Plastic flow and anisotropy of a low-carbon steel over a range of strain-rates

Abstract

The plastic flow and anisotropy of a low-carbon steel (AISI 1018) across a range of strain-rates is probed using compression experiments. Material models are then calibrated from these results. The strain-rates examined were 10−3 /s, 1 /s and 3.5 × 103 /s. It was found that the strain-hardening behavior is similar between the 10−3 /s and 1 /s families of experiments, with the latter showing a higher flow stress, as expected. However, the 3.5 × 103 /s experiments show not only an even higher flow stress, but a different strain-hardening behavior as well: they exhibit almost perfect plasticity, due to deformation-induced thermal-softening at larger strains. Comparing experiments in 3 mutually perpendicular directions, some mild plastic anisotropy was discovered. The initial yield and plastic flow of the material in 2 of these directions is comparable, and higher than in the 3rd one. It was also found that the plastic anisotropy evolves differently between the three directions, and also non-linearly with the strain-rate. These results were used to calibrate 3 versions of the Johnson–Cook (J–C) material model (original and 2 modified). The J–C modifications involve strain-rate-dependent model coefficients and exponents, as well as modified functional dependencies of the flow stress on the strain-rate and yield the best agreement with the experiments across the 6 orders of magnitude variation of the strain-rate. Assuming symmetry in tension and compression, and pressure-independence of yield, the plastic anisotropy was represented using the Hill 1948 yield criterion and 2 versions of the Karafillis–Boyce (K–B) one. The calibrations were performed at 5 levels of reference true strain: 0.075, 0.1, 0.15, 0.2, 0.25. For the material and experiments in this work, the Hill criterion provides good representation of anisotropy in the stress space. To capture the evolving plastic anisotropy, the parameters of the Hill criterion were evolved with plastic strain. Despite this, the criterion failed to provide accurate descriptions of the shape of the deformed specimens. In contrast, the performance of the 2 versions of K–B is significantly better, which would justify the higher effort required for calibration.