(西安交通大学 金属材料强度国家重点实验室， 西安 710049)
摘 要: 首先用Kroner模型计算了具有丝织构的TiN薄膜的弹性矩阵。当材料具有较强的丝织构时，材料弹性矩阵的对称关系将发生变化，得到的弹性矩阵与各向同性同种材料的弹性矩阵相差很大，相同分量的值一般相差在13～20 GPa之间。然后计算了TiN薄膜的弹性常数曲线随ψ 角的分布。当应力测试方向不同时，即使是同一晶面，弹性常数也会产生差异，而且弹性常数随ψ角的分布在低ψ 角区发生了弯曲。计算的TiN薄膜X射线弹性常数曲线的弯曲情况与实测的PVD TiN薄膜应力测试曲线相似。
关键字: 弹性矩阵； 丝织构； 薄膜； X射线衍射
of anisotropic films using Kroner method
（State Key Laboratory for Mechanical Behavior of Materials,
Xi′an Jiaotong University, Xi′an 710049, P. R. China）
Abstract:In order to study the effect of the fiber texture, the elastic matrix of TiN film using the Kroner models was calculated. When fiber texture is involved in films, the symmetry of the elastic matrix will change and there is a large difference of the elastic constants between the textured film and the isotropic. The same tensors of the textured and the isotropic films in the elastic matrix can be discrepant greatly, e.g. the difference is generally in 13～20 GPa. The distribution of the elastic constants of TiN film vs ψ angle was also calculated. The result shows that the difference can be introduced when the measured direction of the residual stress is different, though the diffraction plane does not change. In addition, the distribution curve of the elastic constants shows curvature in the range of the small ψ angle. The distribution curve of X-ray elastic constants is similar to the measured d—sin2ψ curve.
Key words: elastic matrix； fiber texture； thinfilms； X-ray diffraction
