Properties of true stress diagrams in the areas of necking and fracture of materials under tension

Tensile tests of steel specimens with plotting loaded and unloaded true stress curves were carried out. It is shown that «true stress – true strain» curves in the necked region of the tensile specimen have the form of a sloping ascending straight line up to failure. It is revealed that the straightness of the curve is also observed for austenitic steel in the structure of which martensite is formed under the effect of plastic deformation, whereas «true stress S – true relative area reduction ψ» curves exhibit a violation of the straightness with upward deviation at the final stage of necking. When using Davidenkov correction, the calculated values of the true ultimate tensile stress decrease and approach the straight line. Although the unloaded values of the 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. It is possible to apply Kerber’s rule to «true stress – true relative area reduction ψ» if a sufficiently long rectilinear section of the curve is clearly identified after the true ultimate tensile stress has been reached in order to extrapolate this section to a true relative reduction of area equal to unity. Kerber rule is not applicable for «true stress – true strain» curves despite their straightness in the necked region due to the uncertainty in calculating the true strain at the unit value of true relative area reduction. At the same time the presence of a linear section in these curves during the specimen necking greatly simplifies the derivation of the entire tensile curve up to fracture.

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