An Evolutionary Yield Function Model Based on Plastic Work and Non-Associated Flow Rule

Abstract

A constitutive law was developed based on the evolutionary yield function to account for the evolution of anisotropy induced by the plastic deformation. For the effective description of anisotropy, the yield stress function and plastic potential were separately defined based on the non-associated flow rule. In particular, for the description of the equivalent status, the accumulated plastic work was employed as an alternative to the accumulated plastic strain. Numerical formulations based on the plastic work were also derived in case the hardening rule, as well as the evolution of the plastic potential and yield stress function, were defined in terms of the plastic work. The developed constitutive law was characterized using the mechanical properties of the multi-phase BAO QP980 steel and niobium sheets at room temperature. From the uniaxial tension tests and the balanced biaxial tension test, separate sets of anisotropic coefficients for each of the plastic potential and yield stress functions were obtained as a function of the plastic work. By comparing with non-evolving yield functions, the importance of the developed constitutive law to properly describe the evolution of the plastic potential and yield function were validated.

Keywords

• anisotropic hardening
• evolutionary yield function
• non-associated flow rule
• multi-phase Q&amp
• P 980 steel
• niobium sheet
• earing profile
• cylindrical cup drawing
• earing