中文摘要：

采用有限元方法模拟了纳米压痕中不同曲率半径针尖的压头压入不同材料的加、卸载过程，并对计算结果与实验进行了对比以验证模拟的可靠性．理论分析给出了一个硬度关于压头曲率半径和压入深度的半经验公式．结果显示，相同材料的硬度计算值随着压头针尖曲率半径的增大而增大；另外对于同一针尖曲率半径而言，材料硬度值随着压痕深度的减小而增大，并且随着曲率半径的增大，尺寸效应越明显．理论分析与有限元计算结果吻合得较好．分析表明，由于尖端曲率半径的增大而导致过低估计压头与材料的接触面积是产生针尖尺寸效应的主要原因．进一步分析显示，理论推导中对于尖端曲率半径较大（R〉60nm）的压头，在压入深度较浅时（h≤60nm）将其等效为理想压头相对粗糙，其硬度计算结果存在一定的高估．

英文摘要：

Finite element method （FEM） was used to explore the nanoindentation process of several materials under Berkovich indenter. The simulated nanoindentation results with different tip radii were compared with experiments. A semi-empirical relation which depicts hardness with tip radius and indentation depth was derived by theoretical analysis. Results show that the measured hardness with blunt indenter increases with the tip radius and decreases with the depth of indentation. As the tip radius increases, the variation on indentation size effect becomes much more prominent. The results by theoretical analysis and FEM simulation are in good agreement. The analyzed results indicate that the tip effect in nanoindentaion is caused mainly by the underestimation of the contact area as the tip radius increases. Further results show that it is inaccurate to treat the nonideal tips as the ideal tips in theoretical analysis when the tip radius is large （R〉60 nm） and the indentation depth is shallow （h≤60 nm）simultaneously, and that the hardness values tend to be overestimated.