213 先端の鋭い圧子を用いたナノインデンテーションで評価される代表インデンテーション弾性率

抄録

This paper proposes the modification of the Sneddon's solution in a wide range of ν from 0 to 0.5 through the numerical analysis on the unloading behavior of a simulated conical nanoindentation with a finite element method. As a result of the modification, the coefficient of linearity between the indentation elastic parameter k_e and Young's modulus E is empirically given as a function of v and the inclined face angle of the indenter, β, where k_e is defined as k_e≡P/h^2 with the indentation load P and penetration depth of the indenter h. According to the linear relationship between k_e and E, it is found that elastic rebound during unloading of a nanoindentation is uniquely characterized by a representative indentation elastic modulus E^* defined in terms of E, ν and β, and that the value of E^* can be evaluated from the P-h relationship with k_e and β. For an isotropic elastoplastic solid, the indentation unloading parameter k_2 defined as k_2≡P/(h-h_r)^2 for a residual depth h_r is different from k_e even though a linearly elastic solid with k_e and elastoplastic solid with k_2 have a common E^*. In order to evaluate E^* of an elastoplastic solid, the corresponding k_e is estimated from k_2 with an empirical equation as a function of the relative residual depth ξ defined as ξ≡h_r/h_<max> for the maximum penetration depth h_<max>. A nanoindentation experiment confirmed the validity of the numerical analysis for evaluating the elastic modulus