Experimental Characterization and Constitutive Modeling of AZ31B and ZEK100 Magnesium Alloys for Monotonic and Reverse Loading Paths

Abstract

Finite element (FE) simulations are widely used in automotive design processes to model the forming behavior of sheet metals. Comprehensive material characterization and the availability of suitable constitutive models are prerequisites for accurate modeling of these forming operations. In the current research, monotonic tension, compression and large strain compression-tension-compression (CTC) and tension-compression-tension (TCT) experiments have been performed to characterize the mechanical behavior of AZ31B and ZEK100 magnesium sheets at room temperature. A digital image correlation system is used to measure the surface strains during monotonic tension and compression testing. The data is later processed to calculate the evolution of r-values with plastic deformation. Texture measurements of the annealed materials and fractography of deformed specimens under monotonic tension and compression are also performed. The results of mechanical testing are discussed in light of the crystallographic texture and deformation mechanisms such as slip, twinning and untwinning. It is observed that annealed AZ31B sheet has a strong basal texture where the majority of crystallographic c-axes are aligned in the sheet normal (ND) direction whereas the annealed ZEK100 sheet exhibits a comparatively weak basal texture, with significant basal pole spreading in sheet transverse direction (TD). The AZ31B sheet specimens exhibit higher in-plane flow stresses and lower ductility as compared to ZEK100 sheet specimens. The tension-compression yield asymmetry is found to be more pronounced in AZ31B sheet as compared to ZEK100 sheet. In addition to this, the ZEK100 sheet specimens exhibit a strong in-plane orientation dependency of flow stress when subjected to uniaxial tension. Furthermore, a significantly greater evolution of plastic anisotropy (r-values) is observed for AZ31B sheet specimens as compared to ZEK100 sheet specimens. Moreover, the unusual S-shaped hardening behavior is observed during reverse tension following previous compression portions of CTC and TCT flow curves of AZ31B and ZEK100 sheets.

A constitutive model is proposed to capture the evolving asymmetric/anisotropic hardening response of magnesium alloys considering both monotonic and reverse loading paths. The hardening behaviour of magnesium alloys is classified into three deformation modes (i.e. Monotonic Loading [ML], Reverse Compression [RT], and Reverse Tension [RT]). A multi-yield surface modeling approach is used where a CPB06 type anisotropic yield surface is assigned to each deformation mode. For each deformation mode, the yielding criterion is modified to capture the evolution of subsequent yield loci with accumulated plastic deformation. A strain rate independent elasto-plastic formulation is used to implement the proposed constitutive model as a UMAT in LS-DYNA. The predictions of the model are compared against the experimental monotonic and cyclic (CTC and TCT) flow stresses of AZ31B and ZEK100 sheets along different test directions. An excellent agreement is found between the simulated and experimental results.