Table 3 Expressions, abbreviations, and units used to evaluate elastic moduli.

From: Sol–gel synthesized calcium borate glass and glass–ceramics: effect of CrCl3 doping on structure, mechanics, and gamma-ray shielding efficiency

Eq. no.

Parameter

Abbreviations

Unit

Equation

8

Young’s modulus

Y

GPa

\(\:Y=2\:{G}_{t\:}{V}_{t\:}\)

9

Bulk modulus

B

GPa

\(\:B=2.4\:{G}_{t\:}{V}_{t}^{2}\)

10

Shear modulus

S

GPa

\(\:S=\frac{3BY}{(9B-Y)}\)

11

Longitudinal modulus

L

GPa

\(\:L=B+\frac{4}{3}S\)

12

Poisson ratio

\(\:\sigma\:\)

 

\(\:\sigma\:=0.5-\frac{1}{7.2{V}_{t\:}}\)

13

Microhardness

\(\:H\)

GPa

\(\:H=\frac{Y-2\sigma\:Y}{(6+6\sigma\:)}\)