Practical nano-indentation theory and experiments of the pyramidal indenter (1st. theoretical equation including both terms about the elastic deformation of the tester and the truncation of the round tip)

摘要

In the practical load range of the nano-indentation test with the pyramidal indenter, the influences of the elastic deformation of the tester and the truncation of the round tip on the measured displacements cannot be neglected. For this load range, following the practical nano-indentation theory, which includes both terms about the elastic deformation of the tester and the truncation of the round tip, is proposed. L{sub}M = (4/(3×(the square root of π)))×({K{sub}(0(Tri)) or K{sub}(0(Qua))})/(F(E){sub}(IS))×(δ{sub}t - C·L{sub}M + T)(δ{sub}r - C·L{sub}M) where, K{sub}(0(Tri)) = 3{sup}(3/4)/f(α{sub}(Tri)), f(α{sub}(Tri)) = [{sin(α{sub}(Tri)/2)}{sup}(-2) - {cos(π/6)}{sup}(-2)]{sup}(1/2), α{sub}(Tri): adjacent edge angle of the triangular pyramidal indenter, K{sub}(0(Qua)) = 2tan(β{sub}(Qua)/2), β{sub}(Qua): opposed face angle of the quadrangular pyramidal indenter, L{sub}M: load, δ{sub}t: measured indentation depth, δ{sub}r: measured elastic recovery displacement, C: spring constant of the tester. C·L{sub}M: elastic deformation of the tester, T: truncation of the round tip, E{sub}I, E{sub}S and μ{sub}I, μ{sub}S: Young's Moduli and Poisson's ratios of the indenter and the specimen, F(E){sub}(IS) = {(1 - μ {sub}I{sup}2)/E{sub}I + (1 - μ {sub}S{sup}2)/E{sub}S}: elastic parameter of the indenter and the specimen. This theory can be useful to analyze the practical nano-indentation test and also to calculate the mechanical properties of the small and thin specimens.