Analysis of Percent Elongation for Ductile Metal in Uniaxial Tension

Percent elongation of ductile metal in uniaxial tension due to non-homogeneity was analyzed based on gradient-dependent plasticity. Three assumptions are used to get the analytical solution of percent elongation: one is static equilibrium condition in axial direction; another is that plastic volumetric strain is zero in necking zone; the other is that the diameter in unloading zone remains constant after strain localization is initiated. The strain gradient term was introduced into the yield function of classical plastic mechanics to obtain the analytical solution of distributed plastic strain. Integrating the plastic strain and considering the influence of necking on plastic elongation, a one-dimensional analytical solution of percent elongation was proposed. The analytical solution shows that the percent elongation is inversely proportional to the gauge length, and the solution is formally similar to earlier empirical formula proposed by Barba. Comparisons of existing experimental results and present analytical solutions for relation between load and total elongation and for relation between percent elongation and gauge length were carried out and the new mechanical model for percent elongation was verified. Moreover, higher ductility, toughness and heterogeneity can cause much larger percentage elongation, which coincides with usual viewpoints.