Modeling of the cross-section ovality of single crystal nickel-based superalloy samples under tension

The problem of uniaxial tension of a cylindrical body from a single-crystal material with a cubic symmetry is considered. The loss of the initial circular shape of the cross section of a cylindrical specimen under tension or compression in conditions of misalignment of the sample axis with the anisotropy axes is one of the characteristic external manifestations of the mechanical properties anisotropy. The problem is solved in elastic, elasto-plastic and elasto-visco-plastic formulations. Both analytical and numerical (three-dimensional finite element modeling) methods are used to solve boundary value problems. The dimensionless ovality parameter is introduced as a ratio of the difference between the largest and smallest diameters to the smallest ones aiming to estimate the change of the cross-section shape. The results of the calculations are compared with the experimental data concerning the high-temperature creep of the single-crystal nickel-based superalloy VZhM4. The deviation effect of the sample axis orientation from the anisotropy axes on the cross-section shape under loading and unloading is investigated. Both micromechanical (crystallographic) and phenomenological models are used to solve inelastic problems; and later the obtained results are compared. Taking into account the geometric nonlinearity in the solution of the elasto-plastic boundary value problem makes it possible to describe the evolution of the neck formation process which can be non-axisymmetric for anisotropic materials. The obtained results indicate the need to abandon the measurement methods when performing the mechanical tests of anisotropic materials under uniaxial tension related to recording the change in the cross-section size in order to determine the axial deformation. The ovality can be directly used to estimate the axial strain, and also to compensate the missing information about the crystallographic orientation of the sample.