On the non-linear unloading behavior of a biaxially loaded dual-phase steel sheet

Abstract

The response of the dual-phase steel DP 590 under continuous loading and unloading from a biaxial stress state is examined using a combination of experiments and analysis. The experiments utilize cruciform specimens of a custom geometry that develop quite uniform strain fields in the test-section and allow the development of large strains (>12%, depending on the loading path). Experiments along 9 radial stress paths in the first quadrant of the plane-stress space were performed. The first part of each unloading and reloading follows the prediction of orthotropic elasticity using the initial elastic properties. A second linear slope is observed, before the responses become fully non-linear. The non-linear strain recovery is measured to be about 1/5 of the linearly elastic strain for this material. Furthermore, the chord modulus reduces exponentially to a value of ∼90% of the initial. The biaxial cruciform experiments are also used to determine contours of constant plastic work and to calibrate the Yld2000-2D anisotropic yield function. A combined isotropic/kinematic hardening model with a simple exponential-decay shrinkage of the yield surface is adopted. The non-linear unloading response is represented by a 4-term Chaboche non-linear kinematic hardening model using the Ziegler back-stress evolution rule. Plasticity during unloading is assumed to occur as soon as deviation from proportionality is detected. The 4 terms are necessary for capturing both the second linear slope after (re-) yielding and the work-hardening stagnation observed in the experiments. The agreement between experiments and predictions for the induced strain paths is very good. The predictions of the non-linear strain recovery are good overall, and are independent of the yield surface adopted. In summary, it is proposed to capture the biaxial unloading behavior using a constitutive model that includes an anisotropic yield function suitable for predicting the induced strain paths, and a non-linear kinematic hardening rule suitable for predicting the tension–compression behavior of the material at hand.