equations. Numerical results indicate that the soft interphase layer can effectively decrease the surface stress concentration inside inclusion and matrix; The hard interphase layer can also effectively decrease the surface stress concentration inside inclusion, however the reverse effectiveness will appear inside matrix; In general, the increasing of the thermal expansion coefficient of interphase layer relative to inclusion and matrix is disadvantage to reduce the surface stress concentration.