On strain hardening of cast iron with proportional and complex loading

The behavior of thin-walled tubular specimens of cast iron SCH 15-32 are modeled using loaded tension with internal pressure. The experimental data for this iron has been obtained by V.M. Zhigalkin and O.M. Usoltseva. This material is orthotropic according to the experimental diagrams of the axial and circumferential strains. Proportional and complex loadings are considered. Biaxial tension which has been carried out in the experiment corresponded to pure shear (characterized by the parameter of Lode-Nadai), where axial or circumferential stress prevailed. The trajectory of complex loading is given as a two-tier sloping in stress space; the first link path is consistent with axial tension, the second one is consistent with the circumferential tensile either under constant axial strain, or at a certain ratio of the increment of axial tension to the circumferential stress. In the latter case it produces an intermediate full unloading, then repeated complex loading at a high value of the first link path. Yield points are defined according to the initial elastic anisotropy, which is detected at a sufficiently small limit for residual maximum principal strain. Strain strengthening is described based on the concept of slipping and loosening. It is shown that the mechanism of flat plastic deformation is realized in the form of an idealized slipping on the plane of main shear stresses due to the initial anisotropy of materials. Priority inclusion in the work of these planes is characterized by the level and kind of stress. Single dependence on the principal stresses is proposed for maximum principal purely plastic component inelastic deformation (independent of the type of stress state). This dependence is a monotonically increasing function. It describes the change planes of slipping when changing the state of stress. The deformation loosening is considered occurring simultaneously and uniformly in all directions in accordance with V.V.Novozhilov’s hypothesis, which is associated with the plastic deformation. The coefficient of loosening is defined by comparing the longitudinal and lateral strain in uniaxial tension. In all the cases of tension beyond the elasticity, the lateral strain is remained close to its corresponding elastic value according to the interaction of local slipping and loosening. The revealed features of cast iron strain hardening are reflected with the proposed defining relations in the form of uniform relationships between the finite values of the stress and strain both under proportional and complex loadings.