The Variation Of Poisson's Equation

The variation of poisson’s ratio (σ), depends on the variation of the values and relative values of (E) and (G) in Equation (10) and (Ul) and (Us) in Equation (11). For any material (E) and (G) as well as (Ul) and (Us) tends to increase or decrease together. Therefore, we cannot decide the variation of (σ) in the same or opposite direction to that of (E) and (G). Using Equations 10 and 11 we can predict the behavior of (σ) according to which of the two elastic constants varies more than the other. If Equations (10) and (11) are positive, then (σ) varies in the same direction of (E or Ul) and (G or Us) and vice versa. However, for isotropic solids, (σ) is bounded practically by 0 and 1/2.
A high cross-link density material has poisson's ratio in order of 0.1 to 0.2, while low cross link density materials have Poisson's ratio between 0.3 and 0.5 (55 ,56). Accordingly, Poisson's ratio of the investigated glass is about 0.2 for 0 mole% and 0.5 mole% Er2O3 content, while it is greater than 0.2 up 0.33 at 2 mole% Er2O3 content, Figure (11).
Micro-hardness expresses the required …show more content…
In the three dimensional tetrahedral coordination polyhedron such as SiO2 the value of the d ratio is 3 and in the two dimensional layer structures it equals 2. The second important parameter is the ratio G/C12 (58), which considered as an indicator of the character of the force field. This parameter equals to 1 in case of the central force type; otherwise the force is not central. On the other hand, the G/C12 ratio approaches to unity as the central force field may reduce the fraction of the broken bonds in the network structure of the glass (57). Another parameter is the ratio between Young's modulus and shear modulus E/G. The results indicated 2-dimensional network with non central