对称热流载荷下一维六方准晶体币状裂纹的热-弹性解析解

Steady-state Thermo-elastic Field in An Infinite 1D Hexagonal Quasi-crystal Medium Containing A Penny-shaped Crack under Symmetric Heat Flux

针对一维六方准晶无限体中币状裂纹问题,给出了裂纹面作用对称热流载荷时的解析解.在准晶热-弹性通解的基础上,采用广义势理论方法,得到了准晶体中稳态的三维精确热-弹性场.同时,给出了裂纹所在平面上多个重要物理量的封闭解,其中包括裂纹面位移、法向应力、应力强度因子等.通过数值算例,验证了当前解析解的正确性,并分析了三维热-弹性场的分布情况.通过对声子场和相位子场耦合与解耦前后的对比,可知相位子场对结果的影响非常显著.所得解析解可作为针对准晶体断裂问题数值方法(如扩展有限元法)和实验方法(红外热成像无损检测方法)的校核基准.

This paper develops an analytical solution for the problem of an infinite 1D hexagonal quasi-crystal medium weakened by a penny-shaped crack and symmetrically subjected to a pair of heat flux on the upper and lower crack surfaces.Based on the general solution,the steady-state 3D thermo-elastic field in the quasi-crystal is obtained by the generalized potential theory method.Several important physical quantities on the cracked plane,such as crack surface displacements,normal stresses,and stress intensity factors,are obtained in closed forms.An illustrative numerical calculation is performed to verify the present analytical solution and to show the distribution of the 3D thermo-elastic field.It is indicated that the influence of the phason field on the results is pronounced and the phason field variables reduce to zero in the case of decoupling the phonon and phason fields.The present analytical solution can serve as a benchmark for various numerical codes for simulations of quasi-crystal fracture.