Indentation theory and experiments of the truncated conical indenter (1st. extended indentation theory based on the ball indentation theory and experiments by the instrumented rockwell hardness tester)

摘要

Rockwell Hardness test is simple and quick for evaluating mechanical properties of the industrial materials. Up to now, we have been proposed the evaluation method of material properties by the ball indentation theory and also the pyramidal indentation theory. In this paper, the ball indentation theory proposed by authors is extended and applied to the indentation of the truncated conical indenter. As a result, theoretical equation of the truncated conical indenter is deduced as follows: E{sub}(s(c))=(1-μ{sup}2)/[4/3{the square root of}π k{sub}(0(Con))/L{sub}M (δ{sub}t-c·L{sub}m-T{sub}(Con)(δ{sub}r-C·L{sub}m - I(E)] where K{sub}(0(con))= {the square root of}π·tan(β{sub}(Con)/2)，β{sub}(Con): apex angle, L{sub}M load δ{sub}t,δr: measured indentation and elastic recovery displacements respectively, C: spring constant of the tester, C·LM: elastic deformation of the tester, T{sub}(Con): truncation of the indenter's 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)} elastic parameter of the indenter and the specimen. Indentation experiments are carried out for the following specimens: Carbon steel (HV 500, HRC 60, HR 30 N 60) and Cu-Zn alloy (HRB 72): over the load ranging from 144 N to 441 N. Then, implementation processes of the theory are described in detail for the specimen HV 500 considered as the calibration specimen. so that the spring constant of the tester C and the truncation of the conical indenter T{sub}(Con) are obtained. Using theses values of C and T{sub}(Con), Young's moduli E{sub}(S(C)) for the arbitrary specimens are calculated with the deduced theoretical equation. These values of E{sub}S(C) and supposed values E5 show reasonably good agreement. When the load L{sub}M is 147 N. indentation depths of experimental value of Carbon steels (HV 500, HRC 60, HR 30 N 60) are smaller than the height of the indenter's tip ball part, so that this deduced theoretical equation will also be applied to the indentation of the indenter's spherical tip part. Namely, this deduced theoretical equation will be useful for wide range of load.