Non-associated and Non-quadratic Characteristics in Plastic Anisotropy of Automotive Lightweight Sheet Metals

Lightweight sheet metals are highly desirable for automotive applications due to their exceptional strength-to-density ratio. An accurate description of the pronounced plastic anisotropy exhibited by these materials in finite element analysis requires advanced plasticity models. In recent years, significant efforts have been devoted to developing plasticity models and numerical analysis methods based on the non-associated flow rule (non-AFR). In this work, a newly proposed coupled quadratic and non-quadratic model under non-AFR is utilized to comprehensively investigate the non-associated and non-quadratic characteristics during the yielding of three lightweight sheet metals, i.e., dual-phase steel DP980, TRIP-assisted steel QP980, and aluminum alloy AA5754-O. These materials are subjected to various proportional loading paths, including uniaxial tensile tests with a 15° increment, uniaxial compressive tests with a 45° increment, in-plane torsion tests, and biaxial tensile tests using laser-deposited arm-strengthened cruciform specimens. Results show that the non-AFR approach provides an effective means for accurately modeling the yield behavior, including yield stresses and the direction of plastic strain rates, simultaneously, utilizing two separate functions and a simple calibration procedure. The introduction of the non-quadratic plastic potential reduces the average errors in angle when predicting plastic strain directions by the quadratic plastic potential function. Specifically, for DP980, the average error is reduced from 3.1° to 0.9°, for QP980 it is reduced from 6.1° to 3.9°, and for AA5754-O it is reduced from 7.0° to 0.2°. This highlights the importance of considering the non-quadratic characteristic in plasticity modeling, especially for aluminum alloys such as AA5754-O.