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基于Hertz方程,修正了平头压痕薄膜系统的力学模型,建立了用于评估球头压痕确定薄膜弹性模量的等效膜厚法。采用有限元方法对模型进行计算分析,结果发现,当薄膜弹性模量大于基体时,计算误差小于Ranjana和William(RW)模型[1];当薄膜弹性模量小于基体时,对于较深的压痕计算得到的结果仍然和理论值相符,说明本模型可以用于比较深的压痕情况。另外,研究了薄膜屈服强度和球压头半径对计算结果的影响,结果显示,薄膜的压缩屈服强度越大,等效膜厚法得到的结果越准确;而在同一压痕深度下,较大的压头半径会带来较大的误差,当压痕深度较小时,薄膜的弹性模量受压头半径的影响较小。最后通过TiN/sapphire在球压头和三棱锥压头下的试验,验证了本方法。
Based on the Hertz equation, the mechanical model of the flat indentation film system was modified and the equivalent film thickness method was established to evaluate the elastic modulus of the ball indentation film. The finite element method is used to calculate and analyze the model. The results show that when the elastic modulus of the film is larger than that of the matrix, the calculation error is smaller than that of the Ranjana and William (RW) model [1]; when the elastic modulus of the film is smaller than that of the matrix, The calculated results are still consistent with the theoretical values, indicating that the model can be used for deeper indentations. In addition, the influence of film yield strength and ball-head radius on the calculation results is studied. The results show that the greater the compressive yield strength of the film, the more accurate the result obtained by the equivalent film thickness method; while at the same indentation depth, Of the head radius will bring greater error, when the indentation depth is small, the elastic modulus of the film by the head radius less affected. Finally, the method was validated by TiN / sapphire under the ball-indenter and triangular-pyramid indenter.