Nonlinear elastic behaviors of low and high strength steels in unloading and reloading

The elastic moduli of four sheet steels were measured in continuous loading–unloading–loading (LUL) tests after different amounts of plastic pre-strain. The four materials were a low-strength steel (Mild270), a bake-hardenable steel (BH340) and two advanced high-strength steels (AHSS), DP490 and DP590. Hysteresis loops were observed due to a non-linearity of the elastic modulus during the unloading and reloading cycles. The total strain recovery during unloading could be separated into a linear part and a non-linear part. The latter was found to be proportional to the unloading stress for all materials. The unloading and reloading elastic moduli decreased as the plastic pre-strain increased and reached saturation towards specific constant values. They could well be approximated as a function of the plastic strain with an empirical exponential-type model, although there were some deviations for BH340. The baking heat treatment and different strain rate had little influence on the unloading and reloading elastic moduli. The increase of the non-linear elastic strain component as a function of the unloading stress could be explained by the Kocks–Mecking (KM) model in which the micro-plastic strain is related to the mobile dislocation density.