A modified yield function for modeling of the evolving yielding behavior and micro-mechanism in biaxial deformation of sheet metals

In-depth understanding of the evolving plastic yielding behaviors and insight into their microscaled mechanisms are critical for fully exploiting of the formability of sheet metals, accurately forming of the needed shape and geometries, and precisely tailoring of the needed quality and property of the deformed parts. In this research, the in-plane yielding behaviors of dual-phase steel and aluminum alloy sheets were extensively investigated by biaxial tension experiments with the original and pre-strained specimens. It is found that the profile of the experimental plastic work contours changes with the increase of plastic deformation, no matter what the proportional or complex loading condition is. This indicates that the evolving yield behavior cannot be neglected. Based on the Yld2000-2d yield function, a modified yield function with introducing a variable exponent to represent the evolving yield behavior was proposed and then employed to model the evolving yielding of the given metallic sheets. To investigate the yielding micro-mechanisms, the simulated biaxial tension tests were conducted by using the established representative volume elements (RVEs) with a crystal plasticity model. The simulation results showed that the texture of the given sheet metals has a significant effect on the profile of the yield loci. Moreover, when the hard secondary phase is added into the polycrystalline aggregate, the optimum exponent of yield function for the given RVEs is increased, instead of decrease within a certain range of the plastic strain. The micro-mechanism of the evolving yielding behavior could be attributed to the 'pinning' effect of hard inclusions to the polycrystalline grains, i.e. the hardlydeformable particles strengthening the kinetic constraints to the polycrystalline matrix and further obstructing the rotation and plastic deformation of the neighboring grains. This research thus provides a comprehensive understanding of the effect of microscopic structure (crystal structure, texture and secondary hard phase) on the macroscopic plastic yielding behavior of metallic materials as well as a new high-fidelity modelling technique to describe the evolving yielding behavior phenomenologically, in such a way to support the application of FE simulation in sheet metal forming processes.