Practical nano-indentation theory and experiment of the pyramidal indenter (3rd. expanded theory to highly elastic material using tester with linear elastic deformation)

摘要

In the previous paper proposed by the authors, when the theoretical formula is applied to the experimental data of highly elastic, homogeneous and amorphous material, e.g. a glass specimen using a tester with linear elastic deformation, the calculated Young's modulus is rather in disagreement with the expected value. The cause of this result is due to the ratio δ{sub}r/δ{sub}t, δ{sub}r: elastic recovery displacement and δ{sub}t: maximum indentation depth, because the ratio δ{sub}r/δ{sub}t, is very high for a glass specimen but low for a metal specimen. Therefore the ratio δ{sub}r/δ{sub}t is tested to be introduced in the authors' former formula as follows: F(E){sub}(IS): elastic parameter of the indenter and the specimen, δ{sub}(rf)( = δ{sub}t – T{sub}(Tri) -δ{sub}E): final corrected indentation depth of the indenter, S{sub}(rf) ( = δ{sub}r - δ {sub}E): final corrected elastic recovery displacement of the indenter, δ{sub}E ( = C × L{sub}M) elastic deformation of the tester, L{sub}M: maximum indentation load, C : spring constant of the tester, T{sub}(Tri): truncation at the tip of the indenter, k{sub}(0Tri): geometrical constant of the indenter; namely, the expanded formula: F(E){sub}(IS) = {1/E{sup}*} = {((4/3){the square root of}π)k{sub}(0Tri)/L{sub}M}δ{sub}(tf)·δ{sub}(rf){1-x(δ{sub}(rf)/δ{sub}(tf))} : [E{sup}* is the reduced modulus, in the other paper] Under the condition that Young's modulus of a glass specimen is constant, the term x, T{sub}(Tri) and C are obtained from this expanded formula. Next, the applications to the experimental data of metal specimens in the former paper are carried out with these values of x and C, the calculated Young's moduli are fairly in agreement with the expected values rather than the former paper's results. At the same time, the hardness value during indentation HI{sub}(Berk0.) is defined with the terms δ{sub}(tf) and L{sub}M as HI{sub}(Berk0.)=C{sub}(Berk0.)×L{sub}M/(δ{sub}(tf)){sup}2. [C{sub}(Berk0.) : geometrical constant of the indenter) It is shown that the hardness values HI{sub}(Berk0.) calculated for a glass specimen are almost uniform over the load ranging from 0.98 mN to 49 mN. This is a very reasonable result in the homogeneous and amorphous specimen. Also, the hardness values are calculated with the metal specimens, and almost uniformities of hardness in the direction of depth are shown in detail. As a result, the expanded practical nano-indentation theory using the tester with linear elastic deformation proposed in this paper is confirmed to be useful for a wide variety of material.