Elastic and elastic-plastic deformation of fibers under axial loading in twisted yarn

The paper discusses developed of theoretical model of deformation of the fibers, depending on the values of axial force and the twist angle of the yarn. To describe the development of plastic fibers deformation zone it is proposed to use the Prandtl scheme, according to which the connection between the fiber strain and axial stress is represented by two straight lines (bilinear diagram). The condition of axial strain is found when all fibers in the yarn are in a state of plastic deformation. In the absence of hardening the tension in the plastic zone for the twist angle between some values may decrease up to 1.5-3 times. Thus, with the presence in the yarn fibers deformable by elastically plastic according Prandtl law scheme, the yarn may form a core layer of fibers with irreversible deformations