The relation between the shear modulus of elasticity and the indentation hardness of vulcanized rubber is derived, from the theory of elasticity.Hooke's law, isotropy and incompressibility of rubber are assumed in the derivation.Indentor shape is presumed as a cylinder of average diameter instead of a truncated cone. An approximate conclusion is expressed as follows.
H
s=G/G+G
50×100
where H
s is indentation hardness degree of rubber, G is shear modulus of rubber and G
50 is a constant.
(If G=G
50, then H
s=50 and it shows the meaning of the constant G
50.) The calculated value of G
50 for JIS A hardness scale is 7.53kgf/cm
2, but the measured value of shear modulus for rubber of hardness degree 50is sometimes smaller than the calculated G
50.The disagreement is caused by the stress relaxation, because the measurement of modulus of elasticity requires longer time than that of indentation hardness.
The above expression for Shore A scale agrees fairly well with the IRHD probit curve shown in ISO Recommendation R48.
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