From the summary: We study first- and second-order characteristics of two meso-scale random fields for anti-plane elastic response of random matrix-inclusion composites over a wide range of contrasts and aspect ratios. Special attention is given to the convergence of effective responses obtained from the essential and natural boundary conditions, which sheds light on the minimum size of a representative volume element. Additionally, we study the spatial correlation structure of the crack density tensor with the meso-scale moduli.