用路径守恒积分计算平面准晶裂纹扩展的能量释放率

将准晶（包括点群５，５ｍ，８ｍｍ，１０，１０ｍｍ，１２ｍｍ）弹性边值问题化为广义能量泛函的变分问题，建立了求解准晶弹性变形的有限元法，并提出了含裂纹准晶的路径守恒Ｅ－积分，指出Ｅ－积分在数值上等于准晶裂纹扩展的能量释放率，作为实例，计算了平面五次、八次、十二次对称准晶裂纹扩展的能量释放率，数值计算表明准晶中路径积分具有较好的守恒性，同时数值结果表明准晶中相位子场的出现使准晶裂纹扩展的能量释放率增大

Energy release rate of plane quasicrystals with crack determined by path-independent E-integral

This paper firstly presents the FEM\|method to solve the mixed boundary problem equations of plane quasicrystals(including point group 5,5m,8mm,10,12mm)by transforming the elastic equilibrium equations of plane quasicrystals into the variation of a kind of general potential function and to determine the energy release rate (ERR) of plane quasicrystals with crack by extended path independent J\|integral, namely E\|integral. A numerical example caring about the ERRs of those plane quasicrystals is provided and its numerical results show that the ERRs given numerically are equal to the analytic ones very well. The ERRs of plane quasicrystals with crack are greater than those materials without coupled phason filed.