Numerical re-examination of the micro-scale mechanism of the Bauschinger effect in carbon steels

The micro-scale mechanism of the Bauschinger effect in carbon steels is re-examined by the numerical analyses on the periodic microstructures (unit cells) with elaborate illustrations and with our vocabulary in continuum mechanics. With the help of mathematical homogenization theory, we apply the finite element method to evaluate the mechanical behavior of unit cells, which are modeled as two-phase composites of ferrite and cementite, and simulate the uniaxial tension/compression tests for (medium) carbon steel. It is confirmed that the macroscopic responses obtained by the numerical simulations are qualitatively consistent with the experimental ones and that the extent of the Bauschinger effect is found to be sensitive to both the micro-scale morphology and the volume fraction of cementite. Then, by using illustrations of the transient states of stress and plastic strain in the unit cells, we search for the reasonable explanation for the micro-scale mechanism of the strain hardening from the initial yielding and the Bauschinger effect in the first macroscopic reverse loading.