The Measuring Method about Young's Modulus of Plastics Using the Indenting Hardness Test by a Spherical Indenter

• Published in: Transactions of the Japan Society of Mechanical Engineers Series A Vol. 53; no. 495; pp. 2193 - 2202
• Main Authors: ISHIBASHI, Tatsuya, SHIMODA, Shigeru, FURUKAWA, Tooru, NITTA, Isami, YOSHIDA, Hidetoshi
• Format: Journal Article
• Language: English; Japanese
• Published: The Japan Society of Mechanical Engineers 1987
• Subjects: Material Testing; Measuring Method; Performance of Hardness Machine; Spherical Indenter Mean Strain Rate; Young's Modulus of Plastics
• ISSN: 0387-5008; 1884-8338
• DOI: 10.1299/kikaia.53.2193

This study aims at investigating the performance of a hardness testing machine. First, the phenomenon of a contact between a rigid sperical indenter and a plastic material is considered. By using Hertz's elastic contact law, the Young's modulus of plastics Es can be calculated from Eq. (1) using the cordal diameter of an indentation d, the elastic recovery of an indentation δr and the indenting load L : Es = 0.9(3/2) L/(d δr)…(1) From the geometrical relation at the contact part, the contacting diameter dc and the surface level diameter dl are derived as follows. (δt : the total depth) : dc = 2[D(δt-δr/2){1-(δt-δr/2)/D}]1/2…(2), dl = 2[Dδt×(1-δt/D)}1/2…(3) Furthermore, the mean strain rate under the elastic recovery by a spherical indenter is related to the strain rate under the uniaxial stress field. Finally, the indenting experiments are carried out, δr and δt are measured so that a cordal diameter d is formulated as follows : d = dl{1.71-0.707(dl/dc)}…(4) When the Young's moduli calculated from δt and δr using Eqs. (1)-(4) are compared to the Young's moduli measured from a compression test, their Young's values consist within an accuracy of about ±5-10%. Therefore, the measuring method about Young's modulus of plastics using the indenting hardness test by a spherical indenter can be applied to the present hardness testing machines.