Estimating concentrations of cracks and platelets from their traces in 2D cross-sections

The effect of cracks on the overall elastic and conductive properties is expressed in terms of the 3D crack density parameter. Similarly, in composites, the effect of thin platelets (perfectly rigid, in the context of elasticity, or perfect conductor/insulator, in the context of conductivity) on the said properties is expressed in terms of the same parameter. However, it may be difficult to estimate experimentally and it cannot, generally, be related to volume fractions. Its estimation from the 2D density of line traces of cracks/platelets observed on a surface (say, specimen face) is derived in a simple form - thus allowing estimates of the said properties directly from the traces on specimen faces. This 2D-3D relation is verified by direct numerical simulations. The related statistical aspects are discussed.