Phase-field modeling for anisotropic ductile damage of magnesium alloys at finite deformations

Abstract

The damage anisotropy of an extruded ZK60 Mg alloy is characterized using tensile tests and scanning electronic microscopy. The accumulation of anisotropic deformations leads to the great differences of the dimple evolution and strains at fracture along different loading directions. To introduce the anisotropic deformation information into the damage constitutive relationship, a thermodynamically consistent phase-field model of ductile damage fully coupled with elastoplastic finite deformations is developed in this study. Using the user-defined constitutive relationship and displacement-temperature coupling element, the finite element simulations are conducted. The results show that: (1) ZK60 Mg alloys presents clear R-value difference in 0°, 45°, and 90° tests of intact specimens. The 45° test possesses the greatest R-value (1.50) and the greatest strain at fracture, however, the R-value for 0° is less than 1, indicating the thinning is preferential. (2) The higher ultimate stress leads to a larger average dimension of the dimples, whereas the higher density correlates with a larger elongation ratio at the fracture. The disappearance of the stress-bearing area indicates that the phase-field assumption on stress degradation is completely compatible with the dimple analysis on fractography. (3) The simulation results of the stress-strain relationships and damage paths correlate well with the experimental ductile damage of magnesium alloys at 200 ℃. Slight errors are basically attributed to the modeling parameters and finite element iteration algorithm. The proposed model presents fine applicability and reliability for the predictions of plastic deformations, ductile damage, and fracture of anisotropic Mg alloys.

Keywords

• Ductile damage
• Anisotropy
• Phase field
• Constitutive relationship
• Magnesium