Modeling shear band interaction in 1D torsion

When two shear bands are being formed at close distance from each other they interact, and further development of one of them may be quenched down. As a result there should be a minimum distance between shear bands. In the literature there are at least three analytical models for this minimum distance. Predictions of these models do not generally agree with each other and with test results. Recently we developed a 1D numerical scheme to predict the formation of shear bands in a torsion test of a thin walled pipe. We validated our code by reproducing results of the pioneering experiments of Marchand and Duffy, and then used it to investigate the mechanics of shear localization and shear band formation. We describe our shear band code in a separate publication, and here we use it only as a tool to investigate the interaction between two neighboring shear bands during the process of their formation. We trigger the formation of shear bands by specifying two perturbations of the initial strength. We vary the perturbations in terms of their amplitude and/or their width. Usually, the stronger perturbation triggers a faster developing shear band, which then prevails and quenches the development of the other shear band. We change the distance between the two shear bands and find, that up to a certain distance one of the shear bands becomes fully developed, and the other stays only partially developed. Beyond this distance the two shear bands are both fully developed. Finally, we check the influence of certain material and loading parameters on the interaction between the two shear bands, and compare the results to predictions of the analytical models from the literature.