Nonlinear behavior of steel sheets during unloading and reloading

Abstract

The elastic moduli of four automotive sheet steels were measured during unloading and reloading after different amounts of plastic deformation. The four materials were: a low-strength steel (Mild270), a high-strength bake-hardenable steel (BH340) and two advanced high-strength steel (AHSS) sheets (DP490 and DP590). First, standard uniaxial tensile tests were conducted to obtain the basic mechanical properties. The level of pre-strains, at which the loading-unloading cycles were performed, was determined based on the results of the monotonic standard tests. Then, continuous loading-unloading-loading (LUL) tests were carried out at different pre-strain levels to determine plastic-deformation-dependent elastic moduli during unloading and reloading. 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 decomposed into an elastic part and a non-elastic part. The latter was proportional to the unloading stress for all materials. The unloading and reloading elastic moduli decreased as the plastic pre-strain increases and saturated towards specific constant values. They could well be approximated as a function of the plastic strain with an exponential-type empirical model, although some deviations were observed for the BH340 steel sheet. These deviations, mostly in the early stage of plastic deformation, are thought to result from the inhomogeneous deformation, or yield point elongation phenomenon, which is typically exhibited by BH steels. The effects of baking and strain rate on the elastic modulus change during unloading were investigated as well. However, the influences of both of these factors on the unloading and reloading elastic modulus were insignificant. The increase of the non-elastic strain component as a function of the unloading stress was explained by the concept of micro-plastic strain related to the mobile dislocation density. A simple approach based on the Kocks-Mecking (KM) model was proposed to relate this non-elastic strain component to the unloading stress.KEYWORDSSpringback, Nonlinear elastic modulus, Inelastic recovery, AHSS, loading-unloading test