A concise analytical framework for describing asymmetric yield behavior based on the concept of shape functions

A fully analytical framework of yield criterion is constructed under non-associated flow rule to describe asymmetric yielding and anisotropic hardening based on the concept of shape functions. For the yield function, eight parameters are identified by employing the corresponding tensile and compressive hardening functions along the four directions, i.e., uniaxial directions along 0°, 45°, 90° in relation to the rolling direction and equi-biaxial direction. This function can describe continuous non-uniform evolution of yield loci during anisotropic hardening. Besides, a new analytical plastic potential function is also developed to predict the asymmetric R-values along uniaxial tension and compression. Subsequently, a simpler curvature control method is proposed to control the curvature of yield surface, especially suitable for materials with large anisotropy. The effectiveness and accuracy of the proposed criterion are validated with HCP, FCC and BCC crystal structure materials for predicting asymmetric uniaxial yield stress curves, R-value curves, and non-uniform evolution of yield loci. The validations indicate that this new criterion has concise mathematical structure and great capability of asymmetry description. Eventually, an extension method for the yield criterion from 2D to 3D is discussed in the reasonability and incompressibility.