Proportional and non-proportional hardening behavior of dual-phase steels

The elastic-plastic response of sheet materials during non-proportional paths is seldom incorporated in constitutive equations used for routine sheet forming simulation, but can have a significant effect on formability and springback. Monotonic tension and compression, coaxial tension-compression (T-C), coaxial compression-tension (C-T), and two-stage/non-coaxial tensile tests were performed for three grades of dual phase steels: DP590, DP780, and DP980. The reverse flow curves have three characteristics: reduced yield stress (Bauschinger effect), rapid transient strain hardening over a few percent strain, and long-term or "permanent" softening. The departure of the reverse hardening curves from monotonic ones is larger than with other typical sheet forming alloys, presumably because of the effects of large second-phase martensite particles in dual-phase steels. A Modified Chaboche type model was applied in this paper to simulate the elastic-plastic behavior of DP steels. In addition to one or more standard nonlinear components of the back stress, a linear term was added to represent the "permanent" offset of hardening following a stress reversal. The parameters for the model were fit using the monotonic and reverse tensile test results only, and the model predictions were then compared with large-strain balanced biaxial bulge test, non-coaxial, two-stage tensile tests, and draw-bend springback tests. The Modified Chaboche model captured the response following a path change much better than isotropic hardening models, but there is a fundamental difference between large-strain hardening after a path change that occurs between path reversals and changes of principal strain axis. The Chaboche model can reproduce either behaviors, but not both simultaneously. (C) 2013 Elsevier Ltd. All rights reserved.