Prediction of the Work-Hardening Exponent for 3104 Aluminum Sheets with Different Grain Sizes

Abstract

A practical approach to predict the yield strength and work-hardening exponent (<i>n</i> value) to evaluate the deep-drawing performance of annealed 3104 aluminum sheets is presented in the present work by only measuring and analyzing the grain size of the sheet. The various grain sizes were obtained through the different annealing treatment and then the evolution of the <i>n</i> value under different strains and the yield strength of annealed 3104 aluminum sheet were evaluated. Results showed that the <i>n</i> value and yield strength vary greatly with the grain size. A mathematical model relating grain size <i>d</i>, work-hardening exponent <i>n</i>, target strain <i>ε</i>, and yield strength <i>R</i>_p0.2 was developed in the present work. Within the studied grain size range <i>d</i> (12-29 μm), the <i>n</i> value generally increased with <i>d</i> in a strain-dependent manner, such that n = 0.1875 - 85.03 × exp [ - d / 1.94 ] when the <i>ε</i> was less than 0.5%, but n = 0.3 - 0.15 d - 1 / 2 when the <i>ε</i> was greater than 2%. On the other hand, the <i>n</i> value was found to depend on the target strain <i>ε</i> as n = 0.276 - A 1 × exp [ - e / 1.0435 ] , where <i>A</i>₁ varies with <i>d</i> and its value is in the range of 0.132-0.364. In addition, the relationship between <i>R</i>_p0.2 and <i>d</i> followed the Hall-Petch equation ( R p 0.2 = 36.273 + 139.8 × d - 1 / 2 ).