中文摘要：

用有限元法建立了铜/钨酸锆缓和热应力功能梯度薄膜的数学模型,讨论了梯度薄膜的层数N,成分分布指数P,梯度层厚度Hf,基片厚度Hm与纯铜层厚度Hc,以及不同工作环境温度θ对薄膜热应力分布的影响。由热力学计算可知：梯度层数越多,缓和热应力效果越好。考虑到制备工艺复杂程度,参考数值模拟结果可知：当N≥5,P=1时,可以减小热应力最大值,热应力最大值出现在基体与梯度层的界面处;当N=5,2≤P≤3,热应力最大值位于梯度层内;适量增加梯度层厚度Hf和基片厚度Hm有利于减小热应力最大值,此梯度缓冲层在室温到α相钨酸锆陶瓷的相变温度（120℃）区间内,对于各厚度的功能铜层都有良好的保护作用。

英文摘要：

A mathematical model of the copper/zirconium tungstate（Cu/ZrW2O8） functionally graded films was proposed by means of a finite element method.Effects of the parameters,such as the quantity of layers （N）,distribution of components （P）,thickness of graded films （Hf）,thickness of substrate （Hm）,thickness of pure Cu layer （Hc） and temperature （θ）,on the thermal stress fields of Cu/ZrW2O8 functionally graded films were discussed.The results of thermodynamic calculation show that the more layers of the functionally graded films,the more the thermal stress can be reduced.When N≥5 and P=1,the maximum value of heat stress between the substrate and the functionally graded films decreased.When N=5 and 2≤P≤3,the maximum value of heat stress appeared inside the functionally graded films.The increased values of Hf and Hm can favor the reduction of the maximum value of heat stress.This functionally graded film can protect the pure Cu layer from room temperature to the α-ZrW2O8 phase transformation temperature （120 ℃）.