Properties of True Stress Diagrams in Areas of Necking and Fracture of Materials under Tension

Abstract—Tensile testing of steel samples has been carried out, and loaded and unloaded true stress curves have been plotted. It has been shown that the true stress–true strain curves in the area of necking have the shape of an inclined ascending straight line until fracture. It has been established that the straightness of the diagram is also observed for austenitic steel, in the structure of which martensite is formed under plastic deformation. In contrast to these diagrams, the true stress–conditional relative area reduction curves exhibit a straightness violation with the upward deviation at the final stage of necking. The true ultimate tensile stresses calculated using the Davidenkov correction decrease and approach the straight line of the diagram. Although the unloaded values of true stresses and true strains exceed the loaded values at the same tensile force, they fit on the same curves at different stages of the material deformation. The Kerber rule can be applied to the true stress–conditional relative area reduction curves if a sufficiently long rectilinear curve section is clearly identified after the true ultimate tensile stress has been attained, in order to extrapolate this section to the true relative area reduction equal to unity. The Kerber rule is inapplicable to the true stress–true strain curves, despite their straightness in the area of necking, because of the uncertainty in calculating the true logarithmic strain at the unit true relative area reduction. At the same time, the presence of a linear section in these curves over the entire area of necking greatly simplifies the plotting of the entire tensile curve until fracture.