Stress—strain and contraction ratio curves for polycrystalline steel

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Abstract
Tensile tests of flat bars made of polycrystalline steel have been carried out in the elastoplastic domain of straining to determine true-stress, true-strain curves as well as lateral contraction ratio curves versus true strain or stress. Four types of steels were tested, i.e. low carbon steels of designation DIN. St. 33, St. 34 and St. 42, and a low carbon high-yield-strength alloy steel, quenched and tempered, under commercial designation U.S.S. [T 1]. The differential Moiré method was used for the measurement of longitudinal and transverse strains at the elastic, as well as at the plastic domain of deformation. The method yielded the state of deformation over a large gauge area and it was very sensitive to strain-variations. Therefore, it was proved to be convenient for the study of non-uniform fields of deformation with great accuracy. The nucleation and propagation of Lüders fronts in all specimens were studied and the distribution of plastic strain in Lüders bands was measured. Lateral contraction ratio-true strain curves resulted from longitudinal and transverse true strain measurements followed second degree curves (branches of hyperbolas) starting from the elastic constant value of contraction ratio and tending asymptotically to the limiting value of 0•50 of the incompressible material. All curves presented an unstable part, corresponding to the Lüders band region, where contraction ratio increased over 0•50, reached a maximum of the order of 0•65 and then decreased tending to the stable hyperbolic branch of the curve. The same phenomenon appeared in the contraction ratio-true stress curves which presented a sigmoid shape.

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