Characterization and modelling of evolving plasticity behaviour up to fracture for FCC and BCC metals

Abstract

Yield surfaces evolve depending on loading directions (anisotropic hardening) and stress states (differential hardening) during plastic deformation of sheet metals. A new analytical yield function is proposed by coupling an enhanced pDrucker function and SY2009 anisotropic hardening functions to model both the differential and anisotropic hardening behavior. All the parameters are solved analytically for the proposed function so that the proposed function can model the differential hardening from uniaxial compression to equibiaxial tension and anisotropic hardening of uniaxial tension with three different loading directions. Its convexity during evolution is analysed from plasticity onset to ultimate fracture by a geometry-inspired numerical convex analysis approach. Several tests were conducted for an aluminium alloy 2A12-O and a high-strength steel QP1180 including uniaxial tension/compression, simple shear, notched tension and bulge tests. The proposed yield function is applied to describe the plastic behaviour of AA2A12-O and QP1180 steel under the non-associated flow rule. Parameter calibration is conducted at pre-necking and post-necking stages for modelling yield surface evolution more accurately under large deformation especially at shear and equibiaxial tension states. The applications to the two metals show that the proposed function is more suitable for pressure-sensitive face-centered cubic (FCC) and body-centered cubic (BCC) metals compared to the pressure-coupled Yld2000–2d and CQN models since both the anisotropic and differential hardening behaviours are precisely modelled by the proposed yield function. The proposed function could also be utilized as a stress-based fracture criterion to model four stress states fracture from uniaxial compression to equibiaxial tension.