Stochastic modeling of multi-filament yarns: II. Random properties over the length and size effect

The present study addresses the influence of variations in material properties along the multi-filament yarn on the overall response in the tensile test. In Part I (Chudoba, Vorˇechovsky´ and Konrad, 2006), we have described the applied model and studied the influence of scatter of material characteristics varying in the cross-section with no variations along the filaments. In particular, we analyzed the influence of varying cross-sectional area, filament length and delayed activation. Inclusion of these effects has lead to a better interpretation of the experimental data, especially with respect to the gradual stiffness activation, post-peak behavior and some form of size effect. In the present paper, the lengthrelated distributions of local stiffness and strength are included in terms of theoretical considerations and by applying the Monte Carlo type simulation of random fields. Such an approach allows us (1) to demonstrate the strong need for including length scale to random fluctuation of strength along the filaments and (2) to combine several sources of randomness in a single analysis so that their significance can be evaluated from the tensile test response.