The variation of the strain-hardening exponent due to grain size distributions in engineering metallic sheet materials.

Abstract

Grain-size distributions of commercially pure aluminum, copper and 6-4 brass are well approximated by a log-normal distribution function, and it is shown that the strain-hardening exponents of copper and 6-4 brass under tension increase with their median and standard deviation. Based on the nth-power flow curve and the distribution function whose upper grain-size is limited to 3.5 times the mean-grain diameter, the composite flow curve for a metal comprising various grain sizes is expressed by either an equal-strain or an equal-stress model. The equal-strain model gives the lower flow stress limit snd the equal-stress model yields the upper one, and the experimental data appears in between or closely around these two neighboring limits. The relation between the strain hardening exponent and statistical variables can be calculated from these. The former model predicts the upper boundary of the strain-hardening exponent and the latter predicts the lower boundary, with respect to the median and the standard deviation, and the experimental data on 6-4 brass are given in between them.