Stochastic modeling of multi-filament yarns. I. Random properties within the cross-section and size effect

The paper presents a thorough study of sources of randomness/disorder in multi-filament yarns that are relevant for their performance in textile reinforced concrete. For the analysis of bundles with infinite number of fibers we use a continuous analytical model with refined kinematic hypothesis. In parallel, we apply a more general discrete numerical bundle model covering the cases of finite number of fibers and spatial variations of material properties. The considered distributions of material properties include variations of parameters (local stiffness and strength) both from filament to filament and over the length of each filament. In the present paper, we study the influence of variations in filament properties across the bundle. In the companion paper (Vořechovský, M., Chudoba, R., 2006. Stochastic modeling of multi-filament yarns. II. Random properties over the length and size effect. International Journal of Solids and Structures), the variations of material properties over the length are considered. Both papers provide the basis for correct interpretation of the data obtained from the tensile test on multi-filament yarn with varied specimen length. As the actual goal of the present work is to derive yarn characteristics relevant for crack bridges in cementitious composites we systematically assess the significance of the studied sources of disorder in the context of extremely short bundle lengths.